July 15, 2014

This game is from Mr. Bailey, one of my mentor teachers from my credential days. I still remember him teaching it to me during one of our lunch breaks, with his hand full of dice. I was skeptical at first, because I had never really played “math games,” but then I started to really get into it! Like, I spent the rest of my lunch break trying to make math expressions. Just for fun. Yeah, really.

It was in this sixth grade classroom that I first saw what a great tool a good math game could be to help kids have an enjoyable time practicing math! I love this game because it really pushes kids to think mathematically in different ways. I suppose it can be used for kids who only have addition and subtraction under their belts, but it is probably most challenging and fun for kids who have learned the order of operations: PEMDAS, anyone?

A quick refresher on PEMDAS:

- First, do portions in
**P**arentheses. - Next, work out any
**E**xponents. - Next, do all
**M**ultiplication and**D**ivision problems*from left to right.*

Note that multiplication does not always come before division– it’s just whichever shows up first in your problem going left to right. The acronym could have been “PEDMAS” but it just doesn’t have the same ring to it, so it’s PEMDAS… but multiplication and division are actually tied for third. - Finally, do all
**A**ddition and**S**ubtraction problems from left to right. Same deal here– it’s not that addition always comes first– just whichever one shows up first from left to right. In other words, addition and subtraction are tied for fourth.

This game would work well for your fourth grader who can use parentheses, multiplication, division, addition, and subtraction to play. A fifth grader can employ exponents, and a sixth grader can use it to exercise and grow in their thinking with using all of the parts of PEMDAS.

I can see this game working well for families that have children of different ages. Younger children can participate and try to get numbers close to the target number, even if they can’t hit it right on the head. Those with more math chops can look for multiple ways of reaching the target number, which keeps them occupied until everyone is ready to share solutions. There are endless ways to talk strategy here, which is an important exercise; being able to understand others’ and explain your own mathematical thinking is HUGE in the Common Core Standards (see p.6).

If you only try one of the math games I share in this series, I think you should pick this one because you get the most mathematical bang for your buck. (But don’t do that– try them all! :])

**>>>CLICK HERE FOR A PRINTER-FRIENDLY VERSION WITH THE SCORING TEMPLATE AND INSTRUCTIONS.<<<**

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**Math Skills Covered:** Addition, subtraction, multiplication, division, parentheses, exponents, order of operations (“PEMDAS”)**Materials: **5 dice**# of Players: **1+

**Grades: **4-6

**OBJECT OF THE GAME: **Write an expression to get as close to the target number as you can.

**SET UP YOUR GAME BOARD: **Use this template, or use a whiteboard by setting up the space as shown below.

**HOW TO PLAY:**

**Roll two dice to determine the target number.**For example, rolling a 3 and a 5 could mean your “target number” is either 35*or*53. It doesn’t really matter which one you pick. For this example, I’m going to use 53. All players write this number on their boards.

**2. Roll 5 dice to determine the 5 digits you will play with:**

I like to put mine in order from least to greatest. Record these 5 numbers on your game board.

**3. Using each of the digits exactly once, write an expression to get you as close to the target number as possible. **

In this example, you must use the digits 1, 1, 3, 6, and 6 to make a number as close to 53 as you can get. How about (1+1) x 3 x 6 + 6 = 42?

It’s *kinda* close, but… can you think of a better expression to use?

Here another option, and I explain my thinking below:

- I see that 53 is close to 54, so I look for a way to do 54-1.
- I realize that 9 x 6 makes 54!
- I have a way to make 9 by adding 3 and 6.
- Tip: Put a little dot above each digit as you use it to keep track of which numbers you have used (and which ones you still need to use!).

**4. Write out the complete expression and then check to see if it works**:

It works! Woohoo we hit the target number!

**5. Now wait for everyone else to be ready, and then share results.** Be sure to check each other’s work and make sure they are doing their math correctly. After all, the real point of this is to get some mathematical thinking in, and it would be counterproductive if we were practicing incorrectly!

Ready to share? Okay. Here’s a look at all the boards:

Player #1: “I used 3 x 6 to make *9*, and 1 x 1 to get *1*. Then I multiplied 9 x 6 to get 54, and subtracted the 1 to get 53.”

Player #2: My final answer was 50, which is just 3 away from 53. I wanted to make 5 x 10, so I used 6-1 to make 5, and then 6+3+1 to make 10! 5 x 10 is 50!

Player #3: Well, I didn’t get exactly 53, but I got 54 two different ways. The first way was to do *six squared* (I got a two using 1+1), then I used (3 x 6) to make 18 and added 36 + 18 to get 54. Then I found another way. I used (1+1) to get 2, and did *two cubed* to get 8. From there, I did 8 x 6 is 48, then added 6 and got 54 again. I was going to try another way with two to the sixth power, but didn’t finish…

Players should always check each other’s work or even try each other’s problems. It’s up to you to look at other players’ work and see that they actually used every digit and/or didn’t add any extras, which can easily happen on accident. This is a good game to catch and correct any misunderstandings on the order of operations!

When you’re all done, start over and play again! Some rounds will be easy, and some can be extremely hard. I think they’re all fun, though!

**>>>CLICK HERE FOR A PRINTER-FRIENDLY VERSION WITH THE SCORING TEMPLATE AND INSTRUCTIONS.<<<**

Q: Can we put digits together to make 2-digit numbers? For example, if the five numbers we roll are 1, 2, 3, 4, and 5, can we put 2 and 4 together to make “24” for our expression?

*A: No. The only time you do this is when you are determining the target number in step #1. Otherwise, the rolled numbers should always remain 1-digit numbers. *

Q: Do I have to use *all* five numbers in my expression?

*A: Yes.*

Q: Can I use a number more than once?

*A: You can use it exactly the number of times it is rolled. For example, if you roll two 5’s, then you can/must use 5 twice. If you only rolled one 5, though, then you can only use it once.*

Q: Can I use just 4 of the rolled numbers?

*A: No. You must use all five of them. This is part of the challenge!*

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**Variations:**

To make it more challenging, just say, “Nice expression! Can you think of *another* way to do it?” And continue challenging them to come up with more paths to the target number. Even if they can’t think of one, they’ll probably do a lot of mathematical thinking *trying to*, and mathematical thinking is the point.

In my class, I used to have a couple volunteers show their expression, and the rest of the students would have to solve it to check and see if it worked. This way, everyone got a little more math practice in.

**Discuss Strategies:**

Try to coach your child to consider different options and strategies after they’ve made their expressions. It varies based on each child’s level and results, so I’ll just offer some examples of how you can analyze their board and see what you could teach them next.

Example 1: Using multiplication to get closer to the target number.

This child just used straightforward multiplication and addition to get the biggest number they could think of. The next step is to show them how to use parentheses to create new numbers. Talk to your child about using factors of 24, such as 3 x 8 or 4 x 6 or 12 x 2 to get to the target number. If they say, “Well, I didn’t have 3 or 8 or 6 or 12!” then try to help them discover how to use parentheses to make numbers they need, even if they’re not obviously available:

- 3 x 8: (1+2) x (2 x 4) x 1
- 4 x 6: (1 + 1 + 2 + 2) x 4 -or- (1 + 2) x 2 x 4 x 1
- 12 x 2: (4 x (1 + 2)) x 2 x 1

Example #2: Strategies to get rid of extra small numbers.

On this board, the child ended up 1 above the target number. They actually reached the target number (in the second to last step), but had to use up the *1 *digit, so they just tacked it on at the end with + 1. Here you have an opportunity to talk about employing the *Identity Property of Multiplication*, or “anything multiplied by 1 stays the same.” Show them how instead of *adding* 1, they could *multiply* the final answer by 1 to keep it at 31 and stay on the target number.

There are endless opportunities for rich math talk with this game, and you’ll find that your own strategy will probably improve as you play more! It’s pretty simple and it can be challenging for any age. I hope you have fun with it!

See more fun math games in my series on *Fun Math Games for Children!*

You should check out the British gameshow Countdown on Youtube. It combines a game like this and a word unscrambling game.

Fun! Thanks for sharing!

I love this thanks!!

YAYY thanks for the encouragement, Amanda! 😀 Enjoy! I love this game, too!

Awesome game! I made a similar game for the iPad called 5 Dice –> https://itunes.apple.com/us/app/5-dice-order-operations-game/id572774867?ls=1&mt=8

Nice! Thanks for sharing.