# 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.

- Measure the circumference of circles.
- State the relationship between the circumference and diameter of a circle.

find approximate value of pi from measurement

find the circumference and area of a circle

find the area of a cylinder

fidnt he volume of a cuboid

Use area formulas of circles and squares to solve problems

- Find areas of shapes.
- Find simple two-variable linear patterns relating to areas.

- Showing that a polygon is composed of rectangles and triangles.
- Showing that a non-right angled triangle is composed of two right-angled triangles.
- Given the length of one side, finding the area of a regular polygon.

order distances

use rates to solve problems involving measuring units

find the perimeter (cicumference) of a circle

find the area of a circle

**or**applying a formula.

calculate circumference of a sphere

explore the radius and circumference relationship

- Draw a plan to scale, of an object based on a rectangle and two semi-circles.
- Understand the relation of length on the plan to actual length.
- Find lengths and areas use these for costing purposes.
- Be able to link speed, distance and time (given two find the third).
- Estimate distances and300

- Use scale factors to investigate areas being enlarged.
- Use scale factors to investigate volumes being enlarged.
- Solve real life context problems involving scale factors.

- Use translations, reflections and rotations to create friezes and Escher type tessellations.
- Create tivaevae and other symmetric patterns and describe the lines of symmetry and rotational symmetry.
- Apply knowledge of circles (perimeters, area and surface area) to create nets for cylinders.