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How many trapeziums, of various sizes, are hidden in this picture?

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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This challenge is about finding the difference between numbers which have the same tens digit.

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The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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My coat has three buttons. How many ways can you find to do up all the buttons?

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Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Can you fill in the empty boxes in the grid with the right shape and colour?

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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?

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Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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Can you find the chosen number from the grid using the clues?

Number problems for lower primary that will get you thinking.

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Can you find out in which order the children are standing in this line?

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In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

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These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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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.

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Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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

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Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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An activity making various patterns with 2 x 1 rectangular tiles.

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There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.