{FREE} Multiply & Divide by Powers of Ten Game: Includes Exponents

Help your students better understand how to multiply & divide by powers of ten using this hands-on math game. Or use the game pieces as manipulatives for students to learn & practice.

We work in a base ten number system. Therefore, helping students understand place value & powers of ten in this number system is essential for developing deep number sense. But far too often, students are told facts or ‘tricks’ to memorize rather than being given time to play with numbers and make sense of this number system on their own.

The goal of this math center game is to aid 5th grade students in their understanding of powers of ten and the impact multiplying and dividing by powers of ten has on numbers.

In this game, students will also see powers of ten written with exponents. This allows them to begin to understand exponents as repeated multiplication, while working with only powers of ten.

Multiply & Divide by Powers of Ten on a Place Value Mat:

In this game, each student works with their number using a place value mat. There are 2 different place value mats included:

Whole Numbers Place Value Mat to Billions
Decimal Place Value Mat: Millions to Thousandths

If your students are not yet ready to work with decimals, you can print the whole number mat for them.

Why Use a Place Value Mat?

The main goal of this game is to help students see the connection between multiplying and dividing by powers of ten and place value within our base ten system.

Oftentimes, when kids learn this skill they are told to just ‘add zeros’ to the number or ‘move the decimal point.’

But this doesn’t help them understand WHY. Using the place value mat, students can see that it’s actually the DIGITS of a number that shift with each power of ten rather than just adding zeros or moving the decimal (the decimal doesn’t move).

Before allowing students to play the game, spend some time working on basic multiplication & division problems with the place value mat so students can see & think about what’s happening.

Start with a simple number like 5. Then ask students, what happens when we multiply 5 x 10?

They may know right away that the answer is 50. But remind them that 5 x 10 means 5 groups of 10. And because we work in a base ten system, that means we now have 5 tens instead of 5 ones.

Then show then how the 5 shifts from the ones place to the tens place.

Do this with a few more examples, increasing in difficulty and also thinking through division examples.

Powers of Ten with Exponents:

Once students are comfortable using the place value mat to multiply & divide by 10, you can introduce them (if you haven’t already) to exponents.

You may want to start with a review of multiplication as repeated addition. Then explain that just as we use multiplication to show repeated addition, we use exponents to show repeated multiplication.

So if we want to multiply a number by 10 four times, meaning 10x10x10x10, we can write it as 10^4 (10 to the power of 4).

Do some work with powers of ten written with exponents to be sure students are comfortable & familiar with the notation before playing the game.

Powers of Ten Math Center Game Set Up:

This game does require a bit of prep. But hopefully the prep will be worth it when it gives students a more solid understanding of multiplying & dividing by powers of ten.

Plus, you can prep most of the materials once to use again and again!

In addition to printing the materials in the download, you will need a single die and some game markers for each player.

First, print the place value mat of your choice on card stock paper. There is one for whole numbers and one that includes decimals. You will need a mat for each student.

Cut the place value mat on the dotted line and tape together so the place values go in order.

Then print the ‘digit’ cards and game directions on card stock paper of a different color and laminate for durability, then cut out all the cards.

You will notice there’s an additional sheet of ‘zero’ digits. This is because as students multiply, they may need additional zeros as place holders on their place value mat. Keep this stack face up next to the game board to use as needed.

Cut out the additional digit cards, shuffle and stack face down. This will be the pile they draw from. Leave a copy of the game directions for students to reference.

Print the game board on card stock paper of another color and laminate. You only need one game board for each small group.

Lastly, print score cards for each student. You can print these on regular paper for students to record their thinking and scores as they play, or you can print on card stock, laminate and provide dry erase markers. At the end of the game, students can then erase the score cards to be used again another day.

I recommend 3-4 students per game. If you will have multiple groups playing at the same time, complete the prep above for each game set.

Here’s a summary of what you need to print & prep:

One game board per small group
One set of ‘Digit’ cards & game directions per small group, cut out & shuffled (separate the ‘zero’ digits for students to use as needed)
One place value mat per student, cut & taped together
One score card per student

Provide a die & a set of game markers and you’re all set!

Multiply & Divide by Powers of Ten: How to Play the Game

The goal of the game is to be the player with the largest number at the end of the game.

To begin, each player draws 2 digits from the deck. They then start with any 2-digit number, placing the digits on the tens and ones place, or the ones and tenths place.

Players then take turns rolling a die and moving their game piece along the board. They then follow the directions depending on where they land:

Power of ten: multiply the number on your place value mat if the number you rolled was even or divide the number on your place value mat if the roll was odd.
New Digit: draw a card from the ‘digit deck’ to add to the beginning or end of the number on your place value mat. This will be your new score and value used on your next turn.
Digit Swap: player MUST swap one of the digits on their place value mat. They can either swap 2 of their own to form a new number or they can swap one of their digits with another player.

Once all players have made it to the finish, the player with the largest number on their place value mat wins. Each player then writes the final values in order from least to greatest at the bottom of their score card.

A quick note:students will keep a running tally on their score card, meaning they always start with their current value and multiply/divide from there. They do not start over with their original 2-digit number on each subsequent turn.

And that’s it! I hope this provides a fun way for students to make sense of place value, large numbers, decimals, powers of ten & exponents.

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