Short Blocks

# Maths Year 5/6 Spring Measures

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Units of measurement (suggested as 3 days)

### Objectives

Units of measurement
Unit 1: ID# 56572

Y5: Units of measurement, line graphs.
Y6: Units of measurement, line graphs

National Curriculum
Y5: Measures (i) (ii); Stats (i)
Y6: Measures (i) (ii) (iii); Stats (i)

Y5 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.

Y6 Hamilton objectives
40. Use, read and write, and convert between, standard units including miles and kilometres, using decimal numbers with up to three places as appropriate.
41. Solve problems using standard units and convert between them.
47. Interpret and construct (pie charts and) line graphs and use these to solve problems.

### Planning and Activities

Day 1
Hang a 0 card at one end of a washing line and 1000g with 1kg pegged beneath it at the other. Children peg different numbers of grams and kg (up to 2dp) along the line, then convert to kg/grams. Repeat for litres and ml.
Further Teaching with Y6
Write 0.458kg, 500g, 0.4kg, 250g, 0.678kg, 785g on cards and repeat as above.
Group Activities: T with Y6
Y5 -- Play a game converting between grams and kilograms (1 decimal place).
Fill in missing amounts on a 0–1kg line. Estimate to order containers by capacity; measure to check. Convert between litres and millilitres.
Y6 -- Play a game converting between grams and kilograms (1 or 3 decimal places).

Day 2
Write a variety of distances on the board and use these to convert between metres and kilometres (place value multiplication or division by 1000).
Introduce conversion between miles and kilometres. Together, draw a line graph for the conversion; read intermediate points of interest.
Group Activities: T with Y5
Y5/Y6 -- Construct a line graph to convert between miles and km.

Day 3
List 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 metric units.
Group Activities: T with either or both
Use the in-depth problem-solving investigation ‘Inches and Barleycorns’ from NRICH as today’s group activity.
Or, use these activities:
Y5/Y6 -- Use known facts to convert between centimetres and inches, kilograms and stones/pounds, litres and pints.
Y5/Y6 -- Measure height in cm, convert to inches, draw line graph to check. Find out how many grams are in a pound.

### You Will Need

• 1kg weight
• Washing line with pegs and cards
• ‘Converting metric units’ (see resources)
• Scissors; Tape measures
• ‘Equivalent measures’ (see resources)
• Weighing scales; Measuring cylinder
• Range of containers with capacities between 100ml and 2l
• Graph paper, Squared paper, A3 paper
• ‘Conversion graph’ (see resources)
• Bag of crisps
• 30cm ruler; Pint glass
• Bathroom scales (that weigh in kg and stones); Kitchen scales (that weigh in g and oz)

### Short Mental Workouts

Day 1

Day 2
Multiply and divide by 10 and 100

Day 3

### Worksheets

Day 1
Y5/Y6: Convert from litres to millilitres, and vice versa; order by capacity.

Day 2
Y5/Y6: Convert between miles and kilometres.

Day 3
Y5/Y6: Convert between centimetres and inches.

### Mastery: Reasoning and Problem-Solving

Y5

• 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
35 km is ☐ miles
☐ miles = 2.5 km
• 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?

Y6

• Write a familiar object that weighs:
(a) 5 kg
(b) 1 pound
(c) 100g
• Write a familiar container that holds:
(a) 1 pint
(b) 5 ml
(c) 2 gallons
• True or false?
10 lots of 100 grams is 10 kilograms.
One tenth of a litre is 10ml.
Half a pint is about 1/4 of a litre.
You can weigh people in stones.
• Use this fact: 5 miles = 8km
15 miles is ☐ km.
☐ miles is 4 km.
64 km is ☐ miles.
Roughly how many miles is 250 km?

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

Y5
Baby Weigh In
Reading scales in kilograms to the nearest 0.1kg.

Weighty Conversions
Converting grams to kilograms.

Y6
Decimals Measure Up
Converting kilograms to grams and vice versa; Converting litres to millilitres and vice versa.

## Unit 2 Area, perimeter, scaled shapes (suggested as 5 days)

### Objectives

Area, perimeter, scaled shapes
Unit 3: ID# 56602

Y5 Area, perimeter and polygons
Y6 Area, perimeter and scaled shapes

National Curriculum
Y5: Measures (iii) (iv); Geom (PoS) (v) (vi)
Y6: Measures (iv) (v) (vi)

Y5 Hamilton Objectives
37. Measure and calculate perimeters of composite rectilinear shapes using SI units.
38. Understand the concept of area, estimate areas of irregular shapes and count squares to find these; calculate areas of rectangles using standard units.
Y6 Hamilton objectives
42. Measure areas and perimeters; understand that area is a measurement of covering and is measured in square units, and perimeter is a length, measured in mm, cm, m or km; recognise that shapes with the same area can have different perimeters and vice versa.
43. Calculate the area of parallelograms and triangles.

### Planning and Activities

Day 1
Draw a rectangle with two sides labelled, discuss how we know the length of the other two sides and how we can calculate the perimeter.
Further Teaching with Y6
Draw right-angled triangles and discuss how to find their areas by considering each as half of a rectangle.
Group Activities: T with Y6
Y5 -- Find the perimeters of rectangles. Find the perimeter of compound shapes made from two rectangles.
Y6 -- Find the areas of rectangles and then divide these to find the areas of triangles.
-- Generalise how to find the area of right-angled triangles. Test with other types of triangle.

Day 2
Model how to split composite shapes into rectangles in order to find missing lengths of sides, then perimeter.
Further Teaching with Y6
Show a set of quadrilaterals and identify parallelograms. Demonstrate how to find the area by splitting into two triangles and a rectangle.
Group Activities: T with Y6
Y5 -- Draw composite shapes and find perimeters. Some children will investigate the minimum number of known side lengths of a composite shape in order to be able to find the perimeter.
Y6 -- Derive a formula for finding the area of a parallelogram (then share it with Y5).

Day 3
Draw an 8cm by 5cm rectangle on a squared background. Y6 explain how to calculate the area of the rectangle without counting squares. Discuss the units of measurement used.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Through the Window’ from NRICH as today’s group activity.

Or, use these activities:
Y5/Y6 -- Children draw as many rectangles as they can with a perimeter of 48cm on squared paper; find the maximum and minimum possible areas.
Y6 -- Find the area of a regular octagon with perimeter 48cm OR Find rectilinear shapes with a given area.

Day 4
Children sketch a right-angle triangle where the sides along the right angle are 4cm and 7cm long. They measure the longest side. Draw a similar triangle with each side next to the right angle twice the length. Compare the longest side lengths.
Further Teaching with Y5
Show a large picture of a garden. Calculate areas of rectangular shapes with in it. Then discuss how to estimate an irregular area (a pond), counting whole squares and half squares to find a total. Children then measure the area of their hand.
Group Activities: T with Y5
Y5 -- Estimate then count squares to find area of leaves by drawing around them on squared paper.
Y6 -- Scale up rectangles, triangles and parallelograms by a factor of 2 and 3; observe what happens to their area.

Day 5
Ask children to draw a polygon, then to hold it up if it has a stated property.
Further Teaching with Y6
Define similar shapes as identical in shape, but not in area. Using ‘Similar shapes’, children find two rectangles which look similar. Measure the sides of each. Children calculate the scale factor. Repeat for triangles. Where is scaling used in ‘real life’?
Group Activities: T with Y6
Y5 -- Draw polygons with 3 to 8 sides, with certain features stipulated.
Y6 -- Identify pairs of similar rectangles and triangles. Use the scale factor to calculate side lengths. Or, draw similar shapes, using a scale factor of 2 or 3 or 1.5. Identify pairs of similar shapes drawn by others and find the scale factor.

### You Will Need

• Mini-whiteboards and pens
• 0–9 dice
• cm squared paper
• Plain paper
• ‘Areas of triangles’ (see resources)
• ‘Garden design’ (sheets 1 and 2, see resources)
• A range of dry leaves for each pair/group
• ‘Scaling up’ (see resources)
• ‘Similar shapes’ (see resources)
• ‘Similar shapes – rectangles’ (see resources)
• ‘Similar shapes – triangles’ (see resources)

### Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Multiply and divide by 10 and 100

Day 3
Multiply by 100 and 1000

Day 4
Multiply 3 numbers together

Day 5
Repeated doubling

### Worksheets

Day 1
Y5: Find ‘garden’ perimeters.
Y6: Find the area of triangles and a compound shape made from triangles and a rectangle.

Day 2
Y5: Find the perimeter of compound shapes. Calculate missing sides in order to find perimeters.
Y6: Find area of parallelograms.

Day 3
Y5: Find areas of rectangles.
Y6: Draw rectangles with the same perimeter, but different areas.

Day 4
Y5: Order shapes according to estimates of area, then count squares to approximate the area of each.
Y6: Calculate the dimensions of toys, given scale factors.

Day 5
Y5: Explore the properties of polygons.
Y6: Identify pairs of similar rectangles and triangles. Use a scale factor to calculate side lengths.

### Mastery: Reasoning and Problem-Solving

Y5

• Sam has 2 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 sentences to explain how she might do this.

Y6

• Find the area of the triangle (see download). The perpendicular height = 6cm and the base = 5cm.
• What is the area of the shape (see download)? The total length = 12cm and the base of the triangle is half the length of the rectangle. The triangle has two equal sides.
• Draw two rectilinear shapes, one L-shaped and one T-shaped, with equal areas but different perimeters.
• True or false?
-- If one triangle is scaled up to have sides 3 times as long as another, the area is also 3 times as large.
-- If two rectangles are similar and the scale factor is 4, then the area of the larger rectangle is 16 times that of the smaller rectangle.
• Calculate the area of the triangle whose sides are half the length of the one drawn (see download). Compare the two areas. What do you notice?

In-depth investigation: Through the Window
The local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices? Through the Window from nrich.org.uk.

### Extra Support

Y5
Ali Ant’s Long Walk
Finding perimeters.

Rapid Rectangles
Finding the area of rectangles.

Y6
Folding Areas
Finding areas of rectangles and triangles.

Function Blocks
Use Function Blocks ITP to generate multiplication by 3. Can children work out the function? Repeat with other single-step × and ÷ functions.

## Unit 3 Finding volumes (suggested as 2 days)

### Objectives

Finding volumes
Unit 4: ID# 56618

Y5: Finding volumes
Y6: Finding volumes

National Curriculum
Y5: Meas (v)
Y6: Meas (vii

Y5 Hamilton Objectives
39. Estimate volumes of cubes and cuboids.

Y6 Hamilton objectives
44. Calculate, estimate and compare volume of cubes and cuboids using standard units, cm³, m³, mm³ and km³.

### Planning and Activities

Day 1
Show a centimetre cube, and show how its volume is written. Show cuboids made from centimetre cubes, and discuss how to find how many cubes are in the shape. Show how the volume is written. Derive the formula l × w × h.
Group Activities: T with Y5
Y5 -- Sketch cuboids, calculate their volume, then check by making the cuboids from centimetre cubes.
Y6 -- Find the volume of cuboids with given dimensions. Or, experiment systematically to make/sketch all possible cuboids with a volume of 24cm3, then 36cm3.

Day 2
Revise calculating the volume of a cuboid; discuss other cubic measures. Complete demonstrations of how one millilitre takes up one cubic centimetre.
Further Teaching with Y6
Show children a cuboid made from 2 by 3 by 5 cubes. Calculate volume as 30 cubes, observing how 2, 3 and 5 are the prime factors of 30.
Group Activities: T with Y6
Use either the ‘Roomy Boxes’ or ‘Queued Cubes’ in-depth problem-solving investigations as today’s group activity.
Or, use these activities:
Y5 -- Investigate which cuboids could have a volume of 24cm3.
Y6 -- Explore creating cubes with dimensions which are prime numbers less than 15.

### You Will Need

• Centimetre cubes
• ‘Find volumes of cuboids’ (see resources)
• Measuring cylinder (200ml+)
• 100ml coloured water

### Short Mental Workouts

Day 1
Multiply 3 numbers together

Day 2
Factors

### Worksheets

Day 1
Y5: Find volumes of drawn cuboids made from cm cubes.
Y6: Calculate volumes of cubes and cuboids.

Day 2
Y5: Calculate volumes of cuboids.
Y6: Calculate the missing lengths of edges of cuboids, given two edge lengths and the volume.

### Mastery: Reasoning and Problem-Solving

Y5

• A box exactly holds seventy-five 1cm3 dice. Inside, it has a square base with sides 5cm. What is its inside height?

Y6

• A 6cm x 6cm x 6cm cube is chopped in half three times (see download for diagram).
Find the volume of each cuboid after each of the three cuts and write the lengths of their edges.

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.
OR
Queued Cubes
Children apply a combination of knowledge of 3-D shape, area and volume to solve a problem that introduces surface area.

### Extra Support

Y5/Y6
Hidden Volumes
Finding the volumes of cuboids.