# Stage 5 - algebraic techniques – substitute into simple quadratic equations

## Strategy

Students can:

• Substitute non-integer values into a simple quadratic equation and evaluate the result using a calculator

## Activities to support the strategy

Students should be given the opportunity to practice substitution into a variety of formulas. These should include simple linear equations and more complicated quadratic equations. Students should also be given a number of real-life practical formula to use. It is also important for students to understand and use the correct terminology when dealing with equations. The concepts around independent and dependent variables, constant terms and the subject of an equation should be explained. In each case, students should be provided with the independent variables and constant terms and asked to determine the dependent variable (or subject) or each equation. Once students have gained confidence they may then be given the subject and asked to find the matching independent variable as an extension activity. In addition, as calculators may be used, appropriate rounding strategies should be reinforced.

### Activity 1

Students should first review basic substitution into linear formulas. The Substitute values into simple linear equations activity allows students to review the process of substitution.

Once students have developed confidence, they should then move to the Evaluating formulas activity which provides a number of practical and real-life formulas to investigate.

### Activity 2

Students could then work to synthesise their understanding of a variety of mathematical skills to investigate one practical area. An example of this is the Wheat: from seed to market activity. This is a unit of work designed for year 9 students that provides mathematics activities in the context of wheat production in Australia. Activities focus on authentic data and include using rainfall data to identify potential wheat-growing areas and comparing this with existing major wheat-producing areas; using a formula to predict wheat yields based on rainfall patterns and displaying results in a spreadsheet; comparing predictions with actual yields; calculating wheat yield per hectare; estimating the number of wheat silos required to house the annual wheat crop; and displaying data for Asian export destinations for Australian wheat by constructing back-to-back stem-and-leaf plots. The resource provides links to useful resources - Scootle

## References

### Australian curriculum

ACMNA234: Substitute values into formulas to determine an unknown

### NSW syllabus

MA5.2-8NA: Solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques

## Student resources

• Substitute values into simple linear equations - this five-page HTML resource is about solving problems concerning substitution into simple linear equations. It contains four questions, one of which is interactive, and one video. The resource discusses and explains substitution into simple linear equations to reinforce students' understanding.
• Evaluating formulas - this six-page HTML resource is about solving problems involving substitution into algebraic expressions and formulas. It contains one video and three questions, one of which is interactive. The resource discusses and explains solving problems with substituting into algebraic expressions and formulas to reinforce students' understanding.
• TIMES Module 36: Number and Algebra: formulas - teacher guide - this 13-page guide for teachers introduces the use of formulas, and includes substitution and the solution of the resulting equations.