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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?

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?

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?

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?

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?

Number Pyramids

Stage: 3 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

Cunning Card Trick

Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

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.

Fault-free Rectangles

Stage: 2 Challenge Level:

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

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.

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?

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?

Polygonals

Stage: 2 Challenge Level:

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

Pentanim

Stage: 2, 3 and 4 Challenge Level:

A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

Have You Got It?

Stage: 3 Challenge Level:

Can you explain the strategy for winning this game with any target?

Sliding Puzzle

Stage: 1, 2, 3 and 4 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Broken Toaster

Stage: 2 Short Challenge Level:

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

Card Trick 2

Stage: 3 Challenge Level:

Can you explain how this card trick works?

Summing Consecutive Numbers

Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Spirals, Spirals

Stage: 2 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice?

Picturing Triangle Numbers

Stage: 3 Challenge Level:

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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?

Up and Down Staircases

Stage: 2 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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.

Games Related to Nim

Stage: 1, 2, 3 and 4

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

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.

One, Three, Five, Seven

Stage: 3 and 4 Challenge Level:

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

Centred Squares

Stage: 2 Challenge Level:

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

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

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?

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 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?

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?

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?

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"?

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?

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.

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.

Build it Up

Stage: 2 Challenge Level:

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

Build it up More

Stage: 2 Challenge Level:

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

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?

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?

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?

Sums and Differences 1

Stage: 2 Challenge Level:

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

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?