Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This problem is designed to help children to learn, and to use, the two and three times tables.
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
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
Number problems at primary level that require careful consideration.
Can you replace the letters with numbers? Is there only one solution in each case?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Find the next number in this pattern: 3, 7, 19, 55 ...
What is happening at each box in these machines?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Have a go at balancing this equation. Can you find different ways of doing it?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
What is the sum of all the three digit whole numbers?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Find a great variety of ways of asking questions which make 8.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This task combines spatial awareness with addition and multiplication.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .