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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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Areas and volumes

Level Four
Geometry and Measurement
Units of Work
This unit is about finding the areas of triangles, and parallelograms, using what students already know about the areas of rectangle. Students will apply multiplication and division strategies as they calculate areas. The ideas are extended to finding the volumes of cuboids (rectangular prisms).
  • Recognise that two identical triangles can be partitioned and 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’.
  • Connect the area of a parallelogram to the area of300
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Bigger Triangles

Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.
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Books in Boxes

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement strand activity from the Figure It Out series. A PDF of the student activity is included.

solve problems with mass and volume

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Castle Construction

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement strand activity from the Figure It Out series. A PDF of the student activity is included.

measure length and area to construct a model

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Cosmo's Kennel

Level Four
Integrated
Figure It Out activities
This is a level 4 measurement and number activity from the Figure It Out theme series. A PDF of the student activity is available.

calculate area of rectangles

draw a scale diagram

find the best buy using simple proportions

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Covering Up

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement activity from the Figure it Out series.A PDF of the student activity is included.

calculate volume and area of a cuboid

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Cubic Conundrums

Level Four
Integrated
Units of Work
This unit provides a set of learning tasks that integrate across the strands of the Mathematics and Statistics learning area of the New Zealand Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially...

Session One
Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.

Session Two
Use tables, graphs, and word rules to represent growing patterns.

Session Three
Draw cube models using plan views.

Session Four
Draw cube models using isometric projections.

Session Five300

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Divide and Prosper

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement strand activity from the Figure It Out series. A PDF of the student activity is included.

draw scale diagrams for length and area problems

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Fascinated by Fibonacci

Level Four
Integrated
Units of Work
This unit looks at Fibonacci numbers and how they occur in nature. Fibonacci numbers provide a rich context in which to apply algebra at Level 4. It is recommended that students already have some experience with Level 4 algebra, prior to the introduction of this unit.
  • Use a recursive rule to generate the sequence of Fibonacci numbers.
  • Create a Fibonacci spiral using squares with Fibonacci side lengths.
  • Find a pattern of odd and even numbers in the sequence.
  • Identify and represent patterns we find for consecutive numbers in the sequence.
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Fertiliser

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Calculate the area of rectangles using m2.
  • Use remainders within the context of a problem.
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Finding areas and perimeters from decimal side lengths

Level Four
Geometry and Measurement

The purpose of this activity is to support students in measuring the areas and perimeters of a rectangle when the side lengths are given in decimal measurements.

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Finding surface area

Level Four
Geometry and Measurement
The purpose of this activity is to support students in calculating the surface areas of cuboids in an efficient manner, using multiplication and addition.
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Finding volumes and surface areas from decimal side lengths

Level Four
Geometry and Measurement
The purpose of this activity is to support students in measuring the volumes and surface areas of cuboids when the side lengths are given in decimal measurements.
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Great Gardens

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement strand activity from the Figure It Out series. A PDF of the student activity is included.

explore area, perimeter and volume

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How long is a slinky?

Level Four
Geometry and Measurement
Units of Work
In this unit students take part in a variety of measurement tasks including measuring the length of a slinky, working out how many slices of tomato will fit around the edge of a pizza and accurately drawing the label from a can.
  • Describe a method to measure the length of circular objects.
  • Measure length using metres, centimeters and millimeters.
  • Calculate the circumference of a circle from a measurement of diameter.
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It's a Wrap

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement activity from the Figure it Out series.A PDF of the student activity is included.

investigate areas and perimeters of cuboids

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Looking for Lift

Level Four
Geometry and Measurement
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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Measurement Investigations 1

Level Four
Geometry and Measurement
Units of Work
In this unit students complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings.
  • Apply measurement knowledge to solving word problems.
  • Plan a mathematical investigation.
  • Take measurements and make calculations to complete an investigation.
  • Interpret the accuracy of the investigation.
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Melissa's Room

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement activity from the Figure It Out theme series. A PDF of the student activity is available.

calculate volume of cuboids

make scale models

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Perimeter = area rectangles

Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in finding the perimeter and area of rectangles. They engage in trying to find rectangles where the number measure of the perimeter equals the number measure of the area.
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Peter's string

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Determine the area of a rectangle with a given perimeter.
  • Pose questions for mathematical exploration.
  • Make conjectures in a mathematical context.
  • Prove or refute mathematical conjectures.
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Ps for Ever

Level Four
Integrated
Figure It Out activities
These are level 4 measurement, number and algebra problems from the Figure It Out series.A PDF of the student activity is included.

investigate the relationship between area and perimeter (Problem 1)

solve problems involving proportions (Problem 2)

investigate a sequential pattern (Problem 3)

use multiplication and addition to solve money problems (Problem 4)

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Stretching Exercises

Level Four
Integrated
Figure It Out activities
These are level 4 number and measurement problems from the Figure It Out series.A PDF of the student activity is included.

use number strategies to solve puzzles (Problems 1, 2 and 4)

explore areas of geometric shapes on geoboards (Problem 3)

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Talk About: Four

Level Four
Integrated
Figure It Out activities
These are level 4 measurement and algebra problems from the Figure It Out series.A PDF of the student activity is included.

find volume of a cuboid (Problems 2 and 3)

solve problems involving sequential patterns (Problem 4)

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The Big Drip

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement strand activity from the Figure It Out series. A PDF of the student activity is included.

find the area and the volume