Year 8 Mathematics Curriculum Map Topic Algebra 1 & 2 Number 1 Title (Levels of Exercise) Objectives Sequences *To generate sequences using term-to-term and position-to-term rule. (5-6) Quadratic Sequences *To generate sequences using term-to-term and position-to-term rule. *To write an expression to describe the nth term of an arithmetic sequence Functions *To find the inverse of a linear function Graphs *To construct functions arising from real-life problems. *To plot their corresponding graphs Limits of Sequences *To generate sequences *To recognise limits of a sequence Functional Maths Mobile Tariffs The Four rules *To add, subtract, multiply and divide fractions. governing Fractions *To cancel common factors *To change between mixed numbers and improper fractions Sequence, nth term, Keywords Prediction, quadratic sequence, first and second difference inverse Axes, gradient, acceleration Sequence, term-to-term, limit Convert, equivalent, mixed number, top-heavy, improper, LCM Algebra 3 Percentages and Compound Interest (7-8) Reverse Percentages and Percentage change Direct and Inverse Proportion (6) Ratio in Area and Volume Reciprocal of a number Rounding and Estimation (7-8) Equations, Formulae and Identities (6) Simultaneous equations *To find a percentage of an amount *To understand and calculate compound interest *To use a multiplier to calculate a reverse percentage. *To know and use the formula for percentage change. *To use proportional reasoning to solve problems *To use known facts to derive unknown facts *To calculate scale factors of length, area and Vol *To understand and calculate the ratio between scale factors *To round numbers to 1 significant figures. *To use this to estimate answers to calculations *To distinguish between an equation, formulae and identity *To solve linear equations *To solve simultaneous equations by simplifying algebraic expressions Compound, multiplier Reverse percentage, multiplier, power Ratio, unit, direct proportion, indirect proportion Scale factor linear, area, volume Approximate, significant figure Equation, expression, term, coefficient, variable, formula, identity Simultaneous equation, elimination, substitution
Measures 1 Statistics 1 Solving by substitution *To substitute numbers into expressions and formulae Substitution, variable Equations with *To solve equations involving fractions Denominator, cancelling fractions (7 8) Inequalities *To manipulate algebraic expressions and inequalities Inequality *To use accurate inequality notation Simultaneous equations by graphs *To solve simultaneous equations by plotting straight-line graphs intersection Pythagoras Theorem *To investigate Pythagoras Theorem Hypotenuse, Pythagoras Theorem, *To understand and apply Pythagoras theorem square, square root Solving problems using *To investigate Pythagoras Theorem Hypotenuse, Pythagoras Theorem, Pythagoras *To understand and apply Pythagoras theorem square, square root Loci *To find the locus of a point that moves according to a simple rule. Angle bisector, perpendicular bisector, equidistant, locus, loci, region Congruent triangles *To understand the mathematical definition of congruent. Congruent, congruence *To apply this to triangles Circle theorems *To know the definition of a circle and name its parts Chord, tangent, radius * To know the tangent at any point on a circle is perpendicular to the radius *To know that the perpendicular bisector of a chord passes through the centre of the circle. *To use these to calculate unknown angles. Tessellations and *To solve problems using properties of angles of polygons. Exterior angles, interior angles, regular regular polygons (5-6) *To calculate and use the interior angles of regular polygons polygon, tessellate Practical Pythagoras *To investigate Pythagoras Theorem through proof Proof, prove, Pythagoras Theorem *To distinguish between practical demonstration and proof Functional Maths Garden Design - Worksheet required In the teachers book Scatter graphs and *To plot scatter graphs correlation *To interpret and understand correlation of a graph Scatter graphs and lines of best fit *To plot scatter graphs * To draw a line of best fit * To use the line of best fit to estimate results Correlation positive, no and negative Line of best fit, interpret, correlation Time series graphs *To compare two or more distributions over a period of time Time series, raw data, key features, line graphs Two-way tables (6 7) *To design and use two-way tables Two-way table, relationship, data, tally, frequency Cumulative frequency *To plot cumulative frequency graphs from a table * To calculate medians and quartiles from CF graphs Cumulative frequency, quartile, lower, upper, IQR, polygon, curve Estimation of mean from grouped data. *To estimate the mean from a grouped frequency table Grouped data, estimate, median, mean, mid-class value, frequency table
Measures 2 Statistical investigations *To plan and understand the various stages of a statistical investigation Questionnaire, printed table, database, survey, statistic, bias, census Similar Triangles *To understand the meaning of similar shapes similar *To identify and justify similar triangles *To solve problems involving similar triangles Metric units for area *To convert between metric units of area and volume Cm 2, mm 2, m 2, mm 3, cm 3, m 3, hectare, and volume volume (5-6) Arc Length and Sector area *To know and use the formulae for circumference and area of a circle *To know and use the formulae for arc length and sector area Volume of cylinder *To calculate the volume of right prisms (7-8) Rate of change *To solve problems involving compound measures Number 2 Standard form *To turn ordinary numbers into standard form *To turn standard form numbers back to ordinary numbers Multiplying and *To use index notation in order to multiply and divide numbers in standard form Dividing with standard form Arc, circumference, radius, sector Cross section, cylinder, radius, volume Density, pressure, speed Standard form, integer, less than Standard form, addition of powers, subtraction of powers Upper and lower *To calculate upper and lower bounds for numbers to various degrees of accuracy Upper bound, lower bound, bounds 1 Upper and lower *To calculate upper and lower bounds within calculations. Upper bound, lower bound, bounds 2 Recurring decimals *To convert a recurring decimal to a fraction Recurring decimal, terminating decimal *To convert a fraction to a recurring decimal Algebra 4 Index notation *To use index notation for integer powers Power, index Negative powers (7-8) *To know and use the index laws Roots and other *To calculate and estimate square and cube roots Square root, cube root fractional powers (5-8) *To understand fractional indices Quadratic graphs *To generate and plot simple quadratic functions Quadratic, intercept, gradient Cubic Graphs (7-8) *To generate and plot simple cubic functions Cubic, turning points Statistics 2 Probability Statements & Mutually exclusive and exhaustive events (6) *To interpret results involving uncertainty and prediction *To understand and identify all mutually exclusive outcomes *To know that the sum of all mutually exclusive outcomes is 1 and use this to solve problems Certain, even, probability, probable, mutually exclusive, exhaustive, probability, expectation Combining probabilities and tree diagrams Estimates of probability *To identify all mutually exclusive outcomes *To draw a tree diagram *To use the tree diagram to solve probability questions *To compare experimental and theoretical probabilities. Tree diagram, mutually exclusive, independent Relative frequency, estimate, probability, expectation, limit
Measures 3 Fractional Enlargements Trigonometry Tangent Trigonometry Cosine and Sine Problems using Trigonometry Functional Maths *To enlarge 2D shapes given a centre of enlargement and a fractional scale factor *To understand and use the Tangent relationship in right angle triangles to find unknown sides and angles *To understand and use the Sine and Cosine relationships in right angle triangles to find unknown sides and angles *To use all 3 trigonometric relationships to find unknown sides and angles in various problems. Map Reading *To use enlargement and trigonometry in map reading Object, image, centre of enlargement, scale factor, similar Adjacent, hypotenuse, opposite, tangent Adjacent, hypotenuse, opposite, sine, cosine Cosine, sine, tangent Algebra 5 Expansion (5-7) *To expand single brackets and simplify expressions Dimension, expansion Factorisation *To factorise expressions into single brackets Factorisation Quadratic expansion *To expand two brackets and simplify to a quadratic Expand, quadratic Solving Problems and Statistics 3 & Geometry & Measures 4 and revision Quadratic factorisation *To factorise a quadratic into two brackets Factorisation Change of subject *To change the subject of the formula Subject Graphs from equations in the form Ay±Bx= C * To draw graphs from this format Cover up method, gradient, intercept Fractions, Percentages and Decimals (6-8) The first four rules, ratios and standard form Rules of algebra and solving equations Graphs Geometry and measures (6-8) Statistics Statistical techniques G & M revision & investigation *To review and solve problems involving fractions, decimals and percentages *To review and solve problems involving the first four rules, ratios and standard form *To review and solve problems involving the Rules of algebra and solving equations *To review and solve problems involving the Graphs *To review and solve problems involving the Geometry and measures *To review and solve problems involving the Statistics * To revise key techniques * To revise the work of the year on Geometry and Measure Symmetry * To revise work on symmetry
Statistics 4 & GCSE Prep of Probability * To revise work on probability Solving Quadratic Equations (B) Quadratic Equation a 1 (B-A) The difference of two squares ( B A) * To factorise & solve quadratics of the form Quadratic, factorise, root ax 2 + bx + c * To factorise quadratics of the form ax 2 + bx + c with a 1 Quadratic, factorise, root To factorise and recognise the difference of two squares Factorise difference of two squares (DOTS)