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?
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
This is an adding game for two players.
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Find the sum of all three-digit numbers each of whose digits is
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Can you substitute numbers for the letters in these sums?
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?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
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!
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Investigate what happens when you add house numbers along a street
in different ways.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
This task combines spatial awareness with addition and multiplication.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?