Resources tagged with: Generalising

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There are 149 results

Broad Topics > Thinking Mathematically > Generalising

Nim-7

Age 5 to 14Challenge Level

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

Nim-7 for Two

Age 5 to 14Challenge Level

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

Card Trick 2

Age 11 to 14Challenge Level

Can you explain how this card trick works?

Strike it Out

Age 5 to 11Challenge Level

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

Pentanim

Age 7 to 16Challenge Level

A game for 2 players with similarities 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.

Maths Trails

Age 7 to 14

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.

Have You Got It?

Age 11 to 14Challenge Level

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

Dotty Circle

Age 7 to 11Challenge 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?

Button-up Some More

Age 7 to 11Challenge Level

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

Window Frames

Age 5 to 14Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

One, Three, Five, Seven

Age 11 to 16Challenge 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.

Sitting Round the Party Tables

Age 5 to 11Challenge 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.

Cunning Card Trick

Age 11 to 14Challenge Level

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

Strike it Out for Two

Age 5 to 11Challenge Level

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

Play to 37

Age 7 to 11Challenge 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.

Broken Toaster

Age 7 to 11 ShortChallenge 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?

Games Related to Nim

Age 5 to 16

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.

Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Truth or Lie

Age 7 to 11Challenge Level

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Build it Up

Age 7 to 11Challenge Level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Age 11 to 14Challenge Level

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

Number Pyramids

Age 11 to 14Challenge Level

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

Arithmagons

Age 11 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges?

Snake Coils

Age 7 to 11Challenge Level

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

Egyptian Fractions

Age 11 to 14Challenge Level

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Consecutive Negative Numbers

Age 11 to 14Challenge Level

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

Magic Letters

Age 11 to 14Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Keep it Simple

Age 11 to 14Challenge Level

Can all unit fractions be written as the sum of two unit fractions?

Journeys in Numberland

Age 7 to 11Challenge Level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Circles, Circles

Age 5 to 11Challenge 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?

Taking Steps

Age 7 to 11Challenge Level

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

Sliding Puzzle

Age 11 to 16Challenge 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.

Centred Squares

Age 7 to 11Challenge Level

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

Nim-like Games

Age 7 to 16Challenge Level

A collection of games on the NIM theme

Got It

Age 7 to 14Challenge 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.

Build it up More

Age 7 to 11Challenge Level

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

More Magic Potting Sheds

Age 11 to 14Challenge 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?

Squares in Rectangles

Age 11 to 14Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Sums and Differences 1

Age 7 to 11Challenge Level

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

One O Five

Age 11 to 14Challenge Level

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Sums and Differences 2

Age 7 to 11Challenge 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?

Got it for Two

Age 7 to 14Challenge Level

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

Always, Sometimes or Never? Number

Age 7 to 11Challenge Level

Are these statements always true, sometimes true or never true?

Tiling

Age 7 to 11Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

Spirals, Spirals

Age 7 to 11Challenge Level

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

Charitable Pennies

Age 7 to 14Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Triangle Pin-down

Age 7 to 11Challenge Level

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

Partitioning Revisited

Age 11 to 14Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Walking the Squares

Age 7 to 11Challenge Level

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

More Number Pyramids

Age 11 to 14Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...