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This task requires learners to explain and help others, asking and answering questions.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
There are nasty versions of this dice game but we'll start with the nice ones...
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Play this game and see if you can figure out the computer's chosen number.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
A game in which players take it in turns to choose a number. Can you block your opponent?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
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?
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
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 work out how to win this game of Nim? Does it matter if you go first or second?
Can you make square numbers by adding two prime numbers together?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
What do you notice about these squares of numbers? What is the same? What is different?
There are six numbers written in five different scripts. Can you sort out which is which?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.