# Using Games to practice multi-digit multiplication

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## Objective

SWBAT demonstrate an understanding of place value for multi-digit whole numbers and an understanding of solving multi-digit multiplication problems.

#### Big Idea

Students will create factors to make the largest product and explain their reasoning to deepen their understanding about place value and multiplication.

## Warm Up

5 minutes

I start this warm up by writing 24 on the board. I ask students to list all the factors of 24. This is a skill required by CCSS 4.OA.B.4.  This will be a skill I revisit in future lessons to ensure my students are solid in identifying factors. Based on previous lessons and warm ups, many students need organizational methods to ensure they've found all factors.  Once most students are finished, I model one organization method of starting with 1 and 24 and then moving to 2 and 12, and then to 3 etc, and proceeding until you get two numbers that are very close or next to each other on a number line, like 4 and 6.  5 is the only number between them, and 5 is not a factor of 24.

## Concept Development

45 minutes

Students work to refine their understanding of CCSS 4.NBT.5 through a multiplication game in this lesson.  Some students work to finish an assessment from a previous lesson before they begin playing.

I start this lesson by reviewing an example of 2 digit by 2 digit multiplication. Students then play a game I call Largest Product Wins!

I explain that I have placed 9 cards numbered 1-9 in a pile.  (I use regular playing cards for this lesson) I model how to play the game by playing against a student. I draw lines on a personal whiteboard for two double digit factors. I record the numbers in the spaces as I draw a card for each digit. I tell students they may NOT wait until they have drawn all 4 numbers to place them into the double digit factors.  When modeling the game, I do not explain my reasoning but rather allow the time for students to figure strategies out.

To Play:

Draw one card at a time with the intentions of trying to make the largest product possible. (Example: if a student draws a 9 on the very first pull, students would recognize they should place it in the tens place of a factor, the next number drawn is a 7, students might use logical thinking to place this number in the other tens place of the other factor (the likelihood of drawing an 8 is small if compared to drawing another number (0-6). This is one way students work on Math Practice Standards 7 and 8 as they look for patterns in number and place value to make the largest product)

This is a sample of what students draw on their whiteboards with their card pile at top. During play I  circulate the room to monitor students understanding. I use these kinds of questions to guide students thinking.

How does knowing how to set up a multiplication problem help you solve them?

Why is it important to know place value when solving multi-digit problems?

Where would you place your largest number? Why?

Where would you place the third largest number? Why?

Why does this arrangement of the numbers make the largest product?

What patterns in the placement of the digits in the factors do you see happening? Why does this work?

What strategies are you using? Why?

How can you tell what your outcome will be?

What number am I most likely to draw next?

As I circulate the room, I also make sure to connect with students who did not score proficient or advanced on the multiplication assessment from a previous lesson.  In order to best meet their needs, I need to understand where they are making mistakes in order to re-direct and re-teach efficiently.

A great value in playing games, is to encourage students to develop strategies for winning. The strategies of placing the largest two digits in the largest place value spot and the third largest digit in the ones place with the smallest ten really requires students to think about the nature of multiplication. I try to use questioning to guide them to discover this rather than telling them and allow them to prove  their thinking while encouraging them to develop strategies.

Students play with an assigned partner for most of the class period. I assign mixed ability student partner groups.  I want to encourage students to learn from each other and question each other's strategies, therefore, mixed ability groups is the best pairing for this lesson. This is also an excellent way students work on Math Practice Standard 3 and communicate their mathematical ideas.

This video shows a student's thinking about where to place numbers. You can hear the types of questions I ask this student in order to progress student thinking.  At one point, I ask this student how many numbers are higher than 5, and she responds with 3.  I don't correct her at this point, because then I ask her how many numbers are lower than five, and she responds with 4 and very puzzled look.  Later, I did go back to this student and ask her again how many numbers are higher than 5, that she could draw, and she did say 4.

## Student Debrief

10 minutes

I led a brief class discussion by asking some of these questions.  I don't expect that all students will have answers to all of these questions at this point since this was the first time playing this game.  I will use this game again in future lessons as time allows.

How does knowing how to set up a multiplication problem help you solve them?

Why is it important to know place value when solving multi-digit problems?

Where would you place your largest number? Why?

Where would you place the third largest number? Why?

Why does this arrangement of the numbers make the largest product?

What patterns in the placement of the digits in the factors do you see happening? Why does this work?

What strategies are you using? Why?

How can you tell what your outcome will be?

What number am I most likely to pull out of the bag next?

Note:  I had some students communicate to me that they knew the third largest number would go with the smallest ten because the smallest ten needs to "get bigger".  (students words)