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Resources tagged with Generalising similar to Using Questioning to Stimulate Mathematical Thinking:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising

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Maths Trails

Stage: 2 and 3

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.

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Spirals, Spirals

Stage: 2 Challenge Level: Challenge Level:1

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

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Always, Sometimes or Never? KS1

Stage: 1 Challenge Level: Challenge Level:1

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

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Always, Sometimes or Never? Shape

Stage: 2 Challenge Level: Challenge Level:1

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

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More Numbers in the Ring

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

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

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Button-up Some More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Polygonals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Play to 37

Stage: 2 Challenge Level: Challenge Level:1

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.

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Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

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

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Steps to the Podium

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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The Add and Take-away Path

Stage: 1 Challenge Level: Challenge Level:1

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?

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

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

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Sliding Puzzle

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

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.

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

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

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Rope Mat

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Strike it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Three Dice

Stage: 2 Challenge Level: Challenge Level:1

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

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Round the Four Dice

Stage: 2 Challenge Level: Challenge Level:1

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

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How Odd

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Magic Vs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Round the Two Dice

Stage: 1 Challenge Level: Challenge Level:1

This activity focuses on rounding to the nearest 10.

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Always, Sometimes or Never?

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Stop the Clock for Two

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Strike it Out for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Nim-7 for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Walking the Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Dice Stairs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Always, Sometimes or Never? Number

Stage: 2 Challenge Level: Challenge Level:1

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

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Build it Up

Stage: 2 Challenge Level: Challenge Level:1

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

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Build it up More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Got it for Two

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Roll over the Dice

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Round the Dice Decimals 1

Stage: 2 Challenge Level: Challenge Level:1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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Round the Three Dice

Stage: 2 Challenge Level: Challenge Level:1

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

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

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

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What Could it Be?

Stage: 1 Challenge Level: Challenge Level:1

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

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Unit Differences

Stage: 1 Challenge Level: Challenge Level:1

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

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Division Rules

Stage: 2 Challenge Level: Challenge Level:1

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

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Sums and Differences 2

Stage: 2 Challenge Level: Challenge Level:1

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?

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Sums and Differences 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Round the Dice Decimals 2

Stage: 2 Challenge Level: Challenge Level:1

What happens when you round these numbers to the nearest whole number?

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Circles, Circles

Stage: 1 and 2 Challenge Level: Challenge Level:1

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?

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Nim-7

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

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

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Move a Match

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Dotty Circle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Magic Circles

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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GOT IT Now

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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Calendar Calculations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?