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#### Resources tagged with Working systematically similar to Fair Exchange:

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

### Fair Exchange

##### Stage: 1 Challenge Level:

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

### Making Trains

##### Stage: 1 Challenge Level:

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

### 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?

### Five Coins

##### Stage: 2 Challenge Level:

Ben has five coins in his pocket. How much money might he have?

### Winning the Lottery

##### Stage: 2 Challenge Level:

Try out the lottery that is played in a far-away land. What is the chance of winning?

### 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?

### Code Breaker

##### Stage: 2 Challenge Level:

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

### Junior Frogs

##### Stage: 1 and 2 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?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

### Multiples Grid

##### Stage: 2 Challenge Level:

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

### Money Bags

##### Stage: 2 Challenge Level:

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

### 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?

### 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.

### 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.

### 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....?

### Combining Cuisenaire

##### Stage: 2 Challenge Level:

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

### 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.

### 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.

### Here to There 1 2 3

##### Stage: 1 Challenge Level:

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

### Robot Monsters

##### Stage: 1 Challenge Level:

Use these head, body and leg pieces to make Robot Monsters which are different heights.

### Matching Time

##### Stage: 1 Challenge Level:

Try this matching game which will help you recognise different ways of saying the same time interval.

### Coloured Squares

##### Stage: 1 Challenge Level:

Use the clues to colour each square.

### Cover the Camel

##### Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

### Worms

##### Stage: 2 Challenge Level:

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

### 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?

### Greater Than or Less Than?

##### Stage: 2 Challenge Level:

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

### Getting the Balance

##### Stage: 1 Challenge Level:

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

### Tessellate the Triominoes

##### Stage: 1 Challenge Level:

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

### How Long Does it Take?

##### Stage: 2 Challenge Level:

In this matching game, you have to decide how long different events take.

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### 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?

### Triangle Edges

##### Stage: 1 Challenge Level:

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

### 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.

### 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?

### 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.

### 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?

### 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?

### 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?

### Is a Square a Rectangle?

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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.

### Jumping Cricket

##### Stage: 1 Challenge Level:

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

### Whose Face?

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

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

### Nineteen Hexagons

##### Stage: 1 Challenge Level:

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

##### Stage: 2 Challenge Level:

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

### 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?

### Geoboards

##### Stage: 2 Challenge Level:

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