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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Primary Interactive Summer Challenges 2022

### Seeing Squares

### Robot Monsters

### First Connect Three

### Got It

### Coded Hundred Square

### Four Triangles Puzzle

### Factors and Multiples Game

### The Remainders Game

### Sort the Street

### Growing Garlic

### Remainders

### Latin Lilies

### Gathering Gems

### Largest Even

### Carroll Diagrams

### Phiddlywinks

### Number Balance

### Tangram Browser

### Seesaw Shenanigans

### Countdown

### Matching Fractions

### Matching Numbers

### Same Length Trains

### Train Tactics

### Number Lines in Disguise

### Sizing Them Up

### Treasure Hunt

### Poly Plug Rectangles

### Ducking and Dividing

### Your Number Is...

### Light the Lights

### Tables Teaser

### Fruity Totals

### The Number Jumbler

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

We have a challenge a day for you throughout the summer break...

Each weekday, from 18 July to 2 September, a new interactive game or puzzle will appear on this page.

After you've had a go at the day's challenge you may be able to compare your approach to the solutions we have published, which are based on students' work.

You can also find Secondary Interactive Summer Challenges 2022.

Age 5 to 11

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Age 5 to 7

Challenge Level

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

Age 7 to 11

Challenge Level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Age 7 to 14

Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Age 7 to 11

Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Age 5 to 11

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?

Age 7 to 16

Challenge Level

A game in which players take it in turns to choose a number. Can you block your opponent?

Age 7 to 14

Challenge Level

Play this game and see if you can figure out the computer's chosen number.

Age 5 to 7

Challenge Level

Sort the houses in my street into different groups. Can you do it in any other ways?

Age 5 to 11

Challenge Level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Age 7 to 14

Challenge Level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Age 7 to 14

Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

Age 5 to 11

Challenge Level

Using compass points, can you describe up to ten paths on this map so that you bring as many gems back home as possible?

Age 5 to 11

Challenge Level

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Age 5 to 11

Challenge Level

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Age 7 to 18

Challenge Level

Have a go at this version of John Conway's game. Do you have any good strategies for winning?

Age 5 to 7

Challenge Level

Can you hang weights in the right place to make the the number balance balanced?

Age 7 to 11

Explore our selection of interactive tangrams. Can you use the tangram pieces to re-create each picture?

Age 3 to 7

Challenge Level

A group of animals has made a seesaw in the woods. How can you make the seesaw balance?

Age 7 to 14

Challenge Level

Here is a chance to play a version of the classic Countdown Game.

Age 7 to 11

Challenge Level

Can you find different ways of showing the same fraction? Try this matching game and see.

Age 5 to 7

Challenge Level

Can you find different ways of showing the same number? Try this matching game and see!

Age 5 to 7

Challenge Level

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Age 7 to 11

Challenge Level

A train building game for two players. Can you be the one to complete the train?

Age 7 to 14

Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Age 5 to 7

Challenge Level

Can you put these shapes in order of size? Start with the smallest.

Age 7 to 14

Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Age 5 to 11

Challenge Level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Age 7 to 11

Challenge Level

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Age 7 to 14

Challenge Level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Age 5 to 7

Challenge Level

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Age 5 to 7

Challenge Level

How will you work out which numbers have been used to create this multiplication square?

Age 7 to 16

Challenge Level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Age 7 to 14

Challenge Level

The Number Jumbler can always work out your chosen symbol. Can you work out how?