Year 8 Whole Project

Area and Volume Unit

VELS Progresion Points:

Measurement, Chance and Data

4.25*development and use of formulas for the area and perimeter of triangles and parallelograms

4.25*appropriate use of zero to indicate accuracy of measurement; for example, a piece of timber 2.100m long is accurate to the nearest mm

4.25*recognition of the mean value of a set of measurements as the best estimate, and that the range could represent the associated error

4.5*use of appropriate units and measurement of length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature, in context

4.5*calculation of total surface area of prisms, including cylinders, by considering their nets

4.5*understanding of the distinction between error and percentage error

5.0*students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context.

5.0*they interpret and use measurement formulas for the area and perimeter of circles, triangles and parallelograms and simple composite shapes.

5.0* They calculate the surface area and volume of prisms and cylinders.

5.0*Students estimate the accuracy of measurements and give suitable lower and upper bounds for measurement values.

5.0*They calculate absolute percentage error of estimated values.

Working Mathematically

5.0*students formulate conjectures and follow simple mathematical deductions (for example, if the side length of a cube is doubled, then the surface area increases by a factor of four, and the volume increases by a factor of eight).

Number

5.0*They use approximations to π in related measurement calculations (for example, π × 52 = 25π = 78.5

correct to two decimal places).

WEBSITE REFERENCES:

Maths 300

300

Concepts / Key Skills / Activities
  • Units of Measurement – Length and Area
  • Calculation of Perimeter
  • Calculation of Area
/ *Understanding of units of measurement used for length Vs units of measurement used for area
*Examination of the key terms – Perimeter and Area. What is the difference
* Calculation of the area of shapes to gain a sense of area – as covering / Worksheet #1

  • Area of an Enclosure
  • Area and Perimeter of Composite Shapes
/ *To gain an understanding that different shapes can have the same area but different perimeters
*To gain an understanding that some shapes are combinations of other smaller shapes which can help us to calculate Perimeter and Area / Worksheet #2

  • Area of Parallelograms
  • Area of Triangles
/ *To investigate how to find the area of a parallelogram
*To revise finding the area of a triangle
*To reach the understanding as to why the formula is not length times width / Worksheet #3

  • Additional Applications in Area
/ *To explore ways to calculate areas of shapes that may require two separate calculations / Worksheet #4

  • Area given a diagram to scale
/ *Explore finding area when given a
Scale diagram of a country.
*Revise the use of scale / Outline of Lesson

Map of Australia

Maths 300 - Lesson #122
How many people can stand?
  • Circumference and Area of Circle
/ *To develop an understanding of π as a common ratio in finding the circumference of a circle
-To explore how to find the area of a circle / *Maths 300 – Lesson #45
Circumference of a Circle
*Maths 300 – Lesson #43
Area of a Circle
  • Area and Perimeter of Composite shapes involving whole circles and part circles.
/ *Finding Perimeter and Area of composite shapes including circles
*Conversion of Units / Activity:
*Get the students to design a garden bed which includes rectangle, circles and triangles. Get them to calculate the perimeter and area of the garden bed
*Give the students a length of edging to design a garden bed. It must include rectangles, circles and triangles. Get them to calculate the area of the garden bed.
  • Exploration of 3D shapes
  • Key aspects of 3D shapes – width, length and height
  • Volume
/ *To revise the drawing of rectangular
prisms
*To explore the relationship
between the lengths of the sides of
rectangular prisms and their volume / Worksheet #5

Maths 300 – Lesson #166
Newspaper cubes and Volume of a room.
  • Developing the area of the end x the length rule
/ *Using diagrams to calculate volume / Worksheet #6

  • To investigate Volume with changing dimensions
/ *To connect 2 –D and 3-D
representations
*For the student to focus on the
dimensions of a shape
*Describing different boxes
*Use a real life situations of building
open boxes to explore the changing
volumes.
*Integrate the use of Computer
software to explore the problem
further. / Worksheet #7

*Maths 300 – Lesson #81
Biggest Volume
  • To investigate the Volume of cylinder
/ *Revise the drawing of a cylinder
*Introduce the idea of calculating the
volume of cylinders
*To use the
‘Volume = area of the end x length’
relationship to calculate the
volume of a cylinder / Worksheet #8

  • To investigate a ‘realistic’ problem involving volume and capacity
/ *Revise the drawing of rectangular
prisms
*To pose an extended investigation / Worksheet #9

  • Volume of Composite Shapes
/ *Investigate the volume and
dimensions of composite shapes. / Worksheet #10

  • Dimensions of 3D Shapes
/ *To investigate a ‘realistic’ problem
drawing students’ attention to
representations and dimensions. / Worksheet #11

  • Calculating Surface Area
/ *To introduce surface area
*To explore the use of nets to assist
In finding Surface Area
*For students to focus on the
dimensions of a shape / Worksheet #12

Worksheet #13

  • Revision of key concepts covered so far
/ *Area of basic shapes
*Area of composite shapes
*Surface Area
*Volume / Task Centre – Area Problems
Take the following tasks and individually place them around the room with the necessary resources. Students then move around the tasks in groups to complete each task.
Tasks

  • Assessment Task

Useful Websites: