Mathematics / Year 9 / Measurement and Geometry / Geometric reasoning

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Solve problems using ratio and scale factors in similar figures (ACMMG221)

Elaborations
  • establishing the relationship between areas of similar figures and the ratio of corresponding sides (scale factor)
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Ratios,  Scale (Proportions),  Similarity (Geometry)

Interactive resource

Exploring ratios and proportions

Explore ratios by comparing the dimensions of two rectangles. Choose a scale to enlarge the smaller shape and identify whether its sides are proportional to those of the larger rectangle. For example, a rectangle with sides in the ratio 4:5 has an equivalent ratio to a rectangle with sides in the ratio 12:15. Watch a video ...

Interactive resource

Trigonometry: measuring with triangles

Compare the shadows cast by a small stick and a larger object such as a column of a Greek building. Check the angles at which the shadows are cast and confirm whether the two objects create similar triangles. Use equivalent ratios to calculate the lengths of a triangle's sides: the height of an object or the length of a ...

Interactive resource

Measures: scaling up

Compare the areas of squares, rectangles and triangles before and after being scaled up (enlarged). Notice that 'similar shapes' in the mathematical sense have the same shape but different areas. Explore the relationship between side-length enlargement and area enlargement when scaling up shapes. This learning object is ...

Interactive resource

EagleCat: scale it

Explore changes in area when a shape is acted on by a scale factor. Examine changes in volume when an object is acted on by a scale factor. Analyse the changes using whole numbers.

Teacher resource

reSolve: Tree Biomass

In this sequence of two lessons, students investigate how many trees would be required to supply paper for their school for a year. Students use similar triangles, Pythagoras' Theorem and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree. They measure trees, calculate their ...

Teacher resource

reSolve: Pythagoras' Theorem - Phone finding

This lesson challenges students to apply Pythagoras' Theorem to explore a practical real-world problem. Students explore technology reliant on mathematical concepts. The lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources such as ...

Interactive resource

Measures: similar shapes

Compare the sizes and angles of a range of triangles, squares and rectangles. Notice that 'similar shapes' in the mathematical sense have the same shape and possibly different sizes. Corresponding sides are in proportion, and corresponding angles are equal. Identify shapes that are similar and create shapes similar to given ...

Interactive resource

Measures: scaling down

Compare the areas of squares, rectangles and triangles before and after being scaled down (reduced). Notice that 'similar shapes' in the mathematical sense have the same shape but different areas. Explore the relationship between side-length reduction and area reduction when scaling down shapes. This learning object is ...

Interactive resource

Trigonometry: finding angles

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Set the cosine, sine and tangent values of angles from 0–90 degrees. Identify the angle for each of the values. This learning object is one in a series of ...

Interactive resource

In proportion: graphs of ratios, rates and scales

Complete customer orders for a large hardware store by interpreting ratios, rates and scales. Work in the manager's office and discover how ratios, rates and scales can be represented as graphs. Use the graphs to discover quantities for garden fertiliser ingredients, the cost of mulch, and for finding lengths of timber ...

Interactive resource

In proportion: variables in ratios

Complete customer orders for a large hardware store by interpreting the ratios. Work in the gardening department to fill orders for liquid fertiliser (expressed as ratios). Examine the equations suggested to you by your colleagues. Choose and solve the correct equation to complete each order. This learning object is the ...

Assessment resource

Vitality drinks: assessment

Assess your ability to make drinks from a menu to match customer orders. For example, calculate the volume of each juice type required when given the ratio of juices for a drink of a particular total volume. Watch an animation to determine the ratio of juices in a new recipe. Calculate the volume of each juice in the new ...

Interactive resource

In proportion: variables in rates and scales

Complete customer orders for a large hardware store by interpreting rates and scales. Work in the gardening department to fill orders for mulch (expressed as rates), and help out with scale plans in the timber department. Examine the equations suggested to you by your colleagues. Choose and solve the correct equation to ...

Interactive Resource

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Interactive resource

Exploring powers of 10

Examine a table of numbers expressed using base 10 exponents. Look at their equivalents expressed in other numeric formats such as expanded values and fractional exponents. Arrange the numbers within each group in descending order of magnitude. Use a scalable viewer to examine a scene within a valley in Canada. Look at ...

Dataset

Australia's population: countries of birth - dataset

The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is included in the list of related datasets on the page in MS Excel format.

Teacher resource

Very large and very small numbers

This is a website designed for both teachers and students, which addresses very large and very small numbers from the Australian Curriculum for year 9 students. It contains material on the vocabulary and notation for dealing with very large and very small numbers using scientific notation. There are pages for both teachers ...

Interactive resource

Measures: scaling surface area

Compare the surface area of cubes and rectangular prisms before and after being scaled up (enlarged) or scaled down (reduced). Notice that 'similar shapes' in the mathematical sense have the same shape but different surface areas. Explore the relationship between side length and surface area when scaling solids. This learning ...

Moving Image

Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Assessment resource

Biscuit factory: three gears: assessment

Test your understanding of ratios by interpreting three-wheel gear systems where the wheels have different numbers of teeth. For example, how many rotations does a 10-tooth gear wheel make when driven by two driver wheels having 20 and 10 teeth? Also, choose a combination of three gear wheels to achieve a required number ...