Factors and multiples

problem
Old nuts

Age

16 to 18

Challenge level

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
problem
What's left?

Age

5 to 7

Challenge level

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
problem
Little squares

Age

5 to 7

Challenge level

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?
problem
Grouping goodies

Age

5 to 7

Challenge level

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
problem
Making sticks

Age

5 to 7

Challenge level

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
problem
Skip counting

Age

5 to 7

Challenge level

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
problem
Number detective

Age

5 to 11

Challenge level

Follow the clues to find the mystery number.
problem
Constant counting

Age

5 to 7

Challenge level

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?
problem
Biscuit decorations

Age

5 to 7

Challenge level

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
problem
Adding all nine

Age

11 to 14

Challenge level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!