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Resources tagged with Working systematically similar to Chain of Changes:

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

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Chain of Changes

Age 5 to 7 Challenge Level:

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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A Shapely Network

Age 7 to 11 Challenge Level:

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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Peg and Pin Boards

Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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Torn Shapes

Age 7 to 11 Challenge Level:

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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Brush Loads

Age 7 to 11 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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Arranging the Tables

Age 7 to 11 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.

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Six Is the Sum

Age 7 to 11 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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Egyptian Rope

Age 7 to 11 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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Whose Sandwich?

Age 5 to 7 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.

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Briefcase Lock

Age 5 to 7 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?

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A Mixed-up Clock

Age 7 to 11 Challenge Level:

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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Adding Plus

Age 7 to 11 Challenge Level:

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?

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Tri.'s

Age 7 to 11 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard?

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Routes 1 and 5

Age 5 to 7 Challenge Level:

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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Two by One

Age 7 to 11 Challenge Level:

An activity making various patterns with 2 x 1 rectangular tiles.

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How Much Did it Cost?

Age 7 to 11 Challenge Level:

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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Uncanny Triangles

Age 7 to 11 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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All Seated

Age 7 to 11 Challenge Level:

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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Paw Prints

Age 7 to 11 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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Triangle Animals

Age 5 to 7 Challenge Level:

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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Polydron

Age 7 to 11 Challenge Level:

This activity investigates how you might make squares and pentominoes from Polydron.

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Jumping Cricket

Age 5 to 7 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?

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Seven Square Numbers

Age 7 to 11 Challenge Level:

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.

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Spell by Numbers

Age 7 to 11 Challenge Level:

Can you substitute numbers for the letters in these sums?

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Inside Triangles

Age 5 to 7 Challenge Level:

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

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Four Colours

Age 5 to 11 Challenge Level:

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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A Square of Numbers

Age 7 to 11 Challenge Level:

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

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Triangles All Around

Age 7 to 11 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

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Square Corners

Age 7 to 11 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Five Coins

Age 7 to 11 Challenge Level:

Ben has five coins in his pocket. How much money might he have?

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Two Primes Make One Square

Age 7 to 11 Challenge Level:

Can you make square numbers by adding two prime numbers together?

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Zargon Glasses

Age 7 to 11 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?

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Code Breaker

Age 7 to 11 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?

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The Pied Piper of Hamelin

Age 7 to 11 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!

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Pouring the Punch Drink

Age 7 to 11 Challenge Level:

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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Making Squares

Age 7 to 11

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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Bean Bags for Bernard's Bag

Age 7 to 11 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?

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A-magical Number Maze

Age 7 to 11 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!

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Mrs Beeswax

Age 5 to 7 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?

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Rabbits in the Pen

Age 7 to 11 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Here to There 1 2 3

Age 5 to 7 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?

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Triangle Edges

Age 5 to 7 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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Polo Square

Age 7 to 11 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.

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Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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Area and Perimeter

Age 7 to 11 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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Journeys in Numberland

Age 7 to 11 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Button-up

Age 5 to 7 Challenge Level:

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

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Jumping Squares

Age 5 to 7 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.

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Fifteen Cards

Age 7 to 11 Challenge Level:

Can you use the information to find out which cards I have used?

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Junior Frogs

Age 5 to 11 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?