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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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Arithmagons

Level Four
Number and Algebra
Units of Work
In this unit students explore patterns and relationships among the circle numbers and box numbers that form different arithmagons. Students identify, and use rule-based patterns, and linear equations to solve a range of arithmagons, beginning with square and triangular arithmagons. They establish...
  • Devise rules based on numerical patterns to solve triangular arithmagons.
  • Explain the condition for the solution of any square arithmagon.
  • Form and use linear equations to solve triangular arithmagons.
  • Develop proofs of rules and conditions for the solution of arithmagons.
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Bailey Bridges

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 numbr pattern

use an equation to describe a patter

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Balancing Act

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

find unknowns to balance a linear equation represented by a balance scales diagram

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Balancing Acts

Level Four
Number and Algebra
Units of Work
The unit involves students in solving problems that can be modeled with algebraic equations or expressions. Students are required to describe patterns and relationships using letters to represent variables.
  • Predict further members in patterns of equations using relationships within the equations.
  • Develop function rules to describe relationships.
  • Find specific values for variables from given relationships.
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Bathroom Tiles

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 relationship as a linear equation

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Beefing Up Business

Level Four
Integrated
Figure It Out activities
This is a level 4 number, algebra and statistics activity from the Figure It Out series. A PDF of the student activity is included.

use addition to sovle money problems

use multiplication and division to solve problems

find percentage of a number

solve problems involving ratios

find fraction of a number

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Catering for Size

Level Four
Integrated
The purpose of this unit is to engage students in applying their knowledge of measurement to solve problems involving food technology.
  • Identify, quantify, and represent, using graphs and expressions, the effect of a scale in time contexts.
  • Describe, apply, and graph linear relationships to solve problems involving time, temperature, and mass.
  • Scale, convert, compare, and apply metric measurements to solve problems involving grams and300
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Cats and bods

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a problem involving the multiplicative strategies that form the basis of early algebraic investigation.
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Charu in a Pickle

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number and algebra activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.A PDF of the student activity is included.

find a percentage of a decimal number

solve addition and subtraction problems

compare prices by using proportions

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Choices

Level Four
Number and Algebra
Units of Work
This unit is about making best option decisions in real-life situations based on cost. Common examples of such decisions are explored, including the cost of taxis, cooking times, hire cars, and mobile phones.
  • Calculate the cost of hiring a taxi, hiring a car, and using a phone, and the cooking time for meat.
  • Compare the costs of different plans.
  • Represent linear relationships using graphs.
  • Use graphs to make decisions about the best deal.
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Design Day

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.

complete a table to find a pattern

use a linear equation to describe a relationship

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Domino Delight

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.

sovle problems with possibilites and constraints

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Down on the farm

Level Four
Number and Algebra
Units of Work
The unit is designed as a simple introduction to systems of linear equations. Students solve problems in which they meet two constraints to find a single solution. Both constraints can be expressed as linear equations.
  • 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 and ratios.
  • Solve problems in which two or more conditions must be met.
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Food for thought: Using equations

Level Four
Number and Algebra
Units of Work
The purpose of this unit is to support students to represent number problems as equations, and to strategically choose the best operation to solve problems in context.
  • Understand that an unknown amount or number can be represented with a symbol: a question mark, a shape or a letter.
  • Recognise that to find the value of the missing number, you have to ‘undo’ what has been done to it.
  • Write word problems of real-life situations and express these with equations that300
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Four Fours Challenge

Level Four
Number and Algebra
Units of Work
This unit provides an opportunity for students to use all the arithmetic operations, investigate the effect of combinations of arithmetic operations, communicate mathematical thinking using brackets and other mathematical signs and symbols correctly, and use their calculators correctly.
  • Write and calculate arithmetic expressions precisely using the order of operations.
  • Recognise the importance of the order of operations when using a calculator.
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Free Cell

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Solve problems involving fractions and percentages.
  • Devise and use problem solving strategies (guess and check, be systematic, look for a pattern, make a table).
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Frieze

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 pattern

use a linear equation to describe the relationship

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Going bananas

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving problems using integer values.
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How high is the table?

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is for students to find the value of a specific unknown given two relationships among three variables. The relationships are expressed diagrammatically.
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Improbable sports

Level Four
Integrated
The purpose of this unit is to engage the student in applying their knowledge and skills of measurement and algebra within the science learning area; to investigate a physical system.

Students develop their skills and knowledge on the mathematics learning progressions measurement sense and using symbols and expressions to think mathematically, in the context of time and motion in sports. 

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Initials Logo

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 patter

write the rule for a relationship as a linear equation

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Letter 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 pattern

use a linear equation to describe the relationship

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Moving On

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

use a formula to solve calculations

write a linear formula to express a linear relationship

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Number Crunching

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.

write the rule as a simple linear equation

use a rule to complete a number pattern

 

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Number Puzzles

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.

write an equations to generalise a pattern