Stage 4 content (Yr.7 & 8)

Stage 4 Overview

Mathematics - Year 7

 

Term 1

Mathematics is used in many different areas in everyday life. The first term builds a student's confidence with numbers, order of operations and properties of common shapes.

Students learn about:

Computation with integers

  • Addition, subtraction, multiplication, division.

  • Order of operation; apply associative, commutative & distributive laws.

  • Compare, order, add, subtract, multiply and divide integers.

Fractions, decimals and percentages (Part 1)

  • Compare fractions, mixed numerals, place fractions on an integer number line.

  • Add, subtract, multiply and divide fractions with same and different denominators.

  • Express one quantity as a fraction of another.

  • Operate with decimals & percentages.

Angle Relationships, Properties of Geometric  Figures

  • Review types of angles, classify triangles, describe quadrilaterals according to sides and angles.

  • Properties of quadrilaterals.

  • Identify line and rotational symmetry.

  • Angle sum of a triangle and quadrilateral.

  • Solve simple numerical problems using properties of 2D shapes.


Term 2

Time, Index form and Algebra will be covered in this term. Students will become familiar with both 12 and 24 hour time and will be introduced to the basics of mathematical terminology and techniques for solving equations.

Students learn about:

Time

  • Solving problems involving 12 and 24 hour time within a single time zone and international time zones.

Indices with numerical bases

  • Operating with positive integers and the zero index of numerical bases.

  • Investigate index numbers and represent whole numbers as products of primes.

  • Find square roots, cube roots.

  • Apply divisibility tests.

Introductory Algebra, Algebraic Techniques (Part 1)

  • Generalises number properties to operate with algebraic expressions.

  • Use letters to represent numbers

  • Recognise and use simple algebraic expressions

  • Simplify algebraic expression using the four operations.

 

Term 3

Students will be calculating the dimensions of common shapes. They will also learn about mathematics involved in everyday finances.

Students learn about:

Length, Perimeter, Circumference

  • Calculating the perimeter of plane shapes and circumference of circles.

Area of Quadrilaterals, circles, unit conversion

  • Converting between metric units of area.

  • Establish and use formulas to find the areas of triangles, special quadrilaterals and circles. Solve area problems.

Calculating Percentages & Financial Mathematics

  • Performing calculations involving GST, discounts and best buys.

 

Term 4

The mathematics behind predicting events is investigated in this term. We will introduce the Cartesian plane. Students will also discover why we need to collect data and how to represent our findings mathematically.

Students learn about:

Simple Probability

  • Constructing simple sample spaces for single step experiments with equally likely outcomes.

  • Finding probabilities of events in single step experiments.

Linear Relationships (Part 1)

  • Locate and describe points on the Cartesian plane using coordinates. 

  • Describe translations and reflections in an axis on the Cartesian plane.

Data Collection and representation

  • Collecting, representing and interpreting single sets of data, using appropriate statistical displays.

 

 

Mathematics - Year 8 | Stage 4

Term 1

After reviewing year 7 work students will further explore fractions, decimals, percentages and properties of common shapes. The concept of writing number in index form is introduced.

 

Students learn about:

Computation with integers

  • Review¿¿ the ¿four¿ operations¿ with¿ integers.¿

  • Review fractions,¿ decimals¿ and¿ percentages.

Fractions, decimals and percentages - Part 2

  • Rounding ¿decimals¿.¿
  • Terminating¿ &¿ recurring¿ decimals¿,¿ irrational¿ numbers,¿
  • Percentages¿ of¿ quantities¿,¿ percentage¿ increase,¿ decrease,¿ percentage¿ problems¿ involving¿ money. 

Indices

  • Positive¿ integers¿ and¿ zero¿ indices¿
  • Numerical¿ bases.

Angle Relationships, Properties of Geometric  Figures

  • Apply¿ the¿ properties¿ of¿ corresponding¿,¿ alternate¿ and¿ co-interior¿ angles¿ on¿ parallel¿ lines¿ to¿ find¿ unknown¿ angles¿ with¿ reasoning.¿ Determine¿ and¿ justify¿ that¿ particular¿ lines¿ are¿ parallel.¿
  • Solve numerical¿exercises.¿

 

Term 2

This term focuses on determining the area of regular shapes such as rectangles and circles.  Students will also further their skills in gaining information from a set of data, function on a graph and algebra.

 

Students learn about:

Area of Plane Figures

  • Area¿ of¿ quadrilaterals¿ and¿ circles.

Data Analysis

  • Analyses¿ single¿ sets¿ of¿ data¿ using¿ measures¿ of¿ location¿ and¿ range.

Linear Relationships 2

  • Graphing¿ linear¿ relationships¿ and¿ equations.

Algebraic Techniques 2

  • Substitution, expansion and¿ factorisation¿ of¿ simple¿ algebraic¿ expressions.
     

Term 3

Students will continue to build on their understanding of algebra and link this to how to solve an equation. Pythagoras will be introduced, as will volume and congruency.

 

Students learn about:

Equations

  • Solve ¿simple¿ linear¿ equations¿ using¿ algebraic¿ techniques.¿
  • Solve¿ simple¿ quadratic¿ equations¿ of¿ the¿ form¿ x2¿ =¿ c.

Pythagoras' Theorem

  • Applying¿ Pythagoras¿'¿ theorem¿ to¿ find¿ sides¿ of¿ right¿ angled¿ triangles¿ and¿ solve¿ associated problems.

Volume

  • Convert¿ing  between¿ metric¿ units¿ of¿ volume¿ & capacity.¿
  • Solve¿ volume¿ and¿ capacity¿ problems.

Geometry and Congruency

  • Identify¿ congruent¿ figures¿.
  • identify¿ congruent¿ triangles¿ using¿ the¿ four¿ tests.

 

Term 4

The idea of profit and loss is investigated in the final term and linked to other areas of finance. Rates and ratios are explained and students will do some more in-depth work on probability.

 

Students learn about:

Percentages and Financial Mathematics

  • Solve¿ problems¿ involving¿ profit¿ and¿ loss.

Rates and Ratios

  • Apply¿ ratios¿ and¿ rates¿ to¿ solve¿ problems.¿
  • Interpret¿ and¿ draw¿ distance/¿time¿ graphs.

Probability 2       

  1. Probability¿ of¿ compound¿ events.¿
    Venn¿ diagrams