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Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?
You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
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?
These pictures show squares split into halves. Can you find other ways?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Find at least one way to put in some operation signs to make these digits come to 100.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
What do you notice about these squares of numbers? What is the same? What is different?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
There are six numbers written in five different scripts. Can you sort out which is which?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Use these four dominoes to make a square that has the same number of dots on each side.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
How many faces can you see when you arrange these three cubes in different ways?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.