Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Freedom and Constraints

### Two and Two

### Gabriel's Problem

### American Billions

### How Much Can We Spend?

### Largest Product

### Perimeter Expressions

### Cinema Problem

### What Numbers Can We Make?

### Weights

### 1 Step 2 Step

### What Numbers Can We Make Now?

### Peaches Today, Peaches Tomorrow...

### Take Three from Five

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Mathematicians often explore structures, notice patterns, find rules and make generalisations. Once they feel they understand a structure, they then push at the boundaries, change the problem, and explore the new structures that emerge.

The Freedom and Constraints pathway on wild.maths.org offers**students** some situations which may initially seem constrained, but on closer inspection they may find there is more room to manoeuvre than they imagined.

The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.

The Freedom and Constraints pathway on wild.maths.org offers

The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.

Age 7 to 16

Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Age 11 to 14

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Age 11 to 14

Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Age 11 to 14

Challenge Level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Age 11 to 14

Challenge Level

Which set of numbers that add to 100 have the largest product?

Age 11 to 14

Challenge Level

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Age 11 to 14

Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Age 11 to 14

Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Age 11 to 14

Challenge Level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Age 11 to 14

Challenge Level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Age 11 to 14

Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Age 11 to 14

Challenge Level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Age 11 to 16

Challenge Level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?