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#### Resources tagged with Working systematically similar to Transformations on a Pegboard:

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

### Geoboards

##### Stage: 2 Challenge Level:

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

### Making Squares

##### Stage: 2

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?

### Through the Window

##### Stage: 2 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?

### Numerically Equal

##### Stage: 2 Challenge Level:

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

### Polydron

##### Stage: 2 Challenge Level:

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

### Torn Shapes

##### Stage: 2 Challenge Level:

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

### More Transformations on a Pegboard

##### Stage: 2 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.

### Triangles All Around

##### Stage: 2 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

### Uncanny Triangles

##### Stage: 2 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

### 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.

### 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.

### Dicey Perimeter, Dicey Area

##### Stage: 2 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?

### 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?

### Peg and Pin Boards

##### Stage: 1 and 2

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

### My New Patio

##### Stage: 2 Challenge Level:

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

##### Stage: 2 Challenge Level:

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

### 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?

### Shaping Up

##### Stage: 2 Challenge Level:

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

### Shapes on the Playground

##### Stage: 2 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?

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### Fault-free Rectangles

##### Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

### Tiling

##### Stage: 2 Challenge Level:

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

### Two by One

##### Stage: 2 Challenge Level:

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

### Ribbon Squares

##### Stage: 2 Challenge Level:

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

### 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?

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

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

### 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?

### Cover the Tray

##### Stage: 2 Challenge Level:

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

### Tri.'s

##### Stage: 2 Challenge Level:

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

### Family Tree

##### Stage: 2 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

### All Seated

##### Stage: 2 Challenge Level:

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

### Combining Cuisenaire

##### Stage: 2 Challenge Level:

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

### Chocoholics

##### Stage: 2 Challenge Level:

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

### 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?

### 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?

### How Much Did it Cost?

##### Stage: 2 Challenge Level:

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

### Being Thoughtful - Primary Number

##### Stage: 1 and 2 Challenge Level:

Number problems at primary level that require careful consideration.

### Cereal Packets

##### Stage: 2 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

### Dart Target

##### Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

### 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?

### 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?

### Open Squares

##### Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

### Home Time

##### Stage: 2 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.

### 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?

### Polo Square

##### Stage: 2 Challenge Level:

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

### LOGO Challenge - the Logic of LOGO

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

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

### Finding Fifteen

##### Stage: 2 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?

### Arrangements

##### Stage: 2 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....?

### Zargon Glasses

##### Stage: 2 Challenge Level:

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

### All the Digits

##### Stage: 2 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?