1. Home

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

Thanks for visiting NZMaths.
We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.
 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

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
Resource logo

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

Resource logo

A Parabolic Investigation

Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in an investigation of parabolas in a practical context.
Resource logo

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.
Resource logo

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.
Resource logo

Circuit Problems

Level Five
Number and Algebra
The purpose of this unit is to engage students in applying their understanding of algebra to solve problems within the science - physical world context of electrical circuits. Subsequently, students develop their skills and knowledge on the following mathematics learning progression: Using Symbols...
  • use algebra to generalise the results of a practical investigation.
  • apply knowledge of circuits, power, voltage, currents, and resistance to problem solving.
  • use graphical techniques to identify and describe a linear relationship found in a practical investigation. 
Resource logo

Displaying postcards

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • 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).
Resource logo

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

Resource logo

Doubling up

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • 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.
Resource logo

Jackson's consecutive numbers

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe a rule for the general term.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
Resource logo

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. In doing this, they recognise the key features of a parabola, find unknowns from the graph of a parabola, and find unknowns from simple quadratic equations. Procedural fluency and...
  • 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, including the300
Resource logo

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

Resource logo

Olympic training

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Form and solve linear equations.
  • Use ratios.
  • Devise and use problem solving strategies to explore situations mathematically (draw a diagram).
Resource logo

Overlapping powers

Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using algebraic equations, graphs and/or tables to solve a problem.
Resource logo

Playdough balls

Level Five
Integrated
Problem solving activities
This problem solving activity has a measurement focus.
  • Compare the volume of a sphere and a cylinder by measuring or applying a formula.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
Resource logo

Quadratics in context

Level Five
Number and Algebra
Units of Work
In this unit procedural fluency and conceptual understanding are developed together. Students will represent quadratic relationships, particularly using graphs and equations, and will use quadratic functions to model phenomena such as paths of projectiles, stopping distances and profits. In turn...
  • 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, including the300
Resource logo

Renting a Car

Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using their knowledge of linear relationships to solve a problem.
Resource logo

Slingshots

Level Five
Integrated
The purpose of this unit is to engage students in applying their understanding of measurement and algebra in investigating a physical system.
  • Solve problems involving the conservation of mechanical energy. 
  • Find elastic potential energy using graphs.
  • Determine the nature of the relationship between physical quantities (height and elastic stored energy) using a graph.
  • Use a physical property, elastic potential energy, to find an unknown300
Resource logo

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 with negative300
Resource logo

Square and triangular numbers

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • 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.
Resource logo

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: T he 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.
Resource logo

The magic squares

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use algebra as required.
  • Construct magic squares.
Resource logo

The painting triplets

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Form and solve linear equations.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
Resource logo

Three in a row

Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using operations on integers to solve a problem.
Resource logo

Transforming a square

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • 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).
Resource logo

Working backwards

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use their mathematical knowledge to invent problems.
  • Devise and use problem solving strategies to explore situations mathematically.