Faye Schmidt Lesson 8
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Dakota State University College of Education Lesson 4: Equivalent Fractions Name: Faye Schmidt Grade Level: 4th Grade School: Sioux Valley Elementary Date: Friday, March 1st, 2019 Time: 9:00-10:00 AM Reflection from prior lesson: ● In the previous lesson, students used learned about modelling equivalent fractions using fraction tiles and number lines. Using these manipulatives, especially the number line resource, they were successfully able to compare two fractions and identify if they were equal. They completed examples during class as a group and individually, submitted and informal exit ticket, and handed in a Math Workbook homework page to be graded. Students were assessed in various ways, both informally and formally, and the results were used to construct future lessons. Overall, the students have done well on the previous lessons in this chapter and have met the objectives set in the previous lesson plans. As a class, they seem to have a good grasp on the knowledge needed to move forward onto this next part, which dives even deeper into equivalent fractions. Lesson Goal(s) / Standards: ● Domain: Number and Operations - Fractions ● Major Cluster: Extending understanding of fraction equivalence and ordering. ○ 4.NF.1 - Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. ○ 4.NF.5 - Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. ● Math Practice Standards: ○ MP1: Make sense of problems and persevere in solving them. ○ MP2: Reason abstractly and quantitatively. ○ MP4: Model with mathematics. ○ MP7: Look for and make use of structure. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 1
○ MP8: Look for and express regularity in repeated reasoning.
Lesson Objectives: ● By the end of the lesson, the students will be able to define the term equivalent fractions in their own words verbally and in writing. ● By the end of the lesson, the students will identify equivalent fractions correctly with 70% accuracy without the use of manipulatives. Materials Needed: ● Each Student will need their: ○ Math Notebook ○ Pencil ○ Whiteboard marker and eraser ○ Number line handout inside a plastic sheet (27 total) (attached) ○ Math Workbook ● Teacher will need: ○ Promethean Interactive Board ○ Projector ○ Whiteboard marker and eraser ○ Paper to complete example problems on ○ Pencil ○ List of example problems to complete during lesson ○ Exit tickets to check for understanding after the lesson (attached) Contextual Factors/ Learner Characteristics: ● This classroom is made up of 28 total 4th-graders, aged 9-11. 27 of these students will be in the classroom to complete this math lesson as a large-group, teacher-led learning experience. When it comes to independent work time, 2 students work on their homework assignments in an alternative setting, and 25 complete their work independently in the general classroom. I, the student teacher, will be leading this lesson, and my cooperating teacher, who is the classroom’s primary teacher, will be observing and assisting students. This diverse classroom is made up of students from a various backgrounds and learning levels, which have been considered when planning this lesson. ● This lesson will be begin at about 9:15 AM, right after students are finished with their Morning Meeting and complete a brief multiplication fact assessment. At this time, the students should begin to get settled in to their normal daily math routine. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 2
Also, this class will take a break at about 10:00, when the students leave the classroom for their scheduled Library check out time. The students return to the classroom at about 10:15, and will spend the remainder of the class time working on their assignment and fact fluency before using the restrooms and washing for Lunch. Flex seating is also utilized in this classroom, with several different options available each week for the students to choose. In this classroom, there is a strict seating chart, and students are expected to find their seats and remain in their assigned seats for the lesson. Because of the size of the group and the arrangements of the desks, the teacher is to remain mindful of unnecessary behaviors, such as irrelevant conversations. These situations should be approached immediately if any issues arise during the lesson. A. The Lesson 1. Introduction (10 min) ● First, the teacher should ask the students about what they learned the previous days in the first few lessons, as it will likely be helpful as they begin today’s lesson. Students will provide definitions and other information about factors, multiples, prime and composite numbers, and what they learned about modelling equivalent fractions from the lesson the day before. They will also have the opportunity to share information that they have withheld from the previous days. ● Before beginning the lesson, the teacher will ask the following review questions to the class, and call on volunteers to share their definitions and other information regarding these terms. ○ What is a numerator? ○ What is a denominator? ○ What are equivalent fractions? ● After this brief discussion, the students will then be instructed to take out their Math Notebooks, a pencil, number line handout, and a whiteboard marker. ● As a quick review, the teacher will show the following question on the Promethean board by using the projector for the students to answer as a refresher. The students will record their answers on the next open page in their Math Notebooks, and show the teacher that they are finished by putting their pencil down. The teacher will read the problem to the students, and encourage them to use their number line handout from the previous lesson if they need extra assistance. When finished, they will then volunteer to share their answers and explain their thinking. Additional examples may be provided to the class if more review is needed. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 3
○ Betty needs 12 cup of milk for her recipe. How many fractions can you find to represent 12 ? ■ 24 , 36 , 48 , etc.. ● After this brief review is complete, remind the students that the information that was learned in the last couple of days will help us with this lesson, and the ones that follow. Today, our focus is to continue to learn about equivalent fractions, but to try to rely less on manipulatives and other resources. ● The teacher will then share the objective with the class, and then begin the lesson. ○ “By the end of the lesson, the students will identify equivalent fractions correctly without the use of manipulatives.” 2. Content Delivery (35 min) ● Since the goal of this lesson is to draw back the students’ reliance on manipulatives, the number line fraction chart that the student have been using will gradually be used less and less throughout the lesson. To begin, they will be allowed to use this chart as a guide. ● To begin the guided practice, the following example will be shown. To complete this problem, the teacher will read it aloud to the class, and ask what they think would be a good strategy to use to solve this problem. After taking suggestions, slowly and clearly write out the fraction, and explain how you can multiply the numerator and the denominator by the same number to get a new equivalent fraction. Some students may have noticed this in the previous day’s lesson as well. Use this method to find at least two fractions equal to 34 . ○ A recipe for spaghetti and meatballs calls for 34 pound of ground beef. Find two fractions that are equivalent to 34 . 9 ■ Answer: 68 and 12 ● After learning this multiplication strategy to find equivalent fractions, complete a few more examples with the class. At this time, any manipulatives and the number line handout should be put away. Also, discuss that you can also divide to find equivalent fractions as well, as long as you use the same number to divide both the numerator and the denominator of a fraction. Challenge students to find one smaller equivalent fraction and one larger equivalent fraction for the third and forth examples listed below. ○ Find two equivalent fractions of 13 ■ 26 , 39 , etc. ○ Find two equivalent fractions of 25 Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 4
■
4 10
,
6 15
, etc.
○ Find two equivalent fractions of 8 ■ 12 , 16 , etc.
4 8
○ Find two equivalent fractions of
6 10
■
3 5
,
12 20
, etc.
● Next, challenge the students even more by providing practice questions with “mystery numbers.” To solve, they will have to identify what the given fraction is multiplied or divided by to get the new number provided in the problem. Then, they will have to find the other number that goes in the empty space to create the equivalent fraction. Complete the following examples with students as guided practice. ? ○ 38 = 16 ○
7 10
■ Answer: 6 = 70 ?
■ Answer: 100 ● For this next set of questions, the students will work independently to solve the missing number. After questions are given, the teacher will walk around the room to work with students as they solve the problems. After everyone is finished, volunteers will raise their hands to share and explain their answers. ○ 37 = 9? ○
■ Answer: 21 8 ? = 81 9
○
■ Answer: 72 11 = 2? 22
○
■ Answer: 1 25 = 5? 35
■ Answer: 7 ● Lastly, the class will work through two word problems together so that they are more familiar with it when they see it on their assignment. For the first one, the teacher should help guide the students in solving, and ask prompting questions to encourage critical thinking. The second question should be given to the students to complete on their own, and volunteers will raise their hands to answer. ○ There are 10 cars in a parking lot. 6 of the cars are white. First, rewrite this information in the form of a fraction, then find two equivalent fractions. 6 12 ■ Answer: White cars: 10 , 35 or 20 etc.
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 5
○ There are 15 marbles in a bowl. 5 of the marbles are blue, 9 of the marbles are red, and 1 marble is green. Write two fractions that describe the fraction of marbles that are blue. 5 10 15 ■ Answer: Blue marbles: 15 = 13 = 30 = 45 etc. 3. Closure (15 min) ● At this time, the teacher will ask the students if they have any questions regarding the new information from the lesson. If there are any concerns or confusion, these should be addressed as a group so that all students can benefit. ● Now, the teacher will ask the following questions to the class to discuss. Students will then volunteer to share their answers to these terms. ○ What is a numerator? ○ What is a denominator? ○ What are equivalent fractions? ○ How do we find equivalent fractions using math facts? ● After this class sharing and discussion, the teacher will review correct answers and clear up any confusion regarding these concepts. The teacher will then ask the students to show a quiet thumbs up if they feel confident with their understanding of the lesson or a thumbs down if they feel like they could use more practice. ● After the informal assessment of thumbs up/down, each student will be given an exit ticket (attached below) to complete before beginning their homework assignment for the day. ● As soon as the students begin working on their exit ticket, the teacher will write their Math Workbook assignment on the whiteboard (pg. 509-510). As soon as their exit ticket is handed in, they can begin to work on their assignment with the remaining class time available. B. Assessments Used ● Informal Assessment: Observations ○ Observations were gathered when working with students during the guided practice questions and also while walking around and working one-on-one during independent practice. ● Informal Assessment: Thumbs up/Thumbs down ○ By asking students to demonstrate their comfort level in using this method, you can get a better understanding of how confident they may be in this skill. If many showed that their thumbs were up and they were getting it, Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 6
use that to plan more advanced lessons. However, if many showed a lack of confidence, you know that more work and support is needed to reach proficiency in this skill. ● Informal Assessment: Exit Ticket ○ Exit tickets will be collected upon completion at the end of the lesson, but not graded for correctness. These will be analyzed by the teacher to identify which students may need more assistance or any common problem areas that could use more explanation the following day. ● Formal Assessment: Collection of Workbook Assignment ○ Assignments completed from the Math Workbook are to be finished and handed in the following day for grading. These grades are entered and used to determine students’ midterm and quarter grades in math class. C. Differentiated Instruction ● For those needing additional support: ○ Work one-on-one with students needing more help to ensure that they are learning foundational skills to help them with math later on. The specific students who showed a quiet thumbs down at the end of the lesson could be invited to the front table to work with a teacher on more examples to gain more practice and confidence. ● For those in need of enrichment/challenging: ○ Offer more complex or additional problems to them, or ask them to explain their thinking and reasoning more in depth. ○ Also, have them work with those who may need more support. Pair them with struggling students so that both parties may benefit from this interaction. ● For those in need of specific language support: ○ Provide additional wait time for students who take a bit longer to complete the exercises. Make sure to speak slowly and articulate vocabulary and steps to the strategy, and use multiple phrases to describe and explain the same idea or concept. D. Resources Adapted from: McGraw-Hill Education. (2014). My math. Lesson 8.4 Equivalent Fractions (p.505A-510). Columbus, OH: McGraw-Hill Education. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 7
Lesson 4 Exit Ticket ____________________ 1. How can we find equivalent fractions without using manipulatives? _____________________________________________________________________ 2. Write the fraction for the shaded part of the shape. Then, find one equivalent fraction for each. a. b. ____ = ____ ____ = ____ 3. Identify two equivalent fractions for each fraction: 1 3 a. 5 b. 6
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 8
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 9
Page 1
○ MP8: Look for and express regularity in repeated reasoning.
Lesson Objectives: ● By the end of the lesson, the students will be able to define the term equivalent fractions in their own words verbally and in writing. ● By the end of the lesson, the students will identify equivalent fractions correctly with 70% accuracy without the use of manipulatives. Materials Needed: ● Each Student will need their: ○ Math Notebook ○ Pencil ○ Whiteboard marker and eraser ○ Number line handout inside a plastic sheet (27 total) (attached) ○ Math Workbook ● Teacher will need: ○ Promethean Interactive Board ○ Projector ○ Whiteboard marker and eraser ○ Paper to complete example problems on ○ Pencil ○ List of example problems to complete during lesson ○ Exit tickets to check for understanding after the lesson (attached) Contextual Factors/ Learner Characteristics: ● This classroom is made up of 28 total 4th-graders, aged 9-11. 27 of these students will be in the classroom to complete this math lesson as a large-group, teacher-led learning experience. When it comes to independent work time, 2 students work on their homework assignments in an alternative setting, and 25 complete their work independently in the general classroom. I, the student teacher, will be leading this lesson, and my cooperating teacher, who is the classroom’s primary teacher, will be observing and assisting students. This diverse classroom is made up of students from a various backgrounds and learning levels, which have been considered when planning this lesson. ● This lesson will be begin at about 9:15 AM, right after students are finished with their Morning Meeting and complete a brief multiplication fact assessment. At this time, the students should begin to get settled in to their normal daily math routine. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 2
Also, this class will take a break at about 10:00, when the students leave the classroom for their scheduled Library check out time. The students return to the classroom at about 10:15, and will spend the remainder of the class time working on their assignment and fact fluency before using the restrooms and washing for Lunch. Flex seating is also utilized in this classroom, with several different options available each week for the students to choose. In this classroom, there is a strict seating chart, and students are expected to find their seats and remain in their assigned seats for the lesson. Because of the size of the group and the arrangements of the desks, the teacher is to remain mindful of unnecessary behaviors, such as irrelevant conversations. These situations should be approached immediately if any issues arise during the lesson. A. The Lesson 1. Introduction (10 min) ● First, the teacher should ask the students about what they learned the previous days in the first few lessons, as it will likely be helpful as they begin today’s lesson. Students will provide definitions and other information about factors, multiples, prime and composite numbers, and what they learned about modelling equivalent fractions from the lesson the day before. They will also have the opportunity to share information that they have withheld from the previous days. ● Before beginning the lesson, the teacher will ask the following review questions to the class, and call on volunteers to share their definitions and other information regarding these terms. ○ What is a numerator? ○ What is a denominator? ○ What are equivalent fractions? ● After this brief discussion, the students will then be instructed to take out their Math Notebooks, a pencil, number line handout, and a whiteboard marker. ● As a quick review, the teacher will show the following question on the Promethean board by using the projector for the students to answer as a refresher. The students will record their answers on the next open page in their Math Notebooks, and show the teacher that they are finished by putting their pencil down. The teacher will read the problem to the students, and encourage them to use their number line handout from the previous lesson if they need extra assistance. When finished, they will then volunteer to share their answers and explain their thinking. Additional examples may be provided to the class if more review is needed. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 3
○ Betty needs 12 cup of milk for her recipe. How many fractions can you find to represent 12 ? ■ 24 , 36 , 48 , etc.. ● After this brief review is complete, remind the students that the information that was learned in the last couple of days will help us with this lesson, and the ones that follow. Today, our focus is to continue to learn about equivalent fractions, but to try to rely less on manipulatives and other resources. ● The teacher will then share the objective with the class, and then begin the lesson. ○ “By the end of the lesson, the students will identify equivalent fractions correctly without the use of manipulatives.” 2. Content Delivery (35 min) ● Since the goal of this lesson is to draw back the students’ reliance on manipulatives, the number line fraction chart that the student have been using will gradually be used less and less throughout the lesson. To begin, they will be allowed to use this chart as a guide. ● To begin the guided practice, the following example will be shown. To complete this problem, the teacher will read it aloud to the class, and ask what they think would be a good strategy to use to solve this problem. After taking suggestions, slowly and clearly write out the fraction, and explain how you can multiply the numerator and the denominator by the same number to get a new equivalent fraction. Some students may have noticed this in the previous day’s lesson as well. Use this method to find at least two fractions equal to 34 . ○ A recipe for spaghetti and meatballs calls for 34 pound of ground beef. Find two fractions that are equivalent to 34 . 9 ■ Answer: 68 and 12 ● After learning this multiplication strategy to find equivalent fractions, complete a few more examples with the class. At this time, any manipulatives and the number line handout should be put away. Also, discuss that you can also divide to find equivalent fractions as well, as long as you use the same number to divide both the numerator and the denominator of a fraction. Challenge students to find one smaller equivalent fraction and one larger equivalent fraction for the third and forth examples listed below. ○ Find two equivalent fractions of 13 ■ 26 , 39 , etc. ○ Find two equivalent fractions of 25 Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 4
■
4 10
,
6 15
, etc.
○ Find two equivalent fractions of 8 ■ 12 , 16 , etc.
4 8
○ Find two equivalent fractions of
6 10
■
3 5
,
12 20
, etc.
● Next, challenge the students even more by providing practice questions with “mystery numbers.” To solve, they will have to identify what the given fraction is multiplied or divided by to get the new number provided in the problem. Then, they will have to find the other number that goes in the empty space to create the equivalent fraction. Complete the following examples with students as guided practice. ? ○ 38 = 16 ○
7 10
■ Answer: 6 = 70 ?
■ Answer: 100 ● For this next set of questions, the students will work independently to solve the missing number. After questions are given, the teacher will walk around the room to work with students as they solve the problems. After everyone is finished, volunteers will raise their hands to share and explain their answers. ○ 37 = 9? ○
■ Answer: 21 8 ? = 81 9
○
■ Answer: 72 11 = 2? 22
○
■ Answer: 1 25 = 5? 35
■ Answer: 7 ● Lastly, the class will work through two word problems together so that they are more familiar with it when they see it on their assignment. For the first one, the teacher should help guide the students in solving, and ask prompting questions to encourage critical thinking. The second question should be given to the students to complete on their own, and volunteers will raise their hands to answer. ○ There are 10 cars in a parking lot. 6 of the cars are white. First, rewrite this information in the form of a fraction, then find two equivalent fractions. 6 12 ■ Answer: White cars: 10 , 35 or 20 etc.
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 5
○ There are 15 marbles in a bowl. 5 of the marbles are blue, 9 of the marbles are red, and 1 marble is green. Write two fractions that describe the fraction of marbles that are blue. 5 10 15 ■ Answer: Blue marbles: 15 = 13 = 30 = 45 etc. 3. Closure (15 min) ● At this time, the teacher will ask the students if they have any questions regarding the new information from the lesson. If there are any concerns or confusion, these should be addressed as a group so that all students can benefit. ● Now, the teacher will ask the following questions to the class to discuss. Students will then volunteer to share their answers to these terms. ○ What is a numerator? ○ What is a denominator? ○ What are equivalent fractions? ○ How do we find equivalent fractions using math facts? ● After this class sharing and discussion, the teacher will review correct answers and clear up any confusion regarding these concepts. The teacher will then ask the students to show a quiet thumbs up if they feel confident with their understanding of the lesson or a thumbs down if they feel like they could use more practice. ● After the informal assessment of thumbs up/down, each student will be given an exit ticket (attached below) to complete before beginning their homework assignment for the day. ● As soon as the students begin working on their exit ticket, the teacher will write their Math Workbook assignment on the whiteboard (pg. 509-510). As soon as their exit ticket is handed in, they can begin to work on their assignment with the remaining class time available. B. Assessments Used ● Informal Assessment: Observations ○ Observations were gathered when working with students during the guided practice questions and also while walking around and working one-on-one during independent practice. ● Informal Assessment: Thumbs up/Thumbs down ○ By asking students to demonstrate their comfort level in using this method, you can get a better understanding of how confident they may be in this skill. If many showed that their thumbs were up and they were getting it, Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 6
use that to plan more advanced lessons. However, if many showed a lack of confidence, you know that more work and support is needed to reach proficiency in this skill. ● Informal Assessment: Exit Ticket ○ Exit tickets will be collected upon completion at the end of the lesson, but not graded for correctness. These will be analyzed by the teacher to identify which students may need more assistance or any common problem areas that could use more explanation the following day. ● Formal Assessment: Collection of Workbook Assignment ○ Assignments completed from the Math Workbook are to be finished and handed in the following day for grading. These grades are entered and used to determine students’ midterm and quarter grades in math class. C. Differentiated Instruction ● For those needing additional support: ○ Work one-on-one with students needing more help to ensure that they are learning foundational skills to help them with math later on. The specific students who showed a quiet thumbs down at the end of the lesson could be invited to the front table to work with a teacher on more examples to gain more practice and confidence. ● For those in need of enrichment/challenging: ○ Offer more complex or additional problems to them, or ask them to explain their thinking and reasoning more in depth. ○ Also, have them work with those who may need more support. Pair them with struggling students so that both parties may benefit from this interaction. ● For those in need of specific language support: ○ Provide additional wait time for students who take a bit longer to complete the exercises. Make sure to speak slowly and articulate vocabulary and steps to the strategy, and use multiple phrases to describe and explain the same idea or concept. D. Resources Adapted from: McGraw-Hill Education. (2014). My math. Lesson 8.4 Equivalent Fractions (p.505A-510). Columbus, OH: McGraw-Hill Education. Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 7
Lesson 4 Exit Ticket ____________________ 1. How can we find equivalent fractions without using manipulatives? _____________________________________________________________________ 2. Write the fraction for the shaded part of the shape. Then, find one equivalent fraction for each. a. b. ____ = ____ ____ = ____ 3. Identify two equivalent fractions for each fraction: 1 3 a. 5 b. 6
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 8
Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions
Page 9
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