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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

Unit Differences

Stage: 1 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

Stage: 1 Challenge Level:

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?

Stage: 1 and 2 Challenge Level:

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Whose Sandwich?

Stage: 1 Challenge Level:

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Jumping Cricket

Stage: 1 Challenge Level:

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Mixed-up Socks

Stage: 1 Challenge Level:

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Teddy Town

Stage: 1, 2 and 3 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Briefcase Lock

Stage: 1 Challenge Level:

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Zargon Glasses

Stage: 2 Challenge Level:

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?

Mrs Beeswax

Stage: 1 Challenge Level:

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?

Polo Square

Stage: 2 Challenge Level:

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Here to There 1 2 3

Stage: 1 Challenge Level:

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?

Bean Bags for Bernard's Bag

Stage: 2 Challenge Level:

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?

Jigsaw Pieces

Stage: 1 Challenge Level:

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Name the Children

Stage: 1 Challenge Level:

Can you find out in which order the children are standing in this line?

The School Trip

Stage: 1 Challenge Level:

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

A Square of Numbers

Stage: 2 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Code Breaker

Stage: 2 Challenge Level:

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?

Robot Monsters

Stage: 1 Challenge Level:

Use these head, body and leg pieces to make Robot Monsters which are different heights.

2,4,6,8

Stage: 1 Challenge Level:

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

The Pied Piper of Hamelin

Stage: 2 Challenge Level:

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!

A-magical Number Maze

Stage: 2 Challenge Level:

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!

Difference

Stage: 2 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Matching Time

Stage: 1 Challenge Level:

Try this matching game which will help you recognise different ways of saying the same time interval.

Finding All Possibilities Lower Primary

Stage: 1 Challenge Level:

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Ordered Ways of Working Lower Primary

Stage: 1 Challenge Level:

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Finding All Possibilities Lower Primary

Stage: 1 Challenge Level:

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

What Could it Be?

Stage: 1 Challenge Level:

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Sums and Differences 1

Stage: 2 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Build it Up

Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

Build it up More

Stage: 2 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

Sums and Differences 2

Stage: 2 Challenge Level:

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?

Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Stage: 1 Challenge Level:

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?

Two Dice

Stage: 1 Challenge Level:

Find all the numbers that can be made by adding the dots on two dice.

Four-triangle Arrangements

Stage: 1 Challenge Level:

How many different shapes can you make by putting four right- angled isosceles triangles together?

Late Again

Stage: 1 Challenge Level:

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Button-up

Stage: 1 Challenge Level:

My coat has three buttons. How many ways can you find to do up all the buttons?

Ordered Ways of Working Lower Primary

Stage: 1 Challenge Level:

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Junior Frogs

Stage: 1 and 2 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Jumping Squares

Stage: 1 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Find the Difference

Stage: 1 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Arranging the Tables

Stage: 2 Challenge Level:

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.

On Target

Stage: 2 Challenge Level:

You have 5 darts and your target score is 44. How many different ways could you score 44?

How Old?

Stage: 2 Challenge Level:

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Hubble, Bubble

Stage: 2 Challenge Level:

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?

Snakes

Stage: 1 Challenge Level:

Explore the different snakes that can be made using 5 cubes.

Red Express Train

Stage: 1 Challenge Level:

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

3 Blocks Towers

Stage: 1 Challenge Level:

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
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