Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Numerically Equal

Age 7 to 11 Challenge Level:

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

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.

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?

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?

Cover the Tray

Age 7 to 11 Challenge Level:

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

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?

Rod Area

Age 7 to 11

This task challenges you to create symmetrical U shapes out of rods and find their areas.

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.

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?

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?

Dicey Perimeter, Dicey Area

Age 7 to 11 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?

Quadrilaterals

Age 7 to 11 Challenge Level:

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

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.

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?

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.

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?

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?

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?

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.

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?

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?

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.

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?

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?

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.

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?

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?

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.

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?

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?

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.

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.

Wag Worms

Age 7 to 11 Challenge 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.

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?

Two Dots

Age 7 to 11 Challenge Level:

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Team Scream

Age 7 to 11 Challenge Level:

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Make Pairs

Age 7 to 11 Challenge Level:

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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?

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?

Polydron

Age 7 to 11 Challenge Level:

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

Buying a Balloon

Age 7 to 11 Challenge Level:

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Folded Number Line

Age 7 to 11 Challenge Level:

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Building with Rods

Age 7 to 11 Challenge Level:

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

Encouraging Primary Children to Work Systematically

Age 3 to 11

This article for primary teachers suggests ways in which to help children become better at working systematically.

Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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?

More and More Buckets

Age 7 to 11 Challenge Level:

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?