Year 8 Reasoning, convincing and proving

problem

Subtraction surprise

Age

7 to 14

Challenge level

Try out some calculations. Are you surprised by the results?

problem

Gabriel's problem

Age

11 to 14

Challenge level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

problem

American billions

Age

11 to 14

Challenge level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

problem

Isosceles triangles

Age

11 to 14

Challenge level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

problem

Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?

problem

Crossed ends

Age

11 to 14

Challenge level

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

problem

What numbers can we make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

problem

Place your orders

Age

11 to 14

Challenge level

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

problem

Olympic measures

Age

11 to 14

Challenge level

These Olympic quantities have been jumbled up! Can you put them back together again?

problem

Triangles in a square

Age

11 to 14

Challenge level

What are the possible areas of triangles drawn in a square?

problem

Multiple surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...

problem

Polygon rings

Age

11 to 14

Challenge level

Join pentagons together edge to edge. Will they form a ring?

problem

Robotic rotations

Age

11 to 16

Challenge level

How did the the rotation robot make these patterns?

problem

All in a jumble

Age

11 to 14

Challenge level

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

problem

Power mad!

Age

11 to 14

Challenge level

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

problem

Always a multiple?

Age

11 to 14

Challenge level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

problem

Fibonacci surprises

Age

11 to 14

Challenge level

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

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

The greedy algorithm

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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Number and algebra

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For younger learners

Year 8 Reasoning, convincing and proving

Subtraction surprise

Gabriel's problem

American billions

Isosceles triangles

Triangles in circles

Crossed ends

What numbers can we make?

Place your orders

Olympic measures

Triangles in a square

Multiple surprises

Polygon rings

Robotic rotations

All in a jumble

Power mad!

Always a multiple?

Fibonacci surprises

Consecutive negative numbers

The greedy algorithm