Resources tagged with: Generalising

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There are 92 results

Broad Topics > Thinking Mathematically > Generalising

Circles, Circles

Age 5 to 11 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?

Triangle Pin-down

Age 7 to 11 Challenge Level:

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

Got It

Age 7 to 14 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

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.

Nim-7 for Two

Age 5 to 14 Challenge Level:

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

Strike it Out for Two

Age 5 to 11 Challenge Level:

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

Make 37

Age 7 to 14 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.

Taking Steps

Age 7 to 11 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.

Finding 3D Stacks

Age 7 to 11 Challenge Level:

Can you find a way of counting the spheres in these arrangements?

Strike it Out

Age 5 to 11 Challenge Level:

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

Odd Squares

Age 7 to 11 Challenge Level:

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

Build it Up

Age 7 to 11 Challenge 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.

Broken Toaster

Age 7 to 11 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?

Winning Lines

Age 7 to 16

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

Nim-like Games

Age 7 to 16 Challenge Level:

A collection of games on the NIM theme

Stop the Clock for Two

Age 5 to 7 Challenge Level:

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

Pentanim

Age 7 to 16 Challenge 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.

Got it for Two

Age 7 to 14 Challenge Level:

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

Cut it Out

Age 7 to 11 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?

Nim-7

Age 5 to 14 Challenge Level:

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

Dotty Circle

Age 7 to 11 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?

Button-up Some More

Age 7 to 11 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 ...?

Window Frames

Age 5 to 14 Challenge Level:

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

Play to 37

Age 7 to 11 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.

Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns!

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.

Stop the Clock

Age 5 to 7 Challenge Level:

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

Snake Coils

Age 7 to 11 Challenge Level:

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

Tumbling Down

Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens?

Unit Differences

Age 5 to 7 Challenge Level:

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

What Could it Be?

Age 5 to 7 Challenge Level:

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

Sitting Round the Party Tables

Age 5 to 11 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.

Rope Mat

Age 7 to 11 Challenge Level:

How many centimetres of rope will I need to make another mat just like the one I have here?

Polygonals

Age 7 to 11 Challenge Level:

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

The Add and Take-away Path

Age 5 to 7 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?

Centred Squares

Age 7 to 11 Challenge Level:

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

Cuisenaire Squares

Age 7 to 11 Challenge Level:

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

Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

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

Dice Stairs

Age 7 to 11 Challenge Level:

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

The Great Tiling Count

Age 7 to 11 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.

Lots of Lollies

Age 5 to 7 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?

Making Maths: Be a Mathemagician

Age 7 to 11 Challenge Level:

Surprise your friends with this magic square trick.

Charitable Pennies

Age 7 to 14 Challenge Level:

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

Lost Books

Age 7 to 11 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?

Growing Garlic

Age 5 to 7 Challenge Level:

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

Sticky Triangles

Age 7 to 11 Challenge Level:

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

Truth or Lie

Age 7 to 11 Challenge Level:

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

Counting Counters

Age 7 to 11 Challenge Level:

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

Move a Match

Age 7 to 11 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?

Generalising

Age 5 to 11

These tasks give learners chance to generalise, which involves identifying an underlying structure.