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Resources tagged with Generalising similar to Round the Four Dice:

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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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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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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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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 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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Repeaters

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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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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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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More Magic Potting Sheds

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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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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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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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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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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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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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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Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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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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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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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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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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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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Three Times Seven

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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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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Chess

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

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

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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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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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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.

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Magic Constants

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

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?

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Mini-max

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

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

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Special Sums and Products

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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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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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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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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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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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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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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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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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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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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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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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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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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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.