Understanding Multiplication With Equal Groups

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Objective

SWBAT create equal groups of items to demonstrate multiplication.

Big Idea

Students develop their understanding of multiplication by grouping objects into equal groups to model the factors and products.

Warm-up

10 minutes

So many times we need to review, and review, and yet review again. The students in my classroom have been struggling with understanding the concept of multiplication consisting of equal groups.  I started thinking about things that are large in number and difficult to count in nature and I thought of stars, fish, and bees.  All of these appear in large quantities, and all are difficult to count because they appear in random forms.  I decided to use these themes to teach students about creating equal groups to multiply and find the total number. 

In this lesson the students will be looking at a sampling of Tropical Fish.  I presented the students with a picture of fish beneath the surface of the ocean and asked them to try to figure out how many fish are in this picture?

I then asked, How can we even begin to count or figure out how many fish are in this school? How would you keep track of the ones that have already been counted?"

Mini Lesson

10 minutes

To begin this lesson, each of the students was given a handful of small chips such as would be used for a bingo game.  I wanted the students to compare both addition and multiplication in this lesson so each part of the mini lesson required them to first build an addition sentence with different amounts of chips in each group.  I started with 3 and 4.  I asked the students, "What is the number sentence represented by these groups?" The students recorded their number sentences on their whiteboards so that I could do a quick observational assessment. Next I asked the students how could these be made into equal groups.  It was easy for them to determine that by adding one more to the group of three would create 4 + 4 = 8.  I then asked them to write a multiplication sentence.  This gave me the opportunity to review the structure of multiplication sentences of 2 groups of 4 chips or 2 x 4 = 8.

I moved quickly through different numbers of chips increasing the difference between the numbers for the addition sentence such as 3 and 7, 4 and 9,  2 and 8.  I encouraged the students to group the chips into two or three equal groups, and then find how many more chips were needed to create equal groups.  

I differentiated this task for students by changing the number of groups.  This allowed me to support students by using two groups and challenging other students with more groups.  

Try It Yourself

20 minutes

Students were given the a page with fish to find different groupings to create multiplication sentences.  The fish on the page were randomly placed so that students would focus on creating groups with an equal number of fish in each group.  After one multiplication sentence was formed, students were challenged to find another way to group the fish to create a second multiplication sentence.