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Resources tagged with Working systematically similar to Four Layers:

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

Stage: 2 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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?

Single Track

Stage: 2 Challenge Level:

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

Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level:

How many models can you find which obey these rules?

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?

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?

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?

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?

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?

Four Triangles Puzzle

Stage: 1 and 2 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?

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?

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.

Tessellate the Triominoes

Stage: 1 Challenge Level:

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

We'll Bang the Drum

Stage: 1 Challenge Level:

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

Coloured Squares

Stage: 1 Challenge Level:

Use the clues to colour each square.

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?

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?

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?

Cubes Here and There

Stage: 2 Challenge Level:

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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?

Counting Cards

Stage: 2 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Cover the Tray

Stage: 2 Challenge Level:

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

Wag Worms

Stage: 2 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.

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?

Two by One

Stage: 2 Challenge Level:

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

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. . . .

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?

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?

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?

Pasta Timing

Stage: 2 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?

Eight Queens

Stage: 2 Challenge Level:

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

Room Doubling

Stage: 2 Challenge Level:

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

1 to 8

Stage: 2 Challenge Level:

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

It Figures

Stage: 2 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?

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.

Chocs, Mints, Jellies

Stage: 2 Challenge Level:

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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?

Route Product

Stage: 2 Challenge Level:

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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?

A Square of Numbers

Stage: 2 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

The Moons of Vuvv

Stage: 2 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Button-up Some More

Stage: 2 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Four Colours

Stage: 1 and 2 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.

The Third Dimension

Stage: 1 and 2 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?

Prison Cells

Stage: 2 Challenge Level:

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?