Year 7 Explaining, convincing and proving

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

In each of these games, you will need a little bit of luck and your knowledge of place value to develop a winning strategy.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Can you make doughnuts by matching these fractions, decimals and percentages?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Are these games fair? How can you tell?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Can you work out which drink has the stronger flavour?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Imagine a very strange bank account where you are only allowed to do two things...

Can you crack these cryptarithms?

Can you deduce the perimeters of the shapes from the information given?

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

Here's a chance to work with large numbers...

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Can you decide whether these short statistical statements are always, sometimes or never true?