Math Lesson Plan 1

Alexis Padgett Mr. G, Plains Elementary School, 5th Grade

ORDER OF OPERATIONS A. LESSON TITLE: Order of Operations B. CONTEXT OF LESSON Towards the beginning of the year, students learned order of operations. Being so, the students will know the basic underlining concepts of order of operations. Because this topic has already been taught and was suggested, by my CT, as a review lesson, the students will be prepared having background knowledge. This lesson is set to be a review based on the scores the children received on a test.  Vertical planning: In 5th grade, the students should already know how to add, subtract, multiply, and divide. Being so, this lesson fits in with their prior knowledge a building on the knowledge they already know and putting all of the facts together. With order of operation, they are requiring putting all of these facts together knowing how to switch between one to another. This will set the students up to furthering their knowledge of order of operations when they are then introduced to exponents.  Horizontal planning: This review of order of operations fits into the progression of this school year because the students are taking a test on the information the following week. The students will also be required to think about their prior knowledge of that was previously learned in multiple grades in their past. This year students also have furthered their knowledge multiplication and division which helps a lot with order of operations. This lesson will prepare students for the test they will be having the following week where they are able to apply the information learned from the lesson. The main source of their confusion is understanding that they are to work from left to right when it comes to multiplication and division, and then addition and subtraction. They struggle in understanding which problem they start with within each group. For example, when it come to a problem such as 10/2+3x4, the student will often be more inclined to start the problem by multiplying instead of dividing. The students understand that multiplication and division come first but are not going from left to right order. Because of this lesson the student will be able to use their previous knowledge to further refine their understanding of order of operations. This has been shown through their interactive notes that they filled out previously. They will be able add to the previous understanding in the order in which they will use to solve the problem. Based on the constructivist theory produced by Bruner, in discovery learning, the students is places in problem solving situations where they are required to draw on past experiences and existing knowledge to discover facts, relationships, and new information.”(University College Dublin)

http://www.ucdoer.ie/index.php/Education_Theory/Constructivism_and_Social_Construc tivism C. STANDARDS – VA SOLs MATH: 5.6 – Students will a) Solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. b) Solve single-step practical problems involving multiplications of whole number, limited to 12 or less, and a proper fraction, with models 5.7 – Students will simplify whole numerical expressions using the order of operations. D. LEARNING OBJECTIVES: Understand – what are the broad generalization/concepts the students should begin to develop?

Know – what are the tools, vocabulary, symbols, etc. the students will gain through this lesson?

The students will understand why the order of operations is completed in specific order.

Students will gain the knowledge of the three stages of solving the operations. 1) Parentheses 2)Multiplication/Division 3) Addition/Subtraction

Do – what are the specific thinking behaviors/procedures students will be able to do through this lesson? The students will be able to do the order of operation from left to right.

E. MATERIALS NEEDED Pencils Small slips with individual order of operations Practice problems Highlighter (3 colors) F. TASKS 1. Students will be asked how comfortable they are with order of operations. They will then be asked what confuses them the most when it comes to solving order of operations. The students will be asked to give the reason for why order of operations is solved in the order that is given and why it is important to go in that order. This will give the students the understanding of the importance of how one should solve the problem to get the right answer. As a group, the students and I will go over the correct order in which the operation should be solved. 2. Together as a small group, students will have a practice problem where together they will work through the problems 9 - 5 ÷ (8 - 3) x 2 + 6, 7×7+1+16÷8-(7 - 6), and (10/2) x 7 + 5 – 4, explaining each part of the problem and why they are doing a certain operation at that time. I will display the problems on a piece of paper to the students and they will then copy it don’t on their own sheet. This will be repeated again with the use of

highlighters to show the different stages of the problem. A different color will indicate a different stage of the problem. The problems that I will have them solve, I will have an answer sheet with the answers so I will be able to pin point where they seem to be struggling or steps that they are missing. 3. Students will then be given their own problem and use the technique they were just given, using the highlighters, to show their understanding. They will then be showing their thinking process to the rest of the group and they answer they got. MISTAKES:  Choosing the wrong operation to first solve  Not solving left to right  Using the wrong numbers solve an operation  Reusing a number in the operation STRATEGIES  Using highlighters to indicate which operation to first solve  Using order of operations Yoga which explains the stages in order G. PROCEDURE Before:  At the beginning of the lesson, in small groups, the time will be used to review what the students understand about Order of Operations and review/demonstrate other ways they have worked through order of operations. As a group, we will make indepth instructions they should follow when solving order of operations. Though out this time the students will be coming with the order with a little help from myself.  Using the instructions that they wrote as a group, we will work through a problem together. I will be working through the problem as the students tell me what to do. When doing so, I will have the students explain why they are solving each step in that order. Throughout, I will ask why is it that a certain operation goes first. During:  While still in small groups, I will introduce a new strategy the students can use to remember which operation they should solve for first. When reviewing the three stages, each stage will be given a highlighter color. I will demonstrate the use of the highlighters in the first problem. o Example – Parenthesis Multiplication/Division Addition/Subtraction o For the first problem, I will be using the highlighters to show the order they will be solving the operation to get the correct answer. The first problem we will work on together is 9 - 5 ÷ (8 - 3) x 2 + 6 o Using the practice problem, all of the children will write the problem down on their sheet and pick the highlighter they want for each stage. I will then ask the students to highlight the parts that are included in the first stage, parenthesis. Example: 9 - 5 ÷ (8 - 3) x 2 + 6 o Once they have done so, I will then ask them to solve for that portion. o After they have solved for the parenthesis and have rewritten the problem, I will then ask what the next stage is, where they will reply, multiplication and

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division. Being so, they will then be asked to highlight all of the multiplication of division operations. Examples: 9 - 5 ÷ 5 x 2 + 6. o Since, there are two that carry either operation, this will then bring in the rule of left to right. It will be explained that they are find the first one, and that is the one to be solved first. Being that in some cases there will be overlap, the same rule applies where they will me taking the first complete operation to solve for first. Once they finish the first operation the process will be repeated. They will write the new problem, highlight the portions that are multiplication or division, and then solve. o 9–1x2+6 o Once there is no more green highlighter on the problem, they will then know that is when you move on to the next stage, addition and subtraction. To begin they are tasked with highlighting all the addition and subtraction operations. Example: 9 – 2 + 6 o Once they have highlighted, they will then explain to me where they believe they start based on the second stage. They will begin, from left to right, until they get to answer. o 7+6 o Answer: 13 After we have gone through the first problem together and they have followed me step by step on their paper, it will then be their turn to work on a problem. 7×7+1+16÷8-(7 - 6). While working on this problem, they will be working together and asking questions to the whole small group when they come across one. This will allow me to see the children’s understand of order of operations. Once all of the students, one by one, the students will be asked how they completed an individual step. o Based on this I will be able to see if the students are understanding the concept or will need another problem that we will work through together. o If an additional problem is needed: (10/2) x 7 + 5 – 4 Once all of the children are one around the same page when using this technique, I will then explain the game they will play to show their skills when doing order of operations. o The game is called “I Have, Who Has.” For this game all of the students will be given their own problem to solve, using the technique that was introduced earlier in the lesson. Once, I have had the ability to talk to all of the students one on one, on their thoughts when doing the problem. Once they have all worked through their individual problem, the students with the word START, above their problem will then state “I got (their answer)” then flip their slip over where there will be a number listed. Best on that number they will then say, “Who has (the number on the back of their slip).” Whoever got the number that the first person stated will then speak, “I have ….” “Who has ….” This process will continue until the last person speaks and has the word STOP on the back of their slip.

After:  At the end of the game, we will have a discussion on the technique and game that experienced during their time in small groups with me. o I will first let the students tell me what they did and didn’t like and overall what they thought of the lesson.

o I will then ask them to show with a thumb up, thumb down, of sideways thumb, how comfortable they are with order of operations. o I then ask questions, “What was your favorite part of the lesson?” “Did this help you with your understanding of order of operations?” and “What are your overall questions or comments about the lesson?” H. DIFFERENTIATION  This lesson will be differentiated for students within each small group. This will be based on the problems that they will be given during the game. Students, during the lesson will also have a choice in the colors they will be using to determine the different stages of order of operations. These groups that the students will be in were predetermined by the teacher based on their level in math. This form of differentiation is based on their readiness. Some students are further along than others and the problem that I will give then to solve individually are based on their readiness of the topic, order of operations. Therefore, the students will be comfortable with each other and be interactive in the learning process. The material and problems that will be used will also be used based on the student’s readiness in this topic of math. Based on this the low, medium, and high grouping will create differentiation in the problems that the children solve. I. WHAT COULD GO WRONG WITH THIS LESSON AND WHAT WILL YOU DO ABOUT IT? Being that this lesson will be a review on the topic because a lot of the students are struggling with it in the classroom, I am worried that the some of the student will find the lesson to be boring because they already know what they are doing, although they could still use the review. Because of this they can be given a harder problem they can solve through to give them more of a drive. Another element that can go wrong would be during highlighting for the different stages, when the operations are right next to each other sharing a number. If this occurs as confusion in the lesson, I will have the students leave a gap in between the operations as I did above. When doing so they will be picking the first complete operation to solve through first.

Group 1

Group 2

Group 3

(3 + 6) × 2 + 6

12 + (4 ×2) + 21 ÷ 3

(15 ÷ 3) × 7 – 20

5 × 2 – 3 + 18 ÷ 6

25 – 9 ÷ 3 × 2 + 11

(17 - 5) + 2 ×12 ÷ 4

25 – 4 × 3 + (7 × 2)

13 + 2 × 2 - (11 – 4)

3 × 8 + 20 – 6 ÷ 2 + 3

(5 + 6) – 1 × 9

12 – 9 ÷ 3 + 4 × 1

(5 × 6) + (4 ÷ 2) - 3

(12 – 6) × 10 – 4

20 –11+ 4 ÷ 2 × 4

(6 ÷ 6) ÷ 9 ÷ 3

6 – 3 + (3 ÷ 1)

(6 + 2) × 8 ÷ 4 – 1

(7 × 2 – 4) ÷ 5

3 × 11 + (10 - 6)

15 ÷ 3 + (6 ×2) - 1

START WHO HAS 10

START WHO HAS 30

START WHO HAS 18

WHO HAS 27

WHO HAS 10

WHO HAS 44

WHO HAS 2

WHO HAS 13

WHO HAS 29

WHO HAS 56

WHO HAS 17

WHO HAS 3

WHO HAS 6

WHO HAS 15

WHO HAS 2

WHO HAS 37

WHO HAS 16

FINISH

FINISH

Group 1       

(3 + 6) × 2 + 6 = 24 5 × 2 – 3 + 18 ÷ 6 = 10 25 – 4 × 3 + (7 × 2) = 27 (5 + 6) – 1 × 9 = 2 (12 – 6) × 10 – 4 = 56 6 – 3 + (3 ÷ 1) = 6 3 × 11 + (10 - 6) = 37

Group 2  12 + (4 × 2) + 21 ÷3 = 27       

25 – 9 ÷ 3 × 2 + 11 = 30 13 + 2 × 2 - (11 – 4) = 10 12 – 9 ÷ 3 + 4 × 1 = 13 20 –11+ 4 ÷ 2 × 4 = 17 (6 + 2) × 8 ÷ 4 – 1 = 15 (15 ÷ 3) × 7 – 20 = 15 15 ÷3 + (6 ×2) – 1 = 16

Group 3      

(15 ÷ 3) × 7 – 20 = 15 (17 - 5) + 2 × 12 ÷ 4 = 18 3 × 8 + 20 – 6 ÷ 2 + 3 = 44 (5 × 6) + (4 ÷ 2) -3 = 29 (6 ÷ 6) ÷ 9 ÷ 3 = 3 (7 × 2 – 4) ÷ 5 = 2

FINISH

Analysis of Teaching Strategies There were several changes that were made when revising the lesson plan. Many of the revisions took place in the context of the lesson specifically in the vertical and horizontal planning. When including this in the lesson, it is important because it helped me understand the why this lesson is being taught at this time. When creating this part of the lesson it was important to know the students and their understanding of the concept up to the lesson. In doing so, I was better able to prepare for the lesson and for individualized problems for the students. Another revision that was made in the lesson plan was differentiation. Differentiation in math is very important based on the student’s readiness level and good way to implement this in the lesson is through the predetermined math groups the students have been a part of in the class. When I implemented this lesson, I believe and effect strategy that was incorporated was through the different visuals that were included. These visuals were the different colors that the students were able to use when solving the problems. Another effective teaching strategy that worked with some of the students were giving them the ability to create their own rules. The students were more willing to follow the rules that they set for themselves. Through some of these teaching strategies, some of the students began to further understand the features of order of operations. Pattern Groups  Distinguishing characteristics – Within the lesson there were three different groups. 1. Experienced – Being that this was a review lesson for the students, these students grasped the topic very well the first time and did not really need to color the different steps. They felt that the color step wasn’t needed. When they are working individually with their problem, they often would not use the strategy that I taught them. They would go through the problem feeling like highlighting was an unneeded step. 2. Moderate – This group, in general, they were fairly understanding of order of operation. They knew that there was a certain order that the operations need to be solved but they are confused about which operations comes first. Specifically, they were set on doing multiplication first rather than find the operation from left to right. It was also the same for addition and subtraction. They were set on adding first even if subtraction comes first when looking at the problem from left to right. 3. Developing – Within this group, the students acted in a manner that they have never touched on order of operations. They were confused about every aspect of the lesson and was almost like they were giving up. They stopped listening as well. There multiplication and division  Sample Responses – 1. Experienced – “This is easy.” 2. Moderate – “Wait do we do multiplication or division first?” 3. Developing – “I’m confused, why are we highlighting numbers?”  Number of students – 1. Experienced – 7 2. Moderate – 6 3. Developing - 6

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New questions – 1. Experienced – “What way can you change the problems that can be a little more challenging?” 2. Moderate – “When doing order of operations, what confuses you the most?” 3. Developing – “What extra support will you like when learning the order of operations?”

Small Group Activity – 1. Experienced – As a small group activity, I believe these students will benefit by having tougher questions such as having multiple operations within the parenthesis. With these tougher questions, they can also play a game such as bingo. The bingo mat would have the answer to the questions and they could set a goal where they fill a whole row and so on. 2. Moderate – After working with these students, I believe the problems they were given were good problems for the students to work with. Because of this, I would like to have the students practice more with these problems. In doing so, I believe these students can work as a group with the same cards that were used during the lesson. The student will work as a group putting the cards in order based on what card leads to the next. If they work well with the cards they are given, they can work with the cards that were given to the students in group one. This will be a good activity for the kids to collaborate with each other. 3. Developing – With this group, I would like to take a step back. I would like to start out giving these students problems that had less operations. I believe these students would benefit from having more instruction on problems that just consisted on multiplication and division and then other problems that just had addition and subtraction. When giving them these problems to work with, the students will strengthen their understanding on working from left to right when dealing with those operations. An activity that I believe that students will benefit from would be a mystery color sheet where you color based on the answers they receive from the problems. When working one this activity sheet the students will be able to collaborate with other students. Reflection:  What I learned about children as learners of mathematics. o When teaching this lesson, I believe it was important to realize that a lot of students, in math, benefit from learning in small groups. When working with the students in small groups I was able to see the difference in the children and their understanding of order of operations. While doing this lesson I was able to see that some students, who do not like math, are more likely to become frustrated with the material. Being that I was teaching something that students had already started learning, some had already decided that they did not like order of operations. Because of this it was hard for the focus to be on the activity I had planned for them. When having mathematics in the classroom, I believe it is so important for the material to be engaging for the students although that can be difficult at times.  What I learned about teaching.

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o When teaching this lesson, the biggest element of teaching is patients. When I was teaching the lesson for one select group, I could tell their attention was just not there. This is difficult as a teacher because you want nothing more than to help them learn. When trying to gain their attention it took a lot of patients. I also found that it was hard to balance between the students who were paying attention and those who were not. I did not what to prevent the students who were trying to learn the ability to. It is hard to know how to balance your attention as the one facilitating a lesson. What I learned about myself. o While doing this lesson, I believe I was able to learn a few things about myself. I will say that during one of the groups I just felt so defeated because some of the students were just not listing nor did they want to do the game I made for them. It was important for me to not take it personally. When performing lesson like these, I was able to learn that it is something to grow. That, I believe was the most important aspect I learned from this lesson.