Reasoning, convincing and proving

problem
Trolley park

Age

14 to 16

Challenge level

In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?
problem
Sevens

Age

11 to 14

Challenge level

What is the largest number Sophie can use to have seven positive integers with a mean of 7?
problem
Multiple surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...
problem
Fibonacci surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!
problem
Colourful cube

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

Can you explain what is going on in these puzzling number tricks?
problem
Towering trapeziums

Age

14 to 16

Challenge level

Can you find the areas of the trapezia in this sequence?
problem
Six numbered cubes

Age

7 to 11

Challenge level

This task combines spatial awareness with addition and multiplication.
problem
Six ten total

Age

7 to 11

Challenge level

This challenge combines addition, multiplication, perseverance and even proof.
article
Reasoning: the journey from novice to expert (article)

This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.