If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you hang weights in the right place to make the equaliser
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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 each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
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?
Ben has five coins in his pocket. How much money might he have?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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.
Can you make square numbers by adding two prime numbers together?
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?
How would you count the number of fingers in these pictures?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
If the answer's 2010, what could the question be?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
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!
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
Choose a symbol to put into the number sentence.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Can you substitute numbers for the letters in these sums?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Use the number weights to find different ways of balancing the equaliser.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.