3rd Grade Multiplication Unit

Lauren McNeela

May 4, 2015

Multiplication Unit

Grade: 3rd

Rationale:

What are the goals for students?

- Students will be able to understand multiplication concepts and be able to apply them in various contexts and subject areas.

- Students will be able to make connections with multiplication and elements of their daily lives and will realize the importance of multiplication concepts in their world.

Why is it important for the students to learn the concepts/skills?

- Students need to be able to develop foundational mathematical skills in multiplication. These skills will help them succeed with more complex mathematical procedures as they move on to higher levels.

- Students need to be taught various strategies and methods of solving multiplication problems and how to apply them so they can find the way(s) that is/are most clear and efficient for each of them.

Prior Knowledge Required:

Students should be able to recognize numbers 1-100.

Students should be able to recall and apply addition strategies and patterns.

How I will incorporate the NCTM Learning Standards

This unit on multiplication will incorporate the five standards of the National Council of Teachers of Mathematics. These standards will help students utilize reasoning, problem solving, and critical thinking skills in mathematics while communicating with peers, making connections, and learning various strategies to solve multiplication problems. I will encourage inquiry, reasoning, and critical thinking skills through my mathematical instruction, activities, and assignments.

Problem Solving: Students will be able to use various strategies in order to solve multiplication problems and word problems. These strategies may include traditional multiplication, memorization or basic multiplication facts, and arrays.

Reasoning: Students will be able to assess a problem and decide which method they should use to solve it efficiently.

Communication: Students will be encouraged to collaborate with peers to confirm or challenge one another’s answers to multiplication problems. Students will have to defend their methods and answers orally and in writing.

Connections: I will reinforce the value of multiplication in other subject areas and in daily life. Multiplication can be used to decide how many pizzas to buy for a party, how large to make a fence for a yard, and how many copies of homework the teacher needs to ensure that each student receives one. Multiplication is integrated in the daily life of the students, so they need to understand its importance.

Representation: Students will be taught various methods and strategies to represent multiplication problems. They can solve in traditional forms, can draw pictures of objects, can illustrate through columns and rows, can use manipulatives, can view multiplication virtually, etc. Students will have a variety of options to learn multiplication.

Implementation of the CCSSM Mathematical Practices

1. Make sense of problems and persevere in solving them

Students will be encouraged to continue working through various problems to develop their understanding of multiplication and their ability to solve them efficiently. Students will also be presented with problems in real-life contexts, making problems more relevant and clear for students. Students will also be asked to explain various components of a problem (that, in 8x7, 8 represents the group and 7 represents the number in each group) so they understand how to approach the problem.

2. Reason abstractly and quantitativelyStudents will be asked to demonstrate understanding of the terms within a multiplication problem. They will be required to represent the problem in numerical values as well as through visual representations. Students will be able to connect meaning to problems in real life situations to comprehend the relevance of multiplication in their lives.

3. Construct viable arguments and critique the reasoning of othersStudents will be asked to support their reasoning and will be asked to agree or disagree with the reasoning and/or answers of their peers in a respectful manner.

4. Model with mathematicsStudents will be exposed to various means of demonstrating mathematical concepts. The teacher will use online manipulatives, counters, pictures/symbols, and other visual models to teach multiplication. Students will be able to utilize these skills and tools to model real life situation, like arranging desks in a room or ordering food for a class party.

5. Use appropriate tools strategicallyStudents will be asked to utilize a times table to solve multiplication problems and will also use counters to demonstrate grouping and arrays for multiplication.

6. Attend to precisionStudents will be asked to solve problems carefully to ensure that answers are correct. Students will also practice skills relating to arrays, repeated addition, times tables, and other multiplication concepts in order to ensure accuracy and precision of these various strategies. Students will also learn proper terminology like repeated addition, array, and times table to explain their reasoning and strategies and to demonstrate comprehension of mathematical concepts.

7. Look for and make use of structureStudents will be able to make connections between various multiplication concepts. For example, students will realize that solving multiplication is based off of addition. They will understand the relationship between repeated addition, arrays, and other grouping strategies in terms of their use for solving problems. Students will also learn structure through the introduction of the commutative property in multiplication problems and its application in addition problems as well.

8. Look for and express regularity in repeated reasoning Once students become more familiar with multiplication, they will learn that multiplication will serve as a more useful practice than addition for more complex problems. Rather than students simply adding 3+3+3+3, they can more easily use the equation 3x4 and become familiar with the product.

Theme and Topic:

This unit will introduce and cover the topic of multiplication. Multiplication knowledge and understanding is a foundational skill for student success at higher levels of mathematical learning. Students will need to understand mathematics in order to learn fractions, percent, algebra, geometry, and so forth. This unit will introduce what multiplication is, why it is valuable to know, and how one can solve multiplication problems in numerous ways.

Concepts:

Traditional Multiplication Multiplication using times tables

Multiplication using arrays Problem solving Multiplying by 5s and 10s

Multiplication using unit squares Finding Area

Patterns in multiplication Multiplication using repeated addition

Major Questions:

Why is multiplication important in our lives?

What are some strategies we can use to solve a multiplication problem?

How can we create a multiplication equation with information from a word problem?

How does an array help us solve multiplication problems?

What patterns do we notice on a multiplication table?

What is area? How do we find it?

What do we notice when we multiply by 10s? What about by 5s?

Illinois Learning Standards:

3.OA.A.1 – Represent and solve problems involving multiplication and division - Interpret products of whole numbers , e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each

3.OA.A.3 – Represent and solve problems involving multiplication and division – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

3.OA.B.5 – Understand properties of multiplication and division – Apply properties of operations as strategies to multiply and divide *Students need not use formal terms for these properties

Subject Areas:

This unit will include a lesson with the reading of One Hundred Hungry Ants by Elinor Pinczes to describe the concept of arrays. This unit will also familiarize students with the planets of the solar system through a game using a times table.

Time: 3-4 weeks

Lesson Plan 1

Lesson Information

Lesson Title: Introduction to MultiplicationGrade Levels: 3rd gradeSubject/Topic Areas: Multiplication and repeated additionKeywords: Repeated additionDesigned By: Lauren McNeelaTime Frame: 1 class period

Illinois Learning Standards

3.OA.A.1 – Represent and solve problems involving multiplication and division – Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.

3.OA.B.5 – Understand properties of multiplication and division – Apply properties of operations as strategies to multiply and divide *Students need not use formal terms for these properties

Objectives

Students will be able to identify a multiplication problem. I will know they understand this because they will recognize the symbolism associated with multiplication (5 x 7).

Students will be able to recognize a multiplication problem as repeated addition. As an introduction to multiplication, repeated addition will build on the students’ knowledge of addition in order to help them understand multiplication. I will know they understand this because they will be able to write or draw out a multiplication problem as repeated addition and solve it.

Text, Materials, Resources

Whiteboard or chalkboard Counters Paper divided into 12 sectionsWhiteboards for each studentOverhead camera to project images

Anticipatory Set

Teacher: Let’s pretend our class is having a party! We need food for a party, right? What food should we order for the party? (Students can give a suggestion and the teacher will use the given food as an example. For the sake of this demonstration, let’s use pizza.) Now, we want to order pizza slices for the party but we want to make sure we will have enough slices for everyone. There are 23 students in our class and I think 3 slices would be enough for each one of you.

Can you think of a strategy to easily decide how many slices we should order altogether? Think about ways you use addition and subtraction. (Students will offer some suggestions. The common suggestion may be to add 23+23+23 in order to find out how many slices to order. This is what the students should suggest. Some may also suggest adding 3+3+3+3… and this option will be acceptable as well.)

The teacher will write the equations on the board for all students to see. He or she will explain that this form is called repeated addition form because the students are adding the same number over and over again. Then he or she will say we can also write this in the form of a multiplication problem (23 x 3 or 3 x 23). He or she will explain that the x is the sign used to indicate multiplication. Students will see these two equations side by side along with the repeated addition equations and will be able to see the similarities in the operations. The teacher will ask, “What do you notice about the two ways I have written?” The class will discuss the various equations.

Modeling

The teacher will write another problem on the board. The teacher will present it as a multiplication problem (6 x 4). She will then show the students how to expand the problem and make it look like a repeated addition problem.

The teacher will then use an overhead camera to demonstrate this concept with counters. He or she will place counters in sections to represent the problem. For example, the teacher will say, “Let’s say we want to have 6 groups of desks organized in our room. If we have 4 desks in each group, how many desks would we have all together?” The students and teacher would identify the problem as 6 x 4. Then, the teacher will place 4 counters (to represent the desks) in each section for a total of 6 sections (to represent the groups of desks). The visual representation will help the students understand the addition process.

The teacher and students will also discuss the meaning of the problem if it is written 4x6 instead of 6x4. The students will work through the problem with the teacher to see if they result in the same answers for both problems. The class will discuss why this is.

Checking for understanding

After the teacher places the 4 counters in each of 6 sections, he or she will ask the students to explain what it means. Students should be able to explain that going through the sections is like adding 4+4+4+4.

Guided Practice

The students will be given a small whiteboard and piece of paper that they will fold or draw on to create 10 sections. They will use this paper and counters to solve multiplication problems on their own with the teacher’s guidance.

The teacher will present the students with a problem (2x5). He or she will ask the students to write this problem out on the whiteboard as a repeated addition problem. The students may also draw pictures (maybe of toy cars or even shapes to represent the numbers shown). He or she will give the students a minute to write it out and will ask all the students to raise their boards for the class and teacher to see. After, he or she will ask, “Student A, what did you write on your board? Can you explain to the class what you have written and why?”

The teacher will then ask, “Does everyone agree with Student A’s answer and explanation? If someone disagrees, can you tell me why?

The students will then use counters and their piece of folded paper to place counters in groups according to the repeated addition form of the multiplication problem. They will be asked to solve the problem using their counters and knowledge of addition.

The teacher can provide the students with one more problem to work on as a class.

Independent Practice

The teacher will provide the students with a worksheet to complete at home or during class time. Students will be asked to write out the given problem in repeated addition form and to draw pictures/counters to represent the problem visually. The students must also document the answer to the problem in the space provided on the worksheet. The teacher will be able to use this worksheet to gauge the students’ conceptual understanding of the concept of repeated addition.

Assessment

Informal – The teacher will assess student understanding while observing their participation and answers during guided practice. He or she will be able to determine if students are grasping the concepts based on their responses to his or her questions and their ability to represent and solve the multiplication problems. If the teacher takes notice of a student who is struggling, he or she will immediately work with this student one-on-one to address any issues when the children begin working independently. If this student needs extra support outside of class, the teacher will jot down a few notes to refer to when working with the student at a later time.

Formal – The teacher will present the students with a short worksheet that has 2 problems listed on it. Students will be asked to write out the given multiplication problem in the form of a repeated addition problem. Students will then be asked to represent the repeated addition problem visually, using circles to represent counters. They must solve the problem as well.

Differentiation

For ELL students or for students who may be struggling, the teacher can offer differentiation on the worksheet. For the first problem on the worksheet, the teacher can provide struggling students with the counters already drawn on the table so all they need to do is count them. This can help the students understand what needs to be done for the second problem. The teacher can also have a copy of the worksheet prepared in which a clue (ex. 2+2+2…) can be written next to the phrase “repeated addition form” so the students understand what they are expected to write if they are unfamiliar with the terminology and so they can make connections to the terminology.

Closure

Teacher: This is just the beginning to our whole unit on multiplication. What we learned today is the first strategy to solving multiplication problems. Can someone tell me what we learned today? The teacher will then ask a student to respond by summing up what was learned during the day’s lesson. Why do we think this strategy is helpful? The teacher will then ask some students to share. As we move on in the unit, you will discover and explore new strategies to solve multiplication problems that don’t involve repeated addition. Today’s lesson was to introduce you to multiplication and to get you to understand what a multiplication problem looks like when you break it down. Moving forward, we can discover other ways that you may even find faster, easier, or more exciting!

Solving Multiplication Problems Using Repeated Addition

Name:____________________________________________________

Directions: For each multiplication problem, please write the problem as a repeated addition problem. Then, in the sections drawn for you, draw counters or pictures to represent the problem. Solve each problem.

1. 5 x 6

Repeated addition form:

_________________________________________________________________________

Draw counters or circles in each section to represent the problem:

5 x 6 = _______________

2. 7 x 8

Repeated addition form:

____________________________________________________________________________

Draw counters or pictures in each section to represent the problem:

7 x 8 = _____________

Solving Multiplication Problems Using Repeated Addition

Name:____________________________________________________

Directions: For each multiplication problem, please write the problem as a repeated addition problem. Then, in the sections drawn for you, draw counters or pictures to represent the problem. Solve each problem.

1. 5 x 6

Repeated addition form: (ex. 2+2+2…)

_________________________________________________________________________

Draw counters or circles in each section to represent the problem:

5 x 6 = _______________

2. 7 x 8

Repeated addition form: (ex. 2+2+2…)

____________________________________________________________________________

Draw counters or pictures in each section to represent the problem:

7 x 8 = _____________

Lesson Plan 2Lesson InformationLesson Title: Multiplication and ArraysGrade Levels: 3rd gradeSubject/Topic Areas: Solving multiplication problems using arrays – Math and LiteratureKeywords: array, rows, columnsDesigned By: Lauren McNeelaTime Frame: 1 class period

Illinois Learning Standards 3.OA.A.1 – Represent and solve problems involving multiplication and division - Interpret products of whole numbers , e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each

3.OA.A.3 – Represent and solve problems involving multiplication and division – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Objectives

Students will be able to solve multiplication problems using arrays. I will know they are able to understand this because they will be able to draw arrays to represent given multiplication problems and solve them.

Text, Materials, ResourcesOnline array manipulative found at http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.htmlOne Hundred Hungry Ants by Elinor PinczesWhiteboardCounters

Anticipatory SetThe teacher will begin by telling students that they are going to be learning another strategy for multiplication today. First, he or she will ask students to recall what they learned previous about multiplication. The teacher may ask, What strategy did we learn last class? and Can someone explain how that strategy is used? He or she will then introduce the new strategy of using arrays, and he or she will explain that an array is like a picture the students can draw with rows and columns to solve a multiplication problem. The teacher will explain that columns are the sets that are vertical and the rows are the sets that are horizontal. We will learn more about arrays in a little bit, but first, I want to share a story with you about some ants who are going to a picnic. They march in rows and columns, just like those that arrays have, to get to the picnic!

I will then read the story, One Hundred Hungry Ants by Elinor Pinczes. While reading, I will stop at times and I will ask the students to point out the ways in which the ants are arranging themselves into rows and columns. This book will give them visual representation of what we will be learning. ModelingAfter we finish the story and have a discussion of the ants and their arrangements, the teacher will revisit the concept of arrays. He or she will present the class with a real-life multiplication problem. When we are going to leave the classroom, we line up in two rows, right? The way we line up can help us understand an array. Let’s say we want to make two rows with an equal amount of students in each row. Since we have 26 students in the class, we should have 13 students in each row. Let me show you what that looks like. The teacher will draw 13 stick figures of students on the board in two rows. When this is drawn, he or she will explain that what the class is looking at is an array and that the rows are the horizontal sets and the columns are the vertical ones.

The teacher will present the students with another problem. Alison places all her marbles in rows on her bedroom floor. She has 4 rows of marbles and she has 5 marbles in each row. How many marbles does Alison have? The teacher will ask students to tell her what the multiplication problem would look like. They should respond by telling him or her 4x5. Then, she will represent this array using on online virtual manipulative found at http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html. The teacher will ask the students What does the 4 represent? and What does the 5 represent? The teacher will walk the students through the process as he or she works on the generated problem and they will discuss the answer together.

Checking for understandingThe teacher will use the same online manipulative resource to generate another problem. He or she will ask the class a series of questions. How many rows do we have in this problem? How many do we have in each row? The students should be able to respond correctly according to the given problem. The teacher will demonstrate how to create the rows and will ask the class for the answer. Based on the questions and student responses, if the teacher notices that some students are still struggling to understand the concept, he or she will work through another couple of problems. Guided PracticeThe teacher will give the students some counters to use at their desks. They will be asked to use the counters to create an array to solve a multiplication problem. The teacher will give the students a problem. Cassandra bought 6 pieces of candy for each of her friends for her birthday celebration. She has 7 friends coming to the celebration. How many pieces of candy does she have in all? The students will work on this problem at their desks with the counter they were given. They will be allowed to talk to classmates or work with a small group to solve the problem if they want. The teacher will walk around to see what students are doing but will not give any assistance. Then, the class

will get together and talk about the problem. The teacher will ask some questions. How many counters should we have in all for this problem? What does the total amount of counters represent? How many columns should we have? What do the columns represent? How many are in each row? What do these represent? What is our final answer?

Independent PracticeThe students will be given a final problem to work on individually during class. The teacher will write the problem on the board. The problem will be 3 x 8. Students will be asked to create an array for this problem using their counters. After the students have created their arrays, they will be asked to compare and converse with the student(s) next to them to check their answers.

Finally, the students will be given a worksheet to complete as an assessment tool. They will be asked to write the number of rows and columns in a given array and to solve that array. They will also be asked to write their own arrays and solve them. The teacher can use this worksheet as an assessment tool to check for student understanding.

AssessmentThe students will be given a worksheet to complete for homework. Students can also work on this during class time if time permits, but it should be turned in the next day as homework. The teacher will assess their level of understanding of the concept of arrays depending on how well they do on the worksheet. DifferentiationDuring independent practice, the teacher can give extra attention to the students who may be struggling with the concept. While students are working individually on the problem, the teacher can bring some students to a separate table or can walk around and provide extra guidance/assistance to them. The various modes of instruction (online manipulative, physical counters, etc.) can help the students who are visual or tactile learners. ELL students may benefits from these resources because they will provide visual representations for the relevant math problems.

ClosureThe teacher will ask the students what strategy they learned today to solve multiplication problems. He or she will also ask a series of other questions. Can someone briefly explain how we use an array model? Why do you think this strategy would be helpful? The teacher can also explain how this model is similar to the repeated addition model. If you look at what we did today, you can see how the array is similar to repeated addition. The number of counters or images in each row is like adding the same number over and over again. This strategy is like repeated addition, but it has a picture that may help some of you understand the problem better.

Name: ___________________________________________________

Use the array of marching ants to write and solve a multiplication problem.

How many rows? _______

How many columns? ______

_______ X _______ = _______

Use the array of picnic baskets to write and solve a multiplication problem.

How many rows? ______

How many columns? ______

_______ X _______ = _______

Multiplication Using Arrays

Create your own array using any image or symbol you would like. Make sure to write and solve the multiplication problem.

_______ X _______ = ________

Create your own array using any image or symbol you would like. Make sure to write and solve the multiplication problem.

_______ X _______ = ________

Lesson Plan 3

Lesson Title: Multiplication using Times Tables

Grade Level: 3rd Grade

Subject/Topic Areas: Multiplication using times tables and the solar system (math and science)

Keywords: Times table, solar system

Designed by: Lauren McNeela

Time Frame: One class period

Learning Standards:

3.OA.A.3 – Represent and solve problems involving multiplication and division – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities

3.OA.B.5 – Understand properties of multiplication and the relationship between multiplication and division - Apply properties of operations as strategies to multiply and divide

Objectives:

Students will be able to navigate a times table to solve a multiplication problem.

Students will be able to recognize the planets of the solar system through a mathematics activity with the times table.

Materials:

Copy of a times table for each student (found at http://www.invention-j.walsall.sch.uk/wp-content/uploads/2014/06/times-tables-grid1.png)

Large copy of some times table chart in the room OR a camera that can project the image of the table onto the wall

Planet Cards (set for each group)

Game Boards (one for each student)

Standard deck of cards (card number 1-10) (set for each group)

Anticipatory Set:

The teacher will show the students a copy of the time table they will be using for the lesson. The teacher will ask, “Can anybody tell me what it is I am holding up? Do you know what it is called

or what its purpose is?” Students may recognize the times table and identify it as such, but if not, the teacher may introduce it. The teacher will explain, “We will be using this times table to help us solve multiplication problems today. Now that we have learned about rows and columns when we looked at arrays, we can use that knowledge to look at the rows and columns on this.” The teacher will then ask students to identify which on the times table are rows and which are columns.

Modeling:

The teacher will ask the students to provide her with a problem. Let’s say the students suggest the problem 8 x 7. The teacher will put it into the context of a word problem. At the zoo, there are 8 different animal exhibits for visitors to see. In each exhibit, there are 7 different types of animals. How many animals are there in all for visitors to see? The teacher will first ask, What does the 7 represent in the problem? What does the 8 represent in the problem? The teacher will then use the times table to demonstrate how to solve this problem. The times table will be placed under a camera to project onto the wall, can be viewed online, or a large copy can be hung up somewhere in the room (any option will suffice). The teacher will explain that the 8 represents the column which are the numbers that run along the top of the times table. The teacher will then explain that the 7 represents the rows which are the numbers that run along the side of the times table. He or she will demonstrate that, in order to find the answer, the students need to find the place on the times table where the 8 column and the 7 row intersect, or meet together. The teacher will identify this spot and point to it for the students to see.

The teacher will then provide another problem to show the students. There are two flavors of ice cream bars sold at the store. Conrad needs 6 of each for all his friends. How many ice cream bars should Conrad buy? The teacher will ask the students what the problem should look like. The teacher will walk the students through the steps again, showing that the 2 represents the columns and the 6 represents the rows. He or she will find the point that meets in the middle and will identify it for the students to see. Now, they will begin trying some on their own.

Guided Practice:

The teacher will give each student a copy of a times table to use for their work. He or she will create a problem for the students to work on at their desks. There are nine planets in the solar system, including Pluto. If scientists want to send 6 satellites to each planet, how many satellites will be sent to outer space? The teacher will ask the students about the rows and columns. Which number represents the column? Which number represents the row? How do we find the answer to the problem? What does this answer mean in regards to our original problem? The students should be able to recall the process the teacher described earlier in his or her modeling. The students will work on the problem individually at their desk and the teacher will have the class discuss their answers as a whole when students are ready/have gotten an answer. The teacher can provide another problem to students (12 x 7) in the context of a word problem. The teacher will

ask the same questions, but will ask an additional question. What happens if we switch the rows and the columns? Will we get the same answer or a different answer? The teacher will encourage students to try reversing the number order with any given problem they choose in order to test their theories and discover an answer to this question. The teacher will explain to students the concept of the commutative property. When we reverse, or switch, the numbers of a problem we still get the same answer. We call this the commutative property. This means that we can always switch the order of the number in a multiplication problem and still get the same answer. So, 12x7 is the same as 7x12. This works the same way with arrays. If we switch the columns and the rows, we would still have the same amount in total.

Independent Practice:

The students will begin practicing independently and with group members when they begin a math game related to science content about the solar system. This game will be explained thoroughly to the students, and the teacher will walk around during the game to make sure the students understand how to play or to answer any questions. Each group will consist of 3 students. Each group member will hold onto his or her times table. Each group will receive three game boards and a set of homemade planet cards, each with pictures of the planets on them (the cards will have the name of the planet as well). Each group will also get a deck of standard cards with the numbers 1-10 contained within the deck (the aces, kings, queens, and jacks will be removed). The students will take turns when playing the game. Student A will pick two cards out of the standards deck of cards. He or she will use those two numbers as a multiplication problem (if he or she draws a 2 and a 7, the problem he or she is solving is 2x7). The student will use the times table to solve that problem. If he or she gets it right (the other students should check the answer), the student can pick one of the planet cards. The student must find the corresponding planet image on his or her game board and cross that planet out on the board. The card should be put back and mixed around after each turn. Then, it is Student B’s turn and so on. If a student does not answer the problem right, he or she ends his turn and does not get to pick a planet card. Whoever fills up their board first wins!

Assessment:

Assessment will be informal. Students will be observed during their game play. The teacher will listen in on each group for a few minutes to assess how each student is doing. If the teacher notices that some students are struggling, he or she will document this and work with these students individually.

Differentiation

During class discussion or game time, the teacher can observe and document students that are struggling with the concepts of the lesson. The teacher can pull them during game time to work additionally with these students. He or she can even form a small game group that is facilitated by the teacher. Then, the teacher can scaffold these students and they can play the game at a

slower pace. The teacher can reinforce the terminology “commutative property’ when working with these students. When playing the game, the teacher can reverse the order of the standard playing cards the student picked so he or she understands that the problem can be the same regardless of the order of the numbers. The board games and playing cards can help ELL students. The standard playing cards will have the numeric value written and will also have an equal number of symbols for students to count if necessary. The board game and planet cards will provide visual aids to the students who have a hard time reading the planet name or understanding complex instructions for games.

Closure:

The teacher will review with the students what was learned during class. What new strategy did we learn today for solving multiplication problems? Why can this method be helpful for us? The teacher will explain that the class is learning many strategies to help them solve multiplication problems. These strategies will help each of you in different ways. We are learning many different ways, although you may prefer one over the other. That is okay! And next class, we will be exploring some patterns on the times table that will help you make connections between numbers.

Times Tables Are Out of thisWorld!

MERCURY MARS

VENUS JUPITER

EARTH SATURN

NEPTUNE

URANUS

PLUTO

Formal Assessment

Let’s pretend your birthday is in one month! You need to start planning for the BIG party you are going to have! There will be 12 people at the party, including yourself. You want this party to have a lot of yummy food and fun games for you and your guests to play! Use your new strategies for multiplication to send invitations, order food for the party, and make goodie bags.

It’s time to send invitations for your party! You need to send 11 invitations, one to each friend you are inviting. Invitations cost $3 each to make. How much will it cost you to make invitations? Use your multiplication strategies to figure out the cost. Write an equation for the problem and use words, pictures, and/or numbers to show how you solved the problem.

Equation: ________x________ = ________ ________________

(label)

Order pizza slices for you and your guests (12 people in total) – you can choose the number of slices for each person, but you have to make sure you order enough. You can figure out how many slices to order using multiplication. Write an equation for the problem and use the times table below to find the answer. On the times table, circle the numbers you use for the column and the row and circle the solution.

Equation: ________x________ = ________ ________________

(label)

A party is not complete without cake! You must order cake for your guests. One cake serves 6 people. Decide how many cakes you need to order to make sure everyone gets at least one piece. Use repeated addition to solve this problem. Also write a multiplication equation to represent the problem.

Equation: ________x________ = ________ ________________

(label)

Finally, you must prepare goodie bags for your party! You want each bag to have 4 pieces of candy in it. Draw an array to show how many pieces of candy you need to give each of your 11 guests 4 pieces of candy. Write an equation to show the problem.

Equation: ________x________ = ________ ________________

(label)

The preceding scenario will be presented to students as a formal assessment, similar to a test. They will be expected to apply the skills and strategies learned regarding multiplication to complete the assignment. This assignment will require them to demonstrate an understanding of how to utilize repeated addition, arrays and times tables, and it will ask them to recognize what a multiplication equation looks like and how to write one.

Equation Strategy Solution Total number of points (6 points each – 2 points for each component)

Question #1 (Cost of invitations)

Student included an equation for the problem with the

proper components

(3x11=33)

Student utilized a learned

multiplication strategy to solve

the problem

The student correctly solved

the problem (answer is $33 for

the invitations)

Question #2 (pizza slices)

Student included an equation for the problem with the

proper components

Student utilized the times table to solve the problem – student correctly

identified the correct numbers

on the table

The student correctly solved

the problem (answer is

dependent on number of chosen

slices)

Question #3 (ordering cakes)

Student included an equation for the problem with the

proper components

(6x2=12)

Student utilized the repeated

addition strategy to solve the

problem

The student correctly solved

the problem (answer is 2 cakes)

Question #4 (candy for goodie bags)

Student included an equation for the problem with the

proper components

(4x11=44)

Student utilized an array to solve the

problem

The student correctly solved

the problem (answer is 44

pieces of candy)

Total:

Each student will be given a bonus point to make the total out of 25 points. Each students total will be multiplied by 4 to make it out of 100. This will be the percentage grade. This assessment will also be a tool for the teacher. He or she will be able to revisit topics that the student(s) struggled with on this assessment.

References

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2010). Elementary and middle

school mathematics: Teaching developmentally. Boston, MA:

Pearson.

Pinczes, E. (1999). One hundred hungry ants. Houghton Mifflin Harcourt.

“Rectangle multiplication.” (2015). National Library of Virtual Manipulatives.

Retrieved from,

http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_ 1.html

“Squeebles times table grid.” Retrieved from, http://www.invention-

j.walsall.sch.uk/wp-content/uploads/2014/06/times-tables-grid1.png

“The new illinois learning standards for mathematics incorporating the common

core.” (2010). Retrieved at, http://www.isbe.net/common_core/

pdf/Math_common_core_standards.pdf

“Times tables grid.” Retrieved from York Learning, http://www.yorklearning.

org.uk/course/view.php?id=1204