# Tug Harder!

## Problem

You might like to try Tug of War before trying this.

This game is for two players.

You will need to draw a number line from -13 to 13 on a piece of paper, and find a counter and two 1-6 dice to use.

Decide who is Positive and who is Negative.

Positive moves the counter from left to right and Negative moves the counter from right to left. (Why do you think we have suggested this way round?)

Place the counter on 0.

Take it in turns to throw the two dice and add the scores then move the counter that number of places in your direction.

If the counter reaches -13, Negative has won. If the counter reaches 13, Positive has won.

Is it better to play a game where you have to reach the end exactly, or where you can go over the end? What do you think and why?

Now change the game. This time, when you throw the dice, you can decide whether to add, subtract, multiply or divide the numbers on the dice. You must reach -13 or 13 exactly to win.

Does this make a better game? What do you think? Why or why not?

How else could you change the game?

## Getting Started

How many do you need to get to your end of the number line?

What do you get if you add the two dice numbers?

What do you get if you take away one of the dice numbers from the other one?

What do you get if you multiply the two dice numbers?

What do you get if you divide one of the dice numbers by the other one?

Do any of these answers give you the right number? If not, which is closest?

## Student Solutions

Using all four operations but extending the number line to +40 and -40 and using a dice from 1-10

Playing the game with one dice but always multiplying the number on the dice by 2

Playing the game with two 1-6 dice and all four operations but having to decide on the operation you are going to use before you roll.

Thank you! I wonder whether you tried out your suggestions to check that they worked well?

## Teachers' Resources

**Why do this problem?**

### Possible approach

### Key questions

### Possible extension

*Using a number line from -20 to +20, each child has a counter on zero. Each child has a positive red dice and a negative blue dice. They take it in turns to throw both their dice together and work out how many places*

they move and in which direction. For example, for red 3 and blue 5, the calculation would be 3-5=-2 so they move 2 towards -20. The first one to fall off either end is the winner. Some children can 'hop' up the positives and down the negatives whilst others may calculate before moving their counter. I often use numbers in a snake on the floor so the kids can hop up and down the number line.

they move and in which direction. For example, for red 3 and blue 5, the calculation would be 3-5=-2 so they move 2 towards -20. The first one to fall off either end is the winner. Some children can 'hop' up the positives and down the negatives whilst others may calculate before moving their counter. I often use numbers in a snake on the floor so the kids can hop up and down the number line.