Resources tagged with: Generalising

Filter by: Content type:
Age range:
Challenge level:

There are 92 results

Broad Topics > Thinking Mathematically > Generalising

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?

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?

Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

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

Always, Sometimes or Never? KS1

Age 5 to 7 Challenge Level:

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Number Tracks

Age 7 to 11 Challenge Level:

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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.

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?

Three Dice

Age 7 to 11 Challenge Level:

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

Digit Addition

Age 5 to 11 Challenge Level:

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

Oddly

Age 7 to 11 Challenge Level:

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

Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

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

Spirals, Spirals

Age 7 to 11 Challenge Level:

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

Generalising

Age 5 to 11

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

Walking the Squares

Age 7 to 11 Challenge Level:

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

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?

Crossings

Age 7 to 11 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?

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?

Neighbourly Addition

Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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.

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.

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?

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.

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?

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 ...?

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?

Snake Coils

Age 7 to 11 Challenge Level:

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

Round the Four Dice

Age 7 to 11 Challenge Level:

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

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.

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?

Division Rules

Age 7 to 11 Challenge Level:

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

Roll over the Dice

Age 7 to 11 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

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?

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?

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?

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!

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.

Charitable Pennies

Age 7 to 14 Challenge Level:

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

Tiling

Age 7 to 11 Challenge Level:

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

Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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.

Centred Squares

Age 7 to 11 Challenge Level:

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

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?

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.

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?

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?

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?

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.

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?

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.