Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
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?
Can you find all the different triangles on these peg boards, and find their angles?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How many triangles can you make on the 3 by 3 pegboard?
An activity making various patterns with 2 x 1 rectangular tiles.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
This challenge is about finding the difference between numbers which have the same tens digit.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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?