Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Map Folding

Age 7 to 11
Challenge Level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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.

Tangram Tangle

Age 5 to 7
Challenge Level

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Polydron

Age 7 to 11
Challenge Level

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

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?

Cover the Tray

Age 7 to 11
Challenge Level

These practical challenges are all about making a 'tray' and covering it with paper.

Cover the Camel

Age 5 to 7
Challenge Level

Can you cover the camel with these pieces?

Painting Possibilities

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Two by One

Age 7 to 11
Challenge Level

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

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?

Jigsaw Pieces

Age 7 to 11
Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Tri.'s

Age 7 to 11
Challenge Level

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

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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?

Tri-five

Age 7 to 11
Challenge Level

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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.

Waiting for Blast Off

Age 7 to 11
Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Making Cuboids

Age 7 to 11
Challenge Level

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Cuboid-in-a-box

Age 7 to 11
Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

More Transformations on a Pegboard

Age 7 to 11
Challenge Level

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Single Track

Age 7 to 11
Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

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?

Shunting Puzzle

Age 7 to 11
Challenge Level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Multilink Cubes

Age 7 to 11
Challenge Level

If you had 36 cubes, what different cuboids could you make?

A City of Towers

Age 5 to 7
Challenge Level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Sticks and Triangles

Age 7 to 11
Challenge Level

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

Counters

Age 7 to 11
Challenge Level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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?

Let's Investigate Triangles

Age 5 to 7
Challenge Level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

My New Patio

Age 7 to 11
Challenge Level

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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?

Dienes' Logiblocs

Age 5 to 7
Challenge Level

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Nine-pin Triangles

Age 7 to 11
Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

The Third Dimension

Age 5 to 11
Challenge Level

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Putting Two and Two Together

Age 7 to 11
Challenge Level

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Display Boards

Age 7 to 11
Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Train Routes

Age 5 to 7
Challenge Level

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

Tiles on a Patio

Age 7 to 11
Challenge Level

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Watch Your Feet

Age 7 to 11
Challenge Level

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

Cereal Packets

Age 7 to 11
Challenge Level

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Triangle Edges

Age 5 to 7
Challenge Level

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

Four Triangles Puzzle

Age 5 to 11
Challenge Level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

Open Boxes

Age 7 to 11
Challenge Level

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

Calcunos

Age 7 to 11
Challenge Level

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Finding All Possibilities Upper Primary

Age 7 to 11
Challenge Level

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