Middle School Mathematics Trimester 1 Subject Overview

Transcription

1 1 Class 7 Topics Number Algebraic Expressions Solving Equations Angles Content Recognise multiples, factors, common factors, primes (all less than 100), making use of simple tests of divisibility; find the lowest common multiple in simple cases; use the sieve for generating primes developed by Eratosthenes Recognise negative numbers as positions on a number line, order, add subtract positive negative integers in context Recognise squares of whole numbers to at least the corresponding square roots; use the notation 7² 49 Write a number in terms of its prime factors, e.g. 500 = 2² x 5³ Construct simple algebraic expressions by using letters to represent numbers Simplify linear expressions, e.g. collect like terms; multiply a constant over a bracket Substitute positive integers into simple linear expressions/formulae Use the order of operations, including brackets, to work out simple more complex calculations Use index notation for small positive integer powers Simplify or transform algebraic expressions by taking out single term common factors Construct solve simple linear equations with integer coefficients (unknown on one side only), e.g. 2x = 8, 3x + 5 = 14, 9 2x = 7 Construct solve linear equations with integer coefficients (unknown on either or both sides, without or with brackets) Underst use inequality signs; construct solve linear inequalities in one variable; represent the solution set on a number line Recognise the angular connections between parallel lines, perpendicular lines transversals Calculate the sum of angles at a point, on a straight line in a triangle, prove that vertically opposite angles are equal; derive use the property that the angle sum of a quadrilateral is 360 Solve simple geometrical problems by using side angle properties to identify equal lengths or calculate unknown angles, explain reasoning Identify alternate angles corresponding angles Solve geometrical problems using properties of angles, of parallel intersecting lines Coordinates Graphs Read plot coordinates of points determined by geometric information in all four quadrants Generate coordinate pairs that satisfy a linear equation, where y is given explicitly in terms of x; plot the corresponding

2 2 Application Problem Solving graphs Recognise straight-line graphs parallel to the x- or y-axis Recognise graphs of the form y=ax Drawing interpreting graphs for real life situations. Development of investigational skills Effective communication of mathematics Drawing/expressing generalizations Applying mathematics to unfamiliar situations RESOURCES: Collins: Mathematics Frame-working Bk 1.3, Pupil book, e book Homework book Online Tool: Myimaths

3 3 Class 8 Topics Algebraic Expressions Content Construct linear expressions Simplify or transform linear expressions with integer coefficients; collect like terms; multiply over a bracket Simplify or transform algebraic expressions involving index notation Know that letters play different roles in equations, formulae functions; know the meanings of formula function Substitute positive negative numbers into expressions formulae Solving Equations Inequalitites Geometry, Shape Angles Construct solve linear equations with integer coefficients (with without brackets, negative signs anywhere in the equation, positive or negative solution) Solve a number problem by constructing solving a linear equation Solve equations with variables on both sides Sole inequations, interpret the solution sets Underst the properties of parallel lines, the angles around parallel lines Solve geometrical problems using properties of angles, of parallel intersecting lines Calculate the interior or exterior angle of any regular polygon; prove use the formula for the sum of the interior angles of any polygon; prove that the sum of the exterior angles of any polygon is 360 Solve problems using properties of angles, of parallel intersecting lines, of triangles, other polygons circles, justifying inferences explaining reasoning with diagrams text Classify quadrilaterals using their geometrical properties Transformations of shapes (translation & enlargement) Construction of perpendicular lines angle bisectors Number Percentages, Fractions Decimals Multiplying dividing negative numbers Find Factors Multiples, use Prime Factorisation to find Highest Common Factors an Lowest Common Multiples Works with Powers roots Powers of 10, using Stard Form, including negative index Significant Figures Read write positive integer powers of 10; multiply divide integers decimals by 0.1, Add subtract fractions mixed numbers; calculate fractions of quantities (fraction answers); multiply divide an integer by a fraction. Calculate solve problems involving percentages of quantities percentage increases or decreases; express one given number as a fraction or percentage of another.

4 4 Recall simple equivalent fractions, decimals percentages Use known facts place value to multiply divide simple fractions. Use known facts place value to multiply divide simple decimals, e.g , Use known facts place value to calculate simple fractions percentages of quantities. Multiply divide integers decimals by decimals such as 0.6 or 0.06, understing where to place the decimal point by considering equivalent calculations, e.g = (4.37 3) 10, = ( ) 6. Application Problem Solving Development of investigational skills Effective communication of mathematics Drawing/expressing generalizations Applying mathematics to unfamiliar situations RESOURCES: Collins: Mathematics Frame-working Bk 2.3, Pupil book, e book Homework book Online Tool: Myimaths

5 5 Class 9 Topics Brackets Equations Money Factors Angles Circles Simultaneous Equations Application Problem Solving Content Substitute positive negative numbers into expressions formulae Construct solve linear equations with integer coefficients (with without brackets, negative signs anywhere in the equation, positive or negative solution); solve a number problem by constructing solving a linear equation Exp the product of two linear expressions of the form x ± n simplify the corresponding quadratic expression Construct algebraic expressions Add subtract algebraic fractions Solve equations involving algebraic fractions Solve problems involving percentage changes, choosing the correct numbers to take as 100% or as a whole, including simple problems involving personal or household finance, e.g. simple interest, discount, profit, loss tax Recognise when two quantities are directly proportional; solve problems involving proportionality, e.g. converting between different currencies Recognise when fractions or percentages are needed to compare different quantities Use index notation for positive powers Apply index laws for multiplication division of simple expressions Simplify or transform expression by taking out a common factor Factorise trinomials, difference of squares Apply understing of angles subtended from diameter Apply understing of tangent radius Apply understing of Arcs, Sectors, angles at the centre of a circle Solve problems involving area Cicumference Find a Graphical solution of simultaneous equations, with without technology Solve simultaneous equations by elimination substitution Creating simultaneous equations from word problems, choose appropriate method for solving Development of investigational skills Effective communication of mathematics Drawing/expressing generalizations Applying mathematics to unfamiliar situations Exploring becoming familiar with IGCSE investigational tasks RESOURCES: Nelson Thornes; New Maths InAction S3 3 Additional Resources: New Maths InAction S4 3 IGCSE for the International Student (Haease Harris)

6 6 Online Tool: Myimaths