 # Multiplicative Patterns on the Place Value Chart: Gamify Your Math Class ## Teaching Every Student – How to Gamify Your Math Class

Multiplicative Patterns on the Place Value Chart

Not all kids are the same.  They don’t look the same or act the same.  And they certainly don’t learn the same.  As teachers, we know that reaching every kid can be a challenge.  Getting every kid to learn the steps of an algorithm or understand the concept of multiplication is not easy.  Think about the types of activities you use in the classroom.  Which do you find to be most successful – when do your students learn best?

I have found that most of my students’ successful learning comes when they are moving.  They may be working and rotating in stations, using manipulatives, or doing a dance.  Movement promotes learning in multiple ways.  Education Week states, “Studies show that children who are more active exhibit better focus, faster cognitive processing, and more successful memory retention than kids who spend the day sitting still. Keeping the body active promotes mental clarity by increasing blood flow to the brain, making activity vital to both learning and physical and neurological health.”

When I need to find ways to make a concept stick, I try to think of ways I can get students moving.  A motivating way to get kids moving is by creating a game.  Gamifying anything in the classroom automatically makes it an exciting learning opportunity.  Gamifying your math class is a game changer!  Finding multiplicative patterns on a place value chart is the perfect lesson to bring in a game that gets kids moving!

## Multiplicative Patterns on the Place Value Chart Game

### Set-up the lesson (Multiplicative Patterns on the Place Value Chart)

• Use painters tape or chalk to create several large place value charts, spread apart to give each group their own space. Students should be able to stand “in” the place value chart. If you have a tiled floor, each square could be a box on this chart.  Create and label each place value chart as shown below: • Put students into groups of four. Predetermine the groups based on who works best together.
• Each student will receive an envelope with the digits 0-9 written on notecards. One student will be the recorder. The other three students will be forming numbers from the digits in their envelope. They will rotate through the activity 4 times, each student being the recorder once.  Have students work through the activity a second time if time allows.

## Launching the Lesson

### Digit vs. Number

I would start with a quick review of the difference between a digit and a number.  A digit is a symbol that is used to make a number.  Numbers can be composed of one digit, or several.  This is an important distinction to make because students will be given digits 0-9 and be asked to make a number.  They will then need to move individual digits on the place value chart according to the number it is multiplied by.

Then review the role of the decimal in a number.  I give each student a place value chart like the one above to keep in their math notebook as a reference tool.  Students could use those charts now to support them in thinking through these questions.

### Guided Instructions

Pose the question – Is it true or not?  Then give students several examples: 4.2 and .42 are the same number.  When students answer no, ask them why not?

The goal is to get students to realize that 4.2 is larger than .42.  More specifically, we want them to begin to understand that 4.2 is 10 times larger than .42.

At this point, introduce the rule that when you multiply by 10, you move all the digits in the number one place to the left. So .42 x 10 = 4.2  Note that the decimal point does not move, but rather the digits “jump” over it when multiplying by 10.

Then ask students to apply that rule: What would happen if they took 4.2 and multiplied it by 10? And if they multiplied by 10 again? Be sure to show students how to add in a zero as needed.

Try other examples like:

• 4,000 and 4,000,000 – is multiplied by 100 (or multiplied by 10 twice)
• .093 and .930 – is multiplied by 10
• 8 and 6,780 – is multiplied by 1,000 (or multiplied by 10 three times)

Spend the next 5-10 minutes demonstrating how to use the charts on the floor to show the patterns of multiplying by 10.  Ask students to come up in front of the class and have them each hold one digit from several of the examples above. Roll the die. Tell them to multiply by 10 the number of times shown on the die and then move to the left that same number of boxes on the chart. Ask students to read out the new number they have become. Then review the rules for the game.

### The Rules of the Game

1. One person in the group is the recorder. They need the recording sheet on a clipboard and a six-sided die.
2. Three people in the group choose one digit from their envelope.
3. The three students will step into the place value chart next to each other, forming a three digit number. They should be looking at the place values. There can be no spaces between each person.  The number needs to make sense with three digits.  For example, they cannot form the number 1,250, because it is a four digit number.
4. The recorder records the starting number on the record sheet.
5. The recorder then rolls the die and circles X10 according to the number rolled.  For example, if the number rolled is three, they will circle three X10s – multiplying the number by 10 three times, or by 1,000.
6. The students will then move to the new squares, based on the number that was rolled.  For example, if the students start with the number 48.2 and roll a three, each student will step to the left three boxes.  They will fill a zero in any box up to the decimal point.
7. The recorder will record the new number in the record sheet.  All group members check the work of the recorder.
8. A new recorder is selected.
9. Students select a new digit from their envelope and repeat the process until each student has been the recorder at least once. ## Get Kids Moving

Once you are confident groups know what to do, send them off to work independently.  Circulate around the room checking students’ work and asking questions to clarify their understanding and to expand their thinking.  Make note of any common misconceptions and pause the game for all the groups to have a discussion when a teachable moment arises.

Just for fun, you could use the lyrics to Beyonce’s ‘Irreplaceable to help your students remember which way to move when multiplying by 10s.  When going over the direction for the activity, you could sing this when moving inboxes to the left.

“To the left, to the left

Multiply by 10 – move a box to the left”

## Reflecting on the Activity

This activity gives students a chance to move their bodies and switch roles. A good wrap up to this activity is a discussion with students still at their place value charts.  This allows them to demonstrate their understanding or ask questions about the activity where they performed it.

In order to give more students an opportunity to verbalize their understandings, have students share within their game groups before asking groups to share out with the whole group.

Here are some discussion questions to guide the conversation:

1. Did moving your body support your understanding of the patterns of multiplying by 10s?
2. How is doing this activity on paper different than having to step into the chart? How is it the same?
3. What does this teach us about place value?
4. How else could you quickly multiply by 10s if you didn’t have the chart?
5. Could you use this method to divide by 10s?  How would that work?
6. What is one thing you learned through doing this activity?

### Extensions/Next Steps

To extend this lesson for students who need more challenge, you could have the students work backward and divide instead of multiply.  Some of your students will make that connection immediately and be ready to move forward. Others may need coaching and explicit teaching. It can also be used as a follow up lesson on dividing by 10s where students play the same game in a new way.

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