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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?

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Constant Counting

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?

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Skip Counting

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.

Nineteen Hexagons

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem is a good way for children to gain familiarity with multiples of two and five. In addition, it encourages a systematic approach to problem solving by asking for all the possible routes.

It might be useful for children to mark all the multiples of two and five on a number line or number square before they start on the maze.

This sheet gives a number of small copies of the maze for rough working and recording the various routes. This blank grid may be useful for pupils to make their own mazes.

Key questions

Have you marked all the multiples of two and five on your number line/ number square?
Would it be a good idea to circle all the multiples of two in red and all the multiples of five in blue to start with?
Can you see an even number/multiple of two?
How can you tell that a number is a multiple of five/in the five times table?
Where can you go from here?
How many ways have you found so far? Can you see any other ways?
How are you going to record your paths so you know where you've been?

Possible extension

Children could be given cards with numbers $1$ to $20$ and challenged to find all the possible ways that a multiple of two followed by a multiple of five could be selected.

Possible support

Suggest using a number line or number square for marking all the multiples of two and five before tackling the maze itself. Then start on the maze by circling all the multiples of two in one colour and all the multiples of five in another colour.