This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

How many different shapes can you make by putting four right- angled isosceles triangles together?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Can you find out in which order the children are standing in this line?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

What is the best way to shunt these carriages so that each train can continue its journey?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

Find all the numbers that can be made by adding the dots on two dice.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Number problems for lower primary that will get you thinking.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

This article for primary teachers suggests ways in which to help children become better at working systematically.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Can you fill in the empty boxes in the grid with the right shape and colour?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?