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Resources tagged with Generalising similar to Adding and Subtracting Positive and Negative Numbers:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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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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Oddly

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

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

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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?

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Cunning Card Trick

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

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

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Card Trick 2

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

Can you explain how this card trick works?

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Up and Down Staircases

Stage: 2 Challenge Level: Challenge Level:1

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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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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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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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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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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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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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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Centred Squares

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

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

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Consecutive Negative Numbers

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

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

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Crossings

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

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?

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Break it Up!

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

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.

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Taking Steps

Stage: 2 Challenge Level: Challenge Level:1

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

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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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Lost Books

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

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?

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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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Make 37

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

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.

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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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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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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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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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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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Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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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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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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Cut it Out

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

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?

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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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Tourism

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

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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Go Forth and Generalise

Stage: 3

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

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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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Cubes Within Cubes Revisited

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

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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Number Tracks

Stage: 2 Challenge Level: Challenge Level:1

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?

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Domino Numbers

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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Nim-interactive

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

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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Cuisenaire Rods

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

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

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Nim-like Games

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

A collection of games on the NIM theme

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Number Differences

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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Number Pyramids

Stage: 3 Challenge Level: Challenge Level:1

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

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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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More Number Pyramids

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

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

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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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Christmas Chocolates

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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Mystic Rose

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

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.