# Countdown fractions

## Problem

*Countdown Fractions printable sheetCountdown Fractions printable sheet - cards*

*If you enjoy playing Countdown you might also enjoy playing this more challenging version with fractions.*

The challenge is to use the numbers and fractions available, and the four standard operations (addition, subtraction, multiplication and division) to hit the target.

Start by choosing any six cards. The top row always contains the numbers 1, 2, 3 and 4 and the bottom row contains a range of fractions. Alternatively you could click on "Quickstart". Then click on "Generate new target" and the computer will choose a target.

You can only use each card once in your solution, and it is always possible to find a solution without needing to use all the cards.

Once you've had a go, click on "Show solutions" to show some possible ways in which the target can be reached.

## Getting Started

If the target is negative, what can you deduce?

What can you deduce from the denominator of the target?

## Teachers' Resources

Why play this game?

Countdown Fractions offers a motivating context in which to practise calculating with fractions. There is usually more than one way of hitting the target, which offers an opportunity for rich discussion on the merits of alternative methods.

### Possible approach

Demonstrate the game to the class.

If the students have access to computers or tablets they can work in pairs on various examples. If they come across a particularly difficult example you could share it with the rest of the class by using the "Replay code" which can be entered in the Settings menu (access using the purple cog in the top right).

If students don't have access to computers or tablets you could generate several examples and write them on the board for students to have a go at with their partner using pencil and paper.

Once students have successfully completed some challenges, bring the class together to share strategies and methods they have used. If students haven't noticed, draw their attention to the "Possible using 2 cards" prompt that the computer offers. How might this influence their strategies?

Finally, set aside some time for students to have a few more goes to put into practice the strategies they have discussed. Students working on the Level 1 examples may want to challenge themselves to always find the solution using just two cards.

### Key questions

If the target is negative, what can I deduce?

What can I deduce from the denominator of the target?

Does it help to know that it is possible to hit the target using just two, or just three, cards?

### Possible support

Suggest students select more whole number cards (from the top row) and fewer fraction cards to start off with.

You could use the "Replay code" facility to share accessible examples (e.g. 3,2,1d4,1d2,1d8,3d4,-1d4) before letting students loose on randomly generated examples.

### Possible extension

Suggest students have a go at some Level 2 examples, in which it is always necessary to use at least three cards.

A suitable follow-up problem could be Twisting and Turning.