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#### Resources tagged with Working systematically similar to A Cartesian Puzzle:

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##### Other tags that relate to A Cartesian Puzzle
Rotations. Coordinates. Area. Practical Activity. Symmetry. Mixed triangles. Visualising. Reflections. Translations. Quadrilaterals.

### There are 333 results

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

### Building with Longer Rods

##### Stage: 2 and 3 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

### 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?

##### Stage: 3 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares?

### Numerically Equal

##### Stage: 2 Challenge Level:

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

### 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?

### 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.

##### Stage: 2 Challenge Level:

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

### Polydron

##### Stage: 2 Challenge Level:

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

### Coordinate Challenge

##### Stage: 2 Challenge Level:

Use the clues about the symmetrical properties of these letters to place them on the grid.

### 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?

### 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.

### Building with Rods

##### Stage: 2 Challenge Level:

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

### Cover the Tray

##### Stage: 2 Challenge Level:

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

### 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?

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

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

### Tri.'s

##### Stage: 2 Challenge Level:

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

### 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.

### 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?

### 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?

### 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?

### 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?

### Making Boxes

##### Stage: 2 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?

### Area and Perimeter

##### Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### 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.

### 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?

### Tiles on a Patio

##### Stage: 2 Challenge Level:

How many ways can you find of tiling the square patio, using square tiles of different sizes?

### Creating Cubes

##### Stage: 2 and 3 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.

### 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.

### 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?

### 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?

### 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.

### Three Sets of Cubes, Two Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### You Owe Me Five Farthings, Say the Bells of St Martin's

##### Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

### Order the Changes

##### Stage: 2 Challenge Level:

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

### Geoboards

##### Stage: 2 Challenge Level:

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

### Fence It

##### Stage: 3 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

### Single Track

##### Stage: 2 Challenge Level:

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

### 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?

### Isosceles Triangles

##### Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Neighbours

##### Stage: 2 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

### 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?

### Making Maths: Double-sided Magic Square

##### Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

### LOGO Challenge - Following On

##### Stage: 3, 4 and 5 Challenge Level:

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

### Triangles to Tetrahedra

##### Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

### Fencing Lambs

##### Stage: 2 Challenge Level:

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

### LOGO Challenge - Triangles-squares-stars

##### Stage: 3 and 4 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

### LOGO Challenge - Pentagram Pylons

##### Stage: 3, 4 and 5 Challenge Level:

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

### 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?

### Tiling

##### Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

### Making Squares

##### Stage: 2 Challenge Level:

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?