3 Vanvliet Math Charts

Rebecca VanVliet EDUC 410-002

LEGEND – Math A – Art CC – Collaboration with Colleagues CE – Current Events CI – Community Involvement – Collaboration with the Community CM – Communication CP – Character Principle CZ – Citizenship DA – Differentiation / Accommodation E – Evaluation GA – Group Activity LA – Language Arts LI – Listening H – Health HS – Home / School Connection – Collaboration with Family HW – Homework M – Math MA – Manipulative Activity MC – Multicultural MO – Movement / Physical Education MU – Music OL – Oral Language / Public Speaking PA – Participation PS – Problem Solving / Critical Thinking Q – Quiz R – Reading S – Science T – Technology TD – Teacher Demonstration VA – Visual Arts W – Writing

Rebecca VanVliet EDUC 410-002

Monday Day 1 RVSOL M 3.1 Place Value

Tuesday Day 2 RVSOL M 3.1 Place Value

M: Teacher will instruct students in the meaning of place value.

M: Teacher will focus on hundreds, tens and ones place values.

MO: Teacher will have students line up across the front of the room (or around the walls, however they fit.) The student at one end will be the “first” place, and the class will number themselves down the line. (If there are 24 kids in the class, the last student in line will be “24th place.”) Teacher will be sure to inform students that this is not a ranking – that first place is not better than second place, etc. Teacher will explain that the number symbolizes where each student is in the line. Students will return to their seats. MO/MA/PA: Teacher will call four students to stand up and form a line like before. Teacher will give each student a card with a single digit on it. Students will write their digits on the board, in the order of their line, and have a seat. Teacher will ask the class to put the four digits together to form one number, without changing the order (ex: digits are 4, 7, 1, and 0. Students will respond with “four thousand seven hundred and ten.”) Teacher will write the place values as the students say them (four thousand… teacher writes “thousand” over the 4; seven hundred… teacher will write “hundred” over the 7, etc.) Teacher will explain that just like the line, the “place value” of a number tells where each digit can be found in a number. Teacher will repeat exercise with another group of students.

MA/TD: Using base ten blocks, teacher will demonstrate the digits of place value: the ones place is represented by the number of individual squares, the tens place is represented by the sticks, and the hundreds place is represented by the flats. Teacher will write one-, two-, and three- digit numbers on the board, and students will practice forming the numbers with the base ten blocks. Then roles will switch, and the teacher will form a number using base ten blocks, and the students will write the numerical equivalent. GA/MA: Students will pair off and continue the practice, with one partner either writing or forming a number, and the other partner forming or writing the same number. T: Students will go to http://www.aaamath.com/ B/g21b_px1.htm to test their knowledge of the hundreds, tens, and ones place values, using the place value calculator in the “practice” section of the page. Once students are comfortable using the place value calculator, they may scroll down the page and play some games using the calculator.

Math – Week 1 Wednesday Day 3 RVSOL M 3.1 Place Value M: Teacher will review hundreds, tens, and ones, and focus on the thousands place value. MA/TD: Teacher will review using base ten blocks. MO/PA: Teacher will write four-digit numbers on the board, and call on volunteers to approach the board and underline the value that the teacher calls out. Teacher will also write 5- and 6- digit numbers on the board, and ask students to identify the thousands place when it is not the first in the number. W/A/VA: Students will choose to either write a short story from the perspective of a number in the thousands place (how it “feels” to be in that place – making note of where it is and what it stands for) or create a picture using drawing, painting, coloring, etc. that represents the same ideas (where the thousands place is and what it stands for in a number). Student responses will be abstract!

Thursday Day 4 RVSOL M 3.1 Place Value

Friday Day 5 RVSOL M 3.1 Place Value

M: Teacher will review the ones, tens, hundreds, and thousands places, and focus on the ten- and hundred- thousands places.

M: Teacher will review the place values up to the hundred-thousands place.

MO/GA: Teacher will divide the class into teams, and do “board races,” in which the teacher will call out a number and a place value, such as “seven hundred eighty-two thousand, nine hundred fifty, ten-thousands place” and teams will work together to write the number numerically and figure out the digit in the desired place value. Once the team has an answer, one student will “race” to the board to be the first to write out the entire number, circling the digit in the specified place value, and sit down again, before all the other teams. The first team that is seated with the correct answer on the board gets a point. Teams will then rotate racers, so that each student has a chance to practice writing and identifying the numbers and place values.

HW: Students will complete a worksheet on thousands place value (1000-9999) from http://www.freemathtest. com/math-PlaceValues.asp

M/SS/MC: Teacher will explain the history of the Quipu (an Incan counting tool, with a rope as a base and different colored strings hanging from it. Each string represents one place value – the rightmost string is ones, the next tens, and so on. Knots are tied in the strings to represent the digit that would fill that place value.) PA: The teacher will give a number, and the students will respond with the number of knots that will be on each string, drawing diagrams if necessary. M/SS/S/MC/MA/PA/A: The students will make Quipus, tying knots in the strings to represent a number of the student’s choosing. The teacher will stress that the students are to place a digit in all of the place values that have been discussed in class (ones to hundred-thousands). Volunteers will tell the class their number, and the teacher will draw a representation of the Quipu on the board, showing the knots on the strings for the digits. The teacher will write the digits above the proper strings, so that students may see the connection.

HW: Students will complete the worksheet (100-999) found at http://www.freemathtest. com/math-PlaceValues.asp DA: Students who are not able to run/walk to the board will have miniature white boards with markers at their seats, and will hold them up with an answer.

Krause, p.41

Rebecca VanVliet EDUC 410-002

Monday Day 6 RVSOL M 3.2 Rounding

Tuesday Day 7 RVSOL M 3.2 Rounding

M: Teacher will introduce rounding as a way to simplify numbers. Teacher will explain when to round up and when to round down, and focus on rounding to the tens place.

M: Teacher will review rounding to the tens place, and instruct the students on rounding to the hundreds place.

TD/PA: Teacher will write examples on the board, calling on students to tell what they would round each number to, and explain why. T: Students will practice rounding to the nearest tens place at http://www.321know .com/est32_x2.htm. HW: Students will complete the “Rounding to the nearest Tens” worksheet from http://www.teachnology.com/worksheets /math/round/2digit/tens/.

TD/PA: Teacher will write examples or four and five digit numbers on the board, and students will round to the nearest place specified by the teacher, up to the ten thousands place. Students will write their answers on miniature white boards and hold them up for the teacher to see on the teacher’s signal. GA: Students will divide into pairs to complete the three-digit “rounding to the nearest tens” worksheet (http://www.teachnology.com/worksheets /math/round/3digit/tens/) . Each student will complete the worksheet, and check the work of their partner.

Math – Week 2 Wednesday Day 8 RVSOL M 3.2 Rounding M: Teacher will review rounding to the tens and hundreds places, and instruct the students on rounding to the thousands place T: Students will practice rounding to the nearest thousands place at http://www.321know .com/est41cx2.htm, and will work in pairs to complete the puzzle by rounding the numbers to the specified place value at http://www.funbrain.com /tens/index.html. Students will use the “Round number,” “easy” game. HW: Students will complete the “Round to the nearest Thousands” worksheet from http://www.teachnology.com/worksheets /math/round/thousands/.

T: Students will practice rounding to the nearest hundreds place at http://www.321know .com/est32_x3.htm. HW: Students will complete the “Rounding to the nearest Hundreds” worksheet from http://www.teachnology.com/worksheets/ math/round/hundreds/3/.

Thursday Day 9 RVSOL M 3.2 Rounding

Friday Day 10 RVSOL M 3.2 Rounding

M: Teacher will explain estimation as an educated guess.

M: Teacher will review estimation.

TD/PA: Teacher will have a small closed box and a marble. Teacher will tell the class that the closed box is full of marbles. Teacher will ask the students to estimate how many marbles they think will fit in the box. Teacher will encourage the students to think about it before they answer, looking at the size of the marble and the size of the box. After a few minutes, the teacher will ask each student to tell his/her estimation, and the teacher will write each guess on the board. A volunteer will be chosen to take the marbles out of the box, counting out loud as they do so. After the marbles have all been counted, the class will find the estimate(s) that came closest to the actual amount. Teacher will explain that the purpose of estimation is to guess as close to the actual number as possible, without having to count every single item.

MO/CM/GA/OL/PA/PS: Students will play “Round About” in which they meet other students in the class (teacher will encourage them to interact with students they do not already know well). Students will learn the names of four other students and turn the names into numbers by assigning each letter a predetermined numerical value (a=1, b=2, etc.). Students will first estimate the sum of the letters, and then add them together to find the actual total. Class will discuss the results, noting who had the name with the largest numerical value, who had the smallest, if there were any the same, and how close students’ estimates were. Students will be asked to explain how they arrived at their estimated values.

M/PS: Teacher will demonstrate estimation using rounding, explaining that it is possible to get close to the correct answer quickly by adding the rounded numbers. (Ex. Teacher will give the students the numbers 678 and 321. If they are each rounded to the nearest hundred, the answer is simply 700 + 300 = 1000. 1000 would be a good estimation for the problem. Teacher will have the students add the original numbers to see how close their estimation was. DA: Gifted students may try the more difficult levels of the internet rounding game while the rest of the class uses the “easy” level. Molyneux, pp.42-43

Rebecca VanVliet EDUC 410-002

Monday Day 11 RVSOL M 3.3 Comparing (>,<,=)

Tuesday Day 12 RVSOL M 3.3 Comparing (>,<,=)

M/LI: Teacher will introduce comparing numbers. Teacher will introduce the signs for comparing numbers, as well as the words that go with them (> means “greater than” or bigger, < means “less than” or smaller, and = means “equal to” or the same.)

M: Teacher will review the comparison signs with the class, and go over the homework.

PS/PA: The class will agree on a way to remember the signs (the sign “eats” the larger number, the bigger side of the sign is next to the bigger number, the “arrow” “points” to the smaller number, etc.) MO/OL: Teacher will write two numbers between 0 and 99 on the board, one on the left and one on the right, and students will stand at their seats and use their arms to form the correct sign. After each example, the teacher will write the correct sign between the numbers on the board, and the class will practice saying the entire number sentence (ex. Numbers are 46 and 29. Students will say “46 is greater than 29.” Numbers are 58 and 73. Students will say “58 is less than 73.”) HW: Students will complete a worksheet on comparing two-digit numbers, made at http://www.superkids. com/aweb/tools/math/ compare/.

MO/OL: Students will stand, and the teacher will hand out colored ribbons to some students. Students will then divide into two groups (ribbons and no ribbons) and decide which group is larger. Once students have decided, they will raise their hands. Teacher will call on one student to use a sentence to compare the two groups, starting with the student’s own group. For example, if there are 24 students, and the teacher gives 9 students ribbons, a student in the ribbon group would say “the ribbon group is less than the no ribbon group, because 9 is less than 15” and a student from the no ribbon group would say “the no ribbon group is greater than the ribbon group, because 15 is greater than 9.” Teacher will call on at least one student from each group every turn. Students will hand the ribbons back to the teacher and return to their desks, and the teacher will pass out ribbons again. M/A: Students will complete the worksheet from http://www.makeworksheets .com/samples/math/ compgrop.html, only in addition to circling the largest group, students will write the number of shapes in each box, and place the comparison symbols >, <, = between each of the boxes. Students will color the shapes.

Math – Week 3 Wednesday Day 13 RVSOL M 3.3 Comparing (>,<,=) M: Teacher will review the comparison signs, and expand the students’ practice to include three digit numbers. PS/OL/GA: Students will be divided into groups of four. Teacher will give every student a card with a three digit number on it. Students will discover whether their number is greater than, less than, or equal to the numbers of their group members, without saying what the number is or showing their card to anyone. Students will describe their number as greater than or less than a rounded hundred, then a rounded ten, then a rounded five. For example: A student’s card has the number 456. Another student has the number 432. Student #1 will say, “my number is greater than 400.” Student #2 will say “my number is greater than 400 also, but less than 450.” Student #1 will say, “my number is greater than your number.” Once someone is able to declare that their number is certainly greater or less than their partner, they will record it (#1 > #2), and move on to another person in their group. Once all comparisons have been made (1-2, 1-3, 1-4, 2-3, 2-4, 3-4), the group will write the names of the students in order from the least number to the greatest number (#4 < #2 < #1 < #3) and students will show each other their numbers, and determine if their conclusion was correct. T: Students will go to http://www.haelmedia. com/html/og_m2_001.html to practice ordering 3-digit numbers from least to greatest. PS: Students will complete a worksheet on comparing threedigit numbers, from http://www.freemathtest. com/MathWorksheet. asp?c=Comparisons& min=100&max=999.

DA: Students who need extra practice will practice at http://www.crickweb.co .uk/assets/resources/ flash.php?&file=ncmenu.

Thursday Day 14 RVSOL M 3.3 Comparing (>,<,=)

Friday Day 15 RVSOL M 3.3 Comparing (>,<,=)

M: Teacher will review the comparison signs, and expand the students’ practice to include fourdigit numbers.

M: Teacher will review comparisons with the class, and instruct the students in comparing number sentences.

PA/PS: Teacher will write a four-digit number on the board, write a comparison sign next to it (>, <, =), and write another number on the other side of the sign, leaving one digit out. Students will raise their hand when they know what digit(s) will make the statement true. (For example: 3456 > 3_99. Ans: 0, 1, 2, or 3.) Teacher will coax students to come up with all possible answers. Teacher will repeat the activity a few more times, then add a third number, to limit the possible answers. (For example: 3456 > 3_99 > 3321. Ans: 3.) Students will observe that doing so organizes the numbers from greatest to least.

TD/PA: Teacher will write two number sentences on the board (4+5 __ 8+2), and ask students for ideas on how to find which is greater. Teacher will explain that each side can be solved to get a single number. Teacher will solve each side, reducing the equation to the single numbers (9 __ 10). Students will provide the proper signal. Teacher will repeat with subtraction equations, and mixed addition/subtraction equations. Teacher will encourage students to write the sum or difference under the number sentence, to provide a visual to compare.

T: Students will use the comparison generator at http://www.aaamath.com/ B/cmp33_x2.htm#section3 to practice comparing numbers up to four digits. T: Students will use the game at http://www.funbrain .com/ofm/index.html to practice ordering numbers from least to greatest and greatest to least.

GA/PS/MA: Partners will be given a deck of flashcards with number sentences on them. They will shuffle the cards and deal them evenly, facedown. Each will draw one card at a time, and compare the number sentences. The student whose card has the greater value keeps both cards. Any that are equal are set aside and go to the winner of the next comparison. The game is over when one student has all of the cards, or the teacher calls time. T: Students will go to http://www.haelmedia. com/html/mc_m3_003. html to practice comparing number sentences.

Rebecca VanVliet EDUC 410-002

Monday Day 16 RVSOL M 3.33 Equivalencies

Tuesday Day 17 RVSOL M 3.33 Equivalencies

M: Teacher will introduce the word “Equivalency.” Teacher will explain that two numbers or number sentences that have the same answer are equivalent. Teacher will use the equal sign to represent equivalencies.

M: Teacher will review the definition of equivalency. Teacher will explain that number sentences are also equivalencies.

W: Students will write the definition of equivalency in their notebooks. PA/MO: Teacher will write a variety of numbers on the board, and call on a student to circle the numbers that are equivalent (the same). Teacher will erase the numbers and write other numbers, calling on different students each time. VA/MA/A: Teacher will provide construction paper for the students. Students will choose one color for the background, and four colors for their activity. Teacher will explain that students are to fold their construction paper down the middle both ways (to form four identical boxes). Students will then choose a number between one and ten, and cut that number of shapes out of each of the four colors they chose (ex. 4: student will cut 4 red hearts, 4 blue circles, 4 yellow stars, and 4 green flowers) and glue each color in one of the four squares on the background paper. Student will relate the boxes by drawing equal signs between them to show that the value of each box is equivalent to the others.

PA/PS/MO: Teacher will write a number sentence on the board, and a variety of numbers. Students will approach the board and circle the number that is equal to the number sentence. Students will copy the whole equation in their notes, using the equal sign. PS/MO/CM: Teacher will divide the class into three equal teams. To each student on two of the teams, the teacher will give a blue card with a number on it. To each student on the third team, the teacher will give a red card with a number on it. Teacher will explain that the students with the red cards will need to find two students with blue cards (one from each team), whose cards combine by addition to make a number equivalent the value of the red card. Once a group of three has been formed, each student will write down the equivalency, they will rotate cards, and rejoin the class to form other equivalencies. PA/OL: Teacher will call on students to name equivalencies that they made.

Math – Week 4 Wednesday Day 18 RVSOL M 3.33 Equivalencies M: Teacher will review the definition of equivalency. Teacher will expand the students’ practice to include equivalent number sentences. TD/PA: Teacher will write two number sentences on the board. Teacher will ask for students to explain how to find out if they are equivalent. Teacher will follow student directions in adding the two number sentences. Teacher will demonstrate writing the sum of each side underneath the number sentence. Students will tell if the sentences are equivalent. MA: Teacher will pass out colored chips to each table. Students will fold a piece of construction paper in half the long way, and unfold to form two long narrow rectangles. Teacher will write two number sentences on the board, such as 4+5 and 3+6, and students will place the corresponding number of chips into each column. (Students would put four of one color and five of another color in column one for the first number sentence, and three of one color and six of another in column two for the second number sentence.) Students will count the chips in each column to see if the sentences are equivalent. If they are, students will write the equivalency using the equal sign. If they are not, teacher will introduce the not equal sign (≠) and students will say that the two sentences are not equivalent. [Optional: teacher will ask students to add or subtract chips from one of the columns to make the sentences equivalent, and re-write the new sentences.]

DA: Gifted students may use the virtual manipulative at http://nlvm.usu.edu/en/nav/ frames_asid_188_g_2_t_ 1.html?open=instructions to practice making equivalencies (all circles must equal 21).

Thursday Day 19 RVSOL M 3.33 Equivalencies

Friday Day 20 TEST

M: Teacher will review equivalency, and practice equivalencies with subtraction.

E/M: Teacher will review place value, rounding, and comparisons. Test will cover these materials.

PS/PA: Teacher will write a subtraction number sentence and a single number on the board, and students will tell if they are equivalent or not. Teacher will write two subtraction number sentences on the board, and students will again say whether or not they are equivalent. MA/GA/MO: Students will stand. Teacher will divide the class into two unequal teams, and have the teams stand on different sides of the room. Teacher will ask the class if the teams are equivalent (no). Teacher will ask a number of students to sit down from each team, leaving five students on each side. Teacher will ask the class if the teams standing are equivalent now (yes). Teacher will ask the students to write a subtraction sentence for each group, and tell if the sentences are equivalent (yes). Ex: 24 students, divided into groups of 15 and 9. The groups are not equivalent. The first team has 10 people sit down, and the second team has 4 people sit down. Students will write the number sentences 15 – 10 and 9 – 4. The sentences are equivalent, because they both equal 5, therefore, 15-10 = 94. The class will repeat the activity, and switch to mixed addition and subtraction (one group loses people, and one group gains people.) Students will write equivalent number sentences for each.

Rebecca VanVliet EDUC 410-002

Monday Day 21 RVSOL M 3.4 Fact Families

Tuesday Day 22 RVSOL M 3.4 Fact Families

M: Teacher will define the term “fact family” as a relationship between number sentences that use the same numbers.

M: Teacher will review the definition of “fact family” and instruct students in forming fact families when no original sentence is given.

W: Students will record the definition in their notebooks. TD/PA: Teacher will write a simple addition problem on the board (5 + 2) and ask student to come up with the answer (7). Teacher will write the number sentence as an equivalency (5 + 2 = 7). Teacher will write the same number sentence on the board, switching the addends (2 + 5), and students will again provide an answer (7). Teacher will write the number sentence underneath the first. Teacher will ask students to try to come up with a subtraction sentence using the same numbers, and work with the class to create both (7 – 2 = 5 and 7 – 5 = 2). Students will see how the sentences relate to one another. GA/PS: Teacher will write another simple number sentence on the board, and ask students to work with a partner to complete the family.

TD/PA: Teacher will write three numbers on the board, which can be arranged to form a fact family. Teacher will call on a student to give one number sentence that can be made with the numbers. Teacher will call on another student to make another number sentence and so on, until all four sentences are made. Teacher will repeat the process with another four students. PS/PA: Teacher will write three numbers on the board that do NOT form a fact family, and ask students to arrange the numbers in a fact family. Class will discuss why the task is impossible. PS: Students will practice forming fact families from three numbers.

Math – Week 5 Wednesday Day 23 RVSOL M 3.4 Fact Families M: Teacher will review the concept of “fact family” and instruct students in forming fact families when one of the numbers is missing. TD/PA: Teacher will write a number sentence on the board, such as 5 + _ = 8, and ask students how they would go about finding the missing number. Teacher will remind students of the other sentences in fact families, and encourage students to find one that has both of the given numbers on the same side of the equal sign, to make it easier to solve. If necessary, teacher will write out the rest of the fact family for students to gain a visual (_ + 5 = 8, 8 – 5 = _, and 8 - _ = 5) and ask students to pick the number sentence that would be easiest to solve, and then complete the rest of the sentences. CP: Teacher will explain that numbers are reliable. The facts in each fact family are the same, no matter what. GA/MO: Teacher will give each student a card with either a number sentence with one number missing, or a number on it (ex. One card will read 5 + _ = 8, and another will read 3), and the students’ goal will be to discover which number fits into their sentence (or which sentence their number fits into), and pair up with the student who has that card. Together the two students will list the fact family for their sentence. Once everyone has written out their fact family, the teacher will collect the cards and redistribute them, and students will repeat the activity. CP/PA: Teacher will discuss the phrase “You can count on me!” with the class, noting the reliability of numbers in counting. Students will discuss ways people can “count on them” to be reliable. CP: Reliability

Thursday Day 24 RVSOL M 3.4 Fact Families

Friday Day 25 RVSOL M 3.4 Fact Families

M: Teacher will review the concept of “fact family.”

M: Teacher will review the concept of “fact family” and the various methods that have been discussed in order to arrive at a completed family (given one sentence, given three numbers, given only two numbers, given only one number).

MA/GA: Pairs of students will be given ten identical wooden blocks. Teacher will explain that students are to use all of the blocks to create a fact family of blocks. Students will be given an amount of time to come up with a fact family using all of the blocks (7 blocks combined with 3 blocks makes 10, etc., which can be manipulated to form the other sentences, OR 1 block plus 4 blocks equals the remaining 5 blocks, which can be rearranged to show the remaining sentences.) Students will be encouraged to be creative. PA/OL/PS: Teacher will call on each pair to tell the numbers and sentences that make up their fact family, and how they used the blocks. Teacher will write sentences on the board. Teacher will ask students if they can come up with any other combinations using the ten blocks. The class will discuss the results.

DA: Learning disabled students will be given different colored blocks (such as three red and seven blue) and asked to form a fact family using the numbers that correspond to the colors.

PA/PS/GA/MO: Each student will be given a number between one and ten. On the teacher’s signal, students must find a partner, and write a fact family that uses both numbers. Once they have both written the fact family, they will find another partner with a different number than the first, and write another fact family. When the teacher calls time, the students will share the fact families they made. Teacher will tell students that this time, they have to find TWO other students, and create a fact family using all THREE numbers. This may take more thought, and may mean they can’t pair up with only friends. Students must work together to craft the fact families, and will again share their results at the end.

Rebecca VanVliet EDUC 410-002

Monday Day 26 RVSOL M 3.10 Add/Subtract Large Numbers

Tuesday Day 27 RVSOL M 3.10 Add/Subtract Large Numbers

Math – Week 6 Wednesday Day 28 RVSOL M 3.10 Add/Subtract Large Numbers

M: Teacher will administer a “speed test” of 100 addition and subtraction problems (with large numbers), and students will complete as much as they can in five minutes.

M: Teacher will administer the same “speed test” of 100 addition and subtraction problems (with large numbers), and students will complete as much as they can in five minutes.

M: Teacher will administer the same “speed test” of 100 addition and subtraction problems (with large numbers), and students will complete as much as they can in five minutes.

M: Teacher will administer the same “speed test” of 100 addition and subtraction problems (with large numbers), and students will complete as much as they can in five minutes.

M: Teacher will administer the same “speed test” of 100 addition and subtraction problems (with large numbers), and students will complete as much as they can in five minutes.

SS: Teacher will explain the background of the game Lu-Lu (Hawaiian).

M: Teacher will review subtraction regrouping with the class.

M: Teacher will focus on addition and subtraction to the thousands place.

MA/GA: Students will play the game Lu-Lu, which involves addition up to 100. Students will practice addition with regrouping during the game.

MA: Students will use unifix cubes singly and in sticks of ten to demonstrate subtraction problems. Students will be able to physically take the sticks and break them into ones, to show the transfer from tens to ones while regrouping. Students will record their answers.

MO/CP: Students will divide into teams of five, and line up facing the board, behind a “starting line” of masking tape. The teacher will write a problem on the board, and the students on each team will work together to complete the problem before the other teams, each student doing only ONE step (first student copies the problem on the board in front of the line, second adds/ subtracts the ones column, third adds/ subtracts the tens column, fourth adds/ subtracts the hundreds column, and fifth adds/ subtracts the thousands column). Before the next student can approach the board, the student doing the previous step must be behind the starting line. When a group is finished, the whole group must raise a hand. The first team finished correctly gets one point. Students will rotate within groups so everyone gets a chance to do each step of a problem. CP: Cooperation

M: Teacher will review estimation, and explain how it can be used in addition and subtraction of large numbers.

M: Teacher will review addition regrouping with the class. MA/CP: Teacher will hand out M&M’s® to the class, as well as place value sheets. Students will use their M&M’s® as counters and place value markers to practice addition of twoand three-digit numbers with regrouping. Students will designate one color of M&M® for each place value (ones = red, tens = green, hundreds = brown, so if I need to regroup my ones, I will exchange ten red M&M’s® for one green one.) Teacher will explain that students are not to eat the M&M’s® until the lesson is over, at which time all students who still have all their M&M’s® will get a sticker on a character chart for displaying self control.

LI/MA/GA: Teacher will redefine the rules of the game, telling the class that this time the disks are worth 10, 20, 30, and 40 (instead of 1, 2, 3, and 4). Students will play the game again, this time to 1000, practicing addition with regrouping larger numbers. HW: Students will complete the addition chart from http://www.makework sheets.com/samples/puzzle s /mathpuzzle.html, making sure that all columns, rows, and diagonals add up to the totals in the boxes along the bottom and side.

CP: Self-Control DA: Students with chocolate allergies will use Skittles® instead. Krause, p.21

HW: Students will complete a subtraction worksheet generated from http://www.apples4 theteacher.com/mathsubtraction-worksheets .html.

Thursday Day 29 RVSOL M 3.10 Add/Subtract Large Numbers

Friday Day 30 RVSOL M 3.10 Add/Subtract Large Numbers

GA: Students will practice estimation by rounding each number in the addition/ subtraction problem, to arrive at an estimated answer, and then compute the actual answer. Students will compare estimated and actual answers with a partner, discussing how close the estimates are to the actual answer. PA: Teacher will discuss the real-world application and usefulness of estimating sums and differences of large numbers.

Rebecca VanVliet EDUC 410-002

Monday Day 31 RVSOL M 3.19 Telling Time

Tuesday Day 32 RVSOL M 3.19 Telling Time

M: Teacher will review reading analog clocks to the hour, half-hour, and fifteen minute intervals, and focus on five minute intervals. Teacher will explain the position of the hour hand in relation to the minutes (almost to the next number when minutes near the end of the hour).

M: Teacher will review measuring time to the five minute intervals, and focus on measuring to the minute.

TD/MA: Teacher will pass out small analog clocks to the students. Teacher will write a time on the board (in five-minute intervals) and show students how to properly position the hands of the clock to demonstrate the time. Students will mimic the teacher. After a few such examples, the teacher will write a time on the board, without demonstrating the time on a clock, and students will manipulate their clocks to show the proper time, and hold them up for the teacher to see.

MA/PS: Students will use manipulative clocks to show times to the minute, and draw their own analog clocks to represent times to the minute. Students will also view an analog clock and write the time digitally (9 : 47) and in words (nine forty-seven, or nine hours and forty-seven minutes). HW: Students will complete the telling time worksheet from http://www.makework sheets.com/samples/math /time.html.

PA: Class will discuss different things that can be measured in five-minute intervals.

DA: Students who are still struggling to master measuring hours and halfhours on analog clocks will practice with “Think It Through®” Tiles (Discovery Toys – Book on measurement, time, and money, pp.12-17) on reading clocks to the nearest hour and half-hour.

Math – Week 7 Wednesday Day 33 RVSOL M 3.19 Telling Time M: The teacher will review telling time with an analog clock, and go over the homework. MO/GA/CP: Teacher will mark a large analog clock on the floor using masking tape. The class will be divided into groups of six. One group will use the clock at a time. One student will be chosen from each group to be the “hub” or center of the clock, two students will hold hands/ link arms to form the hour hand, and three students will hold hands/ link arms to form the minute hand. Both “hands” will also link to the “hub,” who will only pivot on the center spot in order to keep the hands in place on the clock face. The teacher will call out a time, and the “hands” will work together to arrange themselves to display the time that was called. The other groups that are not making the time will decide whether or not the “clock” is showing the correct time. After a few times are called, the groups will switch off.

Thursday Day 34 RVSOL M 3.19 Telling Time

Friday Day 35 RVSOL M 3.19 Telling Time

M: Teacher will explain how to read digital clocks, and compare digital clocks to analog clocks reading the same time.

M: Teacher will explain adding time, reminding students to start over when they get to twelve.

PS: Students will view a digital clock, and place the hands on a corresponding analog clock, and vice versa. OL: Students will practice reading digital clocks out loud, using terms such as “quarter after,” “half past,” and “quarter to.” M: Students will complete the worksheets from http://www.time-fortime.com/worksheets /atodminute.pdf and http://www.time-fortime.com/worksheets /dtoaminute.pdf on translating from digital to analog and analog to digital.

PS/GA: Students will be divided into groups. Teacher will write a time and a length of time on the board (ex. 10:00AM, 7 hours), and each group will work together to find out the ending time. For each problem, the students will draw both an analog clock and a digital clock representing both the starting and ending times. PS: Students will complete the short worksheet on Amy’s Schedule (Tuttle, p.55).

HW: Students will complete the worksheets for homework if they are not finished in class.

HW: Students will complete a worksheet on time from http://themathwork sheetsite.com/cgibin/telling_time.pl by placing the hands on a clock to display the proper time. CP: Cooperation

Cornett, p.320

Tuttle, p. 55

Rebecca VanVliet EDUC 410-002

Monday Day 36 RVSOL M 3.15 Counting Money

Tuesday Day 37 RVSOL M 3.15 Counting Money

M: Students will review the value of the penny, nickel, dime, quarter, half dollar, dollar bill, and five dollar bill.

M: Teacher will instruct students in counting money up to five dollars.

PA/MA: Students will compare the values of the coins using greater than, less than, equal to. Students will use play money to demonstrate each comparison. GA: Students will pair up, and one student will form two groups of coins. The partner will have to count the coins and write a number sentence comparing the two groups. The students will alternate roles. After a few minutes, the teacher will call for a switch, and one partner will write a comparison sentence with amounts of money, and the other partner will count out the coins for each amount. Students will alternate again.

PS: Students will view pictures of coins and bills, and count the total amount each time. PS/MA/GA/SS/CP/CZ: Students will investigate the men whose faces are on the different coins and bills. Teacher will divide the class into groups. Students will use a computer to discover a little about one of the faces. Groups will share with the class how the person they researched was important, and conclude with telling the class how many coins and/or bills with their person’s picture they would need in order to have as close to five dollars as possible.

Math – Week 8 Wednesday Day 38 RVSOL M 3.15 Counting Money

Thursday Day 39 RVSOL M 3.15 Counting Money

Friday Day 40 RVSOL M 3.15 Counting Money

M: Teacher will instruct students in adding money.

M: Teacher will review adding money.

PS: Students will complete the short worksheet on buying snacks (Tuttle, p.43)

PS/PA: Students will “Create their own Sundae” on the short worksheet on cost (Tuttle, p.64). Volunteers will share their sundae combinations with the class, teacher will write them on the board, and the class will compare the sundaes to determine who spent the most, who spent the least, and why. Class will discuss different combinations that would be possible for the same prices.

M: Teacher will explain that there are many ways to arrive at the same total amount of money.

M: Teacher will instruct the class in subtracting money (making change). PS: For each of the questions in the worksheet, the students will be asked to make change for a payment of one dollar. M: Students will complete a worksheet on adding and subtracting money, from http://www.edhelper.com /math/math_tg17.htm.

GA/PS: Students will gather into groups and use the Money Mix chart to determine all the combinations of coins that equal 25¢. Students will keep track of their results in the chart. PA: Class will discuss how many combinations the different groups found. Teacher will record the combinations on the board.

PS: Teacher will then ask the students to pretend they were the ice cream store clerk, and pretend each of the volunteers (whose sundaes were listed) paid for the sundaes with a five dollar bill. Students must compute the correct amount of change for each sundae.

PA: Class will discuss comparisons. CP: Citizenship

DA: Struggling students will use “Think It Through®” Tiles (Discovery Toys – Book on measurement, time, and money, pp.10-11) to make change for smaller amounts (up to one quarter.) Tuttle, p. 43

Tuttle, p. 64

Molyneux, pp. 84-85

Rebecca VanVliet EDUC 410-002

Monday Day 41 RVSOL M 3.11 Multiplication Table

Tuesday Day 42 RVSOL M 3.11 Multiplication Table

Math – Week 9 Wednesday Day 43 RVSOL M 3.11 Multiplication Table

R/LI: Teacher will read 2 x 2 = Boo! by Loreen Leedy.

T: Students will go to http://www.oswego. org/ocsdweb/games/ Mathmagician/maths multi.html to review the multiplication facts for 1 and 2.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 3.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 4.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 5.

M: Teacher will explain the multiplication table for 3.

M: Teacher will explain the multiplication table for 4.

M: Teacher will explain the multiplication table for 5.

M: Teacher will explain the multiplication table for 6.

TD/OL: Teacher will use a number line to assist students in counting out loud by fours, through 40.

OL/MU: Class will count out loud by fives, and create a chant for the products of the fives tables.

MA/GA: Students will cut strips of construction paper, and group the strips to form six groups for each fact. Students will quiz each other, by forming groups that the partner must write the multiplication fact and product for.

M: Teacher will explain the multiplication tables for 0, 1, and 2. Teacher will define “product.” OL: Teacher will teach students to read multiplication sentences as “x groups of y.” (0x1 = zero groups of one OR no groups of one. Zero groups means zero total!) MA: Students will use plastic chips to make zero, one, and two groups of the numbers 0 – 9. PA/GA/OL: Students will gather into groups and find all the patterns they can in the multiplication tables, explaining them to the rest of the group. (Students will notice that the twotimes-tables are simply the number plus itself.) Teacher will explain the patterns. W/MA: Students will make their own flashcards, and quiz each other. W: Students will complete a chart on the facts for 0, 1, and 2. HW: Students will complete a worksheet on multiplication facts up to the 2s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

PA/OL: Students will count out loud by threes. Students will discover any other patterns within the three times tables. TD/PA/VA: Teacher will hold up a triangle, and explain that multiplying by three is like a triangle. Teacher will count the sides, demonstrating that there are three sides to a triangle. Teacher will draw a triangle on the board, and write a fact of three inside the triangle, for example, 3 x 4. Teacher will then write a four outside the triangle, next to each side. Teacher will prompt students to add the sides of the triangle, and teacher will write the total under the fact inside the triangle. Students will practice their own multiplication triangles. MA/VA: Students will gather into groups, and draw pictures, x’s, or other symbols to represent each multiplication fact for threes. (     3x3=9, xxxx xxxx xxxx  3x4=12). W/MA: Students will add the multiplication facts for three to their flashcards. W: Students will complete a chart on the facts for 0, 1, 2, and 3. HW: Students will complete a worksheet on multiplication facts up to the 3s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

MA: Students will use unifix cubes in sticks of four to demonstrate the facts for four. W: Students will complete a chart (grid) of the facts for 0, 1, 2, 3, and 4. Students will highlight the fours column. W/MA/GA: Students will add the fours to their flashcards, and practice with a partner. HW: Students will complete a worksheet on multiplication facts up to the 4s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

Thursday Day 44 RVSOL M 3.11 Multiplication Table

Friday Day 45 RVSOL M 3.11 Multiplication Table

MA/A/VA: Students will use hands to count by fives. Given paint and large papers, students will represent each fact of five with hand prints in lines. (7 hand prints equals 35 fingers. Five hands seven times: 5x7=35.) Students will use one color per line. (First row will have no hand prints (0). Second row will have one [blue] handprint. Third row will have two [red] handprints. Etc.) MA/W: Students will add the fives to their flashcards. W: Students will complete a chart (grid) of the facts for 0, 1, 2, 3, 4, and 5. Students will highlight the fives column. HW: Students will complete a worksheet on multiplication facts up to the 5s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.) DA: Ethnically diverse students will share a culturally different kind of chant, if they know one.

M: Students will practice multiplication up to the sixes using the worksheet from http://www.edhelper. com/math/multiplication_ tg110.htm. W/MA: Students will add the 6s to their flashcards, noticing any multiples (0x6 = 6x0, 1x6 = 6x1, 2x6 = 6x2, etc.) GA/PA/MO: Class will play “Around the World” with the multiplication facts through the 6s. W: Students will complete a chart (grid) of the facts for 0, 1, 2, 3, 4, 5, and 6. Students will highlight the sixes column. HW: Students will complete a worksheet on multiplication facts up to the 6s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

Rebecca VanVliet EDUC 410-002

Monday Day 46 RVSOL M 3.11 Multiplication Table

Tuesday Day 47 RVSOL M 3.11 Multiplication Table

Math – Week 10 Wednesday Day 48 RVSOL M 3.11 Multiplication Table

T: Students will go to http://www.oswego. org/ocsdweb/games/ Mathmagician/maths multi.html to review the multiplication facts for 6.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 7.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 8.

T: Students will go to http://www.oswego. org/ocsd-web/games/ Mathmagician/maths multi.html to review the multiplication facts for 9.

M: Teacher will explain the multiplication table for 8.

M: Teacher will explain the multiplication table for 9.

GA/MA: Pairs of students will be given 8 plastic cups. Teacher will have a large bin of ice, and students will work together to answer the question: how many ice cubes would you need if everyone (of your 8 cups) asked for one ice cube? two ice cubes? three? etc. up to nine. Students will put the ice cubes in the cups as they figure, and draw a quick picture of each equation to help them see how addition and multiplication are related.

MA: Students will be given string and beads, and will place the beads on the string in groups of nine (either the same color or same shape for each group). Students will tie the ends of the string together, to give them a circle of nines.

GA/PA/MO: Class will play “Around the World” to review all of the multiplication tables.

M/PA: Teacher will review the multiplication tables through the 6s, by calling out a problem and having students write their answer on a small white board and holding it up. M: Teacher will introduce the multiplication facts for 7. Students will notice that 7x0 through 7x6 have already been learned within the other multiplication facts. M/GA: Students will complete the worksheet from http://www.edhelper .com/math/multiplication _tg101.htm. Students will have a partner grade the worksheet, and groups will discuss the answers. TD: Teacher will show a class a calendar and point out that because each week is seven days long, the multiples of seven all line up in one column. MA: Students will add the sevens to their flashcards. W: Students will complete a chart (grid) of the facts for 0, through 7. Students will highlight the sevens column. HW: Students will complete a worksheet on multiplication facts up to the 7s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

MA: Students will add the 8s to their flashcards and quiz one another. W: Students will complete a chart (grid) of the facts for 0 through 8. Students will highlight the eights column. HW: Students will complete a worksheet on multiplication facts up to the 8s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.)

T: Students will practice the nines table by “climbing the mountain” at http://www.teaching tables.co.uk/tm/chall /tmchall.html. MA: Students will add the nines to their flashcards and quiz one another.

Thursday Day 49 RVSOL M 3.11 Multiplication Table

Friday Day 50 RVSOL M 3.11 Multiplication Table M: Teacher will review all of the multiplication tables through the nines.

W: Students will complete a grid for all of the tables up through nine. OL/CP: Students will stand up to recite the tables. Teacher will explain that it takes courage to stand up in front of the class, and students will be admonished to be respectful of their classmates. Q: Students will take a quiz on the multiplication facts.

W: Students will complete a chart (grid) of the facts for 0 through 9. Students will notice that the nines column has already been learned through the other eight columns. Students will highlight the nines column. HW: Students will complete a worksheet on multiplication facts up to the 9s. (Made at http://www.superkids.com /aweb/tools/math/multiply/ times1.shtml.) CP: Courage DA: Struggling students will practice using pp. 5, 6, and 15 of Pizza Pepperoni & Practical Math (Multiplication) with “Think It Through®” Tiles (Discovery Toys).

GA: Students will be given a few minutes to practice with a partner using the flashcards that have been made in class. PS/GA: The class will play Math Bingo, in which the teacher will call out a multiplication problem, and students will mark their cards if they have the answer. The winner is the first student to have five correct answers in a row. OL/CP: Students will stand up to recite the tables.

Rebecca VanVliet EDUC 410-002

Monday Day 51 RVSOL M 3.11 Division

Tuesday Day 52 RVSOL M 3.11 Division

M: Teacher will recall students to their knowledge of fact families. Teacher will explain that multiplication and division form fact families in the same way that addition and subtraction do.

M: Teacher will review division.

TD: Teacher will use blocks to show division of one group into many groups. MA/PS: Teacher will give each student 12 blocks, and some string. Students will be asked to use the string to divide off groups of the same number, using all of the blocks. Teacher will ask students to make groups of four. Students will share how many groups they needed. Teacher will write on the board: 12 ÷ 4 = 3. Teacher will ask students to make groups of three, six, and two as well, writing a division sentence for each. PS: Students will complete the division worksheet from http://www.edhelper .com/math/division_tg301 .htm. MA: Students will use “Think It Through ®” Tiles, Pizza Pepperoni & Practical Math (Division) p. 2&3 to practice division into equal groups.

MA/PS/W: Teacher will give students a certain number of unifix cubes, and ask them to place the cubes into even stacks of different amounts. Students will be asked to write a sentence for each division fact they represent. MO/PS/W: Teacher will have the students stand and form groups of four. Teacher will ask students to determine how many groups the class formed. Teacher will have students write a division sentence for the class. Teacher will repeat with different divisions. PS: Students will complete the worksheet from http://www.edhelper.com /math/division_tg307.htm on writing division sentences for a given picture.

Math – Week 11 Wednesday Day 53 RVSOL M 3.11 Division M: Teacher will use fact families to help students with division. TD/PA/PS: Teacher will write a multiplication sentence on the board, and walk students through completing the fact family in the same way fact families were made using addition and subtraction. GA/MO: Students will be given a card with either a multiplication sentence or a division sentence on it, and have to find a partner who has a sentence that is in the same fact family. The pairs will write the entire fact family, and focus on memorizing the division facts. Teacher will collect and redistribute the cards, and students will repeat. MA/PS: Students will use their multiplication flashcards to write corresponding division flashcards. HW: Students will complete the “fill in the missing number” worksheet on related multiplication / division facts from http://www.edhelper.com /math/division_tg312.htm. DA: Students will use “Think It Through ®” Tiles, Pizza Pepperoni & Practical Math (Division) p.10 to relate multiplication to division.

Thursday Day 54 RVSOL M 3.11 Division

Friday Day 55 RVSOL M 3.11 Division

M: Teacher will review division by saying a division fact. Students will write the fact and the answer on a white board, and hold it up for checking at the teacher’s signal.

M/Q: Teacher will review division with an oral quiz. Teacher will say a division fact (such as 36 divided by 6), and call on a student to give the answer. Teacher will stress the importance of students’ knowing these facts.

MA/GA: Students will quiz one another with their division flashcards. GA/PA/MO: Class will play “Around the World” to review the division facts up to 81 ÷ 9.

PS: Students will complete the division review, from http://www.edhelper.com /math/division_tg390.htm. PA: Class will go over and discuss the answers for the review sheet.

Rebecca VanVliet EDUC 410-002

Monday Day 56 RVSOL M 3.12 Multiplication/ Division

Tuesday Day 57 RVSOL M 3.12 Multiplication/ Division

Math – Week 12 Wednesday Day 58 RVSOL M 3.12 Multiplication/ Division

Q: Teacher will begin class with a short, 20-question, written quiz on the basic multiplication and division facts, based on the students’ flashcards.

Q: Teacher will begin class with a short, 20-question, written quiz on the basic multiplication and division facts.

Q: Teacher will begin class with a short, 20-question, written quiz on the basic multiplication and division facts.

Q: Teacher will begin class with a short, 20-question, written quiz on the basic multiplication and division facts.

Q: Teacher will begin class with a short, 20-question, written quiz on the basic multiplication and division facts.

PS/MA: Students will use blocks and other manipulatives to “act out” the word problems on pages 3 and 4 of Wurst, concerning candles.

GA/PS: Students will work in groups to solve the story problems on pages 102 through 104 of Wurst. Groups will discuss how to solve each problem, and agree on an answer.

TD: Teacher will have twenty-five blocks, and ask the class how many groups of four can be made. Teacher will divide the blocks into groups, and ask students what they notice (there is one left over).

M: Teacher will review remainders of one, and explain that remainders can be from one up to one number less than the divisor.

PS: Teacher will call out facts and students will write the answers on a white board and hold them up to be checked. M/T/GA: Students will practice their multiplication and division facts by competing against a partner in “Arithmetic Four” from http://www.shodor.org/ interactivate/activities/ ArithmeticFour/? version=1.5.0_11 &browser=Mozilla &vendor=Sun_Micro systems_Inc (game will be set to “whole number multiplication” and “whole number division.”

Wurst, pp.3-4

GA: Students will share their ideas with a group, and decide which ideas they like best. Groups will explain one method for solving each problem creatively. OL/PA: Class will discuss the different ways to arrive at an answer. PS: Students will complete a worksheet on multiplication story problems from http://www.edhelper.com /math/multiplication_tg 221.htm.

VA: Each student will choose one of the story problems, and create a picture depicting what is happening. Students will be allowed to use magazines, markers, crayons, construction paper, etc. Students will be encouraged to use a lot of color (problems are about jelly beans). PS Students will complete a worksheet on division story problems from http://www.edhelper.com /math/division_tg323.htm.

Wurst, pp.102-104

Thursday Day 59 RVSOL M 3.12 Multiplication/ Division

Friday Day 60 RVSOL M 3.12 Multiplication/ Division

M: Teacher will explain the concept of remainders in division, and show how to write the answer to a problem with remainders of one. MO/PS: Teacher will pass out cards with colored numbers on them and cards with a number of colored dots on them. Students will find the partner with the same color card, and see how many groups of the number can be made by grouping the dots. The left over dot will be the remainder. The students will practice writing the answer with a remainder, and switch colors with another student. DA: Students may use “Think It Through ®” Tiles, Pizza Pepperoni & Practical Math (Division) p.7 to practice more division with remainders of 1.

PA: Teacher will ask students why they think the remainder can only be as big as one less than the divisor? Discuss. PS/PA: Students will complete the word problems for Monday and Thursday on pages 36 and 37 of Wurst. Class will discuss the remainders they found.

Wurst, pp.36-37

Rebecca VanVliet EDUC 410-002

Monday Day 61 RVSOL M 3.32 Commutativity

Tuesday Day 62 RVSOL M 3.32 Commutativity

Math – Week 13 Wednesday Day 63 RVSOL M 3.32 Commutativity

TD: Teacher will hold up a stick of five blocks in one hand and a stick of four blocks in the other. Teacher will ask the class, “If I have five blocks and four blocks, is that the same as having four blocks and five blocks? Why or why not?” Students will respond.

OL: Students will recite the definition of commutativity.

OL/W: Students will recite and write the definition of commutativity.

M: Teacher will review fact families, and explain how the concept of commutativity is essential for the fact families.

TD/PA: Teacher will write the multiplication sentence 6 x 5 = 5 x 6. Teacher will ask students if the sentence is true. How do they know? Teacher will ask students to solve each side to see that the two sentences both equal thirty. Teacher will ask students if all multiplication facts work the same way.

M: Teacher will explain the definition of “commutativity” in terms of addition, by placing the sticks end-to-end: four and then five, and five and then four, to show that both ways form a stick of nine. OL: Students will repeat the definition of commutativity. TD: Teacher will write 5 + 6 = 11 on the board. Teacher will ask students to identify another way to write the same numbers to get the same answer. Teacher will remind students of their fact families from earlier in the year. Students will respond. Teacher will write 5 + 6 = 6 + 5 to illustrate the principle of commutativity.

MO/GA: Teacher will divide the class into groups of three, to be their own fact family. Teacher will write the names of the students in each group on the board. Teacher will ask that each group decide amongst themselves who will be what number (the numbers must all agree, or be part of the same fact family – they can’t be 5, 7, and 8, etc.) Students will each write their number on a piece of paper, and tape it to their shirt. One at a time, teacher will call groups to line up at the front of the room. Students will explain their fact family (how the numbers relate). Teacher will ask the two students on the left to switch (#1-#2-#3  #2-#1-#3). Teacher will ask the class if the students are still the same fact family. Students will understand that order does not matter in addition.

GA: Groups will gather to review the multiplication tables from memory or their flashcards, and decide if all multiplication problems are commutative. M: Teacher will explain commutativity in terms of multiplication. TD: Teacher will show commutativity in multiplication by using a grid and a rectangle of paper to show that the size (total) does not change just by turning the rectangle on the grid (to be, for example, 5 across and 6 down, or 6 across and 5 down).

Thursday Day 64 RVSOL M 3.32 Commutativity

Friday Day 65 RVSOL M 3.32 Commutativity

OL/W: Students will recite the teacher’s definition of commutativity and discuss what it means in their own words.

OL/W: Students will recite the teacher’s definition of commutativity and rewrite it in their own words.

PA/GA/OL: Teacher will write the following on the board: “Find both an addition problem and a multiplication problem that equals 30. Use the commutative property to list another of each.” Students will work in groups to come up with an answer. Groups will be prepared to explain their problems and reasoning to the class. PS: Teacher will list the problems that students come up with on the board, and ask students if they can identify any more addition or multiplication problems that are not listed. The class will compile the problems into an “Amazing Thirty” chart.

M/A/VA: Students will choose a number sentence that represents commutativity in either addition or multiplication, such as 5+6=6+5 or 5x6=6x5. Students will illustrate their number sentence in a picture. Students must include the number sentence, the answer (sum or product), and a definition of commutativity in the students own words. The class will form a collage on one wall, using their pictures.

DA: Students may use the computer to design their picture if needed.

Rebecca VanVliet EDUC 410-002

Monday Day 66 RVSOL M 3.20 Relating Mathematical Relationships to Life

Tuesday Day 67 RVSOL M 3.20 Relating Mathematical Relationships to Life

M: Teacher will explain that math is found everywhere in life.

M: Students will be presented with the scenario of a group of kids out biking, some on bicycles and some on tricycles. If there were 23 wheels, how many kids were there?

PA/PS/GA: The class will brainstorm examples of people using math in everyday activities. MO/GA: Groups of students will choose one activity from the list, and silently act it out for the class. Class must guess the activity and the math concept being used. PA: Class will discuss the activities that were performed.

Cornett, p. 266

GA/PS: In groups, students will discuss all the possible ways to arrive at a solution, and all the possible solutions. Groups must be sure to record all their workable possibilities. M/PA/OL: Teacher will ask each group to give one answer and explain how they arrived at that answer. Teacher will then ask how having more information would affect the possible solutions. Teacher will tell the students that there were more than two tricycles, and ask students to narrow their solutions accordingly. Students will again suggest possible solutions, and discuss the ways gaining more information limited the possible answers.

Molyneux, p.12

Math – Week 14 Wednesday Day 68 RVSOL M 3.20 Relating Mathematical Relationships to Life M: Students will be given a review list of all the topics covered in class so far (place value to commutativity). GA/MO/VA/W: Groups of students will choose a topic from the list, and decide how they want to relate the topic to life. Students may write a short story, act out a drama, sing a song, etc. that somehow connects the topic to something outside of “school.” (Setting can take place in school, but the topic has to be applied to some area of life, and not just be a repeat of the lessons in class.) Presentations need not be more than a few minutes long.

Thursday Day 69 RVSOL M 3.20 Relating Mathematical Relationships to Life

Friday Day 70 TEST

GA: Groups will finish preparing their presentations, and present them to the class.

M/MO/CM/OL: Students will play the game, “Someone Who Can,” which involves finding a student to complete each activity in a grid. Each person who completes an activity must explain their solution to the person whose paper they are filling out, and must sign the box as well. Once everyone has found someone to complete each box, the teacher will review the answers and the topics of each box, and administer the test.

PA: Class will discuss the math concept and the connection to life after each performance. M: Teacher will help students review for the test.

E/M: Test will be on telling time, counting money, multiplication, and division.

TD/PA: Teacher will generate an idea list on the board if students need help. Students will contribute their ideas for other groups to choose from. DA: Students with accommodations will be allowed to leave the room to go to a less distracting testing environment. Molyneux, p.25-27

Rebecca VanVliet EDUC 410-002

Monday Day 71 RVSOL M 3.16 Measuring Length

Tuesday Day 72 RVSOL M 3.16 Measuring Length

Math – Week 15 Wednesday Day 73 RVSOL M 3.16 Measuring Length

M: Teacher will explain length as a distance that can be measured. Students will measure using unconventional units.

M: Teacher will instruct the students on the standard measurement units of inches, feet, and yards.

M: Teacher will instruct students in the metric units of measurement: centimeters and meters.

TD: Teacher will show the class a foot-long inch ruler, and explain the size of inches and explain that twelve inches equals one foot. Teacher will show a yardstick, and explain that three feet equals one yard. Teacher will ask students to think of a way to discover how many inches are in a yard.

PA/TD/T: Teacher will show the class a centimeter ruler, and ask students to compare it to an inch ruler. Students will note similarities and differences, and estimate how long they think the pencil will measure in centimeters, based on the previous two lessons. Teacher will measure the pencil for the class to see. Teacher will also show the class a meter stick, and ask the class to compare it to a yardstick.

TD/T: Teacher will use an overhead projector to show the class that a pencil is approximately equal to 6 paperclips. Therefore, the length of the pencil would be said to be 6 paperclips long. Teacher will explain that this kind of measurement is subjective, because it will change depending on the size of the pencil and the size of the paperclips used to measure it. Students will measure their own pencils using paperclips, and compare results. MA: Students will use “Think It Through®” Tiles (Discovery Toys – Book on measurement, time, and money, pp.24-25) to measure household objects in “units.” MO/W/PA/PS: Students will demonstrate their ability to measure by measuring the length of the room with their foot sizes. Students will walk heel-to-toe across the entire length of the classroom, and record the number of steps (footlengths) it took to get across. The class will compare answers. What was the largest number of footlengths? Smallest? What does that say about the sizes of different students’ feet? W/PS/MA: Students will complete a worksheet on measuring different lengths using unconventional methods (measuring the text book with paperclips, measuring the desk with pencils, etc) using the specified materials to measure the concrete objects in order to gain an answer.

TD/T/PA: Teacher will ask students to determine which unit would be best to measure a pencil with (inches, feet, or yards.) Students will explain their choice. Teacher will use an overhead projector again to show the measurement of the pencil again, this time using inches. Teacher will explain that this measurement is less subject to change, because inches are always the same size. Students will measure their own pencils using an inch ruler, and compare the results, discussing why answers will still be different even though the units are consistent. MO/W/PA/PS/GA/OL: Students will be placed in groups of four, and again measure the length of the room. Each group of four will be split into partners (two and two) and one set of partners will measure using foot rulers, and the other set will measure using yard rulers. Each group will record both measurements on a sheet of paper, and discuss as a group which method worked best, and why. Groups will be prepared to explain their conclusion and reasons to the class. HW: Students will complete a worksheet on measuring using inches, feet, and yards.

PS/GA/CM: Students will gather into groups, and brainstorm a list of items in the classroom that they think are one meter in length, and another list of items in the room that they believe are one centimeter in length. Once the group has at least five items on each of their lists, they will be given meter sticks and centimeter rulers and allowed to measure the objects they chose, to see if their guesses were correct. For any [drastically] incorrect guesses, students will be allowed to measure other objects in order to replace the objects that were not the right size. Each group should end with a list of five items of each length. MA: Students will use “Think It Through®” Tiles (Discovery Toys – Book on measurement, time, and money), and choose between pp.28-29 and 30-31, to practice measuring household objects in cm. HW: Students will complete a worksheet on measuring using meters and centimeters.

Thursday Day 74 RVSOL M 3.16 Measuring Length

Friday Day 75 RVSOL M 3.16 Measuring Length

M: Teacher will review the conventional units that have been taught: inches, feet, yards, centimeters, and meters.

M: Teacher will instruct students in miles and kilometers.

PS/PA/OL: Teacher will ask students how they would measure something that was not flat. Teacher will write all suggestions on the board. LI/MO/W/PS: Teacher will cut a piece of string for each student that is as long as the student is tall, and explain that the students will be using the string to measure parts of their bodies. Each student will use their piece of string to measure different body parts (around the head, down the arm, whole height, length of foot, arm span, etc.) and mark each distance on the string with a marker. Students will then measure each distance (length of string) using all possible appropriate methods and record their measurements. (Ex: length of leg could be 36 inches, 3 feet, 1 yard, 91 cm, and almost 1 meter. Width of hand could only be 3 inches or 8 cm – all other units are too large.) Students will then compare their measurements, and comment on any surprises (arm span approximately the same length as height, etc).

HW: Students who do not finish the worksheet in class will complete it for homework.

DA: Students who are unable to walk will pair up with a partner and help them count steps, and use their results to compare with the rest of the class. Burns, pp. 36-37

LI/PA: Teacher will ask the class, “What unit would you use if you wanted to measure larger distances, say, the distance from your house to school? Or the distance from your house to your grandparents’ house in another state?” Students will respond. Teacher will introduce miles and kilometers, explaining that they are too big to use rulers to measure these, and that there are special functions in a car that allow us to know how far the distances are (odometer). M/PS: Teacher will instruct students in using scale drawings and maps to measure and convert between inches and miles, if each inch represents 500 feet, or between centimeters and kilometers if each centimeter represents 200 meters. A/VA/PS/W: Students will make their own map using their own scale, such as “the width of my hand represents one mile,” and distances will then be labeled in both “handwidths” and miles.

Rebecca VanVliet EDUC 410-002

Monday Day 76 RVSOL M 3.17 Measuring Liquid Volume

Tuesday Day 77 RVSOL M 3.17 Measuring Liquid Volume

M: Teacher will explain the Cup as a measuring tool for liquids.

M: Teacher will explain the Pint and Quart as measuring tools for liquids. Teacher will explain the relationship between cups and pints, and pints and quarts.

PA: Students will generate a list of common liquid measurements using cups (water for drinking, milk and other liquids for cooking, etc.) PS/MA/GA/H: Teacher will present the students with the health fact that people are supposed to drink 6-8 cups of water each day. Teacher will give each group of students a regular size drinking glass, and ask the students how many drinking glasses of water a person would have to drink in order to drink at least 6 cups of water. How many would a person need to drink to get 8 cups? Students will work together to develop an answer. What does this say about the volume of a drinking glass in comparison to a cup of water?

PA: Students will brainstorm a list of common measurements that use the pint, and another list for the quart. GA: In groups, students will complete a chart on conversion facts (how many cups would be in two quarts? etc.)

Math – Week 16 Wednesday Day 78 RVSOL M 3.17 Measuring Liquid Volume M: Teacher will explain the Gallon as a measuring tool for liquids. PA: Students will generate a list of liquids measured in gallons (milk, gasoline, etc.) MA/PS/GA: Teacher will provide groups of students with cup, pint, quart, and gallon measuring tools, and ask students to determine how many cups, pints, and quarts are in one gallon. After the groups are finished, the teacher will ask the students if they noticed anything about the measurements (if there are 4 quarts in a gallon, we don’t need to measure the rest of the units, because we know how many pints are in a quart, and how many cups are in a quart.) HW/HS: Students will find at home some kind of container that holds liquids (water bottle, empty milk jug, empty bottle of engine oil, etc.), wash it, and bring it to school the next day.

DA: Students with special needs will be provided with a printed chart of the conversion facts.

Thursday Day 79 RVSOL M 3.17 Measuring Liquid Volume

Friday Day 80 RVSOL M 3.17 Measuring Liquid Volume

M/PA: Teacher will ask students to find the measurement on their container (PT (pint), QT (quart), etc.). Teacher will ask students if there is any other measurement on their container as well. Most containers are also marked in metric. Teacher will explain that in the same way that length is measured in standard and metric units, so is liquid. Teacher will introduce milliliters.

M: Teacher will explain the Liter as a tool for measuring liquid volume. Teacher will explain the relationship between milliliters and liters.

PA: Students will brainstorm a list of common liquids measured in milliliters (cough medicine, bottled drinks, etc.).

PA: Students will brainstorm liquids that are commonly measured in liters. PS: Teacher will present the class with different scenarios, and the class will determine which measurement tool they would use. Teacher will specify metric or standard (American) units.

Rebecca VanVliet EDUC 410-002

Monday Day 81 RVSOL M 3.18 Measuring Weight/ Mass

Tuesday Day 82 RVSOL M 3.18 Measuring Weight/ Mass

M: Teacher will introduce measuring weight using ounces and pounds.

M: Teacher will review measurement using ounces and pounds.

PA: Teacher will ask for a volunteer to share how much they weigh with the class. Teacher will ask students to notice the unit that the student says: pounds. Teacher will explain the pound as a unit of measurement. TD/PA: Teacher will hold up a pencil, and ask students how much they think the pencil weighs. If students hesitate, teacher will ask them to feel the weight of their own pencil, and take a guess. Teacher will ask students how they can find out the answer. Teacher will introduce a balance/scale as a tool for finding out how much something weighs.

GA/MO/PS: Teacher will set up measuring stations around the room, each with a balance and an item. Students will circulate in pairs or threes, estimating the weight of each item (in ounces or pounds) before measuring it. Students will record their estimates and measurements on a worksheet. Students will use their textbook as a guide for estimation, because it weighs approximately one pound.

MA: Students will use the balance to determine the weight of their pencils. Students should run into a problem – the pencil weighs less than one pound.

T: Students will go to http://www.studyzone.org/ testprep/math4/e/ounces pounds3p.cfm to choose between ounces and pounds for weighing common objects.

M: Teacher will introduce ounces as a unit for measuring small weights. Teacher will explain that there are sixteen ounces in one pound.

PS: Students will complete a worksheet on estimating weights of common items in ounces and pounds.

MA: Students will measure the weight of the pencil in ounces. PS/MA: Teacher will then have students place the following objects in order by weight (by guessing): pencil, baseball, math book, lunchbox, and stapler. Students will guess which would be more appropriate: ounces or pounds, for each item. Students will measure using the balance to find out if they were correct.

Math – Week 17 Wednesday Day 83 RVSOL M 3.18 Measuring Weight/ Mass M: Teacher will introduce the metric units of measurement: grams and kilograms. TD: Teacher will hold up the pencil again, and explain that the class is going to use a different unit of measurement today. Teacher will explain the gram as a unit of measurement. MA/PS: Students will measure the pencil in grams using the balance, and compare the measurement to the measurement in ounces from before. Which is bigger? What does that say about the weight of a gram compared to an ounce? Class will discuss. M: Teacher will explain that just like pounds are larger units than ounces, there is a unit larger than a gram. Teacher will introduce the kilogram as weighing the same as 1000 grams. Teacher will have a kilogram weight for the students to feel. PS/MA: Students will use the balance, and find an item in the classroom that weighs [close to] one kilogram (students may have to try many items before they find one). Students will find one item that weighs one gram as well (paperclips are a good start). PA: Class will discuss the differences in size and weight.

DA: Gifted students may use a computer to look up the weights of the different animals that are shown. Molyneux, p. 151

Thursday Day 84 RVSOL M 3.18 Measuring Weight/ Mass

Friday Day 85 RVSOL M 3.18 Measuring Weight/ Mass

M: Teacher will review measuring weight using grams and kilograms.

TD/VA/PA: Teacher will show pictures of various animals, and students will tell whether they think it would be easier to measure using ounces or pounds. Class will discuss.

GA/MO/PS: Teacher will set up measuring stations around the room, each with a balance and an item. Students will circulate in pairs or threes, estimating the weight of each item (in grams or kilograms) before measuring it. Students will record their estimates and measurements on a worksheet. Teacher will guide the students’ estimates by writing on the board that one kilogram is equal to a little more than two pounds. PS: Students will complete a worksheet on estimating the weights of common items in grams and kilograms.

TD/VA/PA: Teacher will show pictures of different animals, and students will tell whether they think it would be easier to measure using grams or kilograms. Class will discuss. PA: Class will compare the pictures that they guessed “ounces” and “grams” for. Are they the same pictures? Why? GA/MA: Class will be divided in half (one half will work with metric, the other half with standard units). Students will cut pictures from magazines, and divide the pictures into two groups: ounces and pounds (or grams and kilograms). GA/VA: Each group will combine their pictures, and make a collage of weights. Each collage will have two sections: the standard collage will have a section marked “ounces” and a section marked “pounds,” and the metric will have “grams” and “kilograms” sections.

Rebecca VanVliet EDUC 410-002

Monday Day 86 RVSOL M 3.23 Measuring Area with Concrete Models

Tuesday Day 87 RVSOL M 3.23 Measuring Area with Concrete Models

M: Teacher will explain area as the amount of space a surface takes up.

M: Teacher will review the concept of area.

PS: Students will predict the number of different units (small tiles, cubes, square cards, pattern blocks, and a unit of the student’s choice) it will take to cover the surface of their math books. W/MA/PS: Students will record their prediction on the given chart, and then measure the area with the desired units to get the actual value. Students will record this value as well. Students will discuss and determine which unit they feel was the best to use for measuring the book. PS/MA: Students will then use the same units to cover the surface of their desks. Students will discuss what units worked better and why. Were they the same units that worked best for measuring the surface of the book?

TD/PA: Teacher will show the class a shallow cardboard box (paper-box top, or similar) and wooden cubes. Teacher will ask students to estimate how many cubes it would take to cover the bottom of the box. Teacher will write student estimates on the board. Teacher will place a line of cubes along one side of the box, and ask students if that helps them visualize the number of cubes it will take. Students may revise their estimates if they choose. GA/MA: Students will be divided into groups, and each group will be given a box and a bag of cubes. Students will work together to discover how big the area of the box is in cubes. PS/PA: Teacher will ask students to predict what would happen if they were given smaller cubes to measure with. How would that affect the number of cubes used? Would it change the area of the box? Why or why not? Teacher will direct student thinking toward area as unchanging, and the usefulness of standardized units.

Math – Week 18 Wednesday Day 88 RVSOL M 3.22 Measuring Area

Thursday Day 89 RVSOL M 3.22 Measuring Area

Friday Day 90 RVSOL M 3.22 Measuring Area

M: Teacher will instruct the students in measuring area using graph paper/ grid lines.

M: Teacher will teach students to measure the area of rectangular shapes by multiplying the value of two adjacent sides (base x height).

T/TD/PA: Teacher will use overhead graph paper to project shapes onto the board. Students will determine the area of each by counting the squares inside the shapes.

TD/PA: Teacher will show students a rectangle drawn on grid paper, and ask students to find the area (by counting), and teacher will demonstrate counting the squares to find the area. Teacher will then show students another shape on grid paper, but with no visible squares inside (grid visible outside the shape). Teacher will ask for student suggestions on how to find the area of the shape. Teacher will then explain that there is a way to find the area using multiplication. Teacher will refer back to the rectangle with the visible grid inside, and show students how the area is equal to the product of two adjacent sides. Teacher will return to the shape without the grid inside, and count the number of squares along the sides, writing them down. Teacher will ask students if they can now find the area. Once a few students have answered, teacher will demonstrate the multiplication, and place a clear grid over the shape so students can count the squares to prove their answer is correct and that the multiplication method works.

M: Teacher will instruct students in measuring the area of non-rectangular shapes using base x height and subtraction (forming a rectangle around the shape).

VA/PS/PA: Students will trace their shoe on a piece of centimeter graph paper, and estimate the area of their shoe by counting the squares inside the outline. Teacher will ask students what they think they should do about the partial squares. Can any be combined to form whole squares? T: Students will go online to http://www.shodor.org/ interactivate/activities/Area Explorer/?version=1.6.0_02 &browser=MSIE&vendor =Sun_Microsystems_Inc to practice measuring area by counting the squares. Students can adjust the size of the shape by moving the bar at the bottom of the page.

TD/PS: Teacher will pass out grid paper with shapes drawn on it, and show students how to draw a rectangle around the shapes, touching each side. Teacher will demonstrate finding the area of the rectangle by multiplying two adjacent sides, and explain that in order to find the area of only the shaded shape, the extra pieces of the rectangle must be subtracted. Students will complete similar problems on their own. T: Students will go online to http://www.shodor.org/ interactivate/activities/Area Explorer/?version=1.6.0_02 &browser=MSIE&vendor =Sun_Microsystems_Inc and click the “Show Outline” button to practice measuring area by finding the area of the rectangle, and subtracting the white spaces.

GA/PS: Teacher will assign problems that have no grid lines at all, and only have the length of two sides labeled. Students will work with a partner to find the area of each shape using multiplication.

DA: Students with special needs will be given concrete materials instead of graph paper (wooden cutouts of shapes, and a rectangle with grid lines drawn on it, that the student may place the shape on top of). Molyneux, pp.52

Molyneux, p.151

Rebecca VanVliet EDUC 410-002 Math – Week 19 Wednesday Day 93 RVSOL M 3.27 Collecting Data

Monday Day 91 RVSOL M 3.27 Collecting Data

Tuesday Day 92 RVSOL M 3.27 Collecting Data

M: Teacher will instruct the class in different methods of collecting and organizing data.

M: Teacher will review methods for gathering data, and introduce methods of recording data.

M: Teacher will review the methods for gathering and recording data.

PA: Teacher will ask students to imagine they are trying to find out how many birthdays occur every month in their class. Students will give the best method of collecting data (survey). Teacher will ask students for suggestions on how they will keep track of the information. Students will volunteer answers and ideas.

GA/PS/CP: Students will be divided into groups of three. Each group will decide on a topic they want to investigate, using one of the methods of collecting data. Teacher will emphasize that the topic must be one that can be investigated at school, as the class will have the rest of the week in class to work on it. Students will also agree on how to organize their information. Students will take the remaining class time to begin collecting data.

PA: Teacher will ask the class to come up with ways to collect information. For example, the teacher will ask students how they would go about gathering information about the length of the table (“look at it” – observation; “measure it” – measurement; “ask somebody who would know” – survey, “compare it to another table” – experiment). Teacher will record student responses. TD: Teacher will explain each of the four methods of gathering information, and provide examples of how each is used. W: Students will write their own definition for each method, and write their own example of how each would be used. PA: Students will share their examples. (“If I wanted to find out how many people have a birthday in March, I would use a survey.” “If I wanted to find out how many birds visited my birdfeeder every day, I would use observation.” etc.)

TD/PA: Teacher will write down student ideas, and explain tallies, charts, and tables as good ways to organize information. Teacher will make a table on the board, writing students’ names along the side, and the months of the year along the top (it will be a large table). Teacher will ask students to quickly tell the month they were born as their names are called, and teacher will fill in the table, putting a mark for each birthday. Teacher will ask the class if they think a table is a good way to record the information. (No, names are not needed.) Teacher will make a simpler chart: the headings will be the months of the year, and teacher will take the data from the table, to put a star or check mark in each column to represent the birthdays. Teacher will ask students if this was a better way to organize the information. (Yes.) Teacher will then say that there is another similar way to organize the information, and this is the tally system. Teacher will write each month, and tally up the number of birthdays each month. Teacher will explain that the tally method works best for large quantities of information (with birthdays, there may not be enough each month to make tallies any more effective than a simple chart.) W: Students will summarize each form in their notes. DA: Teacher will have premade table and chart outlines for students who need them, and they will be able to copy the information from the board.

TD: Teacher will explain that students must choose a topic that is more than simply measuring a table (as the first example for collecting data was). Teacher must OK the groups’ ideas before they begin gathering data. Teacher will offer suggestions if groups cannot come up with or agree on a topic.

CP: Cooperation

Thursday Day 94 RVSOL M 3.27 Collecting Data

Friday Day 95 RVSOL M 3.27 Collecting Data

M/GA/PS/CP: Students will work together in their groups to gather and record their data. Teacher will check with each group to see that they are properly gathering and recording their data, and to answer any questions.

M: Teacher will review the methods for organizing data. GA/PS: Groups will be encouraged to finish gathering their data. VA: Groups will organize and display their information in a neat and visually appealing tally, chart or table, and decorate the display to fit their topic. Students will be allowed to type the information, use markers or poster board, or any other way of neatly representing their information. Group members will include their names on the display, and turn in the data for the teacher to look over. (Groups will get their information back next week.)

Rebecca VanVliet EDUC 410-002

Monday Day 96 RVSOL M 3.28 Graphing Data

Tuesday Day 97 RVSOL M 3.28 Graphing Data

Math – Week 20 Wednesday Day 98 RVSOL M 3.28 Graphing Data

M: Teacher will introduce methods of displaying information visually.

M: Teacher will review pictographs and bar graphs briefly, and introduce two other methods of visually representing data.

M: Teacher will briefly review the four types of graphs, and give groups back their data from the previous week.

TD: Teacher will introduce pie graphs as a method of plotting information. Teacher will show an example of a pie graph, explain that pie graphs are useful for expressing information in terms of the fraction each piece of information represents of a whole.

PS: Students will practice tallies and bar graphs using p. 32 of Wurst.

TD: Teacher will introduce pictographs as a way to plot information. Returning to the birthday example from the week before, the teacher will demonstrate how each piece of information will be represented by a picture. Teacher will use a birthday graphic to plot all of the birthdays, while explaining the properties of a pictograph. PA: The class will discuss the kinds of things that can be graphed using a pictograph. TD: Teacher will introduce bar graphs as another way to plot information. Similar to a pictograph, except that instead of pictures representing the data for each heading (month) the data is represented by a line of a certain size. Teacher will note that when using a bar graph, a scale is needed along one side, to show how many pieces of information each bar represents. PA: Students will discuss reasons why it might be better to use a bar graph in some cases than a pictograph. (If there is too much information to be represented by individual pictures, etc.)

PA: The class will discuss different reasons for using a pie graph, and the ways in which it is different from pictographs and bar graphs.

GA: Groups will decide which type of graph will work best for the information they gathered, and begin to construct a graph based on their data. Teacher will circulate among the groups, offering suggestions if needed, and answering questions.

PS: Students will complete the pie graph (“circle graph” Wurst, p.35). TD: Teacher will introduce line graphs as another way to plot information. Teacher will show a line graph, and explain that line graphs are good for tracking the way things change over time. The points represent the actual information that was gathered, and the direction of the lines represents whether the data increased, decreased, or remained steady. Teacher will stress the need for a number scale along both the bottom and side (axis) of the graph to show the value of each point. PA: Class will discuss the usefulness of line graphs, and the similarities and differences with the other forms of graphs. DA: Students who struggle with constructing their own graphs may use http://nces.ed.gov/ nceskids/graphing/classic/ to help them. (This site will not work for pictographs.)

Wurst, p.35

Wurst, p.32

Thursday Day 99 RVSOL M 3.28 Graphing Data

Friday Day 100 RVSOL M 3.28 Graphing Data

GA/VA: Groups will finish graphing their data, and combine the graph and the chart/table/tally of information from the week before into a neat and appealing presentation (either a poster or a stand up display). Groups will discuss among their members how they want to present the information. Teacher will remind them that everyone needs to take part in the presentation.

GA/OL: Groups will present their projects to the class, explaining what they chose to investigate, how they gathered the data, and why they chose the type of graph they used to display the information.

Rebecca VanVliet EDUC 410-002

Monday Day 101 RVSOL M 3.29 Interpreting Graphs

Tuesday Day 102 RVSOL M 3.29 Interpreting Graphs

Math – Week 21 Wednesday Day 103 RVSOL M 3.29 Interpreting Graphs

M: Teacher will instruct the class in reading different types of graphs to gain information.

M: Teacher will review reading pictographs and bar graphs, and instruct the class in reading table graphs.

M: Teacher will review reading pictographs, bar graphs, tally graphs, and tables, and introduce reading pie charts.

TD: Teacher will show a table, and explain the different parts. Teacher will call on students to interpret parts of the table.

TD: Teacher will show a pie chart, and review what it is used for. Teacher will call on students to read different aspects of the pie chart, and answer questions based on the information that is given.

TD: Teacher will show a pictograph, and review how a pictograph is constructed. Teacher will call on students to interpret the different symbols on the graph. Teacher will also instruct the class in reading a bar graph, making note of the number scale along the side/bottom. PA: Students will discuss the similarities and differences in the way the two graphs are interpreted. PS: Students will complete a worksheet on reading pictographs from http://www.edhelper.com /math/graphs301.htm, and complete another worksheet on transferring information from a pictograph to a bar graph from http://www.edhelper.com /math/graphs302.htm, and interpreting bar graphs, from http://www.edhelper.com /math/graphs207.htm.

PS: Students will complete a worksheet on interpreting information from a table, from http://www.edhelper.com /math/graphs304.htm. TD: Teacher will show a tally graph, and explain that each tally represents one piece of information. Teacher will call on various students to interpret the graph.

PA: Students will compare the pie chart to the other graphs, noticing similarities and differences.

Thursday Day 104 RVSOL M 3.29 Interpreting Graphs

Friday Day 105 RVSOL M 3.29 Interpreting Graphs

M: Teacher will review the ways to interpret the different kinds of graphs discussed in class.

MO/PS: Students will finish their questions based on interpreting the graphs of the different projects.

MO/PS: Teacher will set up the students’ projects from the past week around the room, and design questions based on the different graphs. Students will be given a sheet with the questions and which project they came from, and use the graphs and charts from the projects to complete the worksheet.

M: Teacher will go over the questions from the projects, and review how to interpret the different kinds of graphs.

PS: Students will complete a worksheet on reading and interpreting pie charts.

PS: Students will complete a worksheet on reading tally graphs from http://www.edhelper.com /math/graphs307.htm.

DA: Students with mobility handicaps will be given photocopies of the important parts of the graphs for interpreting.

TD/PA: Teacher will show an example of each kind of graph, and describe different features and functions of each. Students will guess which kind of graph is being described.

Rebecca VanVliet EDUC 410-002

Monday Day 106 RVSOL M 3.30 Probability

Tuesday Day 107 RVSOL M 3.30 Probability

Math – Week 22 Wednesday Day 108 RVSOL M 3.30 Probability

M: Teacher will instruct students in probability using dice.

M: Teacher will instruct students in probability using coin tosses.

M: Teacher will instruct students in probability using spinners.

GA/MA/CP: Teacher will divide the class into groups of four, and have the students in each group agree on how many times they will have to roll a die to have each number appear. Teacher will write each group’s prediction on the board.

PA/TD: Teacher will ask students to predict the chance of tails coming up when a penny is tossed. Teacher will demonstrate tossing a penny and recording the results. Teacher will explain that the probability is 50-50, or ½. Class will discuss why it is probability.

TD: Teacher will show and explain how a spinner works.

TD/PA: Teacher will explain that students will roll the die and record the number that comes up. Teacher will demonstrate rolling the die, and recording the number. Students will volunteer different ways to record the values: tally marks, a list, a chart, etc. GA/MA: Students will roll and record until either every number comes up, or the teacher asks students to stop. PA: Teacher will call on groups to share their results, and record the results in one list on the board. Class will discuss why they think it took as many rolls as it did, and discuss how close to the predictions they were. Class will discuss the diversity among the groups’ results as well.

GA/CM: Teacher will divide the class into groups, and have them discuss the possible outcomes of tossing two coins. How many ways can the coins possibly turn up? Groups will also discuss how many tosses they think it will take to have all four possibilities come up.

MA: Students will have individual spinners, and teacher will give students a few minutes to spin the spinners twenty times and record the results. Teacher will tally the results on the board, and ask students if they see any similarity in the number of times one color/number was spun, and the times that color/number appears on each spinner. Teacher will explain that the more times the color/number appears on the spinner, the greater the probability of choosing it.

GA/MA: Students will toss the two coins, and record their results.

PA/PS: Students will notice the comparison between spinners and fractions.

PA: Class will come together again and discuss their results. Teacher will make a chart of how many tosses it took, and class will discuss reasons and ideas.

GA/CM: Students will complete the worksheet from http://www.edhelper. com/math/probability_tg 704.htm in groups of three. Students will discuss how they arrive at each answer. HW: Students will complete the worksheet from http://www.edhelper. com/math/probability_tg 705.htm. Teacher will encourage students to shade the spaces with the desired letter to help them see the spinner as a fraction circle.

CP: Cooperation

DA: Gifted students can predict the possible outcomes of three coins, and test their results.

Molyneux, p. 153

Molyneux, p.155

Thursday Day 109 RVSOL M 3.30 Probability

Friday Day 110 RVSOL M 3.30 Probability

M: Teacher will instruct students in probability using marbles.

M: Teacher will review the four kinds of probability discussed in class. Teacher will instruct students in the probability of letters.

TD/PA: Teacher will bring in a bag of marbles to class. Teacher will ask for volunteers to count the marbles. Each volunteer will count one color of marbles. Teacher will record the numbers on the board, and ask the class to determine the total number of marbles in the bag. Teacher will ask students to predict what color marble will be pulled, if the teacher reaches into the bag and pulls out one marble at random. Teacher will record student predictions, and pull out a marble. Class will discuss why they think that color was pulled. Teacher will ask what would happen if a marble was pulled out twenty times at random. Would one color be pulled more often than another? MA/PS: Students will make their own bag of “marbles” using construction paper in the same colors as the teacher’s marbles, cutting one circle per marble, with the same number of each color as the teacher’s bag (written on the board). Students will put their construction paper “marbles” into a brown paper sandwich bag, and pull one out at random twenty times, recording the color each time. PA: Teacher will record student totals on the board, and compare the number of times each color was pulled to the number of that color in the bag. Class will discuss the outcomes. M/PA: Teacher will direct the students in forming a fraction for each color out of the total in the bag, and for each color out of the total that were pulled in the twenty pulls. (Students will have two fractions for each color.)

TD/PA: Teacher will write a word on the board, and explain to the class that the letters are similar to the marbles, except that instead of different colors, this time there are different letters. Teacher will ask students to raise their hands to tell how many letters are in the word. Teacher will record the total on the board next to the word. Teacher will make a frequency chart of the number of each letter in the word, and ask students to predict which letter will be chosen the most/ least often, if one letter is chosen at random. PS/PA: Teacher will ask students to predict the probability of choosing each letter, based on the number of each letter and the number of total letters. Students will write their probabilities down, and teacher will encourage them to express their answers in fraction form. Students will be called on to share their probability fractions. PS: Teacher will write another word on the board, and students will determine the probabilities of each letter on their own. M: Students will complete the worksheet on probability from http://www.edhelper.com /math/probability_tg702. htm. DA: Students who have trouble grasping the abstract concept of probability will be allowed to write the letters on slips of paper and turn them upside down and physically choose one at random.

Rebecca VanVliet EDUC 410-002

Monday Day 111 RVSOL M 3.26 Symmetry

Tuesday Day 112 RVSOL M 3.26 Symmetry

M: Teacher will explain congruency.

TD: Teacher will show pictures of similar shapes. Students will make observations concerning the shapes (“they’re the same shape,” “they’re different sizes,” “they’re not congruent.”)

W: Students will copy the word and definition into their notes. TD: Teacher will show the class two identical shapes, and explain that they are congruent (same size and same shape). Teacher will demonstrate by placing one on top of the other and showing how they line up. MA/GA: Students will work in pairs with geoboards. One student will make a shape on the board, and the partner will try to duplicate the shape exactly on their own board. Then they will switch roles. VA/PS: Students will use “congruency cards” (found at http://www.mcrel.org /PDF/Curriculum/5021 CM_Shapes.pdf) which have two shapes per card, and students must determine whether or not the shapes are exactly the same size and shape. Students must think carefully, because the shapes may be turned or flipped. Students will sort the cards into two groups: those with congruent shapes, and those without.

M: Teacher will explain similarity. W: Students will copy the word and definition into their notes. MO/PS: Teacher will explain that the class is going to go on a “similarity scavenger hunt.” Each student will be given a sheet of paper with a variety of shapes on it. Students will search the classroom for their shapes, writing down where they found objects or shapes similar to the ones on the paper, and trace the objects if possible. PA: Class will re-gather, and the teacher will call on students to share the objects they found that were similar to each shape on the paper. Class will discuss the results.

Math – Week 23 Wednesday Day 113 RVSOL M 3.26 Symmetry TD/PA: Teacher will make two columns on the board, with the headings “I LIKE…” and “I DON’T LIKE…” and teacher will place “symmetry cards” in the columns, one pair at a time. Students will try to guess why the teacher “likes” or “doesn’t like” the cards. Once students can acknowledge a pattern, teacher will give it a name: symmetry. M: Teacher will explain symmetry. W: Students will write the word and definition in their notes. PA: Teacher will ask students to name more objects that would fit into the categories on the board, and the class will discuss how to find out if they fit. TD: Teacher will take one of the paper symmetry cards off the board, and show students that it is symmetrical by folding it in half, and showing that the two sides are the same. PS: Students will complete a worksheet on symmetry. Students will state whether each shape is symmetrical or not.

Thursday Day 114 RVSOL M 3.26 Symmetry

Friday Day 115 RVSOL M 3.26 Symmetry

M: Teacher will explain horizontal and vertical symmetry.

M/PA: Teacher will review horizontal and vertical symmetry. Students will be asked to give a definition of symmetry.

W: Students will write their own definition for each in their notes. VA: Students will view pictures of items that have vertical or horizontal symmetry. MA/GA: Groups of students will be given paper cut-outs of the letters of the alphabet, and asked to group the letters according to the kind of symmetry they have. Students will be encouraged to fold the letters to find the symmetry. Students should come up with four categories for the letters: no symmetry, horizontal symmetry, vertical symmetry, and both horizontal and vertical symmetry. PA: Class will discuss the symmetry they found, and the teacher will reproduce the students’ charts on the board for reinforcement.

S/MA/VA/W/GA: Teacher will hand out mirrors to the class. Students will experiment with letters and pictures that have symmetry. Each student will be given different shapes, that when held against the mirror will produce a letter of the alphabet. Students will record their prediction of the letter formed by each shape, and hold it to the mirror to see if they were correct. They will then record the kind of symmetry (horizontal or vertical). Students will trade shapes with those around them who have different ones. Students will also cut pictures from magazines to fold and hold against the mirror to see if they have symmetry. GA/VA: The class will post all their symmetrical pictures on a “symmetry collage” on a bulletin board in the classroom.

PS: Students will complete a worksheet on symmetry, in which students state whether the picture has horizontal symmetry, vertical symmetry, both, or neither. Students will draw lines of symmetry. Worksheet from http://illuminations.nctm .org/lessons/35/geometryart/Geometry Art-AS-CreatingLines.pdf.

DA: Students with special needs will be allowed to use a virtual geoboard instead of a concrete one (http://standards.nctm.org/ document/eexamples/chap 4/4.2/index.htm#applet). http://www.mcrel.org/PDF /Curriculum/5021CM_ Shapes.pdf, pp. 39-46

Klag, pp.227-229

Rebecca VanVliet EDUC 410-002

Monday Day 116 RVSOL M 3.31 Numeric and Geometric Patterns

Tuesday Day 117 RVSOL M 3.31 Numeric and Geometric Patterns

M: Teacher will define “pattern” as “a regular repetition of numbers, words, or sounds.” (Molyneux, p.73)

M/PA/PS/GA: Teacher will ask students to find a partner, and brainstorm as many different patterns in the world as they can in ten minutes. (Day/night, weeks, sidewalk squares, etc.) Remember, as long as it repeats in a recognizable way, it is a pattern. After ten minutes, students will share their ideas.

TD/PA: Teacher will make a simple AB pattern out of blocks for the students to see. Students will raise their hands to identify the pattern. MA: Students will use pattern blocks to create their own AB pattern. TD/PA/MA: Teacher will make a ABC pattern out of blocks for the students to see. Again, students will volunteer when they see the pattern, and mimic the pattern using their own pattern blocks. Teacher will ask students to extend the pattern in both directions. Teacher will demonstrate other patterns for the students to consider. MA/W/PS: Students will use string and beads to make pattern necklaces. Before they begin making the necklaces, they must first make a chart of the beads they will use. Teacher will encourage students to be creative and original, but still follow a recognizable pattern. Once the chart and pattern have been approved by the teacher, students will be allowed to begin forming their necklaces.

Molyneux, p.94

M: Teacher will explain that patterns exist everywhere. MA/W/GA: Students will use the matrix to design their own patterns for a partner to complete. They will use shapes and symbols, filling in every space except for one, and a partner will determine what goes in the empty space. MA/W: Students who finish early will use another matrix to discover patterns in their names, numbers, and whatever else they can, coloring the first letter, last letter, even numbers, multiples of three, etc. Students will be creative!

Math – Week 24 Wednesday Day 118 RVSOL M 3.31 Numeric and Geometric Patterns

Thursday Day 119 RVSOL M 3.31 Numeric and Geometric Patterns

Friday Day 120 TEST

M: Teacher will explain numerical patterns, beginning with 1,2,3,4,5…

M/S/SS: Teacher will explain the history of Pascal’s Triangle.

M: Teacher will review measurement, probability, symmetry and patterns.

T/TD/PA: Teacher will put a simple number sequence on the board, such as above, and ask the class what would happen if each number was doubled. Teacher will write the resulting numbers underneath the original line. Students will be allowed to discuss the results with their neighbors, and the teacher will call on students to name some observations, which will be listed on the board. Teacher will ask students to predict what will happen if each number is halved instead, or added to the one before it (Fibonacci). Students will begin to identify patterns.

PS/GA: Groups of students will be given copies of Pascal’s Triangle. Students in the groups must work together to find as many patterns as they can. See if anyone can guess how the entire triangle was constructed!

E: Test will be on these topics.

TD: After about twenty minutes, the teacher will guide students in finding more patterns. VA/PS: Students will use crayons and colored pencils to color certain numbers in the Triangle to create patterns.

M: Teacher will then explain how to identify numeric patterns by using the “Galloping V” – finding the difference between two consecutive numbers in a sequence, such as: 7, 11, 15, 19 \/ \/ \/ +4 +4 +4 W/PS/GA: Students will work in pairs to create their own patterns to share with the class. Each pair must show how the pattern works by using the Galloping V.

DA: Kinesthetic students will be allowed to form patterns with pattern blocks in the shape of a matrix instead of drawing the shapes in the blocks. They will still leave one space to be filled by a partner. Molyneux, p. 96-99

Molyneux, pp. 103-104

Klag, p.484-489

Rebecca VanVliet EDUC 410-002

Monday Day 121 RVSOL M 3.5 Fractions

Tuesday Day 122 RVSOL M 3.5 Fractions

M/MO/LI: Teacher will move all desks out of the way. Students will gather in the middle of the floor as one group. Teacher will ask the class how many students there are. Students will count and respond, and teacher will tell class to divide by two, to form two equal groups, one on each side of the room. Students will move. Teacher will ask the class to regroup and divide by three. Teacher will repeat with four. Class will sit down.

M/T: Teacher will use http://www.coolmath.com /fractions/fractions-01what-are-they-02.html to review the concept of fractions.

PA/TD: Teacher will ask students to recap what they just did. Teacher will mimic the class movements (as they are recalled) with fraction circles for the students to see. Teacher will explain fractions as a way to count parts of a whole, using the class (entire group of students) as the “whole.” (“This circle represents the class. Now when the class divided into two equal groups – halves – this is what it looked like, and if we wanted to count only one group, we’d be counting “one HALF” of the whole class…”) TD: Teacher will write each fraction out as well, and explain the denominator (how many pieces make up the whole), and the numerator (how many pieces we’re counting). LI/PS/CM: Teacher will ask students to imagine that the class divided into more than four groups. How would one of those groups be counted? Students will respond, and teacher will write down student responses.

MA: Students will use paper to create fractions. Students will fold one piece of paper into two equal pieces (halves), one paper into three equal pieces (thirds), one into fourths, one into sixths, and one into eighths. Students will shade one of the sections of each paper, and write the fraction in the shaded section. MA/W: Students will use fraction circles and fraction sticks to model fractions. Students will practice writing numerical fractions for each circle and rod. HW: Worksheet on writing a fraction for the shaded area of a whole, from http://www.edhelper.com /math/fractions_tg501.htm.

Math – Week 25 Wednesday Day 123 RVSOL M 3.5 Fractions M: Teacher will instruct the class in recognizing written fractions and providing a corresponding visual. TD/PA: Teacher will explain that to make a visual for a fraction, the first thing to consider is how many pieces does the picture need to have? Teacher will give the example of ¾. Students will respond with the denominator. Teacher will draw a picture with four sections. Teacher will then ask how to represent the fraction with the picture. Students will respond with the numerator. Teacher will shade three sections. Teacher will repeat the practice with a different fraction, and a different shape picture (divided rectangle if the first used a circle, or vice versa). T: Students will practice making a picture from a written fraction using http://www.interactive stuff.org/sums4fun /shade.html to shade in the correct fraction. HW: Students will complete a worksheet on drawing a picture to represent the given fraction, from http://www.edhelper. com/math/fractions_tg 503.htm.

Friday Day 125 RVSOL M 3.5 Fractions

M: Teacher will review writing fractions, and introduce reducing fractions.

CC/GA: Class will have a pizza party.

TD/PA: Teacher will show the class an image of a circle divided into 8 pieces, with 2 of them shaded, and ask for a volunteer to tell the fraction that is shown (2/8). Teacher will explain that when writing fractions, it is desirable to write the smallest number possible in the numerator and the denominator. Teacher will use fraction circles to imitate the image, and take away all but the two shaded pieces. Teacher will ask students if they know any one piece that is the same size as the two ⅛ pieces. Teacher will offer visuals of the other size pieces if necessary. Students will recognize that the ¼ piece is the same size as the two ⅛ pieces. Teacher will write on the board: 2 = 1 . 8 4 Teacher will ask students to notice anything about the numbers (both numbers on the left can be divided by two to equal the numbers on the right). Teacher will explain that for two fractions to be the same, they must follow this rule: Whatever is done to the numerator must be done to the denominator. Teacher will ask the class what would happen if both the numerator and denominator were multiplied by two. Would the fraction change? Teacher will demonstrate with fraction circles or diagrams. Teacher will write 4/16 as also equal to 2/8 and ¼. Teacher will explain that all of them should be written as ¼, because that has the smallest numbers. PS: Students will be given a worksheet from http://www.edhelper.com /math/fractions_tg509.htm to practice writing equivalent fractions. Students will circle the reduced fraction.

DA: Students with fine motor problems may use a computer to generate pictures instead of drawing them. Cornett, p. 266

Thursday Day 124 RVSOL M 3.5 Fractions

M/PS: Teacher will inform the class that there are six pizzas waiting to be eaten, and each is cut into ten pieces. Teacher will write 10 on the board. Teacher will ask the class how many slices of pizza there are altogether. Teacher will write 60 on the board. Teacher will ask each student how many pieces (between zero and three) they think they can eat. Teacher will write each student’s response down, and have the student tell what fraction of one pizza (10 slices total) he/she will be eating, and what fraction of all the pizza (60 slices total) he/she will be eating. Teacher will move on to the next student, and repeat. Once each student has named their fractions, they may eat them! Students will only be allowed to eat more than their fraction if there is extra pizza left over.

Rebecca VanVliet EDUC 410-002

Monday Day 126 RVSOL M 3.6 Comparing Fractions M: Teacher will review comparison using greater than, less than, and equal to. TD/PA: Teacher will show the class two fractions, using fraction manipulatives. Students will determine which is bigger just from looking at them. Teacher will review fractions as parts of a whole, and explain that the fraction that takes up more of the whole is bigger. PS/W: Students will complete the worksheet from http://www.edhelper. com/math/fractions_tg5 05.htm which gives both a picture and written fractions (with the same denominator) for students to compare. HW: Students will complete the worksheet from http://www.edhelper. com/math/fractions_tg504 .htm which gives fractions with the same numerator.

Tuesday Day 127

Math – Week 26 Wednesday Day 128 RVSOL M 3.6 Comparing Fractions M/PA: Teacher will take examples from the homework worksheet, and the worksheet completed in class, and ask students to study the numerical representations of the fractions (as opposed to looking just at the pictures). Teacher will ask for observations about the numbers, prompting students to notice differences and similarities in numerators and denominators, and the effect that has on the comparison. LI/TD: Teacher will explain that if the denominator is the same, the fraction with the larger numerator will always be greater than the fraction with the smaller numerator, because if the pieces are the same size, more pieces will always be greater than fewer pieces. Teacher will demonstrate with fraction circles. Teacher will explain that if two fractions have the same numerator, the fraction with the smaller denominator will always be greater than the fraction with the larger denominator, because the pieces will be bigger, and four big pieces will always be more of the whole than four little pieces. Teacher will demonstrate with fraction circles. M: Teacher will explain equivalent fractions as different fractions that equal the same amount. MO/PS: Teacher will pass out cards with fractions on them. Students will be required to find their “partner” – the student with a fraction that is equivalent to the one on the student’s card. Once students find their partner, they will work together to show how their fractions are the same. PS/PA: Students will complete the pizza fractions word problem (Wurst, p.92). Class will discuss the equivalent fractions, naming any others that are also equivalent to the ones that were used in the problem.

DA: Students with visual difficulties will have their own fraction manipulatives at their seats to work with.

Thursday Day 129 RVSOL M 3.6 Comparing Fractions

Friday Day 130 RVSOL M 3.6 Comparing Fractions

M: Teacher will introduce comparing numbers with different numerators AND different denominators. Teacher will introduce “Lowest Common Denominator” as a math term, and explain how to find it.

M: Teacher will review comparing fractions.

W: Students will write the definition of Lowest Common Denominator in their math notebooks. M: Teacher will review equivalent fractions, and explain that the students will be making equivalent fractions when they find the lowest common denominator. Teacher will instruct students that in order to keep the fraction the same (value), students must multiply the numerator by the same number they multiply the denominator by. PS: Students will practice making equivalent fractions by multiplying the numerator and denominator by the same number. GA/PS: Students will be assigned a partner, and each student will be given a card with a fraction on it. Students will work with their partners to find the LCD of their two fractions. Once the partners find the LCD, they will compare the two fractions and star the one that is bigger. They will show the cards to the teacher, and be given new cards.

LI: Students will listen to the teacher explain the activity – each student will have a fraction, and they are to line up around the room with their fractions in order from least to greatest, Starting and ending at designated points in the classroom. MO/PS/GA/CM: Each student will be given a card with a fraction on it. Students will compare their fractions to those of their classmates, determining which fractions are greater or less than their own. Students must remember who they are greater or less than, in order to line up in the proper order. OL: Once the class is lined up, students will start at one end of the line and read their fractions. Teacher will record the fractions on the board, asking students to reevaluate any problem areas. The students will return to their seats. PA: The class will discuss the methods they used to find their places in line. HW/CP: Students will complete a take-home test on comparing fractions (http://www.makework sheets.com/samples/math /fraccomp.html). Students and parents must both sign saying the student completed the test without help.

CP: Integrity

Wurst, p. 92

Rebecca VanVliet EDUC 410-002

Monday Day 131 RVSOL M 3.13 Add/ Subtract Fractions

Tuesday Day 132 RVSOL M 3.13 Add/ Subtract Fractions

M: Teacher will instruct students in adding fractions with the same denominators.

M: Teacher will review adding fractions with the same denominators, and explain mixed numbers.

TD/PA: Teacher will show a picture of a pizza cut into 10 pieces. Teacher will explain that two friends want to each eat three pieces of the pizza, and they need to know how much of the pizza that will be. Teacher will ask students how they can find out. Teacher will shade three pieces of the pizza one color and three pieces another color, and ask the students to add them together. Students will answer with how many total pieces are shaded, and express the answer as a fraction.

TD: Teacher will show pictures of two pizzas, each cut into 6 pieces: one with 4/6 shaded, and one with 3/6 shaded. Teacher will explain that two friends were really hungry, and one decided he could eat four sixths of a pizza, and the other decided she could eat three sixths of a pizza. If they both started eating from the same pizza, what would happen? Would they have enough pizza?

TD: Teacher will write the fraction sentence on the board: 3 + 3 = 6 and 10 10 10 explain that when adding fractions with the same denominator, or from the same pizza, only the top numbers need to be added – there is still the same total number of pieces. PA: Teacher will write on the board: 3 + 2 and 5 5 students will add the numbers together. Teacher will explain that when the numerator and denominator are the same, the fraction equals one.

PA/PS: Students will add the fractions together, and give an answer (7/6). Teacher will ask for a volunteer to shade 7/6 of a [blank] pizza for the class. Teacher will ask what needs to be done when the student runs out of spaces to color. Teacher will provide a second blank pizza to color. Class will discuss. Teacher will explain improper fractions, and compare them to mixed numbers. PS: Students will complete the worksheet on converting improper fractions to mixed numbers from http://www.edhelper.com /math/fractions_tg604.htm.

Math – Week 27 Wednesday Day 133 RVSOL M 3.13 Add/ Subtract Fractions M: Teacher will review the concept of “Lowest Common Denominator.” Teacher will instruct the students in addition of fractions when the denominators are not the same. TD: Teacher will show students two pizzas again. This time, one will be divided into sixths, and one into tenths. Teacher will tell the class that two friends are eating these pizzas: one ate 4/10 of one, and the other ate 2/6 of the other. Now the two friends want to know how much of a whole pizza they ate altogether. TD/PA/PS: Teacher will explain that in order to find out how much the two friends ate, they have to measure the amount in the same size pieces. Teacher will ask students to recall “lowest common denominator” from last week. Teacher will call on a volunteer to find the lowest common denominator.

Thursday Day 134 RVSOL M 3.13 Add/ Subtract Fractions

Friday Day 135 RVSOL M 3.13 Add/ Subtract Fractions

M: Teacher will instruct the students in subtraction of fractions when the denominators are the same.

M: Teacher will review addition and subtraction of fractions with both the like and unlike denominators, and instruct students in subtracting mixed numbers.

TD/PA: Teacher will show both numerical and visual representations of fraction sentences involving subtraction, and students will write their answers on white boards for the teacher to check. T: Students will use http://fen.com/student activities/MathSplat/ mathsplat.htm to practice adding and subtracting fractions and mixed numbers. PS: Students will complete the worksheet on subtracting fractions from http://www.edhelper.com /math/fractions_tg607.htm.

PS: Once the lowest common denominator has been found, students will work individually to solve the problem. PS/GA: Students will work in pairs to complete the worksheet on adding fractions with unlike denominators from http://www.edhelper.com /math/fractions_ft213.htm. Within pairs, one student will complete the even numbered problems, and the other the odd. Students will check each other’s work.

TD/PA/PS: Teacher will write on the board: 3 ⅛ - 2 ⅝ = ?. Teacher will ask for volunteers to attempt to solve the problem. Teacher will explain that when you are subtracting mixed numbers, they need to be converted to improper fractions first. Teacher will ask for a volunteer to explain what “improper fraction” means. Teacher will instruct students in how to convert a mixed number into an improper fraction. PS: Students will practice converting mixed numbers to improper fractions, and solve the problem on the board. TD/PA/PS: Teacher will then write another problem on the board, this time with different denominators: 4 ⅔ - 1 ½. Teacher will have the students convert the numbers to improper fractions again, and ask for a student to explain what the next step will be (find a common denominator). Teacher will solve the problem for the students, and ask another student to simplify the resulting improper fraction to a mixed number. PS: Students will practice addition and subtraction with mixed numbers by completing the cross-number puzzle at http://www.edhelper.com/ runaway_math_fraction _puzzles.htm.

PS: Students will complete the worksheet on adding fractions from http://www.edhelper.com /math/fractions_tg605.htm. DA: Advanced students may use the worksheet from http://www.edhelper.com /math/fractions_ft227.htm to practice word problems with mixed numbers.

Rebecca VanVliet EDUC 410-002

Monday Day 136 RVSOL M 3.7 Decimals

Tuesday Day 137 RVSOL M 3.7 Decimals

PA: Teacher will ask students to name places they have seen decimals before (counting money, etc.).

M: Teacher will review decimals as tenths, and explain that just like with fractions, decimals can be greater than one as well.

M: Teacher will explain the purpose of a decimal point, and instruct students that numbers that come after a decimal point are called “tenths.” TD: Teacher will introduce decimals by showing fractions in tenths, and explaining decimals as another way of writing tenths. PA: Teacher will show a fraction in tenths, and students will write the corresponding decimal on a white board, to hold up on the teacher’s signal. Teacher will display another fraction, and students will repeat. PS: Students will complete the worksheet on writing decimals from http://www.edhelper.com /math/decimals401.htm.

TD/PA/OL: Teacher will show pictures of decimals over one, and ask students to write the corresponding decimal amount. Teacher will explain that when the amount is greater than one, the decimal point is pronounced “and.” Students will practice saying the amounts out loud. TD: Teacher will show a picture of a whole number, and ask students how they would say and write the number as a decimal to the tenths place. Teacher will have the class practice saying whole numbers as “two and zero tenths” or “two and no tenths” and writing them: 2.0. PS: Students will complete the worksheet on writing mixed numbers as decimals from http://www.edhelper.com /math/decimals402.htm.

Math – Week 28 Wednesday Day 138 RVSOL M 3.7 Decimals M: Teacher will review decimals, and instruct the class in writing fractions as decimals. TD/PA/PS: Teacher will put a simple fraction on the board (3/10) and ask students to write it as a decimal. Students will be encouraged to pronounce the fraction out loud if it helps (“three tenths”). Teacher will call on a volunteer to write the decimal on the board next to the fraction, with an equal sign between them, so the class can see that 3 /10 = 0.3. Teacher will write another fraction on the board: 40/100. Teacher will ask for a volunteer to guess how this number would be written as a decimal. (Hint if necessary: it can be reduced to a simpler fraction first.) PS: Students will practice converting from fractions to decimals and back again. HW: Students will complete the worksheet on converting between fractions and decimals from http://www.edhelper.com /math/decimals404.htm.

Thursday Day 139 RVSOL M 3.7 Decimals

Friday Day 140 RVSOL M 3.7 Decimals

M: Teacher will instruct the class in the hundredths decimal place.

M: Teacher will review the hundredths place and focus on mixed numbers with tenths and hundredths.

TD: Teacher will explain that fractions other than tenths can be written as decimals as well. Teacher will write on the board: 53 /100, and ask students how they think it would be written as a decimal. Teacher will demonstrate, writing 0.53, and explain that it will be read “fiftythree hundredths” because it is “fifty three out of one hundred.” PS/GA/MA: Students will pair off and be given cards with both fractions and decimals on them, to the hundredths place, and students will read the card, saying for example, “fortyseven hundredths” and the partner will have to write both the fraction and the decimal form of the number. The student who wrote the numbers will read them back to the partner with the card, to check their answers. Students will switch roles. PS: Students will complete the worksheet on writing decimals from fractions and words, from http://www.edhelper.com /math/decimals406.htm. DA: Students with visual impairments will be given cards with raised numbers.

TD/PA: Teacher will show pictures of whole numbers, mixed numbers with tenths, and mixed numbers with hundredths. Students will write the corresponding decimals on white boards, and the teacher will call on students to read the numbers aloud. GA/PA/PS/MO: Teacher will divide the class into teams, and write either a decimal or fraction mixed number on the board, and the teams will race to see who can write the other (fraction or decimal equivalent) on the board and sit down again. Teacher will award points to the team that finishes first with the correct answer each time. PS: Students will complete a worksheet on writing fractions as decimals from http://www.edhelper.com /math/decimals408.htm.

Rebecca VanVliet EDUC 410-002

Monday Day 141 RVSOL M 3.14 Add/ Subtract Decimals

Tuesday Day 142 RVSOL M 3.14 Add/ Subtract Decimals

M: Teacher will review the place value of decimals.

M: Teacher will review adding decimals to the tenths.

T: Students will go to http:// www.bbc.co.uk/education /mathsfile/shockwave/games /laddergame.html to practice ordering decimals from least to greatest.

TD/PA: Teacher will write two decimals to the hundreds place on the board: 0.34 and 0.57. Teacher will ask students to find the answer, by lining up the decimal points vertically. Student volunteer will give the answer. Teacher will write another two decimals on the board: 0.88 and 0.67, and ask students to find the answer. Teacher will ask the class why the answer is not 0.155. Students will respond. Teacher will explain that just like with tenths, the decimal points can be lined up, and the decimal point carried to the answer: 0.88 +0.67 1.55

M: Teacher will instruct students in simple addition of decimals, focusing on adding tenths. TD/PA/MO: Teacher will write two decimals on the board: 0.5 and 0.7, and ask students to add them together. Teacher will give students four possible answers to choose from: 0.12, 1.2, 2.1, and 0.2. Teacher will ask students to move to a certain point in the room for each answer. Teacher will ask students why they chose the answer that they did. TD: Teacher will explain that just like adding whole numbers, when the numbers get to ten, they regroup. Why is 0.12 the wrong answer? Teacher will write the decimals on the board vertically: 0.5 +0.7 and explain that although 5 + 7 = 12, the decimal point and the zero provide another column, and the decimal needs to be carried straight down into the answer: 0.5 +0.7 1.2 PS: Students will practice adding single digit decimals. TD: Teacher will explain that the decimal point doesn’t change when numbers are added to the left of the decimal point. PS: Students will complete the worksheet on adding decimals (tenths) with regrouping from http://www.edhelper.com/ math/decimals_addsubtract 101.htm.

PS: Students will practice adding decimals to the hundreds place. TD: Teacher will again explain that numbers to the left of the decimal point do not affect the placement of the decimal in the answer. Teacher will remind students to count the decimal place from the right, and not the left. For example, 6.78 has one digit to the left, and two to the right. 8.43 has one digit to the left, and two to the right. The sum, 15.21, has TWO digits to the left, and two to the right. The answer is NOT 1.521 – keeping only one digit to the left of the decimal point as in the original numbers. Students must keep the decimal values the same. This is easiest to do if the problems are lined up vertically.

Math – Week 29 Wednesday Day 143 RVSOL M 3.14 Add/ Subtract Decimals M: Teacher will review adding decimals, and instruct the students in adding numbers with different decimal places (adding tenths to hundredths). TD/PA: Teacher will ask students how they would add 0.78 and 0.5. Students will respond. Teacher will ask students if the answer should be 1.28, 0.83, or even 0.7.13! Teacher will remind students to always line up the decimal points! Teacher will explain that 0.5 is equal to 0.50. PS: Students will practice adding zeros to the end of tenths to help them line up the decimal points. PA/OL: Class will discuss why adding a zero to the end doesn’t change the value of the number, like it does with whole numbers (0.5 = 0.50, but 5 ≠ 50). M/PA: Teacher will explain that whole numbers can also be represented as decimals, by adding a “.0” or a “.00” after the number. Class will discuss how this will help when adding decimals to whole numbers (it gives a whole number a decimal point that can be lined up with the point in other decimals, without changing the value of the number). PS: Students will complete the worksheet from http://www.edhelper.com /math/decimals_addsubtrac t 102.htm on adding decimals with either one or two decimal places.

Thursday Day 144 RVSOL M 3.14 Add/ Subtract Decimals

Friday Day 145 RVSOL M 3.14 Add/ Subtract Decimals

M: Teacher will review addition of decimals and focus on subtraction with tenths.

M: Teacher will review subtraction of decimals, and focus on subtraction of hundredths.

TD/PA: Teacher will write two decimals on the board: 4.7 and 3.8. Teacher will ask the class to subtract the numbers, and come up with a solution. Teacher will explain that the same process is used as with addition: the decimal points must line up, and it is right to regroup from the ones column – the decimal does not affect the regrouping. Teacher will remind students they need to put a zero to the left of the decimal point, and not just leave it blank.

TD/PA: Teacher will ask a volunteer to solve the following problem on the board: 0.89 - 0.46

PA: Students will complete the worksheet on subtracting decimals from http://www.edhelper.com/ math/decimals_addsubtract 108.htm.

Teacher will explain that just like with addition, a decimal point and any number of zeros can be added to the end of the numbers to help line up the decimal points.

GA: Students will gather into groups to check their answers to the worksheet. Groups will make a list of problems that at least two people missed, and teacher will review the problem questions with the class.

Teacher will ask another students to solve the following: 1.01 - 0.64 Teacher will ask students if it makes a difference if the decimal on the bottom of the second problem is bigger.

PA/PS/MO/GA: Teacher will divide the class into teams, and have board races in which the teams race to add and subtract decimals on the board. Teacher will include numbers with zero, one, and two decimal places, and write the problems both horizontally and vertically. PS: Students will complete a worksheet on adding and subtracting decimals from http://www.edhelper.com /math/decimals_addsubtract 116.htm.

DA: Students who have mobility difficulties may write the answer to the board race problems at their seats, and have a buddy write the answer on the board.

Rebecca VanVliet EDUC 410-002

Monday Day 146 RVSOL M 3.9 Word Problems with Whole Numbers, Fractions, Decimals

Tuesday Day 147 RVSOL M 3.9 Word Problems with Whole Numbers, Fractions, Decimals

M: Teacher will explain the components of word and story problems.

M: Teacher will discuss the different elements of story problems: a situation, a “problem” (question), and enough numerical information to solve the problem.

GA: Students will break into partners, and work together to answer the story problems with “Think It Through®” Tiles (Discovery Toys – Book on measurement, time, and money, pp.32-33). One partner will read the question, and the other will answer it. First student will place the tile in the answer spot, and partners will switch. MO/OL/GA/PA: The class will be divided into groups, and all groups will be given the same story problem. Students will be given half an hour to come up with a short skit acting out the problem and arriving at the correct answer. Each group will present their skit and solution to the class and the class will discuss as a whole what worked and what didn’t work.

TD/PA: Teacher will begin a story problem on the board, asking students to fill in information as they go. Ex: T: “Farmer John has some animals… what kind of animals?” S#1: “Cows.” T: “Farmer John has some cows… how many cows?” S#2: “Eight.” T: “Farmer John has 8 cows. Now we need a problem.” S#3: “Some of his cows died.” T: “How many died?” S#4: “Five.” T: “What do we want to know?” S#5: “How many are left.” T: “So our story problem is this: Farmer John had 8 cows. Five of them died. How many cows does Farmer John have left?”

Math – Week 30 Wednesday Day 148 RVSOL M 3.9 Word Problems with Whole Numbers, Fractions, Decimals M: Teacher will review how to write story problems, and give an example that has either fractions or decimals in it. PS/GA/CP: Students will work in pairs to write original story problems using either fractions or decimals. Pairs of students will find another pair of students, and read and solve the other pair’s problem, and pointing out any problems that may need to be worked out. Teacher will admonish students to use constructive criticism, and not to be negative. Students will show respect for the work of others. PA/MO: Students will nominate story problems written by other groups to be read for the class. Students may act out the problems if appropriate to the problem.

PS/W: Students will write their own simple word problems. PA: Teacher will call on a few students to share their word problems, and the rest of the class will answer.

Thursday Day 149 RVSOL M 3.9 Word Problems with Whole Numbers, Fractions, Decimals

Friday Day 150 TEST

M: Teacher will review the main elements of story problems.

E/M: Teacher will review fractions and decimals. Test will cover these topics.

PS: Each student will be given three different story problems to solve. Students will choose the one they like best of the three to illustrate. VA: Students will use various materials to illustrate or otherwise visually represent the problem they chose. Students will include the words of the problem, either one thought/sentence at a time (to correspond with the different parts of the illustration), or all as one block of text. GA: Students will gather into groups of four and exchange pictures. Students will then use the picture they have (drawn by another student) to write a different story problem that corresponds to the picture. Students will return the pictures to their owners, and the group will divide into partners. Partners will solve each other’s story problems.

CP: Respect

Cornett, p. 266

GA: Students may study with a partner for 10 minutes before the test begins.

DA: Students with accommodations will be allowed to leave the room to take the test elsewhere. Cornett, p.213

Rebecca VanVliet EDUC 410-002

Monday Day 151 RVSOL M 3.24 Properties of Shapes

Tuesday Day 152 RVSOL M 3.24 Properties of Shapes

M: Teacher will review properties of twodimensional shapes (edges, corners)

M: Teacher will discuss properties of the threedimensional shapes of cube and rectangular prism, noting the similarities to twodimensional squares and rectangles.

PA: Students will view two-dimensional shapes and identify the properties of each, and determine different categories that the shapes can be divided into based on number of sides, number of corners, number of square corners, etc. GA/PS: Groups will be assigned a category. Students will list as many shapes that fit into their category as they can. Teacher will write categories and the groupgenerated lists of shapes on the board, and the rest of the class will be allowed to contribute any unmentioned shapes to a group, if they are able to first explain why the shape they are naming belongs in that group. PA: Class will discuss the possibility of certain shapes belonging to more than one category. HW/HS: Students will be asked to find two or three different boxes at home and bring them to school the next day.

PA: Students will list similarities and differences between the 2- and 3dimensional shapes. MA/GA: Students will form groups of four. Each group will compare their boxes, noticing sides, edges, colors, textures, sizes, and shapes, noticing similarities and differences. Students will use math vocabulary to describe their boxes. Students will trace the faces (flat sides) of their boxes onto colored paper, and discuss the shapes they drew. PA: Class will come together and share ideas about how twodimensional shapes are involved in threedimensional shapes. T: Class will go to http://illuminations.nctm .org/ActivityDetail.aspx ? ID=70 and identify the shapes of the faces on the prisms. Students will color find and color the shapes as the teacher names them.

Molyneux, pp.136-137

Math – Week 31 Wednesday Day 153 RVSOL M 3.24 Properties of Shapes PA/TD: Teacher will ask the class, “is an ice cream cone really a cone?” Students will discuss. Teacher will show a cone, and ask students if they want to change their answer. Teacher will guide a discussion on possible reasons the ice cream “cone” isn’t really conical. Ask students to compare the ice cream cone to the actual cone, and note similarities and differences. Teacher will explain the properties of a cone. Students will identify the twodimensional shapes that make up a cone. MA/GA/PS: Given the activities from the day before, groups of students will brainstorm how to find the shape of the side of a cone. Students will predict what shape they think the side will be, then either trace the cone onto paper, or wrap paper around the cone and cut it to reveal the shape of the side. Groups will experiment with different cones, and observe the different shapes that the sides make. PA: Teacher will show the class a sphere, and class will discuss the properties, related 2-dimensional shapes, and similarities and differences to the cone.

Thursday Day 154 RVSOL M 3.24 Properties of Shapes

Friday Day 155 RVSOL M 3.24 Properties of Shapes

M/SS/T/TD: Teacher will explain the history of tangrams (China), and use overhead tangram pieces to explain to the class that all the pieces form a single square.

M/S/MA/VA/LI: The class will experiment with Mobius Strips. Teacher will give every student a piece of printer paper, and the students will follow directions to make four different creations.

M/S/MA/VA/LI: The teacher will hand out large squares of construction paper to each student. The students will follow directions to cut the paper into the proper pieces. Students will experiment with making other twodimensional shapes (trapezoid, triangle, and parallelogram are possible). Class will briefly discuss the properties of each.

OL/PA/PS: Class will discuss the properties of the Mobius Strips, and hypothesize how and why they work the way they do. Class will discuss the properties that the Mobius strips have in common with other two- and threedimensional shapes. Teacher will have copies of the activities for any interested students to take with them.

MA/PA/PS: Teacher will display the tangram pictures (Klag pp. 506-508 and Krause pp.13-15) one at a time, and students will attempt to fit their tangram pieces together to copy the shape, racing to be the first one done. When a student thinks he or she has copied the picture, they will stand up. The teacher will check to see that all the pieces have been used and they match the teacher’s picture. Teacher will then display another picture.

DA: Students who have problems with spatial awareness and cannot translate the pictures that are displayed to their own tangrams will be given printed outlines of the pictures that they can fit their tangrams into. Krause, pp.11-15 Klag, pp.506-508

Klag, pp.500-502

Rebecca VanVliet EDUC 410-002

Monday Day 156 RVSOL M 3.25 Angles & Line Segments

Tuesday Day 157 RVSOL M 3.25 Angles & Line Segments

M/PA: Teacher will introduce vocabulary such as point, line, line segment, and angle, allowing students to help craft the definitions into ones that will be easily remembered.

M: Teacher will instruct students in the use of a ruler/ straightedge for drawing lines and angles. Teacher will explain right angles as square corners.

VA/GA: Groups of students will be given small prints of artwork, cards with the new vocabulary words on them, and cards with pictures that represent the vocabulary words, and asked to identify as many examples of each in the artwork as they can. PA/CM: Class will discuss the presence of different elements in the different pieces of artwork, noting which had more lines, more points, more angles, etc. and why they think that is the case. T: Students will return to http://illuminations.nctm .org/ActivityDetail.aspx ? ID=70 and identify and color points (vertices), line segments (edges), and angles (two edges meeting at a vertex) on the prisms.

MA/PS: Students will find items in the classroom that have straight edges and angles, and trace these onto a sheet of paper. Students will try to get a variety of different size angles, and compare the results. Students will practice drawing their own line segments of different lengths using a straightedge, and angles that are greater than, less than, or equal to right angles. Students will cut apart all the line segments and angles that were traced, and group them by “line segment,” “right angle,” “acute (smaller than right) angle,” and “obtuse (bigger than right) angles.”

Math – Week 32 Wednesday Day 158 RVSOL M 3.25 Angles & Line Segments M: Students will complete the short worksheet on angles (p.94 of Wurst) as a review. Teacher will review angles as necessary. M: Teacher will explain curves as line segments that are part of a circle. MA/PS: Students will find curved or round objects in the classroom that they can trace, and trace short and long curves onto a sheet of paper. Students will also practice drawing curves using a compass. The class will discuss the difference in curves based on the size of the circle it was traced from.

Thursday Day 159 RVSOL M 3.25 Angles & Line Segments

Friday Day 160 RVSOL M 3.25 Angles & Line Segments

M/SS: Teacher will explain the use of line segments and angles in Native American art: the Rain Bird, carved on water jars by the Zuni tribe of the Pueblo Indians, and the Rain Cloud design of the Hopi Indians of Arizona.

M: Teacher will explain that line segments, points, and angles make up a variety of patterns and artwork.

VA/A: Students will view depictions of the rain bird, identifying the use of line segments and angles. Students will draw their own “rain birds” using a straightedge.

MA/VA: Students will create geometric art with string on foam boards, designing and forming patterns. Students will then identify points and line segments within their artwork, and identify and classify angles as either right, smaller than right (acute), or greater than right (obtuse).

VA/A: Students will also view examples of the Hopi rain cloud, identifying how line segments and points are used in the construction of the rain cloud. Students will draw their own Hopi rain clouds, practicing measuring, fractions (1/4 distance), and use of a straightedge and a compass. OL/PA: Students will compare the two Native American artworks, noticing similarities and differences.

DA: Students who are struggling may go to http://www.beaconlearning center.com/WebLessons/ Anglemania/tri2005.htm for a more step-by-step discussion of angles. Cornett, p. 192

Wurst, p.94

Krause, p.52, 58

Klag, p.475

Rebecca VanVliet EDUC 410-002

Monday Day 161 RVSOL M 3.8 Bases

Tuesday Day 162 RVSOL M 3.8 Bases

M: Teacher will explain base ten as a cycle of numbers that starts over when it gets to ten, because you can’t have more than 9 in any one place value space.

M: Teacher will explain that not all things are measured in base 10.

PA/LI: Teacher will put a chart of the board, with “hundreds,” “tens,” and “ones” columns. Students will be asked to list all possible digits that can go in each place (0-9). Teacher will ask, “what about 10?” and elicit the student answer that 10 means you need to regroup. Teacher will explain that this is why it is called base TEN. Teacher will explain that this week the class will be looking at bases other than base ten. Teacher will then address the column headings; asking students to find the PATTERN in the headings (multiply by TEN to get the next one). Teacher will remind the students that it is base TEN. Teacher will ask students to imagine what the headings would be if they were using base NINE.

TD: Teacher will give the example of weeks. Teacher will point to a calendar and review that there are seven days in one week. TD/PA: Teacher will write on the board: 5 days plus 16 days equals how many weeks? Teacher will use the calendar to add the numbers, explaining that each time you reach seven days, you “regroup” the days to form one week. Just like regrouping ones in regular addition. Teacher will continue counting and regrouping days, until the answer of “3 weeks” is reached. Teacher will give another example, and students will answer. PS: Students will be given a printed calendar, and a list of addition and subtraction problems concerning days and weeks. Students will complete the worksheet.

Math – Week 33 Wednesday Day 163 RVSOL M 3.8 Bases M: Teacher will review counting days and weeks, and move on to months and years. Teacher will explain that when counting months, when you get to twelve you regroup. TD: Teacher will have a list of the months of the year, listed for several years. Teacher will tell the class that something great will happen in 46 months, and the class has to figure out how many years that will be. Teacher will use the list of months to demonstrate counting and regrouping at twelve. PA: Teacher will ask the class how many years from now the great something will take place. Teacher will ask what month it will take place in? PS: Teacher will pass out a worksheet with months listed, and ask students questions related to months and years.

Thursday Day 164 RVSOL M 3.8 Bases

Friday Day 165 RVSOL M 3.8 Bases

M: Teacher will review counting days/weeks and months/years. Teacher will move on to counting time in minutes/hours.

M: Teacher will review the lessons in time from the week, and explain that each one was in a base that was not base ten.

TD: Teacher will have a large replica of an analog clock. Teacher will explain that when counting time, we regroup when we get to sixty. Sixty minutes becomes one hour. PA/PS: Teacher will place two different colored sets of hands on the clock, one at two o’clock, and one at four thirty. Teacher will ask students to determine how many minutes passed between the two times. MO/PA/PS: Teacher will remove one of the sets of hands, leaving the other at two o’clock, and ask for volunteers to place the other set of hands to show 30 minutes later, 60 minutes later, 75 minutes later, 100 minutes later, and 200 minutes later. Teacher will ask students to convert the number of minutes to hours each time. PS: Students will complete a worksheet on adding time in minutes and hours.

TD/PA: Teacher will show addition of other bases using numbers instead of manipulatives or pictures. Teacher will explain that when counting days in terms of weeks, it is called base seven. Teacher will re-write the chart from Monday on the board (names of columns for base ten) and review the way to find the headings (multiply each by ten to get the next). Teacher will inform the class that they are going to make a chart for base seven. Teacher will draw a similar chart next to the base ten chart, and ask students to label the headings, based on the pattern that they saw in the base ten chart. Teacher will give students the right-most column (ones). Students will work to discover the others. Teacher will introduce writing numbers in the columns, starting with 5 days (a 5 in the ones column). Teacher will then move to 8 days. Teacher will remind students that with this system, they will need to regroup when they get to seven. So instead of writing “8”, they will be writing “1 1” because they will have 1 “seven” and one left over. So there will be a 1 in the “sevens” column, and a 1 in the “ones” column. PS: Students will practice writing more numbers in this way. GA/MA: Students will divide into groups, and use colored paper and colored chips to make their own manipulative base seven charts. Students will label the headings, and challenge their group members to form numbers using the chips.

DA: Students who are having a hard time following the work on the board will be given small white boards with the chart marked in colored tape. Students will practice writing the numbers in the columns along with the teacher.

Rebecca VanVliet EDUC 410-002

Monday Day 166 REVIEW

Tuesday Day 167 REVIEW

M: Teacher will review using explanation and standardized testing format (practice tests): place value, rounding, comparing using >, <, and =, and equivalencies. DA: Students with testing problems may use a computer for test review.

M: Teacher will review using explanation and standardized testing format (practice tests): addition/ subtraction of large numbers, multiplication and division.

Math – Week 34 Wednesday Day 168 REVIEW M: Teacher will review using explanation and standardized testing format (practice tests): fractions and decimals.

Thursday Day 169 REVIEW

Friday Day 170 REVIEW

M: Teacher will review using explanation and standardized testing format (practice tests): measurement and probability.

M: Teacher will review using explanation and standardized testing format (practice tests): Student requests for review.

Rebecca VanVliet EDUC 410-002 Math – Week 35 Monday Tuesday Wednesday Thursday Friday Day 171 Day 172 Day 173 Day 174 Day 175 STANDARDIZED STANDARDIZED STANDARDIZED STANDARDIZED STANDARDIZED TESTING TESTING TESTING TESTING TESTING

Rebecca VanVliet EDUC 410-002

Monday Day 176 GROUP PROJECTS

Tuesday Day 177 GROUP PROJECTS

Math – Week 36 Wednesday Day 178 GROUP PROJECTS

M/MA/GA/VA/CP: Groups will make “math quilts.” Teacher will provide a list of the important topics covered in class, which should be incorporated into the quilt, and students will decide who will do which blocks. Students will be encouraged to be creative, and do more than just write numbers on the blocks. Points will be given for use of color and creativity as well as accuracy of information.

M/MA/GA/VA/CP: Student will work on their quilts.

M/MA/GA/VA/CP: Student will finish their quilts.

M/MA/GA/VA/CP/OL: Student will present their quilts to the class.

M/MA/GA/VA/CP/OL: Student will present their quilts to the class.

CP: Cooperation

CP: Cooperation

CP: Cooperation DA: Students who need accommodations for extra time will be allowed to use the library instead of watching other students present on this day.

CP: Cooperation

HW: Students should begin to plan their block designs at home, as the time in class will need to be devoted to the actual creation of the quilt. CP: Cooperation

Cornett, p.213

Thursday Day 179 GROUP PROJECTS

Friday Day 180 GROUP PROJECTS

Rebecca VanVliet EDUC 410-002 Works Cited – Math Cornett, Claudia E. Creating Meaning Through Literature and the Arts. NJ: Pearson Education Inc., 2007. “Grade Three Links.” Bernards Township Public Schools. Retrieved Oct. 24, 2007 from http://www.bernardsboe.com/Cedar-Hill/Linked_Pages/gr3links.htm. “Grade Three Math Worksheets.” EdHelper.Com. Retrieved Oct. 29, 2007 from http://www.edhelper.com/math_grade3.htm. “King’s List of Online Math Activities.” King’s Curriculum. Retrieved Nov. 1, 2007 from http://www.k111.k12.il.us/king/math.htm#Fractions. “Math.” Math. Retrieved Nov. 3, 2007 from http://www.redcreekcsd.k12.ny.us/MSmith/Math.htm. “Number & Operations (Grade 3-5).” National Library of Virtual Manipulatives. Retrieved Oct. 31, 2007 from http://nlvm.usu.edu/en/nav/category_g_2_t_1.html. “Shapes, Shapes, Everywhere!” McREL. Retrieved Nov. 2, 2007 from http://www.mcrel.org/PDF/Curriculum/5021CM_Shapes.pdf. “Third Grade Lessons.” AAAMath. Retrieved Oct. 23, 2007 from http://www.aaamath.com/B/grade3.htm#topic3. “Third Grade Mathematics Skills.” I4c: Internet for Classrooms. Retrieved Oct. 19, 2007 from http://www.internet4classrooms.com/skills_3rd_math.htm. Idea Books Burns, Marilyn. The I Hate Mathematics! Book. NY: Little, Brown and Company, 1975. Klag, Prent. Exploring Terrific Opportunities for Young Scientists. UT: Thumbs Up Enterprises, L., 1996.

Rebecca VanVliet EDUC 410-002 Krause, Marina C. Multicultural Mathematics Materials. VA: National Council of Teachers of Mathematics, Inc., 1983. Molyneux, Lynn. Cooperative Learning, Math and Success: Step-by-Step Activities. NY: Trellis Books, 1992. Tuttle, Wes. Daily Math Practice: grade 3. CA: Evan-Moor Educational Publishers, 1999. Wurst, Sharman and Doug Wurst. Daily Word Problems: grade 3. CA: Evan-Moor Educational Publishers, 2001.