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

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Seven Flipped

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Growing Garlic

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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Seven Pots of Plants

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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Red Even

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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Are You Well Balanced?

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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One to Fifteen

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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Twinkle Twinkle

Stage: 2 Challenge Level: Challenge Level:1

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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Nineteen Hexagons

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

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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Same Length Trains

Stage: 1 Challenge Level: Challenge Level:1

How many trains can you make which are the same length as Matt's, using rods that are identical?

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Find the Difference

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

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

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Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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Chocs, Mints, Jellies

Stage: 2 Challenge Level: Challenge Level:1

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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Prison Cells

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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The Pied Piper of Hamelin

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

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!

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Room Doubling

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

Investigate the different ways you could split up these rooms so that you have double the number.

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Pouring the Punch Drink

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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Eight Queens

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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Neighbours

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

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?

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1 to 8

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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Octa Space

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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Two Egg Timers

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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Cubes Here and There

Stage: 2 Challenge Level: Challenge Level:1

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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Colour in the Square

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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Button-up Some More

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Button-up

Stage: 1 Challenge Level: Challenge Level:1

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

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Wag Worms

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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Ordered Ways of Working Upper Primary

Stage: 2 Challenge Level: Challenge Level:1

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

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How Many Times?

Stage: 2 Challenge Level: Challenge Level:1

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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Team Scream

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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Two Dots

Stage: 2 Challenge Level: Challenge Level:1

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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Seating Arrangements

Stage: 2 Challenge Level: Challenge Level:1

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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Late Again

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

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

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Plate Spotting

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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Jigsaw Pieces

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Pasta Timing

Stage: 2 Challenge Level: Challenge Level:1

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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More and More Buckets

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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Inside Triangles

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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Plates of Biscuits

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

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Route Product

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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Three Ball Line Up

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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Here to There 1 2 3

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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The Pet Graph

Stage: 2 Challenge Level: Challenge Level:1

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Whose Sandwich?

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

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

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Snails' Trails

Stage: 2 Challenge Level: Challenge Level:1

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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Calendar Cubes

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Triangle Animals

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Zargon Glasses

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

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?