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Short Blocks

Maths Year 4 Summer Measures and Data (B)

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 added value for Hamilton Friends and School Subscribers.

Unit 1 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)

Procedural Fluency

Day 1
Find the area of rectangles by counting squares.

Day 2
Find the area of rectilinear shapes.

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 2 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.

• 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.

Extra Support

Maths on the Edge
Calculating perimeters