# Resources tagged with: Working systematically

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##### Other tags that relate to Three Fingers and a Loop of String
Visualising. Symmetry. Interactivities. Triangles. Quadrilaterals. Squares. Practical Activity. Investigations. 2D shapes and their properties. Working systematically.

### There are 320 results

Broad Topics > Mathematical Thinking > Working systematically

### 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?

### 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 11 Challenge Level:

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

### 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?

### 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?

### 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?

### Shaping Up

##### Age 7 to 11 Challenge Level:

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

### Triangle Edges

##### Age 5 to 7 Challenge Level:

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

### 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.

### 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?

### Is a Square a Rectangle?

##### Age 7 to 11 Challenge Level:

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

### 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?

### 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?

##### Age 7 to 11 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

### Nine-pin Triangles

##### Age 7 to 11 Challenge Level:

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

### 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?

### Two by One

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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?

### 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.

### 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?

### Count the Trapeziums

##### Age 7 to 11 Challenge Level:

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

### 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?

### Cover the Camel

##### Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

### Tessellate the Triominoes

##### Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

### Seven Flipped

##### Age 7 to 11 Challenge Level:

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

### 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?

### Calendar Cubes

##### Age 7 to 11 Challenge Level:

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

### Roll These Dice

##### Age 7 to 11 Challenge 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?

##### Age 5 to 7 Challenge Level:

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

### 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?

### Mixed-up Socks

##### Age 5 to 7 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?

### Whose Face?

##### Age 5 to 11 Challenge Level:

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

### Numerically Equal

##### Age 7 to 11 Challenge Level:

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

### Fake Gold

##### Age 7 to 11 Challenge Level:

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

### Pasta Timing

##### Age 7 to 11 Challenge Level:

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?

### 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?

### Triangles All Around

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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. . . .

### Creating Cubes

##### Age 7 to 11 Challenge 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.

### 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?

### Knight's Swap

##### Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

### How Many Times?

##### Age 7 to 11 Challenge Level:

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.?

### 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?

### Symmetry Challenge

##### Age 7 to 11 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

### 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.

### Finding All Possibilities Lower Primary

##### Age 5 to 7 Challenge Level:

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

### Ordered Ways of Working Lower Primary

##### Age 5 to 7 Challenge Level:

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

### Ordered Ways of Working Upper Primary

##### Age 7 to 11 Challenge Level:

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