Te Kete Ipurangi
Communities
Schools

# NA4-7: Form and solve simple linear equations.

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:

## Four Fours Challenge

• Units of Work
• Number and Algebra
• Level Four

This unit provides an opportunity for students to use all the arithmetic operations, investigate the effect of combinations of arithmetic operations, communicate with each other using brackets and other mathematical signs and symbols correctly, and use their calculators correctly.

## Balancing Acts

• Units of Work
• Number and Algebra
• Level Four

The unit involves students in solving problems that can be modelled with algebraic equations or expressions. Students are required to describe patterns and relationships using letters to represent variables.

## Magic Squares

• Units of Work
• Number and Algebra
• Level Four

In this unit students develop and use algebraic representations of 3-by-3 magic squares in which the sum of the three numbers in each row, column, and diagonal, add to a constant number known as the Magic Number. Students are posed an array of problems to solve using their algebraic tools.

## Arithmagons

• Units of Work
• Number and Algebra
• Level Four

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 to solve triangular arithmagons and square arithmagons and use linear equations to solve triangular arithmagons. They establish and prove algebraically the general rules for solving arithmagons.

## Fibonacci I

• Units of Work
• Number and Algebra
• Level Four

In this unit we look at Fibonacci numbers and how they occur in nature. We also look at what factors Fibonacci numbers can have.

## Still more lollies

• Problem solving activities
• Number and Algebra
• Level Four
Solve problems that involve simple linear relationships
Write simple linear expressions
Devise and use problem-solving strategies to explore situations mathematically

## Free Cell

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

## Choices

• Units of Work
• Number and Algebra
• Level Four

This unit is about making calculations in the real life situations of taxis, hire cars, and cell phones.

## Squirt Level 4

• Units of Work
• Number and Algebra
• Level Four

This unit explores how the suite of learning objects, "Squirt", can be used to support students’ development of multiplicative thinking. Squirt encourages students to anticipate multiplicative measurement relationships, e.g. three measures of A fit in B, by partially filling a container and imaging how many more squirts will be needed. Since the containers are not always cylindrical it also develops ideas about conservation of volume.

## Strategic Solving Part III

• Secondary activities
• Number and Algebra
• Level Four

These exercises and activities are for students to use independently of the teacher to practise number properties.

## Strategic Solving Part IV

• Secondary activities
• Number and Algebra
• Level Five

These exercises and activities are for students to use independently of the teacher to practise number properties.

## Strategic Solving Part II

• Secondary activities
• Number and Algebra
• Level Four

These exercises and activities are for students to use independently of the teacher to practise number properties.

## Domino Delight

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.
A PDF of the student activity is included.

## Number Tricks

• Figure It Out activities
• Number and Algebra
• Level Three

This is a level 3 and 4 algebra strand activity from the Figure It Out series.
A PDF of the student activity is included.

## Number Crunching

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Bailey Bridges

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Parking Fees

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Number Puzzles

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Table Mats

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Design Day

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Letter Designs

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Problem Smorgasboard

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Frieze

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Initials Logo

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Bathroom Tiles

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Patterns and Designs

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Tiling Spacecraft

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra strand activity from the Figure It Out series.

## Balancing Act

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra activity from the Figure It Out series.
A PDF of the student activity is included.

## Charu in a Pickle

• Figure It Out activities
• Number and Algebra
• Level Four

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.

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 number, algebra, statistics activity and level 5 number activity from the Figure It Out series. It relates to Stage 7 and 8 of the Number Framework.
A PDF of the student activity is included.

## Moving On

• Figure It Out activities
• Number and Algebra
• Level Four

This is a level 4 algebra activity from the Figure It Out theme series.

## Unknowns and variables: Solving one-step equations

• Units of Work
• Number and Algebra
• Level Four

The purpose of this unit is to support students as they read and record equations in which letters (or variables) represent an ‘as yet unknown’ amount.

## Solving multi-step equations

• Units of Work
• Number and Algebra
• Level Four

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.

## Going Bananas

• Rich learning activities
• Number and Algebra
• Level Four

The purpose of this activity is to engage students in solving problems using integer values.

## Cats and bods

• Rich learning activities
• Number and Algebra
• Level Four

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.

## The 50 Day Challenge

• Rich learning activities
• Number and Algebra
• Level Four

The purpose of this activity is to engage students in solving a problem using measurement and arithmetic techniques.

## The Bee Sting Problem

• Number and Algebra
• Level Four

This unit integrates student learning in the mathematics and science learning areas. Students will be developing their use of rates and ratios, exploring linear relationships using tables and graphs, in the context of chemical reactions involving common household acids and bases.

## Solving linear equations

• Units of Work
• Number and Algebra
• Level Four

This unit teaches students to identify linear relationships and solve linear equations in context.

## Catering for Size

• Number and Algebra
• Level Four

The purpose of this unit is to engage the student in applying their knowledge and skills of measurement to solve problems involving food technology.

## Down on the farm

• Units of Work
• Number and Algebra
• Level Four

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.

## Improbable sports

• Units of Work
• Number and Algebra
• Level Four

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.