place value reasoning and problem solving year 5

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Year 5 – 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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Problem Solving with Place Value

February 3, 2021.

Understanding place value provides the essential foundation for so many aspects of mathematics, from multiplying and dividing by powers of ten, understanding the equivalence between fractions, decimals and percentages, and learning how to write and calculate with numbers in standard form.

The videos below show how I use the place value table to teach these topics conceptually.

Writing numbers as words

Multiplying by 10, 100 and 1000

Converting between fractions, decimals and percentages

I designed this problem-solving lesson to deepen students’ understanding of place value to connect it to other aspects of mathematics, including listing permutations, odd and even numbers and money. By linking to these topics, the questions are challenging yet remain accessible to students in key stage 3 and those studying the foundation GCSE course.

The lesson consists of six problem-solving questions, all centred around place value. Here is a sample of three of the questions.

Here is a sample of three of the questions.

Linking place value to arithmetic

In this question, students link their understanding of place value to writing numbers in figures from words. Next, they use column subtraction to find the difference between two numbers.

Linking place value to permutations

In this question, students arrange the four single-digit cards to make the numbers between 230 and 430.

Students link their understanding of place value to listing permutations.

Linking place value to odd and even numbers

To work out the smallest, even number, students need to find two three-digit numbers with the least difference.

To calculate the biggest, odd number, they need to find two numbers with the greatest difference.

Both questions can be completed through a method of trial and improvement. More able students would use:

• odd + odd = even
• odd + even =odd
• even + odd = odd
• even + even = even.

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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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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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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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