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?
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
This challenge extends the Plants investigation so now four or more children are involved.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Replace each letter with a digit to make this addition correct.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you explain how this card trick works?
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.
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
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.
Who said that adding couldn't be fun?
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!
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Number problems at primary level that require careful consideration.
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?
Ben has five coins in his pocket. How much money might he have?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
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?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Can you be the first to complete a row of three?
How is it possible to predict the card?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This is an adding game for two players.
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
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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!
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you substitute numbers for the letters in these sums?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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 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?
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
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?