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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Can you describe this route to infinity? Where will the arrows take you next?
A game in which players take it in turns to choose a number. Can you block your opponent?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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.
Can you find the values at the vertices when you know the values on the edges?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?
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?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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?
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
There are six numbers written in five different scripts. Can you sort out which is which?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Can you explain the strategy for winning this game with any target?
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.
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.