Measure problems for inquiring primary learners.
Measure problems for primary learners to work on with others.
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
Measure problems at primary level that may require determination.
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Measure problems at primary level that require careful consideration.
I cut this square into two different shapes. What can you say about the relationship between them?
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
How many centimetres of rope will I need to make another mat just like the one I have here?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
What do these two triangles have in common? How are they related?
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 number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Here are many ideas for you to investigate - all linked with the number 2000.
Can you draw a square in which the perimeter is numerically equal to the area?
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
This article for teachers gives some food for thought when teaching ideas about area.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Look at the mathematics that is all around us - this circular window is a wonderful example.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
How many tiles do we need to tile these patios?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
An investigation that gives you the opportunity to make and justify predictions.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
A task which depends on members of the group noticing the needs of others and responding.
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
Determine the total shaded area of the 'kissing triangles'.
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .
What fractions of the largest circle are the two shaded regions?