Multiplication As Repeated Addition

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Objective

SWBAT to interpret the product of whole numbers as the total number of objects in equal groups using addition.

Big Idea

Multiplication as adding the same amount over and over and over.

Introduction

5 minutes

Present a repeated addition problem using showing several addends.  I choose one that is difficult for skip counting and write more than 20 addends. 

6+6+6+6+6+6+6+6+6+6+6+6+6+6+66+6+6+6+6+6+6+6+6+6+6+6+6+6+6=____

I explain to the students we are going to figure out a way to solve this addition sentence easily. 

I ask them to identify what they see in this number sentence, trying to elicit the response that see adding the same number over and over.  I have the students talk with a partner to think of a way to make this problem easier to solve.

Modeling

10 minutes

I explain to the students they will be learning about multiplication and the group size must be the same for multiplying. I explain if I have a large box of chocolates to share with my family, and I want to know how many I have.  I may start counting by twos to find out how many chocolates I have.  Or, I may have a bag of oranges to take to soccer practice, and again I need to know how many I have.  Sometimes as a teacher I even need to count the number of pencils we have to make sure each person has at least two pencils.   

Scientists also count large numbers of things.  Sometimes they even try to count how many birds are living in an area, or how many coyotes are living near other people.  Farmers use this skill to determine how much of their fields are planted with different types of crops like corn or soybeans.  

I begin by putting together groups of connecting cubes, putting three or four in each group to show to the students.  I deliberately put a different amount in one group to draw student focus to the idea of equal groups.  I ask them to examine first if each group has the same amount.  I demonstrate that if we put the items in equal groups of easy numbers like groups of two, it is easy to skip count and add.  

Since this lesson is repeated addition, I write and speak the addition sentence to match the manipulative model  4 + 4 + 4 + 4 = ______.   Then I ask how many there are in all?  I repeat this step with several different models as needed for student understanding.  This modeling of the Math Practice 4 from the Common Core standards provides students with the visual information to compare if their answer makes sense.   

Other examples would be 3 + 3 + 3 + 3 + 3 + 3= __________.  I name these cubes represent three pencils, three cookies, three basketballs, three rabbits, or any item to engage the students.  If they are just naming these as cubes, the students may be less engaged. 

Hands On Practice

15 minutes

Next, the students are given sets of counters or other manipulatives to create number sentences with me.  I say a number sentence and the students will create the model.  

Some of the sentences I use are: 

2+2+2+2+2+2=_______

4+4+4=_______

3+3+3+3+3=_________

Because the students were working with approximately 24 counters each, I chose addends of the number sentences to be below that sum.  I also used numbers that would allow students to use some skip counting skills to complete the addition easily.  Using skip counting skills will support their understanding of multiplication in later lessons addressing the big idea of equal groups for multiplication.   

Following this step, I switched from saying the number sentence to creating a model and the students record the number sentence using individual whiteboards or paper and pencil.  

The students should solve the number sentences during each step. Students were using skip counting skills and knowledge of doubling numbers to find the sum for these number sentences.  I encouraged the students to work with a partner or someone in their group to solve and share strategies with each other including drawing and building models with manipulatives.  

Try It Yourself

15 minutes

Working in partners or a group of three, the students take turns going back and forth as the builder using the manipulatives and as the writer recording the number sentences.  Students use a spinner or a dice to determine the different number of addends to use for each repeated addition sentence. Students use nine-sided dice to get their numbers.  This sets the number so that students are working within guidelines of the Common Core Standards for products to 100.  

Using the dice created an element of chance and eliminates the building of a pattern. Other items that could be used to determine the number of items include cards, dominoes, and numbers written on a slip of paper.  If needed to differentiate, students could use a traditional six-sided dice, or you can set the number of addends for the students.    

The students record their sentences on worksheet and solve the problems together. Students use blank paper to solve the problems including using repeated addition and drawing equal groups. Although the main focus of the lesson is repeated addition, some of the students want to use a strategy for equal groups as well.  This was a decision they came to as a team.  There is evidence here of the development of Mathematical Practice 4 (Model with mathematics ) as students develop different ways to represent the problem. 

Wrap-Up

5 minutes

It is important to consider what you've learned before ending a lesson. Today, students explain which groups are easier and which are more difficult to solve for repeated addition and explain their reasoning. The students in partners/groups show and explain how they solved two of the repeated addition problems they completed.

Students can use manipulatives, drawings, or verbal explanations.  I suggest a sentence frame of:  We solved this problem by using ________________ because ____________.  

This allows the students to use what is most comfortable for them.  Other students are allowed to ask questions about their strategy, so they are encouraged to explain the strategy they are most confident in using.