What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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. . . .
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Make a flower design using the same shape made out of different sizes of paper.
Can you fit the tangram pieces into the outline of Granma T?
Can you visualise what shape this piece of paper will make when it is folded?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of Little Ming?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outlines of the candle and sundial?