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?
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.
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?
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!
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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?
Choose a symbol to put into the number sentence.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Can you use the information to find out which cards I have used?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Can you substitute numbers for the letters in these sums?
Find all the numbers that can be made by adding the dots on two dice.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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 hang weights in the right place to make the equaliser
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
This challenge is about finding the difference between numbers which have the same tens digit.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
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.
Ben has five coins in his pocket. How much money might he have?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!