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#### Resources tagged with Working systematically similar to Hexpentas:

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

### 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?

### 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?

### 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?

### 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?

### 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?

### Two by One

##### Stage: 2 Challenge Level:

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

### 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?

### Coloured Squares

##### Stage: 1 Challenge Level:

Use the clues to colour each square.

### 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. . . .

### 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.

### 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?

### 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?

### 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?

### Single Track

##### Stage: 2 Challenge Level:

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

### 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?

### Display Boards

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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?

### 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.

### Cover the Camel

##### Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

### Building with Rods

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### Cover the Tray

##### Stage: 2 Challenge Level:

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

### Tessellate the Triominoes

##### Stage: 1 Challenge Level:

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

### 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?

### Combining Cuisenaire

##### Stage: 2 Challenge Level:

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

### 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.

### 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.

### 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?

### 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?

### 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?

### 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?

### Find the Difference

##### Stage: 1 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

### 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?

### 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?

### Tri.'s

##### Stage: 2 Challenge Level:

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

##### 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.

### Symmetry Challenge

##### Stage: 2 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

### 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?

### 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?

### 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?

### 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?

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### 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?

### 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?

### 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.

### 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.

### 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?