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GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.

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Elaboration on this Achievement Objective

At Level Four students should apply their multiplicative strategies to find perimeters and areas of commonly used polygons and volumes of cuboids where the lengths of sides and edges are given as whole number measures. Calculations required are:

 

area rectangle.

 area parallelogram.

   

area triangle.

Rectangle: Area = base x height
Perimeter = 2 x (base + height)

Parallelogram: Area = base x height
Perimeter = 2 x (base + side length)

Triangle: Area = 1/2 (base x height)
Perimeter = side + side + side

volume cuboid.

Cuboid: Volume = base x height x depth

Students should express the areas and volumes using symbols, for example 48cm3 (48 cubic centimetres).

 

Teaching resources for this Achievement Objective
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The chicken run

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Explain the relationship between the area and perimeter of rectangles.
  • Use a table to solve a problem.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a table, make a drawing).
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The Emperor’s Army

Level Four
Geometry and Measurement
Picture book activities
This is an activity based on the picture book The Emperor’s Army

Students will be able to model their understanding of volume through creating models and calculating volume using a formula.

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The Lawn

Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in finding unknown quantities that fit within the given constraints.
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The Warlord’s Kites

Level Four
Geometry and Measurement
Picture book activities
This is an activity based on the picture book The Warlord’s Kites
  • Students will be able to derive a formula for finding the area of a triangle based on their understanding of the area of a square.
  • Students will be able to accurately calculate the area of triangles and parallelograms and explain how they achieved their answer.
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Triangles

Level Four
Geometry and Measurement
Units of Work
This unit encourages students to discover and apply the rule for area of a triangle (area equals half base times height). Students will practise multiplication and division strategies as they calculate areas.
  • Recognise that two identical right angled triangles can be joined to make a rectangle.
  • Recognise that a triangle has half the area of a rectangle with the same base and height lengths.
  • Apply the rule ‘area of triangle equals half base times height’ to calculate the area of triangles.
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Volumes of Cubes

Level Four
Integrated
Secondary activities
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved with subsequent recording/reporting.
  • Draw 3D shapes on isometric paper.
  • Explore the relationship between edges, faces and vertices of relevant cube structures.
  • Explore the relationship between the dimensions of a cube and its volume.
  • Interpret drawings of 3D cubes.
  • Calculate volume of 3D cube structures.
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What Goes Around

Level Four
Geometry and Measurement
Units of Work
In this unit students investigate the relationships between the area and perimeters of squares and rectangles.
  • Use a formula to calculate the area of rectangles and squares.
  • Investigate the relationship between the perimeter and area of rectangles.
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Working with partial units

Level Four
Geometry and Measurement

The purpose of this activity is to support students measure areas and perimeters of rectangle when the side lengths have simple fractions.

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Working with partial units

Level Four
Geometry and Measurement

The purpose of this activity is to support students measuring the areas and perimeters of rectangle when the side lengths include simple fractions.

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Working with volume and surface area together

Level Four
Geometry and Measurement
The purpose of this activity is to support students in distinguishing between the surface area and volume of cuboids. Students use multiplicative methods for finding the measurements, and record the measurements using appropriate units (square centimetres (cm 2) for surface area and cubic...
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Working with Wool

Level Four
Integrated
Figure It Out activities
This is a level 4 activity from the Figure It Out series.A PDF of the student activity is included.
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Worms at Work

Level Four
Integrated
Figure It Out activities
This is a level 4 activity from the Figure It Out series.A PDF of the student activity is included.
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You can count on squares!

Level Four
Integrated
Units of Work
This unit requires students to form generalisations about the areas of triangles and quadrilaterals. Through exploring the geometry of three and four-sided polygons, students look for relationships that can be expressed algebraically. At this level it is sufficient for the students to express these...
  • Explore the relationship between rows and columns in finding the areas of rectangles.
  • Calculate the area of rectangles, parallelograms, and triangles.