Unit and Lesson Plan for Third Grade, Introduction to Multiplication

Unit & Lesson plan developed by: Adelaida Kim, Cathy Davila, Sarah Chang, Vivian Huang, Yvonne Kang

Title of the Unit:

Textbook: Houghton Mifflin Mathematics, 3rd Grade, Vol. 1, Teacher Edition (published 2002)Brief description of the UnitStudents will be introduced to multiplication using repetitive addition and arrays. Using various methods of strategy, students will learn how multiply with 2's, 5's and 10's.Goals of the Unit: For students to make connections between repeated addition and multiplication using equal groups. For students to model and use multiplication to solve word problems in situations involving arrays. For students to be familiar and use key math vocabulary to communicate: product, factors, array, times, multiplication, commutative property of multiplication For students to explain their method of choice to solve the problem. For students to understand the different methods learned for multiplication of 2,5,10.

Relationship of the Unit to the Standards:

[CCSS.MATH.CONTENT.2.NBT.A.2] Count within 1000; skip-count by 5s, 10s, and 100s. [CCSS.MATH.CONTENT.2.OA.C.3] Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. [CCSS.MATH.CONTENT.2.OA.C.4] Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

This unit

[CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. [CCSS.MATH.CONTENT.3.OA.A.3] Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

[CCSS.MATH.CONTENT.3.OA.B.5] Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) [CCSS.MATH.CONTENT.3.OA.C.7] Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.Background and Rationalea. Students will need to learn the different methods of solving a multiplication problem, so they will be prepared to learn to solve problems with bigger numbers.b. Students will need to memorize the multiplication table later on, but if they forget they can use what they will learn in this unit to help them solve a problem. In a classroom I have done field experience, a student was struggling to remember what 5x7 was but the teacher reminded them the different methods they had learned to solve multiplication problems.c. Students will build their knowledge on multiplication by learning that multiplication is similar to repeated addition and that multiplication is the basic foundation of division. Students will see how and why 5x7 and 7x5 are different of question even though they have the same solution. Consideration for Designing the Unit (Findings from your research) Curriculum that our group used was a resource from a textbook in the education book collection in the DePaul Lincoln Park library. The section used in the book was a chapter on teaching introduction to multiplication.

Article: Teaching for Mastery of Multiplication

Any memory of multiplication for us was memorization. But according to the National Council of Teachers of Mathematics (NCTM) memorization is not fluency. The book Principles and Standards for School Mathematics states, Developing fluency requires a balance and connection between conceptual understanding and computational proficiency. Fluency in multiplication is defined as possessing a deeper understanding and being able to apply what has been learned. While learning and teaching multiplication can seem tedious children need to learn and master multiplication or they will be at a mathematical disadvantage that can hinder mathematical success in the future. The teaching method that should be used is the introduction to all of the multiplications teaching the easiest ones first and moving to those that may be difficult. Once all the multiplications have been covered teaching should consist of multiplication applications and problem solving. The mastery of multiplications will no longer come simply from memorization but must establish a deeper connection. About the Unit and the LessonThe unit plan we have constructed has been divided into 5 sections. Each section requires students to build upon skills and concepts they have learned from the previous section. The first section is composed of lesson 1. The students are introduced to the concept of multiplication for the first time. We will be modeling multiplication through repeated addition. Addition is a skill students have previous learned and mastered. We will be showing students how you can think about multiplication as repeated addition. Students will learn about the symbol that represents multiplication and how to write a multiplication sentence using the symbol. In the second section, students will be learning about arrays and multiplication. Students will learn how to formulate an algorithm (multiplication sentence) from the given array. Students will also learn about the Commutative Property of Multiplication. Through various activities, students will see that the two factors can be multiplied in any order and still come out with the same product. The third section focuses on multiplying by 2. Now that students have learned the basic foundational concepts of multiplication, they are ready to learn how to multiply numbers. In lesson 3 students will learn different ways to multiply when 2 is a factor.The forth section focuses on multiplying with 5. Students will learn different ways to multiply when 5 is a factor. The fifth section focuses on multiplying by 10. Students will learn to find the product, when one of the factors is a 5.

Flow of the UnitLesson NumberTitle and Learning Objectives# of lesson periods

1 (Vivian)Modeling Multiplicationex. 2 + 2+ 2 +2 +2= 2 x 5

Understand that multiplication is similar to repeated addition.Learn about the multiplication symbol and how to write a multiplication sentence.

1 x 60 min.

2 (Sarah)Arrays and Multiplication

Solve word problem in situations involving arrays. Using arrays to find solution to the multiplication problem.2 x 60 min.

3 (Adelaida)Multiply with Five

Using strategies previously learned and applying to multiplication factor of 5.2 x 60 min.

4 (Cathy)Multiply with Two

Becoming familiar with the multiplication factor of 2 by using different ways to multiply.

2 x 60 min.

5 (Yvonne)Multiply with Ten

Deepen understanding of strategies used and another way to remember multiplication factor of 10.2 x 60 min.

Lesson 2: Vivian Pepperoni PizzasGoals of the Lesson:a. [CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.b. For students to extend their prior knowledge and understand multiplication as repeated addition.c. For students to understand numerical representations in a written algorithm expressed by verbal and visual form.

Flow of the lesson based on teaching through problem solvingSteps, Learning ActivitiesTeachers Questions and Expected Student ReactionsTeachers SupportPoints of Evaluation

1. Introduction Find the total number of eggs. Then write an addition equation to express the total of eggs in the carton.

(2+2+2+2+2+2=12; 6+6=12) This serves as a quick review from what students learned in second grade. CCSS.MATH.CONTENT.2.OA.C.4Use addition to find the total number of object arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

2. Posing the Task

Ms. Huangs Uncle works at a pizzeria. He tells Ms. Huang that every day for lunch, he makes four pizzas for his employee and each pizza has exactly five pepperonis. However, he doesnt have enough pepperonis to make pizzas for his employees for tomorrows lunch. How many pepperonis does Ms. Huangs Uncle need total in order to make lunch for his employees tomorrow? Show me a thumbs up if you understand what to do. Are there any additional questions?Students will display thumbs up if they understand their task, a thumb in the middle if they have some questions, or thumbs down if they dont understand the task at all.

3. Anticipated Student Responses

Students will use paper plates to represent pizzas and red counters to represent pepperonis as math manipulatives.

R1: 5+5+5+5=20R2: Students counting each pepperoniR3: 4+4+4+4+1+1+1+1=20R4: 4*5=20

Follow Up Question What is another way Ms. Huangs Uncle can use the same number of pepperonis but with a different number of pizzas? Write an addition algorithm and multiplication algorithm for each visual you draw

R1: 20 pizza 1 pepperoni on each1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=2020x1=20 R2: 10 pizza 2 pepperoni on each (2+2)+(2+2)+(2+2)+(2+2)+(2+2)=20 10x2=20

R3: 2 pizza 10 pepperoni on each (10)+(10)=20 2x10=20

Students will have various ways of responding. As the teacher, I will take note of all the different responses and use it in the class discussion. For students who have incorrect solutions, I will ask them to explain how they got their answer and explain what their algorithm represents. If students finish early, I will instruct them to develop a different algorithm different from the first algorithm they came up with. The teacher will select students who finished early to go to the board and display the various methods used. The purpose of this lesson is for students to see and understand how multiplication is just repeated addition.

4. Comparing and Discussing After the selected students have displayed their method and math work on the board, the teacher will select other students to explain what their classmates did and what their algorithm represented in the image. Despite the order of algorithms presented on the board, the student solutions will be displayed in the order shown above in Anticipated Student Response. Then as a class we will observe and analyze the picture.- There are 4 pizza- Each one has 5 pepperonis- 5+5+5+5=20 pepperonisHow many groups of pepperonis are there?- 4 groupsHow many pepperonis are in each pizza?- 5 pepperonisAnother way we can write the total of pepperonis is using multiplication.- # of groups x # in each group- 4 x 5=20- There are 4 groups of 5 pepperonis

If we had four pizzas with 4 pepperonis on each AND four pizzas with 1 pepperoni on each, what will the math equation look like?

R1: 4+4+4+4+1+1+1+1=20

What do you notice about the math equation?

R: There are a lot of 4s and 1s.

Very good observation. What would you suggest we should do to make the equation look simpler?

R: Group them together!

What do we group together?

R: The number of 4s and the number of 1s

How many groups of each number do we have? Imagine each digit is a pizza group and each number is how many pepperonis are in each group.

R: There are 4 pizza groups and 4 pepperonis on each one. So 4 groups of 4. There are 4 pizza groups and 1 pepperoni on each one.

What will our multiplication equation look like?

R: 4x4 and 4x1

What do we do with these equations now?

R: Add them together! (4x4)+(4x1)= 16+4=20 Ideas to focus on during the discussion are the various algorithms the students use to represent the image. Then students will be shown despite the various methods of solution, the methods will result in the same answer by simplifying the equation. This will also display a method to check their work.The teacher will use student verbal understanding of how the numbers in the algorithm represents aspects of the image will indicate the students are benefiting from the discussion as well as the questions they ask

5. Summing up Today, we learned how to find the total number of objects using multiplication. We know the total can be found using the number of groups multiplied by the number in each group.

Evaluationa) Did students understand how to write an algorithm to represent the images represented?b) Did students understand what the numbers and operation symbols represent in the algorithm?c) Was there enough time for students to investigate the problem and develop a solution?d) How many students were able to understand the problem and methods of solutions they used?e) How comfortable were students using numbers and operation symbols to represent their understanding?

Lesson 2: Sarah An example of lesson plan format for teaching through problem solving (TTP)Goals of the Lesson: a) [CCSS.MATH.CONTENT.3.OA.A.3] Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.b) For students to model and use multiplication to solve word problems in situations involving arrays. c) For students to know and understand the Commutative Property of Multiplication.d) For students to appreciate the usefulness of multiplication and its efficiency.

***This lesson is anticipated to take about 2-3 days to complete. Flow of the lesson based on teaching through problem solvingSteps, Learning ActivitiesTeachers Questions and Expected Student ReactionsTeachers SupportPoints of Evaluation

1. IntroductionIn the previous lesson, students learned about how multiplication is similar to repeated addition. Instead of adding all the numbers up, students can use multiplication to efficiently solve for the solution. They also learned about the multiplication symbol and how to properly write a multiplication sentence.

For part two of the introduction, I will present the students with a story problem. Problem: Jenny collects flags from different states. She has her flags hung up on a wall in her room. How many flags are on her wall?

If you look at the flags on Jennys wall they are arranged in an array. Can anyone take an educated guess on what an array might be? An array is a number of objects arranged into rows and columns. How many rows are there? 4Can someone tell me something you notice about each row? Each row in the array has an equal number of flags. How many flags are in each row? 5How many flags are there altogether? 20

I will ask students to write a multiplication sentence that correlates with the picture. They will be given no more than 2 minutes to complete this.

Once they have written their math sentence, the students and I will go over it as a class. 4 x 5= 20 4 represents the number of rows 5 represents the number of flags in each row 20 represents the total number of flags

Part 2: After we go over part 2, I will present the students with another question in regards to the same problem. Jenny wants to change the layout of the flags, so she turns it around. Does the total number of flags change? Why or why not? Write a math sentence that represents the new design to support your answer.

We will be going over the answer as a class. I will have students share their answers and explanations.

Afterwards we will talk about both multiplication sentences and how the total does not change. This will set me up into introducing the students to a new vocabulary word: Commutative Property of Multiplication. Students will already know about the Commutative Property of Addition and I will explain how it is very similar.

Commutative Property of Multiplication: When multiplying factors, the order in which you multiply the factors does not change the product. If I change the order of the factors it does not change the product. Example: 4 x 5 = 20 and 5 x 4 = 20

**Mention how if I use 4 x 5 = 20 it means that I have four rows with 5 flags in each row. If I use 5 x 4 = 20 it means I have 5 rows with 4 flags in each row.

Give students example: Will 3 x 5 give me the same product as 5 x 3? Will 6 x 7 give me the same product as 7 x 6? Will 5 x 3 give me the same product as 5 x 4? Why? I will be looking for students to say because they do not have the same factors. In order for the commutative property of multiplication

If students are struggling to answer this question, I will ask them what they notice about the picture and how they are arranged. I will point to the picture and show the students how all of Jennys flags are arranged in rows and columns.

Might need to go over how the first number in the multiplication sentence represents the number of groups and the second number represent the number of items in a group.

Part 2: If the students are having a difficult time writing the number sentence then I will ask them a couple of questions to get them thinking. How many rows do you see? How many flags are in each row? How many flags are there altogether?

See if students are able to write a math sentence based off the array they see

If students are able to explain their math sentence and what each factor represents

Part 2: Write a multiplication sentence that correlates with the array

Able to identify the number of rows and the number of flags in each row

Understand the commutative property of multiplication.

2. Posing the TaskStudents will be given a total of 24 m&ms. They will be asked to come up with as many arrays and write a multiplication sentence for each array. They must use all 24 m&ms. I will give them a worksheet to draw and write each array and multiplication sentence they come up with.

Remind students that each row must have the same (equal) amount of m&m (Cannot have 6 in one row, 10 in another, and 8 in another). Because we know the total number of m&ms what should the product of all our math sentences be?

Based of the arrays and multiplication sentences they created and whether or not the two correlate, I will know whether or not students understand arrays and multiplication.

If the array and multiplication sentence do not match, I will know that the students have not mastered this skill yet and something we need to work on more.

3. Anticipated Student ResponsesR1: 1 x 24 = 24 R2: 2 x 12 = 24R3: 3 x 8 = 24R4: 4 x 6 = 24R5: 6 x 4 = 24R6: 8 x 3 = 24R7: 12 x 2 = 24R8: 24 x 1 = 24

I will encourage students to work together and share their solutions with one another. If there are students who are stuck, I will have them ask a peer first and if they are unable to find the answer, then I will step in and help them.

I will also tell students to come up with as many arrays as possible.

If I see an a multiplication sentence that does not correlate with the array they have, I will ask them various questions so that they notice this mistake as well. The goal of this task is not to have students come up with all the arrays. Instead the goal of this lesson is to see whether or not the array students have drawn matches the multiplication sentence they have written. Are students able to write a multiplication sentence based on the array they see?

4. Comparing and DiscussingI will give students 3-5 minutes to come up to the board and draw their array and math sentence (can only come up once).Then as a class, we will go over each array and whether or not the math sentence that is under it is correct.

After we go over each array, we will group the arrays/multiplication sentences based on similar factors. 1 x 24 = 24, 24 x 1 = 24 2 x 12 = 24, 12 x 2 = 24 3 x 8 = 24, 8 x 3 = 24 4 x 6 = 24, 6 x 4 = 24

I will ask the students if they notice anything about the pairs. I will use this opportunity to go over commutative property of multiplication again.

Writing a multiplication sentence Drawing an array using the given number of objects Writing a multiplication sentence that correlates with the array Notice factors Commutative Property of Multiplication When students are able to challenge one anothers solutions/explanations.

Students use vocabulary terms: product, factors, array, multiplication, commutative property of multiplication

5. Summing upToday we learned about how to use multiplication to solve for the total number of objects in an array. We know how to formulate a multiplication sentence using the information we found from looking at the array. We learned about the Commutative Property of Multiplication and how the order in which you multiply the factors does not matter because you get the same answer.

Evaluationa) Do students know and understand what an array is?b) Are students able to see the relationship between the array and multiplication sentence? c) Were students able to write an algorithm that correctly represents the array?d) Were students given enough time to explore the problem and come up with multiple solutions?e) Are the students comfortable with writing a multiplication sentence for each array? How comfortable?

Lesson 3: Adelaida Goals of the Lesson:a. [CCSS.MATH.CONTENT.3.OA.C.7] Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.b. For students to extend their prior knowledge and understand multiplication as repeated addition.c. For students to understand numerical representations in a written algorithm expressed by verbal and visual form. Flow of the lesson based on teaching through problem solving

Steps, Learning ActivitiesTeachers Questions and Expected Student ReactionsTeachers SupportPoints of Evaluation

1. Introduction a. Show students a sequence of multiplication of 5. Ask students if they see any patterns.

b. Show students a hundreds chart with some of multiplication of 5 highlighted. Ask students what other numbers would be highlighted.

c. Ask students if 4,560 and 85,675 can also be highlighted. d. Pass out a sheet that has a blank circle and tell students to make a clock. Tell them to write the numbers 12 and 6 in the outlier of the middle in the clock first and go on from there. If students have hard time remembering the hour hand, tell them they can also write down 3 and 9 first to give them a better image of the clock. e. Once students are done writing down the numbers on their clock, pass out the chart that has numbers written down along with empty minute box. Students are to write the minutes according the number that the minute hand is pointing to.

Students should be familiar with looking at the time. The activity is to give students confidence that the multiplication of 5 is something they already know even without trying to memorize the numbers.Do you see any pattern in this number sequence? Can you tell me the pattern you see? In this hundreds chart, we see that numbers on the washing line are highlighted yellow. What other numbers would be also highlighted? If the this box were to continue for a long time and numbers 4,560 or 85,675 appearedcan these numbers still be highlighted? Now, were going to change our gear just a little bit and make a clock. Dont look at any clocks in the room and try to make your own clock with the sheet of paper I just passed out.Students see the 5 and 0 pattern from the sequence. They should also realize that the numbers are increasing by. Students say any numbers with 0 or 5 tenths or any numbers that are vertical from the highlighted box could be highlighted.Students can explain that any numbers if 0 or 5 at the end could be highlighted. Students can draw the hour hand of the clock accurately.

Students can write down correct minutes according to each number in the box.

2. Posing the TaskMs. Kim decides to give her teacher friends some chocolates. In order to find out how many chocolates she could give to each teacher, Ms. Kim must find out how many chocolate she has in total. There are 4 groups of 5 chocolates inside the box. How many chocolates does Ms Kim have in total?

Once you are done with the problem, solve 9x6 using your prior knowledge on multiplication of 5.Students will have different strategies to solve the problem. The teacher should consider all the anticipated student responses and use some of them in the class discussion.

3. Anticipated Student Responses R1: 5 10 15 20R2: 5+5+5+5R3: 5x4R4: 4 8 12 16 20R5: 4+4+4+4+4R6: 4x5 The teacher will pick three anticipated responses that all have different strategies. The purpose of discussion is too see that all different methods will have the only one solution.Were students able to understand that even if they grouped the circle differently (horizontally or vertically), they would still get the same answer?

4. Comparing and DiscussingSelect three students to come to the board that had different strategy to solve to the problem. R1:

R4:

R5: 4x5=20

5. Summing upToday, we learned that there is a sequence in the multiplication of 5. To find the solution, we need to add 5 continuously. We also know that any number that ends with 0 or 5 can be dividend by 5.

Evaluationa. Did students understand that multiplication is a sequence of numbers?b. Did students understand that that clock is a representation of multiplication of 5?c. Did students understand any number that ends with 0 or 5 could be dividend by 5?d. How many students were able to understand the problem and methods of solutions they used?e. How comfortable were students using numbers and operation symbols to represent their understanding ?Lesson 4: Cathy

Goals of the Lesson:a) [CCSS.MATH.CONTENT.3.OA.A.1]Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.b) For students to model and use multiplication to solve word problems. c) For students to associate addition to multiplication. d) For students to understand there are multiple strategies when multiplying (repeated addition, array, picture, break-apart).

Steps, Learning ActivitiesTeachers Questions and Expected Student ReactionsTeachers SupportPoints of Evaluation

1. Introduction

In previous lessons students have learned: multiplication is repeated addition, the Commutative Property of Multiplication, and how to using arrays to solve word problems.

Part One:

In the beginning of the introduction, we will have a brief review of what the students learned in the previous lesson. Next, students will have the following worksheet:

1. 2+2+2= 2 x 3 2. 2+2+2+2+2= 2 x 53. 2+2= 2 x 2 4. 2+2+2+2+2+2+2+2+2+2+2+2= 2 x 12 5. 2+2+2+2+2+2= 2 x 66. 2+2+2+2+2+2+2+2+2= 2 x 9 7. 2+2+2+2= 2 x 4 8. 2 = 2 x 1 9. 2+2+2+2+2+2+2= 2 x 7 10. 2+2+2+2+2+2+2+2+2+2= 2 x 1011. 2+2+2+2+2+2+2+2= 2 x 8 12. 2+2+2+2+2+2+2+2+2+2=2= 2 x 11

The multiplications on the right side will NOT be present.

I will then ask students to raise there hands to share ideas of how we can solve these 12 problems faster and in an easier manner.

At the end of the lesson we will review this worksheet again.

Part Two:

Before moving forward we will complete one row of the Multiplication Strategy Review Sheet https://www.pinterest.com/pin/514958538615572642/

Part Three:

Students will watch the following video: https://www.youtube.com/watch?v=PE_oUqJ41oI

Part One:

When students have completed worksheet we will have a brief discussion. We just completed this work. Can someone tell me what we have been learning in previous lessons and how this connect to what we did just a few seconds ago. At this time, talk in your table about ways we can show this in a faster and easier way. After write your ideas in your math journal.

Thumbs up if you are done and a thumbs down if you need more time to write your ideas down.

At this time you may put this sheet away. We will be looking at it once again towards the end of class.

Remember we are going to be using the 2s multiplication

Part Three:

Part One:

Students should recognize that it is repeated addition. They should be able to identify that this is the 2s multiplication.

Students should be brainstorming ideas: array, repeated addition, drawings.

Students should mention the following: repeated addition array drawing (possibly)

The array, drawing, repeated addition is not new to students and should know how to complete the chart. If there is a disconnection in any section I will be able to see which students need additional help in a certain area.

Part Three:

Classroom will all be singing.

2. Posing the Task

Students will use the concept of repeated addition to solve the following problem.

Problem: Ms. Davila wants to know how many computers there are at Blank Elementary. There are 12 classrooms at Blank Elementary and each classroom has two computers. Help Ms. Davila figure out how many computers there are.

I will remind students that they can use their Multiplication Strategy Review Sheet or the following chart will also be available.

Students should write the problem in math journal.

As students solve problem they should show all their work and label each part of their work as well.

Students should be able to solve problem using any of the four strategies shown in the Multiplication Strategy Review Sheet.

3. Anticipated Student Responses

R1: 2+2+2+2+2+2+2+2+2+2+2+2 = 24 [correct]

R2: 2 x 12 = 24 [correct]

R3: 12 x 12 = 24 [ incorrect number sentence; correct product]

R4: 12 + 2 = 14 [incorrect]

I would review with the whole class the following:

# of groups x # in each group = product.

Students who finished early could review their 2s flashcards for additional review.

4. Comparing and Discussing

I would have a student with the correct answer and a student with the incorrect answer come to the board and have them walk the class through. I would stop and facilitate in area that need to more attention.As a class we will review both problems and learn together.

I will ask for the students to point to the # of groups and # in each group.

Students will be learning from their peers.

Students will be able to question and comment the work their peers show.

5. Summing up

Students will take out the worksheet completed Part One of the Introduction. Next to the repeated addition they will write the 2s multiplication. 1. 2+2+2= 2 x 3 2. 2+2+2+2+2= 2 x 53. 2+2= 2 x 2 4. 2+2+2+2+2+2+2+2+2+2+2+2= 2 x 12 5. 2+2+2+2+2+2= 2 x 66. 2+2+2+2+2+2+2+2+2= 2 x 9 7. 2+2+2+2= 2 x 4 8. 2 = 2 x 1 9. 2+2+2+2+2+2+2= 2 x 7 10. 2+2+2+2+2+2+2+2+2+2= 2 x 1011. 2+2+2+2+2+2+2+2= 2 x 8 12. 2+2+2+2+2+2+2+2+2+2=2= 2 x 11

Then, as a table students will discuss and brainstorm a summary.

Students will write their tables brainstormed summary and then a classroom/teacher summary.

Student Summary:

Class Summary: Today as a class we reviewed arrays, repeated addition,and the Commutative Property of Multiplication. We also practiced our 2s multiplication understanding that they are doubles.

Students will share out brainstormed summary.

Evaluation

1. Did students understand that the 2s multiplication table is doubles?2. Do students understand # of groups x # in each group = product? 3. Were students able to create a correlation between 2+2+2+2= and 2 x 4 and the concept of repeated addition? 4. What are other ways the 2s can be taught?5. What can I do different next time?

Lesson 5- YvonneGoals of the Lesson:a) [CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.b) For students to explain their method of choice to solve the problem.c) For students to understand the different methods learned for multiplication of 10.

Steps, Learning ActivitiesTeachers Questions and Expected Student ReactionsTeachers SupportPoints of Evaluation

1. IntroductionStudents will review the different ways to solve a one-digit multiplication problem using addition, arrays and the different methods for multiples of five and two.Students will also go over the multiple of 1, as it will lead them into the main lesson of multiple of 10. Two methods of x10.For example, for 10 x 5.1) I will show the students that they can solve it by simply taking the number that is not 10 and then adding a 0 to the end. This examples answer would look like this: 10 x 5= 50Explanation: I used the rule of putting one zero on the end of the number 52) students can use the first method they learned in the beginning of the unit by adding. Students will always use the number 10 and then add the amount of number that 10 is multiplying by. For example,10 x5= 10+10+10+10+10=50I will help them review by asking what those different methods are of solving a one-digit multiplication problem. I may need to give couple problems that relate to what they have learned already.

I will determine to see if the students are understanding the methods but having the students do another practice problem themselves by themselves in the next step of this lesson.

2. Posing the Task-Students will use what they have learned throughout this whole unit to solve a multiplication story problem with the multiple of 10.-The multiplication story problem I will give the students is The monkeys had 7 trees. There were 10 bananas in each tree. How many bananas are there together? -Students will use the number given in the information and multiply those two numbers. Students will be asked to show their work and also explain in one sentence how they have solved this problem as we did in the beginning of the lesson.If students need additional help and dont know where to start, I will have them fill the boxes with the two numbers they will use to solve this problem.

I will see if the students understand by looking at the one sentence explanation. Students will be expected to explain how they got their answer.

3. Anticipated Student ResponsesIf students are not familiar with multiplying, they might add the numbers straight down from the problem. -R1: 10 x 7= 7+7+7+7+7+7+7+7+7+7 [correct]I added the number 7 ten times. - R2: 10 x 7= 170 (incorrect)I put a zero after putting the other numbers. I can help students to fix their answer by questioning them what they did to solve the problem. Their reasoning should be one of the methods the students have learned earlier in the lesson.--The method student one used had the right answer and explanation, but there is also another way to solve that problem. Students can add 10 seven times.R1: 10+10+10+10+10+10+10=70--The method the second student used were correct, but the number they used was incorrect. Students fixed responses should look like this:R2: 10x7=70Explanation: I added a 0 at the end of the number I am multiplying the 10 with.I will know if the students understand the task if they get the right answer and also have a good explanation.

4. Comparing and DiscussingI will have the students share their method depending on how they have solved the problem. I will have one student from each method taught to share their solution methods.I will also share one problem that is incorrect so that the students can discuss why the solution is incorrect.Students should discuss the method that is used in the incorrect problem I have shared. The discussion should include students explaining why the method works or doesnt. I will be able to see if the students are benefiting from the discussion if students are participating and discussing the incorrect problem.

5. Summing upI will summarize the main idea of the lesson by discussing the different methods once again to solve the multiplication of 10s. Students should know how to explain how they have solved a multiplication of 10 problems.I will look to see if I can proceed by giving them additional problems that relate to the ones we have learned today.

Evaluation1. Do students understand the different methods of solving a multiplication of 10s problem?2. Do students understand the information given in the world problem?3. Are students using a method learned for the multiplication of 10?4. Were students giving an accurate explanation of their solution?5. Do students have the right answer?

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