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Resources tagged with Multiplication & division similar to Clever Carl:

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Broad Topics > Calculations and Numerical Methods > Multiplication & division

Slippy Numbers

Stage: 3 Challenge Level:

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Stage: 3 Challenge Level:

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

Thirty Six Exactly

Stage: 3 Challenge Level:

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Like Powers

Stage: 3 Challenge Level:

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

X Marks the Spot

Stage: 3 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Times Right

Stage: 3 and 4 Challenge Level:

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Difficulties with Division

Stage: 1 and 2

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Diggits

Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

As Easy as 1,2,3

Stage: 3 Challenge Level:

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Skeleton

Stage: 3 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

What Is the Question?

Stage: 3 and 4 Challenge Level:

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

What Two ...?

Stage: 2 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers?

Sept03 Sept03 Sept03

Stage: 2 Challenge Level:

This number has 903 digits. What is the sum of all 903 digits?

Oh! Hidden Inside?

Stage: 3 Challenge Level:

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Which Is Quicker?

Stage: 2 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Two Many

Stage: 3 Challenge Level:

What is the least square number which commences with six two's?

How Do You Do It?

Stage: 2 Challenge Level:

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Learning Times Tables

Stage: 1 and 2 Challenge Level:

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

1, 2, 3, 4, 5

Stage: 2 Challenge Level:

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Stage: 2 and 3 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

A One in Seven Chance

Stage: 3 Challenge Level:

What is the remainder when 2^{164}is divided by 7?

Clever Santa

Stage: 2 Challenge Level:

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Remainders

Stage: 2 Challenge Level:

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Tom's Number

Stage: 2 Challenge Level:

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Sending Cards

Stage: 2 Challenge Level:

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Zios and Zepts

Stage: 2 Challenge Level:

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

What's in the Box?

Stage: 2 Challenge Level:

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Stage: 2 Challenge Level:

Use the information to work out how many gifts there are in each pile.

Divide it Out

Stage: 2 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Repeaters

Stage: 3 Challenge Level:

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.

Clock Face

Stage: 2 Challenge Level:

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Napier's Bones

Stage: 2 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Factor-multiple Chains

Stage: 2 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

Highest and Lowest

Stage: 2 Challenge Level:

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Pies

Stage: 2 Challenge Level:

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Practice Run

Stage: 2 Challenge Level:

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

What's My Weight?

Stage: 2 Short Challenge Level:

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

All the Digits

Stage: 2 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Penta Post

Stage: 2 Challenge Level:

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Month Mania

Stage: 1 and 2 Challenge Level:

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Exploring Number Patterns You Make

Stage: 2 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Current Playing with Number Upper Primary Teacher

Stage: 2 Challenge Level:

Resources to support understanding of multiplication and division through playing with number.

Ordering Cards

Stage: 1 and 2 Challenge Level:

This problem is designed to help children to learn, and to use, the two and three times tables.

Square Subtraction

Stage: 2 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Jumping

Stage: 2 Challenge Level:

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

What Is Ziffle?

Stage: 2 Challenge Level:

Can you work out what a ziffle is on the planet Zargon?

Multiply Multiples 1

Stage: 2 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Always, Sometimes or Never? Number

Stage: 2 Challenge Level:

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