Can you each work out the number on your card? What do you notice? How could you sort the cards?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

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

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Investigate what happens when you add house numbers along a street in different ways.

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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

There are nasty versions of this dice game but we'll start with the nice ones...

There were 22 legs creeping across the web. How many flies? How many spiders?