problem solving measurement year 5

Measurement in Year 5 (Ages 9–10)

In Year 5, your child will convert between metric and imperial units. They will also find the area and perimeter of lots of different shapes, will estimate capacity and volume, and will covert between units of time.

The key words for this section are capacity ,  mass ,  rectilinear , and  volume .

What your child will learn

Take a look at the National Curriculum expectations for measurement in Year 5 (age 9–10):

Convert between different units of metric measure

To convert 1.15kg into grams, you can use your knowledge that 1kg is equivalent to 1000g. 0.15kg is therefore equivalent to 150 grams. 1.15 kg is therefore equivalent to 1150 grams .

Your child should be able to convert between:

• kilometres and metres
• metres and centimetres
• millimetres and centimetres
• kilograms and grams
• litres and millilitres.

Use approximate equivalences between metric and common imperial units

Your child will use metric units such as metres, grams, and litres, and imperial units such as inches, pounds, and pints. They will also learn about approximate equivalences between metric and imperial units:

Measure and calculate the perimeter of composite rectilinear shapes

Composite shapes are shapes that can be divided into more than one basic shape (for example, a square and a rectangle).

Calculate the area of rectangles and estimate the area of irregular shapes

Your child will be able to calculate the area of rectangles using standard units, such as square centimetres (cm²) and square metres (m²). They should also be able to calculate area from a scale drawing. For example, they might be given a scaled drawing of a vegetable plot where 1cm is equivalent to 50cm and need to calculate the area.

Your child will use the relationship between perimeter and area to find unknown values. For example:

A square has a perimeter of 36cm. Find the area of the square. As a square has four equal length sides, we can calculate that each side must be 36cm ÷ 4 = 9cm. Then, they can calculate the area, which would be 9cm × 9cm which equals 81cm² .

Your child will be able to estimate the area of irregular shapes.

Estimate volume and capacity

• Volume means the amount of space occupied by a 3D shape. It is measured in cubed units like cm ³ .
• Capacity means the amount a container can hold. Capacity is measured in metric units such as litres or imperial units such as pints.

Solve problems involving converting between units of time

Your child will use multiplication and division to convert between units of time. For example:

Convert 180 minutes into hours. 180 ÷ 60 = 3 hours

Use all four operations to solve measure problems using decimal notation

Your child will use addition, subtraction, multiplication, and division to solve problems involving:

These problems will include:

• Conversions – for example, ‘Convert 24 days into weeks, expressing the answer as weeks and days.’
• Scaling – for example, ‘If an item costs £28.40 and there is a 50% discount, what is the new price?’
• Decimals – for example, ‘If one plank of wood measures 1·6 m and four planks of wood are needed, what is the total length of wood needed?’

How to help at home

There are lots of everyday ways you can help your child to understand measurement. Here are just a few ideas.

1. Understand the difference between capacity and volume

The difference between volume and capacity is quite subtle, and can be difficult to understand:

You could explore capacity with your child using a 1l jug. Gather together some cups and containers. Can your child estimate the capacity of each container? Check how close their estimate was using the 1l jug.

2. Convert between units of measurement

Your child will be using:

• metric units such as kilograms, litres and metres
• imperial units such as inches, pounds, and pints.

Your child may be less familiar with imperial units. Ask them if they know of any items that use imperial measurements – for example, milk is usually sold in pints and the weight of people is often measured in stones and pounds. Point out these examples when you spot them in real life.

On your next trip to the supermarket, ask your child to do any weighing. Can they tell you the weight of some fruit or vegetables in grams and kilograms? Can they convert between metric measurements (like grams) and imperial measurements (like ounces)?

A table like this is useful for getting to grips with approximate equivalences between metric and imperial units:

3. Practise managing money

Budgeting with precise amounts of money can make for great calculating practice.

Try involving your child in some budgeting activities – for example, budgeting for a family day out. Tell them how much they have to spend, and ask them to work out the cost of different options.

Activity: My money

Keep on top of all your money matters.

4. Understand perimeter and area

Perimeter means the distance around the outside of a shape. Area is the size a surface takes up. Your child will learn to find the perimeter and area of rectilinear  shapes, which are shapes with straight sides and right angles.

When finding the area of composite rectilinear shapes (shapes that can be divided into more than one rectangle), encourage your child to divide the shape into smaller squares and rectangles. Here is an example of finding the area and perimeter of a composite rectilinear shape:

Area To find the area of the total shape, your child will need to separate the shape into two rectangles:     The total area of the shape can be found by adding the area of the two rectangles. 10m × 8m = 80m² 12m × 5m = 60m² 80m² + 60m² = 140m²

Perimeter To find the perimeter, your child will first need to find the lengths of the missing sides:     Your child will then add each length of the shape together. 8m + 10m + 3m + 12m + 5m + 22m = 60m

Be sure to remind your child to record their solutions using the appropriate units, such as cm, cm², m, and m².

5. Make a bedroom plan

Ask your child to estimate the area of the floor space in their bedroom, as well as the length of its perimeter. Once they have made their estimates, they can use a tape measure to check them.

Then, see if they can make a plan of their bedroom, measuring the edges of the room and the large pieces of furniture, such as the bed, wardrobes, and so on. This will help your child see how useful accurate measurements of perimeter and area are in the real world. Can they use the skills they have learnt to make a plan of their dream bedroom?

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Measurement Word Problems: Stretch (Year 5)

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Children will help Rachel plan her sister's surprise birthday party with this stretch level worksheet. They will solve different measurement problems involving the price of drinks, the weight of sandwiches and the length of decorations among others.

Answers are included.

An equivalent standard level worksheet is also available.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Units of Measure
• Topic Group: Measurement
• Year(s): Year 5
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 25/10/2023
• Resource Code: M2WHT455
• Curriculum Point(s): Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.

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Year 5 Problem solving - geometry, measurement & statistics

Subject: Mathematics

Age range: 7-11

Resource type: Unit of work

Last updated

26 January 2024

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Like its partner, Year 5 Problem Solving - Number , Y5 Problem solving – measurement, geometry and statistics comprises differentiated activities based upon the relevant problem-solving objectives in the year 5 maths curriculum.

Activities include scaffolded word problems and investigations alongside explanations, teaching notes and answers.

What’s included? 11 comprehensive activities differentiated to three levels Teaching notes, explanations and step-by-step answers Space for workings.

Topics featured: Measurement: length, mass and volume, area and perimeter, metric and imperial units, time Geometry: properties of shapes, reflections and translations, angles Statistics: reading and interpreting tables, interpreting line graphs.

What’s inside? Unit 1 – Measurement: length problems (pages 5-19) Unit 2 – Measurement: length, perimeter and area (pages 20-29) Unit 3 – Measurement: mass problems (pages 30-44) Unit 4 – Measurement: mass and volume (pages 45-54) Unit 5 – Measurement: metric and imperial units (pages 55-67) Unit 6 – Measurement: units of time (pages 68-79) Unit 7 – Geometry: properties of shapes (pages 80-91) Unit 8 – Geometry: reflections and translations (pages 92-99) Unit 9 – Geometry: angles (pages 100-110) Unit 10 – Statistics: interpreting tables (pages 111-117) Unit 11 – Statistics: interpreting line graphs (pages 118-126)

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Years 5 & 6: Measures

This list consists of activities, games and videos designed to support the new curriculum programme of study in Years 5 and 6. Containing tips on using the resources and suggestions for further use it covers:

Year 5 : converting between different units of metric measure, understanding and using equivalences between metric and imperial units, measuring and calculating perimeter and calculating and comparing the area of rectangles.

Year 6 : solving problems involving measure,converting between standard units of measure,converting between miles and kilometres, use formulae for area and volume when possible, calculating areas of parallelograms and triangles and calculate, estimate and compare the volume of cubes and cuboids. using standard units, extending to other units.

Visit the primary mathematics webpage to access all lists.

Mensuration

Quality Assured Category: Mathematics Publisher: Centre for Innovation in Mathematics Teaching

Developed for primary and non-specialist maths teachers, these two booklets are aimed to provide subject knowledge, highlight misconceptions and offer practical tasks on measurement. All highlighted pages refer to booklet A.

Making 2-D nets into a 3-D shapes in the practical tasks on pages 19-26  will help children see that 3-D shapes have volume. Cubes and cuboids of different size could be constructed and then the volumes calculated and compared.

Pages 51 -59 offer examples of calculating the volume of cuboids and examples for use in class. The volume of other shapes is not required at primary level but may be of interest to teachers wishing to extend gifted children.

Pages 27-32 offer example questions on conversion between  metric and imperial measures, including worded problems.

Data, Graphs, Charts, Measures and Money

Quality Assured Category: Mathematics Publisher: Department for Education

Converting measures is a topic that many children find difficult and there is usually a wide range of abilities in every class. These resources may be used to demonstrate and practise converting a variety of metric measures of mass, capacity and length.

The Measures counting stick and Converting measures show the conversions between metric units of capacity and mass, the starting number and steps to take along the stick can be selected. It also shows a conversion graph between miles and kilometres.

Converting units of measure shows the conversions between a variety of metric measures of mass, capacity and length. The units are chosen and then an amount is input, the conversion can then be revealed. Included are two problems in context, the second using imperial measures of length. Teacher guidance is included.

Area and Perimeter Resource Bank

Quality Assured Category: Mathematics Publisher: Resources for Learning Development Unit (RLDU)

This treasure chest of resources contains 19 activities, which investigate area and perimeter. Page 6 asks children to find the area of various rectangles and then come up with the formula to calculate it. Children in Year 6 are asked to recognise when it is possible to use formulae to find the area of shapes so page 16, which investigates how to find the area of circles should give then something to think about. 

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

Double Measures on sheet 22(page 53 on the pdf) investigates shapes with a constant area and different perimeter and shapes with the same perimeter and different areas. It also provides further questions for children to explore.

Dotty Squares on sheet 27(page 63 ) investigates the different sized squares that may be drawn on dotty paper and finding the area of each. It could also be carried out using triangles or rectangles.

Perimeter Dots on sheet 35(page 73) Exploration of different triangles measured in terms of 'perimeter' dots and 'inside' dots.  It looks at different types of triangle: equilateral, isosceles, acute-angled, obtuse-angled and right-angled.

Location, Location, Location (Key Stage Two)

Quality Assured Category: Science Publisher: BLOODHOUND SSC

When considering speed, what better place to start then with the fastest car on Earth! The first part of this lesson uses the BLOODHOUND SSC land speed attempt as a context for teaching about speed. Starting with speeds of familiar things, like a child walking or running then looking at other moving objects is a nice way of introducing children to the units of speed. Through the lesson children develop their understanding of speed by comparing the speeds of different objects and ordering them.

Volume and Capacity: an Activity Pack

Quality Assured Category: Mathematics Publisher: BEAM Education

21 cards containing  practical activities  for children to explore volume and capacity. These tasks allow children to develop their mathematical skill by actively estimating, measuring and comparing capacity and volume. They really get children thinking about measure.

Activities include: • free play with a variety of containers in contrasting shapes and sizes • comparing the capacities of containers by pouring the contents of one into another • measuring and comparing the capacities of containers by filling them with any smaller non-standard containers • measuring and comparing the capacities of cuboid boxes by filling them with small cubes • estimating and finding the capacities of all sorts of containers • using displacement of water as a means of measuring volume

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Length word problems

Measuring length.

These math word problems worksheets involve the measurement of length in both customary (inches, feet, yards) and metric (millimeters, centimeters, meters) units.  No conversions of units between the two systems are needed.

Inches, feet, yards:

Mm. cm. meters:

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Measurement

Estimating, Comparing, Measuring KS1

This collection of KS1 tasks combines the skills of estimating, comparing and measuring.

Estimating, Comparing, Measuring KS2

This collection of KS2 tasks combines the skills of estimating, comparing and measuring.

The KS1 activities in this collection are all related to time.

The KS2 activities in this collection are all related to time.

Area and Perimeter KS2

These resources introduce and explore the concepts of area and perimeter.

Volume and Capacity KS2

These resources introduce and explore the concepts of volume and capacity.