# Resources tagged with: Place value

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Broad Topics > Numbers and the Number System > Place value ### Cayley

##### Age 11 to 14 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"? ### Mini-max

##### Age 11 to 14 Challenge Level:

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. . . . ### Tis Unique

##### Age 11 to 14 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. ### Eleven

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)? ##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 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? ### Football Sum

##### Age 11 to 14 Challenge Level:

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

##### Age 7 to 14 Challenge Level:

Try out some calculations. Are you surprised by the results? ### Song Book

##### Age 7 to 11 Challenge Level:

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed? ### Big Powers

##### Age 11 to 16 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. ### Just Repeat

##### Age 11 to 14 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? ### Which Is Quicker?

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 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? ### Double Digit

##### Age 11 to 14 Challenge Level: ### Which Scripts?

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 14 Challenge Level:

The Number Jumbler can always work out your chosen symbol. Can you work out how? ### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience. ### How Can I Support the Development of Early Number Sense and Place Value?

##### Age 3 to 11

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas. ### Journeys on the Gattegno Tens Chart

##### Age 5 to 11

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division. ### Place Value as a Building Block for Developing Fluency in the Calculation Process

##### Age 5 to 11

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating. ### Place Value: the Ten-ness of Ten

##### Age 3 to 11

This article develops the idea of 'ten-ness' as an important element of place value. ### Ordering

##### Age 5 to 11

This set of activities focuses on ordering, an important aspect of place value. ### Position

##### Age 5 to 11

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea. ### Number Sense and Place Value

##### Age 5 to 11

This feature aims to support you in developing children's early number sense and understanding of place value. ### More Upper Primary Activities on Number Sense and Place Value

##### Age 7 to 11

More upper primary number sense and place value tasks. ##### Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E ### What Do You Need?

##### Age 7 to 11 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? ### Basically

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . . ### Chocolate Maths

##### Age 11 to 14 Challenge Level:

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. . . . ##### Age 7 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible. ### Lesser Digits

##### Age 11 to 14 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

##### Age 11 to 14 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. ### Back to the Planet of Vuvv

##### Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . . ### Six Times Five

##### Age 11 to 14 Challenge Level:

How many six digit numbers are there which DO NOT contain a 5? ### Napier's Bones

##### Age 7 to 11 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? ### Three Times Seven

##### Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why? ### Nice or Nasty for Two

##### Age 7 to 14 Challenge Level:

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent. ### Less Is More

##### Age 5 to 11 Challenge Level:

Use your knowledge of place value to try to win this game. How will you maximise your score? ### Multiply Multiples 2

##### Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation? ### Multiply Multiples 1

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication? ### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it? ### Number Detective

##### Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number. ### Activities on the Gattegno Chart

##### Age 5 to 11

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division. ### Legs Eleven

##### Age 11 to 14 Challenge Level:

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?