Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
The idea of this game is to add or subtract the two numbers on the
dice and cover the result on the grid, trying to get a line of
three. Are there some numbers that are good to aim for?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you hang weights in the right place to make the equaliser
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 make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Use the number weights to find different ways of balancing the equaliser.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
If you have only four weights, where could you place them in order
to balance this equaliser?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
There are nasty versions of this dice game but we'll start with the nice ones...
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
Here is a chance to play a version of the classic Countdown Game.
Choose a symbol to put into the number sentence.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
An environment which simulates working with Cuisenaire rods.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you substitute numbers for the letters in these sums?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
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?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Can you use the information to find out which cards I have used?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Find all the numbers that can be made by adding the dots on two dice.
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
Ben has five coins in his pocket. How much money might he have?
You have 5 darts and your target score is 44. How many different
ways could you score 44?