# GM5-4: Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.

This means that students should find the ratio of the diameter of a circle to its perimeter (π) by measuring several circles and looking for the relationship.

C = 2πr (2 times pi times the radius), or

C = πD (pi times the diameter)

They should apply the formula to find the circumference of any circle, for example the circumference of a bicycle tyre. Students should find the formula for area of a circle by cutting several circles into increasingly small sectors and reassembling the sectors to approximate rectangles, A = πr^{2} (pi times the radius squared). They should apply this formula to finding the area of any circle.

Students will find the perimeters of composite shapes by adding the lengths of the sides together. At Level Five composite shapes are made up of common polygons (for example rectangles, triangles, semicircles). Students will find the area of composite shapes by calculating the areas of the parts and adding them together. Students will find the volumes of prisms by multiplying the area of their cross section by their length, for example for a cylinder multiply the area of the circle by the length of the cylinder.

## Scale Factors for Areas and Volumes

- Units of Work
- Geometry and Measurement
- Level Five

This collection of teaching ideas provides students with the opportunity to discover the effect of a change of length by a given factor on area and volume.

## Round the Track

- Units of Work
- Geometry and Measurement
- Level Five

This unit is about making calculations in the real life situations of athletics.

## Fences and Posts

- Units of Work
- Geometry and Measurement
- Level Five

In this unit a measurement strand objective concerning finding areas of shapes is explored, then a link to the algebra strand is explored.

## A4 Containers

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Describe the relationship between the surface area and volume of a container

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model)

## Bill's Badge

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Construct two intersecting circles where the radius of the second circle is on the circumference of the first.

Use Pythagoras’ theorem to find the area of a rhombus

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model)

## Penny's Box

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Find the volume and surface area of rectangular prisms

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

## Puck's Girdle

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Find the circumference of a circle;

Understand the relationship between changes in the circumference of a circle and changes in the radius.

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

## Tennis Ball Tubes

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Use the formula for the circumference and diameter of a sphere to solve a problem

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model)

## Playdough Balls

- Problem Solving Activities
- Geometry and Measurement
- Level Five

compare the volume of a sphere and a cylinder by either measuring **or** applying a formula.

devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

## Karen's Tiles

- Problem Solving Activities
- Geometry and Measurement
- Level Five

investigate how perimeter changes as area changes

see the relation between area and perimeter for similar shapes

pose questions for mathematical exploration

prove or refute mathematical conjectures

## Peter's Second String

- Problem Solving Activities
- Geometry and Measurement
- Level Five

determine the maximum area of a rectangle with a given perimeter

determine the range of areas of a rectangle with a given perimeter

pose questions for mathematical exploration

prove or refute mathematical conjectures

## Dan's Badge

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Use area formulas of circles and squares to solve problems

## Around We Go

- Units of Work
- Geometry and Measurement
- Level Five

The measurement of circles and the relationships to be found within them are the focus for this unit. Students investigate a range of circles, each with a different radius, diameter and circumference and assemble this information in their search for relationships.

## Circle Links

- Figure It Out Activities
- Geometry and Measurement
- Level Four

This is a level 4 and 5 measurement strand activity from the Figure It Out series.

## Colossal Kiwifruit

- Figure It Out Activities
- Geometry and Measurement
- Level Five

This is a level 5 measurement strand activity from the Figure It Out series.

## Round the Bend

- Figure It Out Activities
- Geometry and Measurement
- Level Five

This is a level 5 measurement strand activity from the Figure It Out series.

## On the Right Track

- Figure It Out Activities
- Geometry and Measurement
- Level Five

This is a level 5 measurement strand activity from the Figure It Out series.

## Gumboot Games

- Figure It Out Activities
- Geometry and Measurement
- Level Five

This is a level 5 measurement strand activity from the Figure It Out series.

## Area of a circle

- Geometry and Measurement
- Level Five

The purpose of this multi-level task is to engage students in an investigation of the area of circles.

## Marketing Tricks

- Geometry and Measurement
- Level Five

The purpose of this multi-level task is to encourage students to use algebraic techniques when solving a measurement problem.