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

### Build it Up

##### Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

### 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?

### Unit Differences

##### Stage: 1 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

### What Could it Be?

##### Stage: 1 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

##### Stage: 2 Challenge Level:

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

### Round the Dice Decimals 1

##### Stage: 2 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 Two Dice

##### Stage: 1 Challenge Level:

This activity focuses on rounding to the nearest 10.

### Round the Dice Decimals 2

##### Stage: 2 Challenge Level:

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

### Multiply Multiples 2

##### Stage: 2 Challenge Level:

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

### Multiply Multiples 1

##### Stage: 2 Challenge Level:

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

### Two Spinners

##### Stage: 1 Challenge Level:

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

### 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?

### 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?

### Matching Time

##### Stage: 1 Challenge Level:

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

### 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?

### School Fair Necklaces

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

How many possible necklaces can you find? And how do you know you've found them all?

### Dice in a Corner

##### Stage: 2 Challenge Level:

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

### This Pied Piper of Hamelin

##### Stage: 2 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### Take Three Numbers

##### Stage: 2 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

### The Games' Medals

##### Stage: 1 Challenge Level:

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

### Fifteen Cards

##### Stage: 2 Challenge Level:

Can you use the information to find out which cards I have used?

### Jumping Squares

##### Stage: 1 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

### Half Time

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

What could the half time scores have been in these Olympic hockey matches?

##### Stage: 1 and 2 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?

### Button-up Some More

##### Stage: 2 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

### Rolling That Cube

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

### Journeys in Numberland

##### Stage: 2 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

### The Add and Take-away Path

##### Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

### 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.

### Inky Cube

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

### Sitting Round the Party Tables

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

### Curious Number

##### Stage: 2 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

### Counters in the Middle

##### Stage: 2 Challenge Level:

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

### 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?

### Magic Vs

##### Stage: 2 Challenge Level:

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

### 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.

### Oh! Harry!

##### Stage: 2 Challenge Level:

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

### 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.

### First Connect Three

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

### Shape Times Shape

##### Stage: 2 Challenge Level:

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

### 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?

### 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?

### Route Product

##### Stage: 2 Challenge Level:

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

### 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.

### 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?

### Coordinate Challenge

##### Stage: 2 Challenge Level:

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

### Intersection Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

### Diagonal Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

### Torn Shapes

##### Stage: 2 Challenge Level:

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