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### Number and algebra

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### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Primary Summer Challenges 2023

### Sealed Solution

### Fifteen Cards

### Roll These Dice

### Factor Track

### Add 3 Dice

### Biscuit Decorations

### Teddy Town

### Sets of Numbers

### Square Corners

### Skip Counting

### More Less Is More

### Seeing Squares

### Family Tree

### A City of Towers

### Seven Flipped

### 4 Dom

### Less Is More

### Robot Monsters

### First Connect Three

### Got It

### Junior Frogs

### Coded Hundred Square

### Make 37

### Incey Wincey Spider

### Nim-7

### Tangrams

### Four Triangles Puzzle

### Making Sticks

### Missing Middles

### Factors and Multiples Game

### Two-digit Targets

### Dicey Operations in Line

### Shape Times Shape

### Butterfly Flowers

### The Remainders Game

### Sort the Street

### Mystery Matrix

### Three Block Towers

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

Each weekday, from 10 July to 1 September, a new problem or game 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 Summer Challenges 2023.

Age 7 to 11

Challenge Level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Age 7 to 11

Challenge Level

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Age 7 to 11

Challenge Level

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?

Age 5 to 7

Challenge Level

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Age 5 to 11

Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Age 7 to 11

Challenge Level

How many different sets of numbers with at least four members can you find in the numbers in this box?

Age 7 to 11

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?

Age 5 to 7

Challenge Level

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

Age 7 to 14

Challenge Level

In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.

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 7 to 11

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.

Age 5 to 7

Challenge Level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Age 7 to 11

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.

Age 5 to 11

Challenge Level

Use these four dominoes to make a square that has the same number of dots on each side.

Age 7 to 11

Challenge Level

Use your knowledge of place value to try to win this game. How will you maximise your score?

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 5 to 11

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?

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 7 to 11

Challenge Level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Age 5 to 7

Challenge Level

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

Age 5 to 11

Challenge Level

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Age 5 to 11

Challenge Level

Can you make five differently sized squares from the interactive tangram pieces?

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 5 to 7

Challenge Level

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Age 5 to 7

Challenge Level

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?

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 5 to 7

Challenge Level

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Age 7 to 11

Challenge Level

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Age 7 to 11

Challenge Level

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

Age 5 to 7

Challenge Level

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

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 7 to 11

Challenge Level

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 5 to 7

Challenge Level

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?