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Resources tagged with Generalising similar to Three Primes:

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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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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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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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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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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Chocolate Maths

Stage: 3 Challenge Level: Challenge Level:1

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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Round and Round the Circle

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

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.

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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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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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Winning Lines

Stage: 2, 3 and 4

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

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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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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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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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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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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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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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Sum Equals Product

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

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .

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Counting Counters

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

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

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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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Games Related to Nim

Stage: 1, 2, 3 and 4

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.

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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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Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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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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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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Tiling

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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Simple Train Journeys

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

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?

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Doplication

Stage: 2 Challenge Level: Challenge Level:1

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?

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The Great Tiling Count

Stage: 2 Challenge Level: Challenge Level:1

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.