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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Finding All Possibilities Upper Primary

### Beads and Bags

### Half Time

### Buying a Balloon

### Fifteen Cards

### Cubes Here and There

### Trebling

### Factor Lines

### Sealed Solution

### Magic Vs

### All the Digits

### Finding Fifteen

### Button-up Some More

### This Pied Piper of Hamelin

### Reach 100

### 5 on the Clock

### Nine-pin Triangles

### Inky Cube

## You may also like

### Geoboards

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)

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These activities ask you to find all possible solutions. If you work in a systematic way, you will be sure not to leave any out!

Age 5 to 11

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?

Age 5 to 11

Challenge Level

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

Age 7 to 11

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?

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

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Age 7 to 11

Challenge Level

Can you replace the letters with numbers? Is there only one solution in each case?

Age 7 to 14

Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

Age 7 to 11

Challenge Level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Age 7 to 11

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?

Age 7 to 11

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 ...?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Age 7 to 11

Challenge Level

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Age 7 to 11

Challenge Level

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

Age 7 to 14

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?

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