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#### Resources tagged with Working systematically similar to Chairs and Tables:

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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.

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### Display Boards

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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?

### 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.

### 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?

### 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?

### Triangle Edges

##### Stage: 1 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

### 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?

### Tessellate the Triominoes

##### Stage: 1 Challenge Level:

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

### 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?

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

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

### 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?

### Inside Triangles

##### Stage: 1 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

### 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.

### 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 Tray

##### Stage: 2 Challenge Level:

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

### We'll Bang the Drum

##### Stage: 1 Challenge Level:

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

### 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. . . .

### Tri.'s

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### Coloured Squares

##### Stage: 1 Challenge Level:

Use the clues to colour each square.

### Three Sets of Cubes, Two Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### The Pet Graph

##### Stage: 2 Challenge Level:

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

### Seven Flipped

##### Stage: 2 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

### A City of Towers

##### Stage: 1 Challenge Level:

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

### Calendar Cubes

##### Stage: 2 Challenge Level:

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

### Triangle Animals

##### Stage: 1 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

### Snails' Trails

##### Stage: 2 Challenge Level:

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

### Making Cuboids

##### Stage: 2 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?

### Pouring the Punch Drink

##### Stage: 2 Challenge Level:

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

### 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.

### 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.

### Room Doubling

##### Stage: 2 Challenge Level:

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

##### Stage: 2 Challenge Level:

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

### Octa Space

##### Stage: 2 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?

### 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?

### Stairs

##### Stage: 1 and 2 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.