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.
problem
Favourite
Make 37
Age
5 to 11
Challenge level
Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
problem
Favourite
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?
problem
Favourite
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.
problem
Favourite
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.
problem
Favourite
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?
problem
Favourite
Three neighbours
Age
7 to 14
Challenge level
Take three consecutive numbers and add them together. What do you notice?
problem
Favourite
Six Ten Total
Age
7 to 11
Challenge level
This challenge combines addition, multiplication, perseverance and even proof.
problem
Favourite
Six Numbered Cubes
Age
7 to 11
Challenge level
This task combines spatial awareness with addition and multiplication.
problem
Favourite
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?
problem
Favourite
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?