Mathematics / Year 10 / Number and Algebra / Patterns and algebra

Curriculum content descriptions

Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)

Elaborations
  • expressing the sum and difference of algebraic fractions with a common denominator
  • using the index laws to simplify products and quotients of algebraic fractions
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Simple fractions,  Algebraic terms,  Number operations

Text

Geometry of water sources and landforms

Indigenous cultures have always been deeply aware of the location of water and its significance. In this resource students will apply geometric, trigonometric, and algebraic techniques to analyse idealised water body shapes and associated landforms. They will calculate surface areas, volumes, angles, and heights of these ...

Text

The Mathematics of Projectiles - Calculate

This activity provides a practical introduction to the motion of projectiles with a focus on angles. It is designed as a lead in to parabolic and quadratic functions.

Text

Factorising Quadratics and Solving - Calculate

This activity explores the properties of the family of functions and their graphs known as parabolas. The unit includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas to take their understanding further. A short quiz at the end ...

Online

Formulate and manipulate expressions: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Formulate and manipulate expressions. Students extend the distributive law to expanding the product of two binomials (ax + b)(cx + d) and the factorisation of non-monic quadratic expressions with integer coefficients. Students practise algebraic manipulation involving ...

Text

Work sample Year 10 Mathematics: Mathematics assignment

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 10 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

Online

Logarithmic scale: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Logarithmic scale. Students read and interpret different types of scales. They understand that that a logarithmic scale uses powers 10 and how it appears on a graph. Students know when the use of such a scale is appropriate and where logarithmic scales are used for ...

Online

reSolve: Algebra: Think of a number- Binomial Equations

This lesson engages students in investigating a 'think of a number' game and then model it visually and algebraically. This develops skills in algebraic operations including expanding, factorising and collecting like terms. Students investigate whether the game will work for any number and are challenged to generate the ...

Interactive

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.

Video

Big data, better hospitals

Overcrowding in hospitals is one of the biggest challenges facing our healthcare system . In order to reduce hospital waiting times, the Patient Admission Prediction Tool (PAPT) uses historical data to predict how many patients, and with what kinds of injuries, are expected to arrive at the emergency department each day ...

Video

MathXplosion, Ep 15: How many times can a sheet of paper be folded?

Why can a regular sheet of paper be folded only about six times? By folding a sheet of paper in half, over and over, the number of layers and the thickness of the paper doesn’t just double, they increase exponentially. Find out how many times a sheet of paper can actually be folded!

Interactive

Laptop wrap: Expanding on algebra

Students make a presentation on the index laws, investigate the visual representation of the binomial expansions and design an acronym to help recall the special products. 

Interactive

Laptop wrap: Taxing times

A laptop-friendly resource with a focus on student use of spreadsheets to calculate various income and taxation problems. A debate on the merits of income sources is included.

Interactive

The Numberline

An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals

Online

TIMES Module 39: Number and Algebra: polynomials - teacher guide

This is a 27-page guide for teachers. This module introduces addition, subtraction, multiplication and division of polynomials. Factorisation of polynomials and the solution of polynomial equations are also discussed.

Online

TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.

Online

TIMES Module 36: Number and Algebra: formulas - teacher guide

This is a 13-page guide for teachers. It introduces the use of formulas, and includes substitution and the solution of the resulting equations.

Online

TIMES Module 35: Number and Algebra: the quadratic function - teacher guide

This is a 29-page guide for teachers. It introduces graphing of quadratic functions.

Online

TIMES Module 33: Number and Algebra: factorisation - teacher guide

This is a 17-page guide for teachers. It continues the discussion of factorisation. In particular, the techniques for the factorisation of quadratic expressions are presented.

Online

TIMES Module 34: Number and Algebra: quadratic equations - teacher guide

This is a 19-page guide for teachers. It introduces quadratic equations and methods for solving them.

Online

TIMES Module 31: Number and Algebra: indices and logarithms - teacher guide

This is a 26-page guide for teachers. It extends the study of indices to rational indices and introduces logarithms.