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#### Resources tagged with Working systematically similar to Different Sizes:

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

### Numerically Equal

##### Age 7 to 11 Challenge Level:

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

### Torn Shapes

##### Age 7 to 11 Challenge Level:

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

### Polydron

##### Age 7 to 11 Challenge Level:

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

### Geoboards

##### Age 7 to 11 Challenge Level:

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

### Dicey Perimeter, Dicey Area

##### Age 7 to 11 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

### Dice in a Corner

##### Age 7 to 11 Challenge Level:

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

### Making Squares

##### Age 7 to 11

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?

### My New Patio

##### Age 7 to 11 Challenge Level:

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

### Fencing Lambs

##### Age 7 to 11 Challenge Level:

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

### Area and Perimeter

##### Age 7 to 11 Challenge Level:

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

### Tiles on a Patio

##### Age 7 to 11 Challenge Level:

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

### Through the Window

##### Age 7 to 11 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?

### Square Corners

##### Age 7 to 11 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?

### Two Spinners

##### Age 5 to 7 Challenge Level:

What two-digit numbers can you make with these two dice? What can't you make?

##### Age 5 to 11 Challenge Level:

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

### More Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

### Junior Frogs

##### Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

### More Children and Plants

##### Age 7 to 14 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

### Home Time

##### Age 7 to 11 Challenge Level:

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

##### Age 7 to 11 Challenge Level:

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

### Troublesome Triangles

##### Age 7 to 14 Challenge Level:

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

### Knight's Swap

##### Age 7 to 11 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?

### Making Boxes

##### Age 7 to 11 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?

### Chain of Changes

##### Age 5 to 7 Challenge Level:

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

### Dodecamagic

##### Age 7 to 11 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?

### Shapes on the Playground

##### Age 7 to 11 Challenge Level:

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

### More Plant Spaces

##### Age 7 to 14 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

### Tiling

##### Age 7 to 11 Challenge Level:

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

### Multiply Multiples 1

##### Age 7 to 11 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

### Round the Two Dice

##### Age 5 to 7 Challenge Level:

This activity focuses on rounding to the nearest 10.

### Is a Square a Rectangle?

##### Age 7 to 11 Challenge Level:

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

### Plants

##### Age 5 to 11 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Ribbon Squares

##### Age 7 to 11 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

### What Could it Be?

##### Age 5 to 7 Challenge Level:

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it?

### Round the Dice Decimals 1

##### Age 7 to 11 Challenge Level:

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

### Round the Three Dice

##### Age 7 to 11 Challenge Level:

What happens when you round these three-digit numbers to the nearest 100?

### A City of Towers

##### Age 5 to 7 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?

### Round the Dice Decimals 2

##### Age 7 to 11 Challenge Level:

What happens when you round these numbers to the nearest whole number?

### Seven Pots of Plants

##### Age 7 to 11 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

### Cover the Tray

##### Age 7 to 11 Challenge Level:

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

### Multiply Multiples 2

##### Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation?

### Peg and Pin Boards

##### Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

### Cuisenaire Counting

##### Age 5 to 7 Challenge Level:

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

### Briefcase Lock

##### Age 5 to 7 Challenge Level:

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

### Putting Two and Two Together

##### Age 7 to 11 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?

### Arrangements

##### Age 7 to 11 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

### Teddy Town

##### Age 5 to 14 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

### Nine-pin Triangles

##### Age 7 to 11 Challenge Level:

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

### Finding Fifteen

##### Age 7 to 11 Challenge Level:

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?