Resources tagged with: Generalising

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There are 92 results

Broad Topics > Thinking Mathematically > Generalising

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.

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 ...?

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?

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?

Centred Squares

Age 7 to 11
Challenge Level

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

Sums and Differences 1

Age 7 to 11
Challenge Level

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

Unit Differences

Age 5 to 7
Challenge Level

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

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?

Build it up More

Age 7 to 11
Challenge Level

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

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?

Tiling

Age 7 to 11
Challenge Level

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

Journeys in Numberland

Age 7 to 11
Challenge Level

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

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.

Sums and Differences 2

Age 7 to 11
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?

Break it Up!

Age 5 to 11
Challenge Level

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Magic Vs

Age 7 to 11
Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Round the Two Dice

Age 5 to 7
Challenge Level

This activity focuses on rounding to the nearest 10.

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.

Round the Three Dice

Age 7 to 11
Challenge Level

What happens when you round these three-digit numbers to the nearest 100?

Doplication

Age 7 to 11
Challenge Level

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

How Odd

Age 5 to 7
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?

Area and Perimeter

Age 7 to 11
Challenge Level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

More Numbers in the Ring

Age 5 to 7
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?

Division Rules

Age 7 to 11
Challenge Level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Digit Addition

Age 5 to 11
Challenge Level

Try out this number trick. What happens with different starting numbers? What do you notice?

Simple Train Journeys

Age 5 to 11
Challenge Level

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Making Maths: Be a Mathemagician

Age 7 to 11
Challenge Level

Surprise your friends with this magic square trick.

Magic Circles

Age 7 to 11
Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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?

Bundles of Cubes

Age 7 to 11
Challenge Level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Magic Constants

Age 7 to 11
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?

Round and Round the Circle

Age 7 to 11
Challenge Level

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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?

Oddly

Age 7 to 11
Challenge Level

Find the sum of all three-digit numbers each of whose digits is odd.

Calendar Calculations

Age 7 to 11
Challenge Level

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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.

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"?

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?

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?

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?

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?

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?

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

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

Next-door Numbers

Age 5 to 7
Challenge Level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Snake Coils

Age 7 to 11
Challenge Level

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

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?

Unexpected Ordering

Age 5 to 7
Challenge Level

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?