Resources tagged with: Working systematically

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

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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?

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Count the Trapeziums

Age 7 to 11 Challenge Level:

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

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Numerically Equal

Age 7 to 11 Challenge Level:

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

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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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Two by One

Age 7 to 11 Challenge Level:

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

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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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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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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?

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Making Boxes

Age 7 to 11 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?

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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?

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Street Party

Age 7 to 11 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.

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Sweets in a Box

Age 7 to 11 Challenge 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?

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Ice Cream

Age 7 to 11 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.

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Fencing Lambs

Age 7 to 11 Challenge Level:

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

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Newspapers

Age 7 to 11 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?

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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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Shapes on the Playground

Age 7 to 11 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?

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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.

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Magazines

Age 7 to 11 Challenge Level:

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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Halloween Investigation

Age 7 to 11 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?

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Cover the Tray

Age 7 to 11 Challenge Level:

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

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Ribbon Squares

Age 7 to 11 Challenge Level:

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

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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?

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Crossing the Town Square

Age 7 to 11 Challenge Level:

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

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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?

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3 Rings

Age 7 to 11 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?

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Two on Five

Age 5 to 11 Challenge 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?

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Room Doubling

Age 7 to 11 Challenge Level:

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

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It Figures

Age 7 to 11 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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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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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?

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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?

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Through the Window

Age 7 to 11 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?

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This Pied Piper of Hamelin

Age 7 to 11 Challenge Level:

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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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.

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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?

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Eight Queens

Age 7 to 11 Challenge Level:

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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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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Building with Rods

Age 7 to 11 Challenge Level:

In how many ways can you stack these rods, following the rules?

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Quadrilaterals

Age 7 to 11 Challenge Level:

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

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Octa Space

Age 7 to 11 Challenge Level:

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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Stairs

Age 5 to 11 Challenge Level:

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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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?

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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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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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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?

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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.

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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. . . .

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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?

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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.