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NA4-7: Form and solve simple linear equations.

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Elaboration on this Achievement Objective

This means students will form and solve simple linear equations in the form y = mx + c, where x and y are related variables and where m is a whole number and c is an integer, for example q = 3p – c, or a + 5 = 4b. When the value of one variable is given the value of the other can be found by solving the equation, for example 3p – 6 = 18. Students should understand the equals sign as a statement of balance and know what operations to both sides of an equation preserve that balance, for example take off the same number from both sides. At Level Four students should be able to find the required value using both sensible estimation and improvement, and by formal methods of applying inverse operations, for example 3p – 6 = 18 so 3p = 24 (adding six to both sides) so p = 8 (dividing both sides by three).

 

Teaching resources for this Achievement Objective
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Number Tricks

Level Three
Level Four
Number and Algebra
Figure It Out activities
This is a level 3 and 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

explore equation puzzles (level 3)

use symbols to generalise the pattern (level 4)

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Parking Fees

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a linear equation to solve a problem

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Patterns and Designs

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a rule for a geometric pattern

write a rule for a relationship as a linear equation

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Perimeter = area rectangles

Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in finding the perimeter and area of rectangles. They engage in trying to find rectangles where the number measure of the perimeter equals the number measure of the area.
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Problem Smorgasboard

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a linear equation to solve a problem

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Solving linear equations

Level Four
Number and Algebra
Units of Work
This unit teaches students to identify linear relationships and solve linear equations in context.
  • Identify and find values for variables in context.
  • Identify linear relationships in context.
  • Represent linear relationships using tables, graphs and simple linear equations.
  • Draw strip diagrams to represent linear equations.
  • Solve simple linear equations and interpret the answers in context.
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Solving multi-step equations

Level Four
Number and Algebra
Units of Work
In this unit students read, write and solve multistep equations that include variables that stand for fixed values. Importantly, students also come to see that a variable can be interpreted in other ways, including representing a quantity that varies in relation to another quantity.
  • Recognise that to find the value of the variable, you have to ‘undo’ what has been done to it.
  • Review and solve single step whole number equations that include a variable.
  • Solve two-step equations and represent the solution using materials.
  • Represent number relationships using words, a table300
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Still more lollies

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Solve multi-step problems that involve simple linear relationships.
  • Write simple linear expressions.
  • Devise and use problem-solving strategies to explore situations mathematically.
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Strategic Solving Part II

Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practise number properties.

solve linear equations with decimal fractions
use appropriate forms of the equation to solve for x.

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Strategic Solving Part III

Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practise number properties.
solve linear equations with integer solutions
 
use a range of add/sub strategies to solve linear equations.
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Strategic Solving Part IV

Level Four
Level Five
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practise number properties.

solve linear equations with fractions.
use appropriate forms of the equation to solve for x.
use a range of add/sub strategies to solve linear equations.

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Table Mats

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a rule for a geometric pattern

write the rule for a relationship as a linear equation

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The 50 Day Challenge

Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in solving a problem using measurement and arithmetic techniques.
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The Bee Sting Problem

Level Four
Number and Algebra
This unit integrates the mathematics and science learning areas, and provides an opportunity for students to explore the context of chemical reactions involving common household acids and bases. In turn, students will develop their use of rates and ratios, and will explore linear relationships using...
  • Identify household acids, bases, and neutral solutions, and pH indicators.
  • Construct a pH indicator scale.
  • Construct appropriate and accurate graphs.
  • Interpret and apply graphed results of a practical investigation.
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Tiling Spacecraft

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 algebra strand activity from the Figure It Out series.

use a rule to describe a relationship