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# Mathematics / Year 8 / Measurement and Geometry / Using units of measurement

Curriculum content descriptions

Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area (ACMMG197)

Elaborations
• investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
• investigating the area of circles using a square grid or by rearranging a circle divided into sectors
General capabilities
• Literacy Literacy
• Numeracy Numeracy
ScOT terms

Area,  Diameter,  Radius,  Circumference

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Year level 7-8
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Learning area Mathematics

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### Exploring area and perimeter

Build a compound shape on a grid from shapes such as rectangles, semicircles and squares. Notice that the total area of the compound shape equals the sum of the areas of all of the component shapes. Build a rectangle to produce a given area and perimeter. Identify shapes used to form a compound shape. Calculate the area ...

### Exploring diameter and circumference

Explore the constant value of 'pi' by investigating the relationship between circumference and diameter. Unroll the circumference of a circle to form a straight line. See how many times the diameter can be placed beside it. Notice the relationship between the circumference and diameter applies no matter what size the circle ...

### Circles

This is a website designed for both teachers and students that refers to the properties of circles including the circumference and area from the Australian Curriculum for year 8 students. It contains material on finding circumferences and areas of circles, and the areas and perimeters of shapes formed from circles and other ...

### TIMES Module 17: Measurement and Geometry: the circle - teacher guide

This is a 15-page guide for teachers. In the module the formulas for finding the circumference and area of a circle are introduced. The history and significance of the number pi is also included in this module.

### reSolve: Area of a circle

This lesson explores the formula for calculating the area of a circle. Students estimate the area of a circle using inscribed and circumscribed squares, and investigate proofs of the area formula. Each lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, supporting PowerPoint ...

### reSolve: Circumference

This sequence of three lessons explores the properties of circles, in particular the relationship between the diameter and circumference. In the first lesson, students use a cylinder containing three tennis balls to understand that a circumference is 'three and a bit' times the diameter. They then complete five different ...

### Area of triangles

Find the area of different types of triangles on a grid. Explore how the formula works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. Practise applying ...

### Exploring the Pythagorean theorem

Adjust the dimensions of a right-angled triangle. Calculate the area of squares bordering each side of the triangle. Notice that the area of the square bordering the hypotenuse is equal to the sum of the areas of the squares bordering the other two sides. Watch a video showing how Pythagoras's theorem is used to determine ...

### Area of triangles: assessment

Test your understanding of how to use the formula for calculating the area of triangles. Find the area of nine different triangles on a grid. First, predict the area of a chosen triangle on a grid. Find the base and height measurements of the triangle using an animation. Then, substitute the base and height measurements ...

### Compound shapes: small shapes

Estimate the area of a simple polygon. Try counting squares on a grid to help your estimate. Cut the shape into rectangles and triangles. Use a formula to calculate the exact area for each of the simple shapes. Then find the total area for the original polygon. Try dividing the shape again into fewer pieces. This learning ...

### Compound shapes

Select from three levels of complexity for working with polygons. Estimate the area of a randomly-generated polygon. Try counting squares on a grid to help your estimate. Cut the shape into rectangles and triangles. Use a formula to calculate the exact area for each of the simple shapes. Then find the total area for the ...

### Compound shapes: large shapes

Estimate the area of a highly complex polygon. Try counting squares on a grid to help your estimate. Cut the shape into rectangles and triangles. Use a formula to calculate the exact area for each of the simple shapes. Then find the total area for the original polygon. Try dividing the shape again into fewer pieces. This ...

### Surface area and volume

This is an interactive resource about investigating the surface areas and volumes of rectangular and triangular prisms. The resource can be used in one of two modes. In the Explore mode, the student can vary the height, width and depth of the prism, and the surface area and volume are calculated automatically. In the Compute ...

### Area of triangles: triangles without vertical or horizontal sides

Find the area of triangles that do not have vertical or horizontal sides. Explore how the formula works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. ...

### Area of a parallelogram

This is a Geogebra activity used to teach the area of a parallelogram. Suitable for use with an interactive whiteboard (IWB).

### Area of triangles: height intersects with the base inside the triangle

Find the area of triangles that have vertical or horizontal sides. In this type of triangle, the height intersects with the base inside the triangle. Explore how the formula for finding the area of a triangle works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling ...

### EagleCat: spin graph

Investigate the beautiful patterns that can emerge from the locus of a point on one circle rolling around another circle. Investigate families of curves that can be produced by: (a) changing the size of the rolling circle only, (b) changing the size of the fixed circle only or (c) changing the position of the point only.

### Exploring square roots

Build a square on a grid to cover a given number of units. Notice that each side of the square equals the square root of the area. Calculate the area of each square and work out the square root. For example, calculate the length of each side needed for a square to cover 81 units. Calculate the area of squares bordering ...

### Area of triangles: triangles with a right angle

Find the area of right-angled triangles. Explore how the formula works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. Practise applying the formula ...

### Compound shapes: medium-sized shapes

Estimate the area of a complex polygon. Try counting squares on a grid to help your estimate. Cut the shape into rectangles and triangles. Use a formula to calculate the exact area for each of the simple shapes. Then find the total area for the original polygon. Try dividing the shape again into fewer pieces. This learning ...