GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
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).
- 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 to300
solve problems with mass and volume
measure length and area to construct a model
calculate area of rectangles
draw a scale diagram
find the best buy using simple proportions
calculate volume and area of a cuboid
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 isometric300
draw scale diagrams for length and area problems
- 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.
explore area, perimeter and volume
- 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.
investigate areas and perimeters of cuboids
- Plan a mathematical investigation in a group.
- Take measurements and make calculations to complete an investigation.
- Interpret the accuracy of the investigation.
calculate volume of cuboids
make scale models
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)
use number strategies to solve puzzles (Problems 1, 2 and 4)
explore areas of geometric shapes on geoboards (Problem 3)
find volume of a cuboid (Problems 2 and 3)
solve problems involving sequential patterns (Problem 4)
find the area and the volume
Students will be able to model their understanding of volume through creating models and calculating volume using a formula.