Investigate the different distances of these car journeys and find out how long they take.
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This article for teachers suggests ideas for activities built around 10 and 2010.
If the answer's 2010, what could the question be?
This challenge is about finding the difference between numbers which have the same tens digit.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
What is happening at each box in these machines?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?