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NA5-7: Form and solve linear and simple quadratic equations.

Elaboration on this Achievement Objective

Students should be able to form the linear equation or simple quadratic (y = ax2 or y = x2 ± c, a and c are integers) to model a given situation (see patterns and relationships). They should understand that solving an equation involves finding the value of a variable when the other variable is defined, and interpret how the solution relates to the original context. Students should be able to solve linear and simple quadratic equations by applying inverse operations with an understanding of the equals sign as a statement of transitive balance, for example (3q + 7)/4 = 16, by multiplying both sides by four, subtracting seven, etc. They should also recognise where it is appropriate to solve an equation through trial and improvement, and find the missing value by systematic calculation.

 

Teaching resources for this Achievement Objective
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Alien Critters

Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a pattern

write a quadratic equations to describe the relationship

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A Parabolic Investigation

Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in an investigation of parabolas in a practical context.
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Array for quadratics

Level Five
Number and Algebra
Units of Work
This unit uses linear and area spatial models to represent and solve linear and simple quadratic equations.
  • Represent algebraic expressions as array diagrams.
  • Solve for specific unknowns, either areas or side, lengths from array diagrams.
  • Expand quadratic expressions with the support of array diagrams.
  • Factorise quadratic expressions with the support of array diagrams.
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Beanies

Level Five
Number and Algebra
Units of Work
This unit supports students to understand ratio problems such as: It takes 4 balls of wool to make 7 beanies. How many balls of wool does it take to make 19 beanies? It provides an entry into solving ratio problems using one simple algebraic equation.
  • investigate situations involving ratios;
  • understand that there are many ways to solve ratio problems;
  • solve simple equations of the form ax = b;
  • see the relevance of algebra to ratio problems.
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Circuit Problems

Level Five
Number and Algebra
The purpose of this unit is to engage the student in applying their knowledge and skills of algebra to solve problems within the context of electrical circuits.

Students develop their skills and knowledge on the mathematics learning progression Using Symbols and Expressions to Think Mathematically, in the science learning area, the physical world.

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Counting Cubes

Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series.

use a rule to make a prediction

write a rule as a quadratic equation

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Displaying postcards

Level Five
Number and Algebra
Problem solving activities
Apply algebra to the solution of a problem
Devise and use problem solving strategies to explore situations mathematically (be systematic, use a table, use algebra).
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Domino Stacks

Level Five
Number and Algebra
Figure It Out activities
This is a level 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

usea  table to continue a pattern

use a rule to describe a prediction

write a rule as a quadratic equation

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Doubling up

Level Five
Number and Algebra
Problem solving activities
Perform calculations with powers of numbers and square roots
Explain the relation between a square root and a square.
Devise and use problem solving strategies to explore situations mathematically. This problem uses be systematic, draw a picture, and think.
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From a square to a rectangle

Level Five
Number and Algebra
Problem solving activities
Solve problems involving percentage increases and decreases
Apply the area formulas for squares and rectangles
Devise and use problem solving strategies to explore situations mathematically (be systematic, use a diagram).
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Jackson's consecutive numbers

Level Five
Number and Algebra
Problem solving activities
Describe a rule for the general term.
Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Mary's Garden

Level Five
Number and Algebra
Units of Work
In this unit students represent a quadratic relationship using spatial patterns, tables, graphs and equations, recognising the key features of a parabola, and finding unknowns from the graph of a parabola and from simple quadratic equations. Procedural fluency and conceptual understanding are...
  • Make a table of one variable against another to represent a quadratic relationship.
  • Represent a quadratic relationship between two variables in words and as an equation.
  • Represent a quadratic relationship as a parabola on the Cartesian Plane.
  • Recognise the key features of a parabola, including300
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Number Juggling

Level Four
Level Five
Number and Algebra
Figure It Out activities
This is a level 4 and 5 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.

write an equation to generalise an equation

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Olympic training

Level Five
Number and Algebra
Problem solving activities
Form and solve linear equations
Use ratios
Devise and use problem solving strategies to explore situations mathematically (draw a diagram).
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Overlapping powers

Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in using algebraic equations, graphs and/or tables to solve a problem.
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Playdough balls

Level Five
Integrated
Problem solving activities
compare the volume of a sphere and a cylinder by either measuring or applying a formula.
devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
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Quadratics in context

Level Five
Number and Algebra
Units of Work
In this unit procedural fluency and conceptual understanding are developed together. Students will be representing quadratic relationships, particularly using graphs and equations. Quadratic functions are used to model phenomena such as paths of projectiles, stopping distances and profits to...
  • Make a table of one variable against another to represent a quadratic relationship.
  • Represent a quadratic relationship between two variables in words and as an equation.
  • Represent a quadratic relationship as a parabola on the Cartesian Plane.
  • Recognise the key features of a parabola, including300
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Renting a Car

Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in using their knowledge of linear relationships to solve a problem.
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Slingshots

Level Five
Integrated
The purpose of this unit is to engage the student in applying their knowledge and skills of measurement and algebra 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. 

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Solving linear equations 2

Level Five
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, including those with negative rates of change.
  • Represent linear relationships using tables, graphs and simple linear equations.
  • Draw strip diagrams to represent linear equations, including those with300
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Square and triangular numbers

Level Five
Number and Algebra
Problem solving activities
Give a general expression for the nth term of a pattern
Describe the links between different patterns
Devise and use problem solving strategies to explore situations mathematically
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Square Xs

Level Five
Number and Algebra
Units of Work
This unit supports students to form and use quadratic equations to solve ratio problems such as: The Square Xs Problem A square has an area, in m², that is a number nine less than six times the length of one side (in m). Find the dimensions of the square.
  • investigate situations involving quadratics
  • understand that there are many ways to solve quadratic problems
  • solve for unknowns in factorised quadratics
  • appreciate the use of algebraic techniques in solving quadratic problems.
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The magic squares

Level Five
Number and Algebra
Problem solving activities
Use algebra as required
Construct magic squares
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The painting triplets

Level Five
Number and Algebra
Problem solving activities
Form and solve linear equations
Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra)
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Three in a row

Level Five
Number and Algebra
Rich learning activities
The purpose of this multi-level task is to engage students in using operations on integers to solve a problem.