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Resources tagged with Place value similar to Plenty of Pens:

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Broad Topics > Numbers and the Number System > Place value

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?

Six Is the Sum

Stage: 2 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Trebling

Stage: 2 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

The Deca Tree

Stage: 2 Challenge Level:

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Becky's Number Plumber

Stage: 2 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Arrange the Digits

Stage: 3 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

ABC

Stage: 2 Challenge Level:

In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Four-digit Targets

Stage: 2 Challenge Level:

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Oddly

Stage: 2 Challenge Level:

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

Which Is Quicker?

Stage: 2 Challenge Level:

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

Spell by Numbers

Stage: 2 Challenge Level:

Can you substitute numbers for the letters in these sums?

Reach 100

Stage: 2 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

Diagonal Sums

Stage: 2 Challenge Level:

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

The Thousands Game

Stage: 2 Challenge Level:

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Coded Hundred Square

Stage: 2 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

One Million to Seven

Stage: 2 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Snail One Hundred

Stage: 1 and 2 Challenge Level:

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

(w)holy Numbers

Stage: 2 Challenge Level:

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Some Games That May Be Nice or Nasty

Stage: 2 and 3 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones...

What Do You Need?

Stage: 2 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Digit Sum

Stage: 3 Challenge Level:

What is the sum of all the digits in all the integers from one to one million?

Cayley

Stage: 3 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Which Scripts?

Stage: 2 Challenge Level:

There are six numbers written in five different scripts. Can you sort out which is which?

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" .

That Number Square!

Stage: 1 and 2 Challenge Level:

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Football Sum

Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Number Detective

Stage: 2 Challenge Level:

Follow the clues to find the mystery number.

Lesser Digits

Stage: 3 Challenge Level:

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

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.

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.

Six Times Five

Stage: 3 Challenge Level:

How many six digit numbers are there which DO NOT contain a 5?

Even Up

Stage: 3 Challenge Level:

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Dicey Operations

Stage: 2 and 3 Challenge Level:

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Stage: 3 Challenge Level:

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

Alien Counting

Stage: 2 Challenge Level:

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Calculator Bingo

Stage: 2 Challenge Level:

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Three Times Seven

Stage: 3 Challenge Level:

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

Exploring Simple Mappings

Stage: 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

Light the Lights

Stage: 2 Challenge Level:

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Stage: 3 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Big Powers

Stage: 3 and 4 Challenge Level:

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

How Many Miles to Go?

Stage: 3 Challenge Level:

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

Eleven

Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

Two and Two

Stage: 2 and 3 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Tis Unique

Stage: 3 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Just Repeat

Stage: 3 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Basically

Stage: 3 Challenge Level:

The number 3723(in base 10) is written as 123 in another base. What is that base?

What an Odd Fact(or)

Stage: 3 Challenge Level:

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?