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More Numbers in the Ring

Stage: 1 Challenge Level:

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Stop the Clock

Stage: 1 Challenge Level:

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Stop the Clock for Two

Stage: 1 Challenge Level:

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Dotty Circle

Stage: 2 Challenge Level:

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Domino Numbers

Stage: 2 Challenge Level:

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

Number Differences

Stage: 2 Challenge Level:

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?

Taking Steps

Stage: 2 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Odd Squares

Stage: 2 Challenge Level:

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

Circles, Circles

Stage: 1 and 2 Challenge Level:

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Counting Counters

Stage: 2 Challenge Level:

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Cuisenaire Rods

Stage: 2 Challenge Level:

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Growing Garlic

Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Lots of Lollies

Stage: 1 Challenge Level:

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?

Nim-7 for Two

Stage: 1 and 2 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Always, Sometimes or Never?

Stage: 1 and 2 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Play to 37

Stage: 2 Challenge Level:

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.

Crossings

Stage: 2 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

How Odd

Stage: 1 Challenge Level:

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Triangle Pin-down

Stage: 2 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Polygonals

Stage: 2 Challenge Level:

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Make 37

Stage: 2 and 3 Challenge Level:

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

Fault-free Rectangles

Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

Move a Match

Stage: 2 Challenge Level:

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Lost Books

Stage: 2 Challenge Level:

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

Cut it Out

Stage: 2 Challenge Level:

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

What Could it Be?

Stage: 1 Challenge Level:

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

Snake Coils

Stage: 2 Challenge Level:

This challenge asks you to imagine a snake coiling on itself.

Round the Four Dice

Stage: 2 Challenge Level:

This activity involves rounding four-digit numbers to the nearest thousand.

Button-up Some More

Stage: 2 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 ...?

Three Dice

Stage: 2 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level:

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

Unit Differences

Stage: 1 Challenge Level:

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

Magic Constants

Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Sums and Differences 1

Stage: 2 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Walking the Squares

Stage: 2 Challenge Level:

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Dice Stairs

Stage: 2 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Build it up More

Stage: 2 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

Build it Up

Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

The Great Tiling Count

Stage: 2 Challenge Level:

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

Strike it Out for Two

Stage: 1 and 2 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Sums and Differences 2

Stage: 2 Challenge Level:

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?

Roll over the Dice

Stage: 2 Challenge Level:

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Got it for Two

Stage: 2 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

Strike it Out

Stage: 1 and 2 Challenge Level:

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Nim-7

Stage: 1, 2 and 3 Challenge Level:

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

Centred Squares

Stage: 2 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Got It

Stage: 2 and 3 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.

Sticky Triangles

Stage: 2 Challenge Level:

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.