Proof: Diving in at the Deep End

This group of tasks forms part of our Generalising and Proof Feature.  Each task below gives you the opportunity to create a proof of your own.

Dicey Addition

Age 5 to 11
Challenge Level

Who said that adding couldn't be fun?

Take Three Numbers

Age 7 to 11
Challenge Level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Three Neighbours

Age 7 to 11
Challenge Level

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Reach 100

Age 7 to 11
Challenge Level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Six Ten Total

Age 7 to 11
Challenge Level

This challenge combines addition, multiplication, perseverance and even proof.

Sealed Solution

Age 7 to 11
Challenge Level

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?

Six Numbered Cubes

Age 7 to 11
Challenge Level

This task combines spatial awareness with addition and multiplication.

Square Subtraction

Age 7 to 11
Challenge Level

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

The Dice Train

Age 7 to 11
Challenge Level

This dice train has been made using specific rules. How many different trains can you make?

Factor Lines

Age 7 to 14
Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Make 37

Age 7 to 14
Challenge Level

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.