### Rationals Between...

What fractions can you find between the square roots of 65 and 67?

### There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

# Countdown Fractions

### 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.