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# Maths Year 5 Autumn Measures and Data

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Understand metric and imperial units (suggested as 3 days)

### Objectives

Revise and deepen understanding of metric units
Imperial units
Unit 1: ID# 5297

National Curriculum
Meas (i) (vii)
Stats (i)

Hamilton Objectives
35. Measure and compare capacities, weights and lengths; convert between different SI units.
36. Understand and use approximate equivalences between common imperial and SI units.
44. Create and interpret line graphs, solving comparison, sum and difference problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a kg weight. How else can we write 1kg? Remind children that ‘kilo’ means 1000. Hang a 0 card at 1 end of a washing line and 1000g with 1kg pegged beneath it at the other. Children peg different nos. of grams along the line. Repeat for litres and ml.
Group Activities
-- Play a game converting from grams to kilograms and vice versa (1 decimal place).
-- Fill in missing amounts on a 0–1kg line. Order containers by eye, then convert from litres to millilitres and vice versa, to check.

Day 2 Teaching
Write a variety of distances on the board and use these to convert between metres and kilometres. Start to convert between miles and km and begin to draw line graph for conversion and read intermediate points.
Group Activities
Use the in-depth problem-solving investigation ‘Inches and Barleycorns’ from NRICH as today’s group activity.
Or, use these activities:
-- Construct a line graph to convert from miles to km and vice versa.

Day 3 Teaching
Brainstorm imperial units other than miles, e.g. pints, pounds, stones, ounces, feet, inches, yards. Do children know the contexts where they are used? Using different familiar contexts (packet of crisps, baby’s weight, milk, etc.) explore equivalent SI units.
Group Activities
-- Use known facts to convert between centimetres and inches, kilograms and stones/pounds, litres and pints.
-- Measure height in cm, convert to inches, draw line graph to check. Work out how many grams are in a pound, use scales to check.

### You Will Need

• 1kg weight.
• Packets weighing less than 1kg.
• Activity sheet of weights cards to cut up (see resources).
• 0–1kg line (see resources).
• Range of containers between 100ml & 2l.
• Measuring cylinder.
• Blank graphs with pre-prepared axes (see resources).
• Bag of crisps & pint glass.
• Bathroom & kitchen scales.
• ITP : Measuring Scales
• ITP: Measuring Cylinder

### Mental/Oral Maths Starters

Day 1

Day 2
Multiply and divide by 10 and 100 (pre-requisite skills)

Suggested for Day 3

### Procedural Fluency

Day 1
Convert from litres to millilitres so as to put a range of capacities in order.

Day 2
Use a line graph to convert from miles to km and vice versa.

Day 3
Use conversions between feet and inches to metres to complete a ‘ready reckoner’ to help people to approximately convert their heights from feet and inches to metres and centimetres, or vice versa.

### Mastery: Reasoning and Problem-Solving

• True or false?
1050g = 1.5Kg.
1 pint is about 1.5 litres.
4 ounces is a bit more than 100g.
2.5 inches = 1 cm.
1 metre is a bit bigger than a yard.
• If we assume 3 miles = 5 kilometres, write the missing numbers.
☐ km = 30 miles.
35km =☐ miles.
☐ miles = 2.5km.
• What imperial unit would be used to measure…
The length of a large dog, nose to tail?
The weight of a child’s lunch box?
The capacity of a baby bath?

In-depth Investigation: Inches and Barleycorns
How many barleycorns are the same length as 1 inch?! Create your own conversion problems using this set of imperial length measurements. Inches and Barleycorns from nrich.maths.org.

### Extra Support

Baby Weigh In
Reading scales in kilograms to the nearest 0.1kg

Weighty Conversions
Converting grams to kilograms

## Unit 2 Timetables and intervals: 24 hour clock (suggested as 2 days)

### Objectives

Read timetables and calculate intervals using 24 hour clock
Unit 2: ID# 5303

National Curriculum
Meas (vi)

Hamilton Objectives
40. Solve problems involving converting between units of time; use 12-hour and 24-hour times, find time intervals and tell the time with confidence.
43. Complete, read and interpret information in tables, including timetables.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Download a timetable showing times in 24-hour format. Children convert the times to 12 hour o’clock times, e.g. quarter to 4. They say if times are morning or afternoon/evening. How do they know? Model calculating time intervals using Frog to count up from 1 time to another.
Group Activities
Use the ‘Digits of Time’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use a help sheet to support reading a 24-hour train timetable and answer questions about it.
-- Calculate lengths of TV programmes.

Day 1 Teaching
Children write 2 times with a difference of 1 hour 25 minutes. Share whiteboards. Then they write pm times using the 24-hour clock. Share whiteboards. Children write different time intervals using the 24-hour clock including crossing midnight. Share different children’s whiteboards.
Group Activities
-- Find possible start finish times of a film lasting 1 hour 50 mins.
-- A gadget has been invented to stop us watching too much television! After 9 hours in a week, it switches off. Work with partner to choose what to watch with a total time of less than 9 hours.

### You Will Need

• A local train/bus timetable showing times in 24-hour format
• Reading timetables sheet (see resources)
• Help sheet (see resources)
• Copies of a page from a current TV guide
• Timeline (see resources)
• TV guides (paper or online)

### Mental/Oral Maths Starters

Day 1
Read the 24-hour clock (pre-requisite skills)

Day 2
Pairs to 60 (pre-requisite skills)

or (suggested)
Units of time (simmering skills)

Day 1

Day 2

### Mastery: Reasoning and Problem-Solving

• Each of these train times is given using 24-hour clock. Write the times as analogue times in words.
13:40 to London.
14:45 to Bristol.
15:13 to Newcastle.
16:05 to Birmingham.
17:35 to Chester.
Calculate the time interval between each pair.
• True or false?
Half an hour after quarter to midnight is 01:15.
16:25 is half an hour before 5 to 5.
00:30 is half past midday.
20 past 3 in the afternoon is 15 minutes before 15:35

In-depth Investigation: Digits of Time
Children find out how many times the digit 9 is used on the 24 hour digital clock between noon and midnight.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 3 Perimeters: composite and rectilinear (suggested as 2 days)

### Objectives

Measure and calculate perimeters of composite rectilinear shapes
Unit 3: ID# 5309

National Curriculum
Meas (iii)

Hamilton Objectives
37. Measure and calculate perimeters of composite rectilinear shapes using SI units.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a rectangle on the board with sides of 20cm and 30cm long. Explain what the perimeter is. Discuss whether we need to measure all 4 sides? Model how we can find 2 sides and calculate the perimeter. We can measure or calculate perimeter.
Group Activities
-- Find the perimeters of rectangles, then put 2 rectangles together and find the perimeter of the compound shape.

Day 2 Teaching
Use Perimeter and area animation to show how we can divide the composite shape into rectangles. Model how to find the lengths of the sides where lengths are not given. Children work in pairs to find the perimeter of the shape on the screen. Take feedback.
Group Activities
Use the in-depth problem-solving investigation ‘Area and Perimeter’ from NRICH as today’s group activity.
Or, use these activities:
-- Carry on using the Perimeter and area animation. Work out missing sides in order to find perimeters.
-- Find the minimum number of known side lengths of a composite shape in order to be able to find the perimeter.

### Mental/Oral Maths Starters

Day 1
Double 2-digit numbers (pre-requisite skills)

Suggested for Day 2
Compare numbers with 1 decimal place and position on a line (simmering skills)

or
Round decimals to the nearest whole or tenth (simmering skills)

### Procedural Fluency

Day 1
Find the perimeters of gardens.

Day 2
Find the perimeters of composite shapes.
Work out missing sides in order to find perimeters.

### Mastery: Reasoning and Problem-Solving

• 2 rectangles have a perimeter of 20 cm.
In both, the sides measure whole number of centimetres.
Give possible measurements for the sides of the 2 rectangles.
• My room is L-shaped (see sketch on download). The longest side is 4 metres. The next longest is 3 metres. Find the perimeter.

In-depth Investigation: Area and Perimeter
Begin to explore the relationship between perimeter and area. Area and Perimeter from nrich.maths.org.

### Extra Support

Ali Ant’s Long Walk
Finding perimeters

## Unit 4 Regular and irregular areas; volumes (suggested as 3 days)

### Objectives

Find area of regular and irregular shapes
Find volumes by calculation

Unit 4: ID# 5323

National Curriculum
Meas (iv) (v)

Hamilton Objectives
38. Understand the concept of area, estimate areas of irregular shapes and count squares to find these; calculate areas of rectangles using standard units.
39. Estimate volumes of cubes and cuboids.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw an 8cm by 5cm rectangle on a squared background. Ask how children might work out the area of the rectangle without counting squares. Draw out that we can multiply the length by the breadth. Discuss the units. Find the area of a school hall in metres squared.
Group Activities
-- Draw as many rectangles as they can with a perimeter of 48cm on squared paper. They find the area of each. The challenge is to find the maximum and minimum possible areas.

Day 2 Teaching
Show children a large picture of a garden. Calculate areas of regular rectangular shapes with in it. Then draw an irregular pond. Discuss how to estimate the area of the pond. Draw a rectangle within it. Discuss the squares around the edge and add half squares to find a total.
Group Activities
-- Estimate then count to find area of leaves by drawing round them on squared paper.
-- Find areas of composite shapes by splitting into rectangles using an animation.

Day 3 Teaching
Use 3-D boxes on a suitable animation (see resources). Show cuboids and discuss how we can calculate how many small 1cm cubes make up the whole cuboid. Point out that the cuboid is made up of several layers of cubes. Show how we can work out the number of cubes in 1 layer and multiply by the number of layers.
Group Activities
Use the ‘Roomy Boxes’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Sketch cuboids, calculate the volume, and then check by making the cuboids from centimetre cubes.

### You Will Need

• Squared background on the IWB.
• Cm² paper.
• Scale drawing of a garden (see resources).
• A range of dry leaves.
• 3D boxes from interactivestuff.org
• Centimetre cubes.

### Mental/Oral Maths Starters

Suggested for Day 1
Multiply and divide by 10 and 100 (simmering skills)

Suggested for Day 2
Multiply by 100 and 1000 (simmering skills)

Day 3
Multiply 3 numbers together (pre-requisite skills)

### Procedural Fluency

Day 1
Find areas of rectangles.

Day 2
Order shapes according to estimates of area, then count squares to approximate area of each.

Day 3
Find volumes of drawn cuboids made from cm cubes.

### Mastery: Reasoning and Problem-Solving

• Sam has two photos. One has an area of 49cm². The other has an area of 56cm². A side length of one photo is equal to one of the sides of the other. What are the side lengths of the two photos?
• The area of a rectangle is 45cm². If one side is 4cm longer than the other, what is the perimeter of the rectangle?
• Mary has an oval table. She wants to find its area as accurately as she can. Write 2 or 3 sentences explaining how she might do this.
• A box exactly holds 75 centimetre cubed dice. Inside, it has a square base with sides 5cm. What is its inside height?
• Challenge:
If the wood is ½ cm thick and the box has a lid, how much space will the box take up in my bag?

In-depth Investigation: Roomy Boxes
Children cut squares from a square piece of paper, fold up the sides to form an open cuboid and find out which size will hold the most 1cm3 cubes.

### Extra Support

Rapid Rectangles
Finding the area of rectangles

## Unit 5 Temperature and negative numbers (suggested as 2 days)

### Objectives

Understand the concept of temperature and relate to negative numbers
Unit 5: ID# 5333

National Curriculum
Meas (vii)
Number (iii)

Hamilton Objectives
41. Begin to read scales of different types; solve scaling problems involving measures.
4. Interpret negative numbers in context, counting backwards and forwards through zero.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Launch ITP Thermometer. Choose a range of -10 to 10. At what sort of temperature might we get ice outside? Why? Agree that as water freezes at 0 Celsius the temperature will be less than this, e.g. minus one, -2, etc. Ask children to label temperatures on the thermometer. Compare temperatures. Calculate temperature rises and falls.
Group Activities
-- Draw vertical number lines to help calculate rises and falls in temperature.
-- Label temperatures on a thermometer, then use this image to calculate falls in temperature.

Day 2 Teaching
Display a table showing the temperatures recorded at a school weather station. Discuss the differences between temperatures. Find how much the temperature rose and fell during the day and night.
Group Activities
Use the ‘Alternating Chains’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Work in pairs to find as many pairs of temperatures with a difference of 10°C as they can. 1 temperature must be above freezing and 1 below.

### You Will Need

• ITP: Thermometer
• Temperature sheet (see resources)
• Flipchart and pens
• A set of -9°C to 9°C cards
• 2 cut-out card arrows
• Blu-tac

### Mental/Oral Maths Starters

Suggested for Day 1
Double 2-digit numbers (simmering skills)

Suggested for Day 2
Pairs to 100 (simmering skills)

### Procedural Fluency

Day 1
Order temperatures and calculate rises and falls in temperature.

Day 2
Find differences in temperatures on a bar chart of temperatures in different cities.

### Mastery: Reasoning and Problem-Solving

• If the temperature starts at 4 degrees and falls 3 degrees each hour from midnight to 6am, what is the temperature at 6 in the morning?
• Today it is minus 3 degrees. What was the temperature yesterday if it was 5 degrees lower than it is today? Tomorrow they say it will be 10 degrees warmer. What will it be then?
• Complete the table:
 4° -6° -1° Falls 3° 1° Rises 4°

In-depth Investigation: Alternating Chains
Children create chains of alternating positive and negative numbers and explore the patterns in their totals.

### Extra Support

This unit has no separate Extra Support activities.