How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Number problems at primary level that require careful consideration.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Here is a chance to play a version of the classic Countdown Game.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
If you have only four weights, where could you place them in order
to balance this equaliser?
Who said that adding couldn't be fun?
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?
Find the sum of all three-digit numbers each of whose digits is
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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?
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?
Can you substitute numbers for the letters in these sums?
A game for 2 players. Practises subtraction or other maths
Investigate what happens when you add house numbers along a street
in different ways.
Can you be the first to complete a row of three?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
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
This is an adding game for two players.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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!
This challenge extends the Plants investigation so now four or more children are involved.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Choose a symbol to put into the number sentence.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
This dice train has been made using specific rules. How many different trains can you make?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three