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Resources tagged with Working systematically similar to Triangle Island:

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

Numerically Equal

Stage: 2 Challenge Level:

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

Through the Window

Stage: 2 Challenge Level:

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Fencing Lambs

Stage: 2 Challenge Level:

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

Polydron

Stage: 2 Challenge Level:

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

Geoboards

Stage: 2 Challenge Level:

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

Torn Shapes

Stage: 2 Challenge Level:

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

Triangles All Around

Stage: 2 Challenge Level:

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

Area and Perimeter

Stage: 2 Challenge Level:

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

Ribbon Squares

Stage: 2 Challenge Level:

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

Making Squares

Stage: 2

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?

Dicey Perimeter, Dicey Area

Stage: 2 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Peg and Pin Boards

Stage: 1 and 2

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

My New Patio

Stage: 2 Challenge Level:

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

Tiles on a Patio

Stage: 2 Challenge Level:

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

Newspapers

Stage: 2 Challenge Level:

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Cover the Tray

Stage: 2 Challenge Level:

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

Egyptian Rope

Stage: 2 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?

Street Party

Stage: 2 Challenge Level:

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Warmsnug Double Glazing

Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Shapes on the Playground

Stage: 2 Challenge Level:

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Two by One

Stage: 2 Challenge Level:

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

Square Corners

Stage: 2 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?

Uncanny Triangles

Stage: 2 Challenge Level:

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

More Transformations on a Pegboard

Stage: 2 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.

Fault-free Rectangles

Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

Shaping Up

Stage: 2 Challenge Level:

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

Tri.'s

Stage: 2 Challenge Level:

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

3 Rings

Stage: 2 Challenge Level:

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Stage: 2 Challenge Level:

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

Sticks and Triangles

Stage: 2 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?

Halloween Investigation

Stage: 2 Challenge Level:

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Nine-pin Triangles

Stage: 2 Challenge Level:

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

Is a Square a Rectangle?

Stage: 2 Challenge Level:

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

Ice Cream

Stage: 2 Challenge Level:

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.

Making Boxes

Stage: 2 Challenge Level:

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

Calcunos

Stage: 2 Challenge Level:

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

Tiling

Stage: 2 Challenge Level:

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

Putting Two and Two Together

Stage: 2 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?

Paw Prints

Stage: 2 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?

All Seated

Stage: 2 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?

Combining Cuisenaire

Stage: 2 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

Counters

Stage: 2 Challenge Level:

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

Zargon Glasses

Stage: 2 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?

LOGO Challenge - the Logic of LOGO

Stage: 3 and 4 Challenge Level:

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Open Squares

Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Home Time

Stage: 2 Challenge Level:

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Chocoholics

Stage: 2 Challenge Level:

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Fence It

Stage: 3 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Arrangements

Stage: 2 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?