Students can:

• generalise an algebraic rules to match the information given
• perform appropriate substitutions with algebraic expressions
• solve equations involving fractions

Activities to support the strategy

When solving this problem students will need to create generalised algebraic equations for each part of the question. Students will then need to perform appropriate substitutions and solve the resulting equation. To do this efficiently, they will need to choose carefully and have a confident understanding of substitutions and solving equations involving fractions.

That is: Kumi is ¾ of the height of Zac. Sue is ⅔ the height of Zac. Kumi is 15 centimetres taller than Sue. How tall is Zac in centimetres?

This should result in the following equations:

K= ¾ Z, S = ⅔ Z, K = S + 15

Taking the equation K=S+15 students need to replace the K with K= ¾ Z and the S with S= ⅔ Z thus creating the equation ¾ Z= ⅔ Z+15

Students then need to recognise and multiply each of the terms by the common denominator 12, and then solve the resulting equation:

Activity 1

Students should first review the process of writing algebraic expressions and equations from a worded description or rule. Particular attention should be given to order of operation, the correct use of mathematical convention and potential problem areas with the use of language

• Three times a particular number plus five is equal to thirty-five - 3 x + 5 = 35
• The difference of six and x 6 − x
• In five years’ time, my son will be half my age ∴ s + 5 = ½ (d+5)

Activity 2

Students should also practice the use of algebraic substitution in a variety of situations including simple numeric substitution into formulas and cases where one algebraic expression is substituted for another.

References

Australian curriculum

ACMNA176: Create algebraic expressions and evaluate them by substituting a given value for each variable, using authentic formulas to perform substitutions

NSW syllabus

MA4-8NA: Generalises number properties to operate with algebraic expressions,

MA4-1WM: communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols,

MA4-2WM: applies appropriate mathematical techniques to solve problems,

MA4-3WM: recognises and explains mathematical relationships using reasoning

Student resources

• TIMES Module 36 - Number and Algebra: formulas - this 13-page guide for teachers introduces the use of formulas, and includes substitution and the solution of the resulting equations.
• Matching a formula to a given context - this five-page HTML resource is about solving problems concerning matching formula in a given context. It contains five questions, two of which are interactive, and one video. The resource discusses and explains determining a formula to reinforce students' understanding.
• TIMES Module 26 - Number and Algebra: linear equations - this 16-page guide for teachers introduces the solution of linear equations and their uses.