# Resources tagged with: Working systematically

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### There are 321 results

Broad Topics > Thinking Mathematically > Working systematically

### Torn Shapes

##### Age 7 to 11Challenge Level

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

### Shaping Up

##### Age 7 to 11Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

### Two by One

##### Age 7 to 11Challenge Level

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

### 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?

### Tiles on a Patio

##### Age 7 to 11Challenge Level

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

### Chain of Changes

##### Age 5 to 7Challenge 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?

### More Transformations on a Pegboard

##### Age 7 to 11Challenge Level

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

### My New Patio

##### Age 7 to 11Challenge Level

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

### Cover the Tray

##### Age 7 to 11Challenge Level

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

### 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.

### Polydron

##### Age 7 to 11Challenge Level

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

### Triangle Animals

##### Age 5 to 7Challenge Level

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

### Geoboards

##### Age 7 to 11Challenge Level

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### A City of Towers

##### Age 5 to 7Challenge 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?

### Putting Two and Two Together

##### Age 7 to 11Challenge 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?

### Nine-pin Triangles

##### Age 7 to 11Challenge Level

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

### Sticks and Triangles

##### Age 7 to 11Challenge 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?

### Square Corners

##### Age 7 to 11Challenge 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?

### Tangram Tangle

##### Age 5 to 7Challenge 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?

### Inside Triangles

##### Age 5 to 7Challenge Level

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

### Tri-five

##### Age 7 to 11Challenge Level

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

### Count the Trapeziums

##### Age 7 to 11Challenge Level

How many trapeziums, of various sizes, are hidden in this picture?

### Crossing the Town Square

##### Age 7 to 11Challenge Level

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

### Egyptian Rope

##### Age 7 to 11Challenge 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?

### Fencing Lambs

##### Age 7 to 11Challenge Level

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

### Tri.'s

##### Age 7 to 11Challenge Level

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

### Four Triangles Puzzle

##### Age 5 to 11Challenge 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?

### Dienes' Logiblocs

##### Age 5 to 7Challenge 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?

### Making Boxes

##### Age 7 to 11Challenge Level

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

### Triangle Edges

##### Age 5 to 7Challenge Level

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

### Numerically Equal

##### Age 7 to 11Challenge Level

Can you draw a square in which the perimeter is numerically equal to the area?

### Let's Investigate Triangles

##### Age 5 to 7Challenge 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?

### Uncanny Triangles

##### Age 7 to 11Challenge Level

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

### Ribbon Squares

##### Age 7 to 11Challenge Level

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

### Tiling

##### Age 7 to 11Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

### What Shape and Colour?

##### Age 5 to 7Challenge Level

Can you fill in the empty boxes in the grid with the right shape and colour?

##### Age 7 to 11Challenge Level

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

### Three Sets of Cubes, Two Surfaces

##### Age 7 to 11Challenge Level

How many models can you find which obey these rules?

### Four Colours

##### Age 5 to 11Challenge 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.

### Room Doubling

##### Age 7 to 11Challenge Level

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

### Polo Square

##### Age 7 to 11Challenge Level

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

### Map Folding

##### Age 7 to 11Challenge 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?

### Order the Changes

##### Age 7 to 11Challenge Level

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

### Painting Possibilities

##### Age 7 to 11Challenge 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. . . .

### Roll These Dice

##### Age 7 to 11Challenge Level

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

### Sweets in a Box

##### Age 7 to 11Challenge Level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

### Creating Cubes

##### Age 7 to 11Challenge Level

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

### Ordered Ways of Working Lower Primary

##### Age 5 to 7Challenge Level

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

### Two on Five

##### Age 5 to 11Challenge Level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

### Wag Worms

##### Age 7 to 11Challenge Level

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.