GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
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:
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Rectangle: Area = base x height | Parallelogram: Area = base x height | Triangle: Area = 1/2 (base x height) |
Cuboid: Volume = base x height x depth |
Students should express the areas and volumes using symbols, for example 48cm^{3} (48 cubic centimetres).
Teaching resources for this Achievement Objective
The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.
Rich learning activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
This is a level 4 measurement and number activity from the Figure It Out theme series.
calculate area of rectangles draw a scale diagram find the best buy using simple proportions
Figure It Out activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
To provide a set of learning tasks that integrate across the strands of the New Zealand Mathematics Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson , especially if students need more time to become...
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....
Number and Algebra
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
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 this unit be used with students that already have some experience with level 4 algebra.
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.
Units of Work
Number and Algebra
Level Four
Calculate the area of rectangles using m 2 Use remainders within the context of a problem
Problem solving activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
This is a level 4 activity from the Figure It Out series. A PDF of the student activity is included.
Figure It Out activities
Geometry and Measurement
Level Four
In this unit students complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings.
plan a mathematical investigation in a group. take measurements and make calculations to complete an investigation Interpret the accuracy of the investigation
Units of Work
Geometry and Measurement
Level Four
This is a level 4 measurement activity from the Figure It Out theme series.
calculate volume of cuboids make scale models
Figure It Out activities
Geometry and Measurement
Level Four
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.
Rich learning activities
Geometry and Measurement
Level Four
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
Problem solving activities
Geometry and Measurement
Level Four
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)
Figure It Out activities
Geometry and Measurement
Level Four
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)
Figure It Out activities
Number and Algebra
Level Four
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)
Figure It Out activities
Geometry and Measurement
Level Four
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
Figure It Out activities
Geometry and Measurement
Level Four
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)
Problem solving activities
Geometry and Measurement
Level Four
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.
Picture book activities
Geometry and Measurement
Level Four
The purpose of this activity is to engage students in finding unknown quantities that fit within the given constraints.
Rich learning activities
Geometry and Measurement
Level Four
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.
Picture book activities
Geometry and Measurement
Level Four
This unit is around discovering and applying the rule for area of a triangle (area equals half base times height). Students will practice 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’
Units of Work
Geometry and Measurement
Level Four