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KS3 Maths Place Value (MEP – Year 7 – Unit 2)
Subject: Mathematics
Age range: 11-14
Resource type: Lesson (complete)

Last updated
7 September 2014
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Place value word problems
This lesson will show you how to solve six interesting place value word problems. Before you start this lesson, review the place value chart .
Problem #1: A number has 5 tens and 2 more ones than tens. What is the number? Solution 2 more ones than tens is equal to 5 + 2 or 7. Therefore, the number has 5 tens and 7 ones. The number is 57.
Problem #2: A number has 8 ones and 2 fewer tens than ones. What is the number? Solution 2 fewer tens than ones is equal to 8 - 2 = 6. Therefore, the number has 6 tens and 8 ones. The number is 68.
Problem #3: A number has 6 tens and the same number of ones as tens. What is the number? Solution The number has 6 tens and 6 ones. The number is 66.
Problem #4: A 4-digit number has a 6 in the thousands place, a 9 in the ones place and 0s elsewhere. What is the number? Solution The number is 6009
Challenging place value word problems
Problem #5: What 3-digit number has the number 5 as its digit in the tens place and the digit in the hundreds place twice as big as the digit in the ones place? (There may be more than 1 correct answer) Solution First, we need to realize that the number has 3 digits and the digit in the middle is 5. So far the number looks like this: a5b The digit in the hundreds place is a and the digit in the ones place is b. Possible choices for a and b: a = 8 and b = 4 a = 6 and b = 3 a = 4 and b = 2 a = 2 and b =1
The number can be 854, 653, 452, or 251
Problem #6: What 3-digit number am I if the digit in my tens place is five more than the digit in my ones place and the digit in my tens place is twice the digit in my hundreds place?
When the digit in the tens place is five more than the digit in the ones place, we have the following scenario for the ones and the tens place: 94, 83, 72, 61, and 50
When the digit in the tens place is twice the digit in the hundreds place, we have the following scenario for the tens and the hundreds place:
48, 36, 24, and 12
The one that satisfies both scenarios is 36 and 61. Therefore, the number is 361.
What is the place value?
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Problems Related to Place Value
Worked-out problems related to place value of digits in a numeral.
Examples on place value: 1. Find the difference between the place value and face value of digit 6 in the numeral 2960543. Solution: Place value of digit 6 in 2960543 = 60000
Face value of digit 6 in 2960543 = 6
Their difference = 60000 - 6 = 59994
2. Find the product of the place values of two 4s in the numeral 30426451.
Solution:
The place value of 4 in hundreds place = 400
The place value of 4 in hundred thousand place = 400000
Their product = 400000 × 400 = 160000000.

3. Write the smallest 5-digit number:
(a) having 5 different digits
(b) having 8 in thousands place
(c) having 9 in ones place Solution: (a) The smallest 5 different digits are 0, 1, 2, 3, 4
Therefore, the smallest 5-digit number having 5-different digits 10234 (b) The smallest 5-digit number having 8 in thousands place is 18023. (c) The smallest 5-digit number having 9 in ones place is 10239.
4. Write the largest 4-digit number:
(a) having 4-different digits
(b) having 3 in tens place
(c) having 5 in hundreds place Solution: (a) The largest 4-different digits are 9, 8, 7, 6.
Therefore, the largest 4-digit number having 4 different digits = 9876 (b) The largest 4-digit number having 3 in tens place = 98 3 7 (c) The largest 4-digit number having 5 in hundreds place = 9 5 87
5. Form a number with:
3 at ten thousands place
5 at lakhs place
7 at thousands place
9 at ones place
1 at hundreds place
9 at tens place.
The number is 5,37,199.
6. Form a number with:
7 at crores place, 8 at ten-thousands place
3 at lakhs place, 4 at ten-lakhs place
7 at hundreds place, 9 at ones place
1 at thousands place, 0 at tens place
The number is 7,43,81,709.
Each digit has a value depending on its place called the place value of the digit are explained and shown above in the problems related to place value using step-by-step explanation.
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Resources tagged with: Place value
Filter by: Content type: ALL Problems Articles Games Age range: All 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level:
There are 126 NRICH Mathematical resources connected to Place value , you may find related items under The Number System and Place Value .

More Less Is More
Age 7 to 14 challenge level.
In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.

Less Is More
Age 7 to 11 challenge level.
Use your knowledge of place value to try to win this game. How will you maximise your score?

The Number Jumbler
The Number Jumbler can always work out your chosen symbol. Can you work out how?

Digit Addition
Age 5 to 11 challenge level.
Try out this number trick. What happens with different starting numbers? What do you notice?

Dicey Addition
Who said that adding couldn't be fun?

Age 11 to 14 Challenge Level
Where should you start, if you want to finish back where you started?

Forwards Add Backwards
What happens when you add a three digit number to its reverse?

By selecting digits for an addition grid, what targets can you make?

Subtraction Surprise
Try out some calculations. Are you surprised by the results?

Multiply Multiples 3
Have a go at balancing this equation. Can you find different ways of doing it?

Round the Dice Decimals 1
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Round the Three Dice
What happens when you round these three-digit numbers to the nearest 100?

Round the Dice Decimals 2
What happens when you round these numbers to the nearest whole number?
Multiply Multiples 2
Can you work out some different ways to balance this equation?
Multiply Multiples 1
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Two Spinners
Age 5 to 7 challenge level.
What two-digit numbers can you make with these two dice? What can't you make?

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

Always a Multiple?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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

Our Numbers
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

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

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

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

What Do You Need?
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?

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

Diagonal Sums
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?

An Easy Way to Multiply by 10?
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

How Many Miles to Go?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

What an Odd Fact(or)
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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

Sixty-seven Squared
Age 16 to 18 challenge level.
Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

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

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


Think of Two Numbers
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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
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?

Number Rules - OK
Age 14 to 16 challenge level.
Can you produce convincing arguments that a selection of statements about numbers are true?

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.

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

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Legs Eleven
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?

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.

2-digit Square
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Latin Numbers
Can you create a Latin Square from multiples of a six digit number?

Number Detective
Follow the clues to find the mystery number.

Writing Digits
Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
BT.. Eat Your Heart Out
If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

Purr-fection
What is the smallest perfect square that ends with the four digits 9009?

Six Is the Sum
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Double Digit
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
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place value word problems
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First Grade Place Value Word Problems

2nd Grade Place Value Math Word Problem Task Cards | Print & Digital

Also included in: 2nd Grade Math Word Problem Task Cards BUNDLE | Printable & Digital

Word Problems Place Value First Grade

Also included in: Word Problems Bundle First Grade

Place Value Word Problems | Daily Math Review

Also included in: Word Problems Bundle for Daily Math Spiral Review in Grade 4 (Math SOLs)

Multi-Step Word Problems Math Worksheets 2nd and 3rd Grade

Also included in: 3rd Grade TOP 25 Math, Language, Science, Social Skills Variety Pack

Math Task Cards - Scoot/Scoot JR - place value, skip counting, & word problems

Also included in: MATH BUNDLE 2nd grade math scoot, anchor charts, and task cards

Would You Rather Math Journal Word Problems 5th Grade Math Review Number Talks

Also included in: Grades 3-5 Would You Rather Math Journal Prompts - Math Review Warmups BUNDLE

3rd Grade Rounding & Place Value Math Word Problem Task Cards | Print & Digital
Also included in: 3rd Grade Math Word Problem Task Cards BUNDLE | Printable & Digital

Addition and Subtraction Word Problems Worksheets First Grade Math 1.OA.1

Also included in: Addition Subtraction and Algebraic Thinking Worksheets for First Grade

4th Grade Word Problems Math Spiral Review Place Value Print and Digital

Also included in: 4th Grade Math Word Problems | Math Spiral Review | Math Test Prep YEARLONG

1st Grade Math Word Problems NBT and Place Value - Short Answer Response

Also included in: 1st Grade Math - Common Core Math Centers, Worksheets, Word Problems, More

3rd Grade Math Word Problems Math Spiral Review Place Value Test Prep
Also included in: 3rd Grade Word Problems | Math Spiral Review | Math Test Prep YEARLONG BUNDLE

Decimal Place Value Word Problems with Comparing and Rounding | Daily Math

Spring Egg Math Craft Addition Word Problems

2nd Grade Math Activities Word Problems Centers Place Value Review

1st Grade Math Worksheets Place Value and Addition and Subtraction to 40

1st Grade Magic of Math Lesson Plans for Place Value and Counting

Also included in: 1st Grade Magic of Math Lesson Plans for THE ENTIRE SCHOOL YEAR

Place Value Logic Puzzles

Place Value Number Riddles

2nd Grade Math BUNDLE Word Problems, Time Tests, Assessments CCSS All Standards

5th Grade Word Problems Math Spiral Review Place Value Print and Digital
Also included in: 5th Grade Word Problems Math | Math Spiral Review | Math Test Prep YEARLONG

Differentiated Word Problem Task Cards: Place Value, Addition, and Subtraction

Also included in: Differentiated Math Word Problem Task Card Bundle

Weekly Word Problems

Understanding Place Value Unit for 5th Grade | Lessons, Practice, Assessment

Also included in: 5th Grade Math Bundle
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Place Value
September 3, 2022.
Scheme of work: Key Stage 3: Year 7: Term 1: Place Value
Prerequisite Knowledge
- Find 1000 more or less than a given number.
- Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- Order and compare numbers beyond 1000
- Identify, represent and estimate numbers using different representations
- Round any number to the nearest 10, 100 or 1000
- Solve number and practical problems involving the above and increasingly large positive numbers.
- Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include zero and place value.
Key Concepts
- The ability to arrange digits in a place value table is crucial to accessing future topics such as fractions, percentages and many more.
- When multiplying and dividing by 10, 100 and 1000, students can benefit from visualising the digit shift between columns in the place value table.
- To interpret a number scale, students need to have a secure understanding of using the place value table.
- Students often confuse the direction of the inequality symbols when comparing numbers.
Working Mathematically
- Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals.
- Reason mathematically
- Extend their understanding of the number system; make connections between number relationships,
- Solve problems
- Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
Subject Content
- understand and use place value for decimals, measures and integers of any size
- order positive and negative integers, decimals and fractions; use the number line as a model for ordering the real numbers; use the symbols =, > and <
- use the four operations, including formal written methods, to integers and decimals.

Writing Numbers using Words and Digits
Comparing the size of numbers, reading and writing numbers on a scale, multiplying a number by a power of ten, dividing a number by a power of ten, alternative number systems, additional resources.

Multiplying and Dividing by 10, 100 and 1000

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- 11-14 Years
Play these fun Maths Games for 7-11 year olds
Choose a category:, place value games.

Place Value Basketball
Place Value Basketball is a fun, base ten blocks game which helps children aged 5 to 8 to know what each digit in a either a two or three digit number represents.

Bead Numbers - Place Value
Bead Numbers is a place value investigation involving a tens and ones abacus. The game provides a good context for encouraging learners to think systematically.

Carroll Diagrams - Odd and Even
Sort numbers on these Carroll Diagrams by whether they are odd or even, by place value or by more or less than a given number.

Place Value Charts
Test your knowledge of place value or hundreds, tens and units. Suitable for use on an interactive whiteboard and desktops.

Daily 10 has maths questions on a range of maths concepts: addition, subtraction, ordering, partitioning, digit values, rounding, multiplication, division, doubles, halves and fractions. Great starter or plenary activity. Useful for mental maths.

Dienes and Coins
Useful place value teaching resources for use on an interactive whiteboard. They cover hundreds, tens and ones and money. With some you will need to drag the Diennes blocks to represent the number you want. Please note the decimals section is faulty.

ITP Beadsticks
Mathsframe has produced a tablet friendly beadsticks resource which can help with understanding place value, partitioning and modelling addition and subtraction.

Shark Numbers
A hundreds, tens and units maths game. Count carefully otherwise the shark will bite your boat.

Decimal Demonstrator
A useful teaching tool to demonstrate decimals and place value.

Starship Sten
Find 1000 more or less than a given number.

Scooter Quest
A place value game which will test your knowledge of digit values. There are 3 levels of difficulty which go from two to four decimal places. Note the currency is dollars but this does not mean the game is not useful in other currency areas.

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Maths worksheets and activities. The topic of Place Value from the Year 7 book of the Mathematics Enhancement Program. For information about these resources
Place value word problems · Problem #1: A number has 5 tens and 2 more ones than tens. · Problem #2: A number has 8 ones and 2 fewer tens than ones. · Problem #3:
Solution: (a) The largest 4-different digits are 9, 8, 7, 6. Therefore, the largest 4-digit number
live. Age 7 to 11. Challenge Level. There are six numbers written in five different scripts. Can you
Can you replace the letters with numbers? Is there only one solution in each case? Sixty-seven Squared. Age 16 to 18. Challenge Level.
5th Grade Word Problems Math Spiral Review Place Value Print and ... Each of the 36 math word problem solving task cards included in
Place Value Activities. Winnipeg School Division. Numeracy Project. 7.
An instructional video showing how to multiply using place value.Please give feedback so future videos can be improved:
Scheme of work: Key Stage 3: Year 7: Term 1: Place Value ... challenged to solve a range of problem solving questions involving place value.
Place Value Basketball is a fun, base ten blocks game which helps children aged 5 to 8 to know what each