Math Grade 8

Overview

The Maths Syllabus at GEMS Wesgreen International Secondary School aims to support students to develop their ability to calculate fluently, to reason and solve problems through application of knowledge and transferable skills. Throughout the year we recover and extend objectives as the focus is on providing a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

Learning Outcomes

The aims of all subjects state what a teacher may expect to teach and what a student may expect to experience and learn. These aims suggest how the student may be changed by the learning experience. The aims of the Math Syllabus are to encourage and enable students to:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Unit Overviews

Term 1

Unit 1 – Percentages

Approximate length: 1 week

In this unit the children will recognise and use relationships between operations including inverse operations; define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages and work with percentages greater than 100%. They will also learn to interpret fractions and percentages as operators.

Specific National Curriculum Objectives Covered:

  • To understand what is meant by simple interest
  • To solve problems involving simple interest
  • To use the multiplier method to calculate the result of a percentage increase or decrease
  • To calculate the percentage change in a value
  • Given the result of a percentage change, to calculate the original value
  • To calculate the result of repeated percentage changes

Unit 2 – Equations and formulae

Approximate length: 1 week

In this unit the children will use and interpret algebraic notation, understand and use standard mathematical formulae; rearrange formulae to change the subject, substitute numerical values into formulae and expressions, including scientific formulae and understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.

Specific National Curriculum Objectives Covered:

  • To expand brackets and simplify more complex expressions
  • To factorise more complex expressions
  • To expand and factorise expressions with more than one variable
  • To solve equations where the variable is in the denominator of a fraction

Unit 3 – Polygons

Approximate length: 1 week

In this unit the children will derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons.

Specific National Curriculum Objectives Covered:

  • To work out the sum of the interior angles of a polygon
  • To work out exterior angles of polygons
  • To calculate the interior and exterior angles of regular polygons
  • To work out which regular polygons tessellate

Unit 4 – Using data

Approximate length: 2 weeks

In this unit the children will describe, interpret and compare observed distributions of a single variable through appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers). They will also learn Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data and be able to describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

Specific National Curriculum Objectives Covered:

  • To infer a correlation from two related scatter graphs
  • To draw a line of best fit to show a correlation
  • To interpret a variety of two-way tables
  • To estimate a mean from grouped data
  • To draw a cumulative frequency diagram
  • To find the interquartile range
  • To plan a statistical investigation

Unit 6 – Pythagoras’ theorem

Approximate length: 1 week

In this unit the children will Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proof and Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles.

Specific National Curriculum Objectives Covered:

  • To use Pythagoras’ theorem in right-angled triangles
  • Using Pythagoras’ theorem to solve problems
  • To use the converse of Pythagoras’ theorem

Term 2

Unit 5 – Applications of graphs

Approximate length: 1 week

In this unit, the children will model situations or procedures by translating them into algebraic expressions or formulae and by using graphs and use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement). They will also work with coordinates in all four quadrants, recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane, interpret mathematical relationships both algebraically and graphically. They will learn to reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically. They would use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations and find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs.

Specific National Curriculum Objectives Covered:

  • To interpret step graphs
  • To interpret and draw time graphs
  • To draw exponential growth graphs

Unit 7 – Fractions

Approximate length: 1 week

  • In this unit the children will use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
  • Specific National Curriculum Objectives Covered:
  • To choose an appropriate method to add or subtract mixed numbers.
  • To multiply two fractions or mixed numbers.
  • To divide one fraction or mixed number by another fraction or mixed number.
  • To add, subtract, multiply or divide fractions containing a variable.

Unit 8 – Algebra

Approximate length: 2 weeks

  • In this unit the children will simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms, multiplying a single term over a bracket, taking out common factors, expanding products of two or more binomials. They will understand and use standard mathematical formulae; rearrange formulae to change the subject. Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs. They will use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement).

Specific National Curriculum Objectives Covered:

  • To multiply out (or expand) two brackets.
  • To multiply out three or more brackets.
  • To factorise quadratic expressions with positive coefficients.
  • To factorise quadratic expressions with negative coefficients.
  • To recognise and use the difference of two squares.

Unit 9 – Decimal Numbers

Approximate length: 1 week

  • In this unit the children will understand and use place value for decimals, measures and integers of any size. They will order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥. They will interpret and compare numbers in standard form A × 10n 1 ≤ A < 10, where n is a positive or negative integer or zero.

Specific National Curriculum Objectives Covered:

  • To understand and work with both positive and negative powers of ten.
  • To understand and work with standard form, using both positive and negative powers of ten.
  • To multiply numbers in standard form, using both positive and negative powers of ten.
  • To divide numbers in standard form, using both positive and negative powers of ten.
  • To understand the limits of accuracy when using rounded data.

Unit 10 – Surface Area and Volume of Cylinders

Approximate length: 2 weeks

  • In this unit the children will derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders). They will use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.

Specific National Curriculum Objectives Covered:

  • To calculate the volume of a cylinder.
  • To calculate the curved surface area of a cylinder.
  • To calculate the total surface area of a cylinder.
  • To calculate the volumes and surface areas of composite shapes.

Term 3

Unit 11 – Solving Equations Graphically

Approximate length: 2 weeks

In this unit the children will use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations. They will learn that there are all sorts of different equations that arise from real situations and pupils will meet some examples in this chapter. They will have met straight-line graphs and quadratics before but this chapter builds on this with more complex examples. It will introduce the idea that many equations that are used to model the real world are difficult to solve by algebraic methods and are more easily solved by drawing a graph.

Specific National Curriculum Objectives Covered:

  • To draw any linear graph from any linear equation.
  • To solve a linear equation from a graph.
  • To solve a pair of simultaneous equations by drawing graphs.
  • To solve quadratic equations by drawing graphs.
  • To solve a cubic equation by drawing a graph.

Unit 12 – Compound Units

Approximate length: 1 week

In this unit the children will use standard units of mass, length, time, money and other measures, including with decimal quantities. They will change freely between related standard units [for example time, length, area, volume/capacity, mass]. They will use compound units such as speed, unit pricing and density to solve problems.

Specific National Curriculum Objectives Covered:

  • To understand and use measures of speed.
  • To understand and use density and other compound units.
  • To understand and use unit pricing.

Unit 13 – Right-Angled Triangles

Approximate length: 2 weeks

In this unit the children will learn that trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. This chapter introduces these important properties of right-angled triangles and demonstrates how this can be used in real life situations such as estimating the height of a tree.

Specific National Curriculum Objectives Covered:

  • To understand trigonometric ratios
  • To understand what the trigonometric ratios sine, cosine and tangent are.
  • To find the angle identified from a trigonometric ratio.
  • To find an unknown length of a right-angled triangle given one side and an angle.

Unit 14 – Revision and GCSE Preparation

Approximate length:

In this unit the children will revise over the following mathematical strands:

  • Number
  • Algebra
  • Geometry and measures
  • Statistics

The material will provide excellent practice so that pupils become mathematically fluent. Encourage pupils to work through this whole chapter before their End of Year 9 tests.

Specific National Curriculum Objectives Covered:

  • Help pupils to practise and revise topics covered in their current course.
  • Get pupils started on their foundation to iGCSE course.

Blended Learning

Throughout this year there will be blended learning and we are using multiple teaching methods in order to help our students learn more effectively. All students whether face to face or learning from home will have the opportunity to access all the lessons and resources. The learning will be linked to the unit objectives and prior knowledge of the concept. Mathematical concepts like Percentages/ Polygons/ Volume and surface area of cylinders / Algebra would be covered using a blend of online learning and teaching tools using Phoenix,Teams, myimaths, class activities and tasks. Effective learning is encouraged through frequent activities and self-assessment questions.

Assessment

Formative: Throughout the units, the children will complete graded work, quizzes and problem solving activities which allows the teacher to assess the students’ attainment and inform their planning.

Summative: At the end of each term we complete internal tests – Unit based and combined Units. Students complete standardized tests. This allows us to measure the students’ progress throughout the term and year. At the end of the academic year, the students sit for the end of year exams.

Next Steps

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