Upper primary working systematically KS2

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

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

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?

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

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

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

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?

How do you know if your set of dominoes is complete?

This challenge combines addition, multiplication, perseverance and even proof.

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?

This task combines spatial awareness with addition and multiplication.

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.

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

Can you make square numbers by adding two prime numbers together?

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?

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?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

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

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

Can you go through this maze so that the numbers you pass add to exactly 100?

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?

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?

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?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

This dice train has been made using specific rules. How many different trains can you make?

These practical challenges are all about making a 'tray' and covering it with paper.