# Dicey Addition

## Problem

*Dicey Addition printable sheet*

*This game can be played before Dicey Operations in Line.*

Find a partner and a 0-9 dice. The interactivity in Dice and Spinners can be used to simulate throwing different dice.**Game 1**

Each of you draw an addition grid like this:

Take turns to throw the dice. After each throw of the dice, you each decide which of your cells to put that number in.

Throw the dice four times until all the cells are full.

#### Whoever has the sum closer to 100 wins.

There are two possible scoring systems:

- A point for a win. The first person to reach 10 wins the game.
- Each player keeps a running total of their "penalty points", the difference between their result and 100 after each round. First to 500 loses.

You can vary the target to make it easier or more difficult.**Game 2**

Each of you draw an addition grid like this:

Take turns to throw the dice, until it has been thrown four times in total. After you have collected all four numbers, each player must decide where to place them on his/her own grid.

**Whoever has the sum closer to 100 wins.**

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 100 after each round. First to 500 loses.

You can vary the target to make it easier or more difficult.

## Student Solutions

We placed the 9,8,7,6 in the units column because if we had 9,8,7,6 in the tens column then it would equal more than 100 by a larger difference.

If we had 5,4,3,2,1, you are more likely to reach 100 if you put these into the tens column.

If we rolled a high number at the start it is quite safe to place this into the tens column and then if you roll a high number again, it is best to place that number in the units.

Thank you Math Magicians. We would be interested to hear from anyone else who had some ideas about this challenge.

## Teachers' Resources

Why play this game?

This game is thought provoking and very engaging. It encourages discussion of place value, mental calculations and estimation, alongside valuable strategic mathematical thinking.

### Possible approach

This game is a simpler version of Dicey Operations in Line.

It can be played with 1-6 die but ideally would be played with a decahedral 0-9 dice or a spinner (an interactive 10-sided spinner is available here).

Invite volunteers (perhaps working in teams of two) to play the game on the board and explain the rules to them and the rest of the class.

When the game is over confirm who has won and explain the scoring system.

Working in teams of two, set learners off on playing the game. Depending on your aims for the lesson, offer the simple or more complicated scoring system.

When appropriate, encourage learners to vary the targets.

Encourage learners to justify their strategies to their partners, and draw their ideas together at the end of the lesson.

### Key questions

How are you deciding where to place the numbers?

How do you decide which targets are appropriate?

### Possible extension

When working on the second version of the game whereby the four numbers are thrown before deciding where to place them, encourage learners to justify and prove that their arrangement is as close to 100 as possible.

You may wish to move learners on to Dicey Operations in Line.

### Possible support

Simplify the calculations by using fewer cells in each game.

Perhaps provide learners with number cards that they can move around the grid to consider different options.

Pupils who find estimation difficult could use calculators to check their estimates.

Choose the easiest scoring system or allow calculators for scoring the more difficult version.

Allow pairs to play against other pairs, so that partners can support each other.