How Many Times!

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SWBAT Interpret a multiplication equation as a comparison.

Big Idea

In this lesson students will explore one-digit multiplication problems to interpret what number is being multiplied, and what number tells how many.

Warm Up

20 minutes

Printable Arrays: Stars.docx

This unit begins the transition for my students to use the four basic operations to solve more complex problems. 

In this lesson I want students to understand what number is being multiplied and which number tells how many times.  I invite students to the carpet. How many of you always ask, “How many times?”  One student response was:   My mom always tells me to take out the garbage. However, when I ask how many times do I have to do it before my little brother gets a chance, she shakes her head and points to the garbage!  I explain that multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity.  I draw an array on the board. I ask students to count the length of the array with me.  We both count 7. Then I ask them to count the width with me. We both count 6. Can someone tell me how I can represent this array in an equation?  7 x 6 =

You are exactly right! Now, I am going to show you how this equation can be represented in a word problem. Are you ready?  Students all scream…. Yes! 


Cameron is 7 years old. His sister is 6 times older. How old is Cameron’s sister?

I point out, that his sister is 6 times older, so 6 tell how many times.

I repeat these steps using additional multiplication problems. I scaffold students until they are able to determine what number is being multiplied and which number tells how many. 

Students tend to jump right to an answer instead of taking their time and creating problem solving steps. In this lesson I want them to think of ways problems can be solved and express it orally and visually.

In this lesson we will be focusing on the following Mathematical Practices:

MP1: Make sense of problems and persevere in solving them. 

MP. 8. Look for and express regularity in repeated reasoning.


Group Work

30 minutes

Write the number sentence for the given array.docx

During this part of the lesson, I ask my students to pair up with their assigned partners.  I want them to give it a go on their own to see how well they respond. Since we have worked on this objective before, students basically need additional practice time to become more fluent. 

I post a multiplication problem on the board. 8 x 5 = 40 I ask students to represent this equation using an array.   I give them about five minutes or so to do this. Some students cannot decide if they want their length or width to be 8, or 5. I explain that it really would not matter because either way they would come up with the same answer. 

Do you think you can compose a word problem that would represent one number being multiplied and the other number telling how many times?  Students seem to be on board. I give each group chart paper, crayons, and pencils. I ask them to be creative, and neat with their work.  As students are working I circle the room to see how well they are thinking their way through.  Some students decide to write their word problem first.  I ask why, and their response was that it would help them focus on choosing the number that was being multiplied verses the number that represents how many.  I may ask a few more questions to check for understanding.  For instance, how do you know? Can you explain how this works? Can you represent this problem in any other way? When students have completed their assignment, I ask student volunteers to share their work with the rest of the class.  During that time I ask students to check for mistakes, and I encourage students to ask questions about concepts they do not understand. 

After this, I wrote additional one-digit problems on the board and allowed students additional work time, so that they can see patterns on their own. MP8



Wrap Up

20 minutes

note taking paper.pdf 

In this portion of the lesson I ask students to return to their original seats, so that they can prepare to write about today’s lesson in their journal.  I remind students of the purpose of this lesson. For instance, I say that today we focused on determining which number was being multiplied and which number tells how many. You guys can construct your own word problems in your journals and explain how and why you would determine the given factors; however, you can use the problem we discussed early on the board, or in your group. I want you guys to gain fluency. Being fluent in knowing how many verse the number being multiplied will help you identify and explain patterns in arithmetic.

I tell them when the given time is up we will have an open discussion, for those who want to share out.    As students are working and expressing their thoughts, I circle the room to reinforce and assist as needed.