reasoning and problem solving year 5 place value

Number & place value in Year 5 (age 9–10)

In Year 5, your child will be reading, writing, and comparing numbers up to 1,000,000. They will round large numbers, interpret negative numbers in lots of contexts, and learn Roman numerals up to 1000 (M).

The key words for this section are number and place value .

What your child will learn

Take a look at the National Curriculum expectations for number and place value in Year 5 (ages 9–10):

Read, write, and compare numbers up to at least 1,000,000

Place value is the basis of our number system and allows us to represent all our numbers with just the digits 0–9. Your child will understand that the position of the digit in a number tells us the value of the digit.

Your child will know the value of each digit in numbers up to at least a million. They will be able to order and compare numbers using their understanding of place value.

Note that the children will use the vocabulary ones and not units when talking about place value.

Count in powers of 10 from any number up to 1,000,000

Your child will be expected to count forwards and backwards in powers of 10 from any number up to a million.

Count forwards in steps of 10 ²  (100) from 25,760: 25,860, 25,960, 26,060, and so on. Count backwards in steps of 10 ³  (1000) from 8151: 7151, 6151, 5151, and so on.

Interpret and use negative numbers

Your child will interpret negative numbers in real-world contexts. For example, they might learn about negative numbers using temperature or money.

Your child will also count forwards and backwards with positive and negative whole numbers, including counting through 0. For example:

Count backwards from 6 to -3: 6, 5, 4, 3, 2, 1, 0, -1, -2, -3.

Round numbers to the nearest 10, 100, 1000, 10,000, and 100,000

Your child will round numbers up to a million up or down to the nearest 10, 100, 1000, 10,000 and 100,000.

537,129 rounded to the nearest 1000: 537,000.   145,674 rounded to the nearest 10,000: 150,000.   832,541 rounded to the nearest 100,000: 800,000.

Solve increasingly complex number problems

Children will solve problems involving:

• Negative numbers
• Roman numerals.

Their knowledge of place value will be very useful for this. They will use physical objects, drawings, diagrams, and mathematical symbols to visualise problems.

Read Roman numerals to 1000 (M)

Your child will be able to read Roman numerals from 1 (I) to 1000 (M). They should be able to recognise years written in Roman numerals.

 1 = I  5 = V  10 = X  50 = L  100 = C  500 = D  1000 = M    1995 = MCMXCV  2019 = MMXIX

How to help at home

There are lots of ways you can help your child to understand number and place value . Here are just a few ideas:

1. Use place value charts

Place value charts can be a great way to help your child represent numbers and understand how the number system works. These charts will help your child to read, write, and compare numbers, as well as to understand how zero is used as a placeholder.

2. Use place value knowledge

When comparing numbers up to 1,000,000, your child should look at the digit with the largest value first. For example, if your child is comparing the numbers 232,765 and 233,276, they would first need to look at the digit with the largest value. In this example, as the hundred thousands and ten thousands digits are the same, we need to look at the thousands digit:

232,765 has 2 thousands, and 233,276 has 3 thousands, so 232,765 is less than 233,276.

Encourage your child to use their knowledge of number and place value to identify patterns when calculating. For example, if you know 4 + 3 = 7, then you also know 0.4 + 0.3 = 0.7. This is because each of the numbers in the calculation is now ten times smaller, so the total will be ten times smaller.

Give your child a simple addition calculation using one-digit numbers such as 5 + 4 = 9. How many related calculations can they record using this fact? For example:

15 + 4 = 19 5 + 14 = 19 50 + 40 = 90 500 + 400 = 900 0.5 + 0.4 = 0.9  +   =  … and so on.

Activity: Place value pandemonium

3. Explore negative numbers

Chatting about the numbers we see around us will help your child use numbers in all parts of their daily lives. Point out negative numbers in the real world, such as temperatures on the weather forecast. Vertical number lines, such as those seen on thermometers, can help your child grasp the concept of negative numbers.

Activity: Negative numbers

4. Make estimates

Being able to make accurate estimates is a valuable skill we use in everyday life. When calculating, encourage your child to use their rounding skills to estimate the answer before calculating precisely. This will help them to check if their answer seems reasonable.

If you are out shopping and you have picked up a few items, ask your child to estimate the total cost of the items. They will need to round the cost of each item to find the estimated total. For example, if you bought items costing £3.82, 82p, £4.10, and £2.45, your child could round each of these items to the nearest pound:

£3.82 to £4 82p to £1 £4.10 to £4 £2.45 to £2

Your child could then add the rounded amounts of £4, £1, £4, and £2 to find the estimated total of £11. When they calculate precisely and come to £11.19, they can feel fairly confident that their calculation was correct.

5. Play Roman numerals bingo

Your child will be expected to be able to read Roman numerals from 1 to 1000. Point out Roman numerals in the modern world. For example, Roman numerals are used on older buildings to show when they were built, or at the end of a film to show the year it was made.

Why not play Roman numeral bingo with your child? Create bingo boards using pieces of A4 paper. Choose and write down six different Roman numerals between 1 and 100 on each piece of paper (one piece of paper per player). One player chooses a number between 1 and 100 and announces it. If a player has that number shown in Roman numerals, they can cover that number. The first player to cover all numbers is the winner.

Here are the Roman numerals up to 1000, with some examples of years written in Roman numerals:

 1 = I 5 = V 10 = X 50 = L 100 = C 500 = D 1000 = M   1995 = MCMXCV 2019 = MMXIX

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In-depth Investigation: Adapt Nice or Nasty (Game 5, Nasty Version) from nrich.maths.org.

Deepen understanding of 6-digit numbers (suggested as 2 days)

In-depth Investigation: Activity Set A from ncetm.org.uk

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Extra Support worksheets come with guidance for a teacher or TA working with small groups. They can make a significant difference to children working below ARE. Extra support is linked to individual objectives-based units, but you can also explore a set for a whole year.

Procedural fluency is fundamental to numeracy, and Hamilton's practice worksheets are carefully differentiated for children working toward Age Related Expectations (ARE), at ARE and at greater depth. Practice is linked to individual objectives-based units, but you can also explore sets of worksheets for the whole year.

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Place Value KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Number Match

A task which depends on members of the group noticing the needs of others and responding.

Dicey Addition

Who said that adding couldn't be fun?

The Thousands Game

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

Take Three Numbers

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Number Differences

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Less Is More

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

Round the Four Dice

This activity involves rounding four-digit numbers to the nearest thousand.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Round the Three Dice Live

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

Four-digit Targets

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?

Coded Hundred Square

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

Which Scripts?

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

The Deca Tree

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.

Dicey Operations in Line

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

Reasoned Rounding

Four strategy dice games to consolidate pupils' understanding of rounding.

Nice or Nasty

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

Number Lines in Disguise

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

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Year 5 Problem Solving with Place Value Maths Challenge

This Year 5 Problem Solving with Place Value Maths Challenge aims to secure your child’s understanding of place value while developing their problem solving skills. Children with use clues to work out which numbers the characters have created and then order them. The problem includes negative numbers, Roman numerals, and rounding.

If you would like to access additional resources which link to this maths challenge, you can purchase a subscription for only £5.31 per month on our sister site, Classroom Secrets .

Teacher Specific Information

This Year 5 Problem Solving with Place Value Maths Challenge checks pupils’ understanding of place value while aiming to develop their problem solving skills. Pupils will use clues to work out which numbers the characters have created and then order them. The problem includes negative numbers, Roman numerals, and rounding.

National Curriculum Objectives

Number – number and place value (5N1) Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000 (5N2) Read, write, order and compare numbers to at least 1,000,000 (5N3a) Determine the value of each digit in numbers up to 1,000,000 (5N3b) Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals (5N4) Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 (5N5) Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero (5N6) Solve number problems and practical problems that involve 5N1 – 5N5

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• National Curriculum Resource Tool

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Year 5: Number and Place Value

• read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
• count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
• interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
• round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
• solve number problems and practical problems that involve all of the above
• read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Year 5: Addition and Subtraction

• add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
• add and subtract numbers mentally with increasingly large numbers
• use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Year 5: Multiplication and Division

identify multiples and factors:

• identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
• know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
• establish whether a number up to 100 is prime and recall prime numbers up to 19
• multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
• multiply and divide numbers mentally, drawing upon known facts
• divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
• multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
• recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
• solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
• solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
• solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Year 5: Fractions (including decimals and percentages)

• compare and order fractions whose denominators are all multiples of the same number
• identify, name and write equivalent fractions of a given fraction, represented visually,including tenths and hundredths
• recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number[for example, 2 ⁄ 5 + 4 ⁄ 5 = 6 ⁄ 5 = 1 1 ⁄ 5 ]
• add and subtract fractions with the same denominator and denominators that are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• read and write decimal numbers as fractions [for example, 0.71 = 71 ⁄ 100 ]
• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
• round decimals with two decimal places to the nearest whole number and to one decimal place
• read, write, order and compare numbers with up to three decimal places
• solve problems involving number up to three decimal places
• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
• solve problems which require knowing percentage and decimal equivalents of 1 ⁄ 2 , 1 ⁄ 4 , 1 ⁄ 5 , 2 ⁄ 5 and those fractions with a denominator of a multiple of 10 or 25.

Year 5: Measurement

• convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
• understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
• calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes
• estimate volume [for example, using 1 cm 3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
• solve problems involving converting between units of time
• use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.

Year 5: Geometry - properties of shapes

• identify 3-D shapes, including cubes and other cuboids, from 2-D representations
• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• draw given angles, and measure them in degrees (°)
• use the properties of rectangles to deduce related facts and find missing lengths and angles
• distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Year 5: Geometry - position and direction

• identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

Year 5: Statistics

• solve comparison, sum and difference problems using information presented in a line graph
• complete, read and interpret information in tables, including timetables.

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Place Value Questions

Place value questions with solutions are provided here for students to practice and enhance their skills. The place value of a digit in a number represents the position or place of that digit. For example, the place value of 2 in 726 is the tens place. Knowledge of place values will help kids to write numbers in words in both Indian and international systems.

Place value charts in Indian and International systems of numerals :

Learn more about Place Values .

Place Value Questions with Solution

Identifying the place value of a digit within a given number are taught to students of grades 1 to 5. These questions on place values will help them affirm their concept regarding place values and the numeral system.

Question 1: Find the place value of 5 for the following numbers:

Question 2: Find the place value of 2 and 7 for the following numbers:

(iii) 28467

Questions 3: Fill in the blanks:

(i) 20600 + ____ + 30 + 5 = 28635.

(ii) _____ + ____ + 86 = 4586.

(iii) 4000 + 3 + 400 + ____ = 4443.

(iv) 34589 = _____ + _____ + ____ + ______ +_____.

(i) 20600 + 8000 + 30 + 5 = 28635.

(ii) 4000 + 500 + 86 = 4586.

(iii) 4000 + 3 + 400 + 40 = 4443.

(iv) 34589 = 30,000 + 4000 + 500 + 80 + 9 .

• Numbers in Words
• Addition and Subtraction
• Number Lines
• Types of Numbers

Question 4: Identify the number which has 4 in tens place and 8 in thousands place. The digit in ones is half the sum of the digits in tens and thousands, and the digit in hundreds place is six less than the digit in ones place. Find the number.

Given, the number has 4 in the tens place and 8 in thousands place.

Digit in ones place = (8 + 4) ÷ 2 = 12/2 = 6

Digit in hundreds place = less than the digit in ones place = 6 – 6 = 0

Thus, the number is –

Question 5: Write following numbers in the place value chart in both Indian and International system:

(ii) 912597

(iii) 213709

(iv) 120986

Question 6: Find the sum and product of the place value and face value of 6 in the number 86245.

Place value of 6 = 6000

Face value of 6 = 6

6000 + 6 = 6006

6000 × 6 = 36000

Question 7: State ‘true’ or ‘false’ for the following statements:

(i) The place value and face value of any digit in ones place are the same.

(ii) Sum of the place values of 3 in the numbers 3986 and 9723 is 3030.

(iii) 300 + 60 + 5 = 356.

(iv) The face value of any digit is either less than or equal to the place value of the digit.

(v) The product of the place value of 4 in 4956 and the face value of 7 in 171 is 280000.

(i) The place value and face value of any digit in ones place are the same. (True)

(ii) Sum of the place values of 3 in the numbers 3986 and 9723 is 3030. (False)

(iii) 300 + 60 + 5 = 356. (False)

(iv) The face value of any digit is either less than or equal to the place value of the digit. (True)

(v) The product of the place value of 4 in 4956 and the face value of 7 in 171 is 280000. (False)

Question 8: Write the following numbers in words according to the Indian system:

(ii) 129644

(iii) 25456

(i) 94562 – Ninety-four thousand five hundred sixty-two.

(ii) 129644 – One lakh twenty-nine thousand six hundred forty-four.

(iii) 2545600 – Twenty-five lakhs forty-five thousand six hundred.

(v) 30764 – Thirty thousand seven hundred sixty-four.

Question 9: Write the following numbers in words according to the International system:

(ii) 5720964

(iii) 40972

(iv) 497114

(i) 34921 – Thirty-four thousand nine hundred twenty-one

(ii) 5720964 – Five million seven hundred twenty thousand nine hundred sixty-four

(iii) 40972 – Forty thousand nine hundred seventy-two

(iv) 497114 – Four hundred ninety-seven thousand one hundred fourteen

Question 10: Compare the following using ‘>’, ‘<’ or ‘=’:

(i) Place value of 3 in 3245 ____ Place value of 6 in 265

(ii) Places value of 5 in 456 ____ Place value of 2 in 234

(iii) Place value of 7 in 7980 ____ Place value of 5 in 5790

(iv) Place value of 4 in 234 ____ Face value of 9 in 494

(i) Place value of 3 in 3245 > Place value of 6 in 265

(ii) Places value of 5 in 456 < Place value of 2 in 234

(iii) Place value of 7 in 7980 > Place value of 5 in 5790

(iv) Place value of 4 in 234 = Face value of 4 in 495

Question 11: Write the following numbers in the place value charts:

(ii) 325.006

(iii) 0.976

Question 12: Fill in the blanks:

(i) 1 × 100 + 2 × 10 + 8 × 1 + 5 × 1/10 + 2 × 1/100 = _____.

(ii) 2 × 1000 + 28 × 10 + 1 × 1/10 + 1 × 1/100 = ________.

(iii) 0.008 + 1.07 + 0.5 = _______.

(iv) 300 + 4 + 45 + 0.0006 + 0.007 + 0.08 = ______.

(i) 1 × 100 + 2 × 10 + 8 × 1 + 5 × 1/10 + 2 × 1/100 = 128.52

(ii) 2 × 1000 + 28 × 10 + 1 × 1/10 + 1 × 1/100 = 2280.11

(iii) 0.008 + 1.07 + 0.5 = 1.578

(iv) 300 + 4 + 45 + 0.0006 + 0.007 + 0.08 = 349.0876

Practice Questions:

1. Find the place value of 6 for the following numbers:

(iii) 497612

2. The digits in the tens and the thousands place of a number are 3 and 9, respectively. The digit in the ones and the ten thousands places are 3 and 4 more than the digit in tens place. If the digit in the hundreds place is three less than the digit in ten thousands place, find the number.

3. Fill in the blanks:

(i) 3000 + 700 + _____ + 8 = 3758.

(ii) 200 + 9050 + 4 = ______.

(iii) 2000 + 0.009 + 12.23 + 300 = _____.

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Decimal Place Value Challenge Questions

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

3 November 2020

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Four problem solving and reasoning style questions linked to decimal place value that are appropriate for Year 5 or 6. The answers are also included.

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