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Resources tagged with Working systematically similar to Fit These Shapes:

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

Waiting for Blast Off

Stage: 2 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?

Cover the Tray

Stage: 2 Challenge Level:

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

Shunting Puzzle

Stage: 2 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Display Boards

Stage: 2 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Open Boxes

Stage: 2 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?

Single Track

Stage: 2 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

Tangram Tangle

Stage: 1 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?

Map Folding

Stage: 2 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

Stage: 2 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. . . .

Hexpentas

Stage: 1 and 2 Challenge Level:

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

Red Even

Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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.

Tetrafit

Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

Are You Well Balanced?

Stage: 1 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Celtic Knot

Stage: 2 Challenge Level:

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Two on Five

Stage: 1 and 2 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?

Tessellate the Triominoes

Stage: 1 Challenge Level:

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

Two by One

Stage: 2 Challenge Level:

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

Cover the Camel

Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

Routes 1 and 5

Stage: 1 Challenge Level:

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

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?

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?

Coloured Squares

Stage: 1 Challenge Level:

Use the clues to colour each square.

Cuisenaire Counting

Stage: 1 Challenge Level:

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Dienes' Logiblocs

Stage: 1 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?

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.

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?

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?

Knight's Swap

Stage: 2 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?

We'll Bang the Drum

Stage: 1 Challenge Level:

How many different rhythms can you make by putting two drums on the wheel?

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?

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?

Same Length Trains

Stage: 1 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical?

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?

One to Fifteen

Stage: 2 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Combining Cuisenaire

Stage: 2 Challenge Level:

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

Three Ball Line Up

Stage: 1 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Geoboards

Stage: 2 Challenge Level:

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

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?

Stage: 2 Challenge Level:

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

Nine-pin Triangles

Stage: 2 Challenge Level:

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

Dodecamagic

Stage: 2 Challenge Level:

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Finding All Possibilities Lower Primary

Stage: 1 Challenge Level:

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

Coded Hundred Square

Stage: 2 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

Two Dots

Stage: 2 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.

Make Pairs

Stage: 2 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.

Difference

Stage: 2 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.