Reasoning, convincing and proving

problem
Consecutive negative numbers

Age

11 to 14

Challenge level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
problem
9 weights

Age

11 to 14

Challenge level

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
problem
The great weights puzzle

Age

14 to 16

Challenge level

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
problem
Gutter

Age

14 to 16

Challenge level

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
problem
Honey bees

Age

14 to 16

Challenge level

How many bees could fly 1000 miles if they had 10 gallons of honey?
problem
Matching triangles

Age

5 to 7

Challenge level

Can you sort these triangles into three different families and explain how you did it?
problem
Nicely similar

Age

14 to 16

Challenge level

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
problem
Route product

Age

7 to 11

Challenge level

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
problem
Growing garlic

Age

5 to 11

Challenge level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
problem
Triangle numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?