Maths Year 4 Summer 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 Measure in m, cm, mm; convert units (suggested as 2 days)

Objectives

Measure in m, cm, mm; convert between units
Unit 1: ID# 4967

National Curriculum
Meas (i) (iv)

Hamilton Objectives
33. Convert between units of measurement, e.g. cm to m.
36. Estimate, compare and calculate different measures.

Teaching and Group Activities for Understanding

Day 1 Teaching
Before the lesson, draw round the outline of two children and an adult from other classes. Bring these to lesson and display. Show a metre stick. Use this to estimate the heights of the outlines. Measure one of the outlines and model how we record this: 134cm is 1 metre and 34cm or 1.34m. Repeat with the other two outlines.
Group Activities
-- Convert height measurements from centimetres to metres and centimetres.
-- Convert distance measurements (aeroplane heights) from metres to kilometres.

Day 2 Teaching
Show some pencils. Discuss what unit to use to measure them. Explain that using millimetres will give a more accurate measurement. Model accurate measuring and show on the IWB with pictures of a pencil and ruler. Write: length = 125mm. Recall that 1cm = 10mm. So, we divide 125mm by 10 to get 12.5cm. Repeat with other millimetres to centimetre conversions.
Group Activities
Use the ‘Timeline’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Measure lines in millimetres and convert them to centimetres.

You Will Need

  • People outlines
  • Metre stick
  • Mini-whiteboards and pens
  • ‘Height’ recording table (see resources)
  • Blank cards
  • Sticky tack
  • Rulers
  • Sharpened coloured pencils

Procedural Fluency

Day 1
Convert measurements from centimetres to metres and vice-versa

Day 2
Measure lines in millimetres and convert them to centimetres.

Mastery: Reasoning and Problem-Solving

  • Look at these lengths. Estimate their accuracy.
    Tick if they look correct.
    -- Car length: 4.5m
    -- Cat, nose to tail: 0.42m
    -- Mobile phone: 15mm
    -- Wax crayon 100mm
    -- Teaspoon: 200cm
  • Write the missing numbers or units.
    3.4cm = ☐mm
    ☐cm = 2.35m
    10m = 1000☐
    129mm = ☐cm
    3400mm = 3.4☐

In-depth Investigation: Timeline
Children use their knowledge about millimetres, centimetres and metres to create a scale timeline from 0 to the current year, and gain some sense of the order of historical events.

Extra Support

Expert Estimates
Estimating in metres and centimetres

Unit 2 Use SI units; bar charts (suggested as 3 days)

Objectives

Measure in and convert between m, cm, mm, kg & g; represent info on bar charts
Unit 2: ID# 4973

National Curriculum
Meas (i) (iv)
Stats (i)

Hamilton Objectives
33. Convert between units of measurement, e.g. kilograms to grams.
36. Estimate, compare and calculate different measures.
38. Interpret and present discreet data using bar charts, pictograms and tables, and continuous data on time graphs. Answer questions re data.

Teaching and Group Activities for Understanding

Day 1 Teaching
Ask children what units we use to weigh things. Agree kilograms and grams. Remind children that 1000g = 1kg. Pass round packets of food and look at the mass/weight on each packet. Use Measuring scales ITP to practise reading a scale, noting various divisions. Show a loaf of bread/ bag of loose apples. Using the class scales to weigh these items. Record, e.g. 1kg and 300g = 1300g = 1.3kg.
Group Activities
-- Weigh food items in grams and convert the mass/weight to kilograms, and vice versa.

Day 2 Teaching
Show a bag of groceries (around 2kg) and a full PE bag (less than 1kg). Invite children to compare each mass/weight with a 1kg weight, and to make an estimate based on this. Weigh the bags, noting how many kilograms and grams each one weighs. Record in three ways: 2kg and 300g, 2.3kg and 2300g. Weigh a selection of toys and record each mass/weight in a table.
Group Activities
-- Use scales to find and compare masses/weights in grams and kilograms. Display these on a bar chart.

Day 3 Teaching
Today children will carry out their own measuring investigations (length or mass). They can choose what their investigation will be about but it must be simple and answer a question. Give some examples, e.g. Do boys have longer arms than girls? Are apples heavier than bananas? Have a variety of toys, books and other objects for children to use.
Group Activities
Use the ‘Pencil power’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Design a measurement enquiry; measure, then record results in a bar chart.
-- Begin to explore averages by weighing a large number of lighter objects and dividing the total as necessary.

You Will Need

  • Packaged foods, weighing scales and flipchart
  • ITP: Measuring Scales
  • A selection of food items to weigh
  • Blank cards for shop signs
  • Bag of groceries (1–3kg) and PE bag (<1kg)
  • 1kg, 500g, 100g weights and Cm² paper
  • Selection of toys
  • Five heavy objects to weigh
  • Variety of toys, books, fruit and vegetables
  • Large sheets of squared paper
  • £1 coin, 50p coin, 1g, 5g and 10g weights
  • Electronic pan balance
  • Knives, forks and dessert spoons

Mental/Oral Maths Starters

Day 1
Convert between units of measurements (pre-requisite skills)

Suggested for Day 2
Mark tenths on a line (simmering skills)

Suggested for Day 3
Place numbers on empty lines of different lengths (simmering skills)

Procedural Fluency

Day 1
Convert masses/weights from grams to kilograms and vice-versa.

Day 2
Compare and order masses/weights in grams and kilograms.

Day 3
Display information about mass/weight in a bar chart.

Mastery: Reasoning and Problem-Solving

  • True or false?
    350g is the same as 1kg and 35g.
    1199mm is the same as 1.199m.
    23.4cm is the same as 234mm.
    72g is the same as 0.72kg
  • Look at the mass/weight of these items. Estimate their accuracy. Tick if they look correct.
    Large dictionary: 2.1kg
    An apple: 500g
    Mobile phone: 0.02g
    Pair of wellies: 400g
    Teaspoon: 0.2kg
  • Convert each measurement to metres
    (a) 600cm
    (b) 180cm
    (c) 1300mm
    (d) 50mm
  • Convert each measurement to kilograms
    (a) 2500g
    (b) 1090g
    (c) 575g

In-depth investigation: Pencil Power
Children use larger weights and numbers to find an accurate weight of one pencil. Collect data on a bar graph.

Extra Support

In the Balance
Continue to practise weighing objects and reading from different scales.

Unit 3 Find the area of rectilinear shapes (suggested as 2 days)

Objectives

Find the area of rectilinear shapes
Unit 3: ID# 4987

National Curriculum
Meas (i) (iii)

Hamilton Objectives
35. Find the area of rectilinear shapes by counting squares.

Teaching and Group Activities for Understanding

Day 1 Teaching
Draw an 8 × 5 rectangle on IWB squared background. Explain that its area is the amount of paper it covers and that we measure this in square units. If each square measured one centimetre by one centimetre, we would call each square one square centimetre: 1cm². Give each child cm² paper. They draw a 5cm × 4cm rectangle. What is its area? Can you draw a different rectangle with an area of 20 whole squares? Now have a go at drawing a shape with an area of 20cm² that is not a rectangle…. Compare shapes. They look different, but all have the same area.
Group Activities
-- Find the area of book covers by counting squares.
-- Calculate areas. Draw rectangles with a given area.

Day 2 Teaching
Remind children how to find the area of a 6 × 4 rectangle by counting the rows and multiplying. Draw a rectilinear L shape (using two rectangles 6 × 4 and 2 × 6). Discuss how we can count the squares it covers to find the area. We can sometimes use a mixture of calculation and counting. Divide the shape into two rectangles and demonstrate how to find the area by adding the two areas.
Draw a second rectilinear shape and model dividing it into rectangles to find its area.
Group Activities
Use the ‘Pete’s pond problem’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Divide rectilinear shapes into rectangles to support finding the area.

You Will Need

  • Cm² paper
  • Selection of books of different sizes
  • Rulers
  • ‘Find the area’ (see resources)
  • Colouring pencils

Mental/Oral Maths Starters

Suggested for Day 1
8 times table (simmering skills)

Suggested for Day 2
9 times table (simmering skills)

Mastery: Reasoning and Problem-Solving

  • John has a rectangular bookmark. It measures 20cm × 6cm.
    Draw it and find its area. It is too long for his book, so he cuts 1cm off the bottom. What is its area now?
  • Tanya has a silk scarf. It measures 60cm × 30cm. Is its area more or less than 100cm²?
  • Find the area of this shape. Each little square is a 1 centimetre square.

In-depth Investigation: Pete's Pond Problem
Children apply knowledge of perimeter and area to make a generalisation and help Pete to fence around his pond.

Extra Support

Polyominoes
Investigating rectilinear shapes and investigating systematically

Unit 4 Perimeters of rectilinear shapes; area (suggested as 3 days)

Objectives

Find perimeters of rectangles and rectilinear shapes; explore relation to area
Unit 4: ID# 4993

National Curriculum
Meas (i) (ii) (iii)

Hamilton Objectives
34. Measure and calculate the perimeter of a rectilinear figure (including squares) in cm and m.
35. Find the area of rectilinear shapes by counting squares.

Teaching and Group Activities for Understanding

Day 1 Teaching
Ask children how long they think the distance all around the whiteboard is? If an ant walked it, how far would it walk? Discuss how we can find out. Show how we can measure two sides, and double each of these, then add them to find the perimeter, or add the length and the width then double. Emphasise that the perimeter is the distance around the outside of a shape. Find perimeter of a 5 × 3 rectangle, modelling both doubling strategies.
Group Activities
-- Find the perimeter of a variety of rectangles.

Day 2 Teaching
Sketch a rectangle, label just two sides – the length and width, e.g. 8cm and 4cm. Children discuss, in pairs, how to find the perimeter – the measurement of the distance once around the outside of the shape. Take feedback. Agree adding two sides and doubling. Draw a non-rectangle shape like an ‘L’. Discuss finding the perimeter. Repeat for a rectilinear ‘T’ shape.
Group Activities
-- Find the perimeter of rectilinear (T and L) shapes made from rectangles.
-- Generalise how to find the perimeter of rectangles.

Day 3 Teaching
Children help you to draw rectangles with areas of 16 squares, on a squared background. Children discuss, in pairs, what is the same and different. (Same area but different perimeters.) Which do you think has the greatest perimeter? And the smallest? Children work out the perimeter of each rectangle to check. Explore the relationship between perimeter and areas of squares.
Group Activities
Use the activity below as the in-depth problem-solving investigation for this unit.
-- Explore patterns and relationships between the perimeter and area of squares and rectangles.

You Will Need

  • Cm² paper
  • Scissors
  • Flipchart

Mental/Oral Maths Starters

Day 1
Doubling (pre-requisite skills)

Suggested for Day 2
Double any 2-digit number (simmering skills)

Suggested for Day 3
Choose suitable units of measure for a range of items (simmering skills)

Procedural Fluency

Day 1
Find the perimeter of a variety of rectangles.

Day 2
Find the perimeter of rectilinear shapes made from rectangles.

Day 3
Match a range of rectilinear shapes to their corresponding area and perimeter.

Mastery: Reasoning and Problem-Solving

  • The sketch below shows the plan of a garden made up of a strip of garden which is 4.5m long and 1m wide and a second strip, which runs at right angles to it, that is 3m long and 2m wide. How many metres of fence are required to fence it all in?
  • How many shapes with an area of 5 squares can you draw? Each square must touch another along the length of at least one side. Choose four and find their perimeters. Which has the longest perimeter?
  • Draw a rectangle with an area of 20cm². Now draw another rectangle with the same area, that has a different perimeter.

In-depth Investigation
Use the group activity on Day 3 as this unit’s investigation.