Year 7 Mathematics Mastery Programme ... - Hilbre High School

Year 7 Mathematics Mastery Programme of Study

Mathematics Mastery © 2018

Autumn 1: Place value, addition and subtraction

Unit 1: place value (1)

Read and write whole numbers in figures and words

Multiply, and divide, any whole number by 10, 100, 1000, or 10 000

Round whole numbers to the nearest 1000, 100 or 10

Unit 2 & 3: Addition and

subtraction (2)

Use mental strategies

Add and subtract using formal algorithms

Calculate and work with perimeters

Model solve word problems

Unit 4: Addition and subtraction of decimals (2)

Understand decimal notation and place values

Read and write decimals in figures and words

Convert between decimals and fractions where the denominator is a factor of 10 or 100

Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 decimal places

Use correctly the symbols <, > etc. and the associated language to order a set of decimals

Multiply and divide decimals by 10, 100, 1000, or 10 000

Solve word problems involving the addition and subtraction of money in decimal notation

Use written methods in column format for addition and subtraction of decimals

Extend existing mental calculation to include decimals

Calculate the perimeter of rectangles, squares and rectilinear figures

Autumn 2: Multiplication and division

Unit 5, 6, 7 & 8: multiplication and

division (5)

Use multiplication facts to solve mental calculations

Use the terms ‘product’, ‘multiple’ and ‘LCM’

Understand and use the column method to multiply integers and decimals

Divide whole numbers and decimals by whole numbers

Use the terms ‘quotient’, ‘remainder’, ‘factor’, ‘HCF’

Represent multiplication word problems using bar models

Find the area of a rectangle and triangle

Solve problems involving length, perimeter and area

Estimate answers in calculations and check that results are reasonable

Measure time, calculate with time and solve time word problems

Find the mean average, interpreting average as “total amount ÷ number of items" and solve word problems involving average

Spring 1: 2D shapes

Unit 9: Working with

units (1)

Record and order measurements using decimal notation

Estimate and/or measure: o length in kilometres (km) /metres (m)/ centimetres (cm)/ millimetres (mm) o mass in kilograms (kg) /grams (g) o volume of liquid in litres (l) / millilitres (ml)

Unit 10: Angles (1)

Draw and measure acute and obtuse angles reliably to the nearest degree

Estimate the size of any given angle

Recognise acute, right, obtuse and reflex angles

Know and use the fact that the angles round a point total 360o, that angles on a straight line total 180o, and that vertically opposite angles are equal

Unit 11 & 12: Triangles and

quadrilaterals (2)

Classify triangles and quadrilaterals according to their properties

Use a ruler and protractor to construct triangles and quadrilaterals from given data

Know and use the fact that the sum of interior angles of a triangle is 180o

know and use the fact that the interior angles of a quadrilateral sum to 360o

Solve problems involving coordinates in the first quadrant

Unit 13: Symmetry and tessellation (1)

Identify lines of symmetry in any shape

Identify the order of rotational symmetry in any shape

Create shapes given details of their symmetries

Investigation and create tessellations

Spring 2: Fractions

Unit 14:

Understand and use fraction (2)

Represent fractions using area diagrams, bar models and number lines

Recognise and name equivalent fractions

Convert fractions to decimals

Convert terminating decimals to fractions in their simplest form

Convert between mixed numbers and improper fractions

Compare and order numbers

Convert simple fractions and decimals to percentages

Express one quantity as a fraction of another

Unit 15: Fractions of amounts (1)

Find a fraction of a set of objects or quantity

Find the whole given a fraction

Unit 16: Multiplying and

dividing decimals (2)

Multiply a whole number or fraction by a whole number or fraction

Multiply a mixed number and a whole number

Divide a whole number or proper fraction by a whole number or proper fraction

Summer 1: Algebra

Unit 17: Order of

operations (2)

Carry out combined operations involving all four operations

Understand and use brackets

Use simple index notation

Unit 18: Introduction to

algebra (2)

Recognise and continue sequences

Represent an unknown number using a letter

Write and understand simple algebraic expressions

Substitute numerical values into formulae and expressions

Collect like terms and simplify expressions

Multiply out brackets, identify and take out common factors to factorise

Recognise that different-looking expressions may be identical and prove simple algebraic identities

Unit 19: Algebraic generalisation project

Summer 2: Percentages and handling data

Unit 20: Percentages (2)

Understand percentage as a fractional operator with denominator of 100

Express a part of a whole as a percentage

Convert between fractions, decimals and percentages

Find fractions and percentages of given quantities

Find the whole given a part and the percentage

Increasing and decreasing by a percentage

Unit 21: Handling data (2)

Understand the difference between types of data

Construct and interpret o Tables (including tally and two way) o Bar charts (including comparative and composite) o Pictograms o Line graphs

Read and interpret pie charts

Draw pie charts from raw data

Explore misleading graphical representations


Autumn 1: Working with number

Unit 1: Primes and factorising

(2 weeks)

Find the factors and multiples of a number

Find the prime factors of a number

Determine HCF and LCM by prime factorisation

Find squares, square roots, cubes and cube roots using prime factorisation

Use indices to record repeated multiplication

Y7 U5, U16

Unit 2: Add and subtract fraction

(3)

Use equivalent fractions

Add and subtract fractions with like and unlike denominators

Add and subtract fractions mixed numbers and improper fractions

Convert between improper fractions and mixed numbers

Add and subtract fractions mixed numbers and improper fractions

Y7 U13, U14, U15

Autumn 2: Number and algebra

Unit 3: Positive and negative

numbers (2)

Represent and order positive and negative integers on a number line (using the

symbols , , , and )

Show addition and subtraction on a number line

Apply the four basic operations on positive and negative integers

Calculate with rational and decimal numbers (including negative numbers)

Y7 U16

Unit 4: Sequences,

expressions and equations

(3)

Recognise and represent number patterns (including finding an algebraic expression for the 𝑛th term)

Distinguish between terms and coefficients in algebraic expressions

Distinguish between like and unlike terms in algebraic expressions

Simplify expressions, collect like terms and expand and factorise linear expressions

Substitute numerical values into formulae and expressions

Solve linear equations in one unknown

Solve simple fractional equations that can be reduced to linear equations

Formulate a linear equation in one unknown to solve problems

Y7 U16, U17 Y8 U3

Spring 1: 2D geometry

Unit 5: Triangles, quadrilaterals and angles in parallel lines

(3)

Construct a triangle from given information (sides/angles)

Classify special quadrilaterals on the basis of their properties: define a parallelogram, rhombus and trapezium

Construct a quadrilaterals from given information (sides/angles)

Identify the different types of angles formed by parallel lines and a transversal such as corresponding angles, alternate angles and interior angles

Use the various properties of angles to find unknown angles

Find unknown angles in geometrical figures involving square, rectangle, parallelogram, rhombus, trapezium and triangle

Y7 U9, U10, U11

Unit 6: Length and area:

parallelograms and trapezia

(2)

Convert between cm2 and m2

Find the area and perimeter of a figure made up of some of the following shapes: square, rectangle, triangle

Find the areas of parallelograms and trapezia

Find the areas and perimeters of composite plane figures

Solve word problems involving area and perimeter

Y7 U4, U7, U8, U10, U11

Spring 2: Proportional reasoning

Unit 7:

Percentage change

(2)

Use percentages greater than 100%

Express one quantity as a percentage of another

Compare two quantities by percentage

Increase or decrease a quantity by a given percentage

Understand how to compare quantities using percentages

Reverse percentages: find the original quantity given a part of it and its percentage

Reverse percentages: find the original quantity when we know its final value after the percentage increase or decrease

Solve problems involving percentages and reverse percentages

Y7 U19

Unit 8: Ratio (and SDT)

(3)

Interpret 𝑎 ∶ 𝑏 and 𝑎 ∶ 𝑏 ∶ 𝑐, where 𝑎, 𝑏 and 𝑐 are whole numbers

Compare two or more quantities by ratio

Understand the relationship between ratios and fractions

Write equivalent ratios, and find the missing term in a pair of equivalent ratios

Express ratios involving rational numbers in their simplest form

Divide a quantity in a given ratio

Find the whole/ one part when a whole is divided into parts in a given ratio

Solve word problems involving ratio

Use the relationship between distance, time and speed

Write speed in different units such as km/h, m/min, m/s and cm/s

Convert from one unit of speed to another (e.g. km/h to m/s)

Solve word problems involving speed, uniform speed and average speed

Y7 U13, U14, U15

Summer 1: 2D and 3D geometry

Unit 9: Rounding (>1)

Round off a number to a required number of decimal places

Round off a number to a required number of significant figures

Estimate the answer to a given problem

Identify rounding and truncation errors

Y7 U1, U4

Unit 10: Circumference and area of a

circle (2)

Use formulae to calculate the area and circumference of a circle

Find the area and perimeter of o semicircle (half circle) o quarter circle

Solve word problems involving area and perimeter

Unit 11: 3D shapes and

nets (1)

Recognise nets of 3D shapes

Build and name 3D shapes

Draw plans and elevations of a given solid

Identify a solid from its plans and elevations

Unit 12: Surface area and volume

(2)

Find the volumes of cubes and cuboids

Find the volumes of prisms and cylinders

Find the volumes of composite solids

Explore the surface area of cubes, cuboids, cylinders other prisms and composite solids

Convert between cm3 and m3

Y7 U6, U8 Y8 U6

Summer 2: Handling data

Unit 13: Statistics (2)

Find the mean, median more and range from raw datasets

Use the mean/median/mode to compare data sets

Use an average plus the range to compare datasets

Find the mode, median and mean from tables and graphical representations (not grouped)

Explore methods of data collection including surveys, questionnaires and the use of secondary data

Appreciate the difference between discrete and continuous data

Classify and tabulate data

Conduct statistical investigations using collected data

Draw, analyse and interpret graphs including those met in year 7

Y7 U20

Y7 Link

Y7 Link

Y7 Link

Y7 Link

Y7 Link

Y7 Link

Note:

The number in the brackets after the unit number and name is the

guided number of weeks to spend.

The learning statements in an italic font are Year 7 objectives

(repeated in Year 8).


Autumn 1 ~ Graphs and proportion

Unit 1 Coordinates

(1 week)

Plot coordinates in all four quadrants

Find the midpoint of a line segment joining two points

Find an endpoint of a line segment, given the midpoint and one endpoint

Solve problems using coordinate grids

Y8 U3

Unit 2 Linear graphs

(2 weeks)

Identify the equations of horizontal and vertical lines

Plot coordinates from a rule to generate a straight line

Identify key features of a linear graph

Make links between the graphical and the algebraic representation

Identify parallel lines from algebraic equations

Y7 U18 Y8 U4

Unit 3 Proportion (2 weeks)

Recognise when two quantities are directly or inversely proportional to each other

Recognise the graphical representation of a proportional relationship

Solve proportion problems

Interpret and use conversion graphs and other graphs of proportional relationships

Y8 U8

Unit 4 Scales and

standard form (1)

Use standard form to express very large and small numbers

Convert between standard form and ordinary numbers

Order large and small numbers

KS4 content: Use standard form to solve simple problems

Use scales to solve distance and area problems in context

Y7 U4

Autumn 2 ~ Algebra

Unit 5 Linear and non-linear sequences

(1 week)

Recognise that linear and quadratic expressions can be used to represent sequences of different types

Recognise arithmetic and geometric sequences and appreciate other sequences that may arise

Solve problems involving linear and non-linear sequences in a variety of contexts

Y7 U18 Y8 U4

Unit 6 Expanding and

factorising (2 weeks)

Multiply a term over a single bracket

Expand products of two or more binomials

Factorise expressions into a single bracket

KS4 Content: Factorise quadratic expressions where the coefficient of 𝑥2 is equal to one

Y7 U18 Y8 U4

Unit 7 Changing the

subject of a formula

(2 weeks)

Write expressions, equations and formulae to represent relationships

Use substitution to find the value of one variable given other values

Make links between solving linear equations and rearranging formulae

Apply “changing the subject” to equations of straight lines

Manipulate familiar formulae such as formulae for area and perimeter

Y7 U18 Y8 U4

Spring 1 ~ 2D geometry

Unit 8 Constructions

(1 week)

Use the standard ruler and compass constructions for: o perpendicular bisector of a line segment o constructing a perpendicular to a given line from/at a given point o bisecting a given angle

Understand and use the perpendicular distance from a point to a line as the shortest distance to the line

Y7 U10 Y7 U11 Y7 U12 Y8 U5

Unit 9 Congruence

(1 week)

Know the criteria for congruence of triangles

Apply properties of plane figures, and the criteria for congruence, using appropriate language

Y7 U11 Y7 U12 Y8 U5

Unit 10 Pythagoras’

theorem (2 weeks)

Derive Pythagoras’ theorem

Use Pythagoras’ theorem to find missing sides in right-angled triangles

Solve associated problems in other shapes where right-angled triangles exist Deduce whether a triangle is right-angled by considering its sides

Y8U1

Unit 11 Angles

in polygons (1 week)

Derive the proof of the sum of the angles in a triangle

Find the formula for sum of the angles of any polygon

Understand and use the sum of the exterior angles of a polygon

Solve problems involving the angles/number of sides in a regular polygon

Y7 U10 Y7 U11 Y7 U12 Y8 U5

Spring 2 ~ Equations and inequalities

Unit 12

Linear equations and inequalities

(3 weeks)

Form and solve linear equations and inequalities in one unknown, including those where the unknown appears on both sides

Rearrange and solve linear equations and inequalities given in any form, including those involving fractions and brackets

Y7 U18 Y8 U4 Y9 U2

Unit 13 Graphical solutions (2 weeks)

Use linear and quadratic graphs to estimate values of 𝑦 for given values of 𝑥

Use linear graphs to find approximate solutions of simultaneous linear equations

KS4 content: Solve simultaneous equations algebraically

Find approximate solutions to contextual problems from given graphs of a variety of functions including:

o Piecewise linear (e.g. real-life linear graphs) o Exponential o Reciprocal

Y9 U1 Y9 U2

Summer 1 ~ Handling data and probability

Unit 14 Probability (3 weeks)

Understand and use the probability scale from 0 to 1

Understand and use the language associated with probability

Understand the relationship between relative frequency and theoretical probability

Understand that different trials of an experiment may produce different outcomes

Systematically list outcomes using a variety of representations

Use Venn diagrams and understand the meaning of union and intersection

KS4 content: Frequency tree diagrams

Y7 U4 Y7 U14 Y7 U15 Y7 U16 Y7 U20

Unit 15 Working with

data (1 week)

Appreciate the difference between discrete and continuous data

Understand why the exact mean cannot be found from grouped data

Find an estimate of the mean from grouped data and continuous data

Describe, interpret and compare distributions, involving appropriate measures of central tendency and spread

Y8 U13

Unit 16 Scatter graphs

(1 week)

Plot scatter graphs

Describe the type of correlation observed

Interpret correlation in context

Y9 U1 Y9 U2

Summer 2 ~ Geometry

Unit 17 Similarity and enlargement

(1 week)

Enlarge shapes from a given centre, with and without coordinate grids

Understand that the corresponding angles of similar shapes are equal

Solve problems involving similar triangles

Y8 U8 Y9 U9

Unit 18 Transformations

(2 weeks)

Translate a shape by a given vector

Reflect a shape in a line, including on coordinate axes

Rotate a shape about a centre, including on coordinate axes

Identify the type of transformation carried out by comparing an object and image

Y8 U3 Y9 U1 Y9 U2

Unit 19 Trigonometry

(2 weeks)

Develop an understanding of the trigonometric ratios

Solve problems using trigonometric ratios in right-angled triangles

Y9 U10 Y9 U17

Hilbre High School Curriculum Website

Key Stage 4

Term Year 10 Year 11

Autumn

Module 3 Module 4 Module 5

Module 3 Module 4 Module 5 Module 6 Module 7

Spring

Module 3 Module 4 Module 5

Module 4 Module 5 Module 6 Module 7

Summer

Module 3 Module 4 Module 5 Module 6

Exam Preparation

MODULE 3 PARENT INFORMATION

MW Learning Objectives: Students will be able to:-

Unit 3A – Number: Decimals and Fractions 66/67 • multiply and divide with decimals.

76 85

• recognise different types of fraction, reciprocal, terminating decimal and recurring decimal • convert terminating decimals to fractions • convert fractions to decimals • find reciprocals of numbers or fractions.

• work out a fraction of a quantity • find one quantity as a fraction of another.

71 • add and subtract fractions with different denominators.

73 74

• multiply proper fractions • multiply mixed numbers • divide by fractions.

• use a calculator to add and subtract fractions • use a calculator to multiply and divide fractions.

UNIT 3A HOMEWORK Unit 3B – Geometry and Measures: Area and Perimeter

53 • calculate the perimeter and area of a rectangle. • calculate the perimeter and area of a compound shape made from rectangles.

54 • calculate the area of a triangle • use the formula for the area of a triangle.

55 • calculate the area of a parallelogram • use the formula for the area of a parallelogram.

56 • calculate the area of a trapezium • use the formula for the area of a trapezium.

118 • recognise terms used for circle work • calculate the circumference of a circle.

117 • calculate the area of a circle. • give answers for circle calculations in terms of π.

UNIT 3B HOMEWORK

UNIT 3A and 3B TEST


33 34

• write an algebraic expression • recognise expressions, equations, formulae and identities.

95 • substitute into, simplify and use algebraic expressions.

100 135a 135b

• solve linear equations such as 3x – 1 = 11 where the variable only appears on one side • use inverse operations and inverse flow diagrams • solve equations by balancing • solve equations in which the variable (the letter) appears in the numerator of a fraction

93 • expand brackets such as 2(x – 3) • expand and simplify brackets.

94 • factorise an algebraic expression.

134 • expand two linear brackets to obtain a quadratic expression.

157 • factorise a quadratic expression of the form x2 + ax + b into two linear brackets.

136 • change the subject of a formula.

UNIT 3C HOMEWORK

Algebra: Linear Graphs

96 • use flow diagrams to draw graphs • work out the equations of horizontal and vertical lines. • draw linear graphs without using flow diagrams.

97 • work out the gradient of a straight line • draw a line with a certain gradient.

159

• draw graphs using the gradient-intercept method • draw graphs using the cover-up method. • work out the equation of a line, using its gradient and y-intercept • work out the equation of a line given two points on the line. • work out the equation of a linear graph that is parallel to another line and passes through a specific point.

107 • convert from one unit to another unit by using a conversion graph • use straight-line graphs to work out formulae.

UNIT 3C HOMEWORK

UNIT 3C and 3D TEST

MW Learning Objectives: Students will be able to:- Unit 3E - Ratio and proportion and rates of change: Ratio, Speed and

Proportion

38 39

106

• simplify a ratio • express a ratio as a fraction • divide amounts into given ratios • complete calculations from a given ratio and partial information.

142

• recognise the relationship between speed, distance and time • calculate average speed from distance and time • calculate distance travelled from the speed and the time taken • calculate the time taken on a journey from the speed and the distance.

42

• recognise and solve problems that involve direct proportion.

• find the cost per unit mass • find the mass per unit cost

UNIT 3E HOMEWORK

Unit 3F – Geometry and Measures: Transformations

120 • calculate angles in parallel lines.

10 • use angle properties in quadrilaterals.

124 • use a bearing to specify a direction.

11 • work out the order of rotational symmetry for a 2D shape • recognise shapes with rotational symmetry.

50 • translate a 2D shape.

48 • reflect a 2D shape in a mirror line.

49 • rotate a 2D shape about a point.

148 • enlarge a 2D shape by a scale factor.

182 • use more than one transformation.

174 • represent vectors • add and subtract vectors.

UNIT 3F HOMEWORK

UNIT 3E and 3F TEST



Unit 4A – Statistics: Complex Statistics

152 • obtain a random sample from a population • collect unbiased and reliable data for a sample.

128a • draw and interpret pie charts.

129 • draw, interpret and use scatter diagrams • draw and use a line of best fit.

130 • identify the modal group • calculate an estimate of the mean from a grouped table.

UNIT 4A HOMEWORK

Unit 4B – Probability: Probability and Events

59 • use the probability scale and the language of probability • calculate the probability of an outcome of an event.

60 • calculate the probability of an outcome not happening when you know the probability of that outcome happening."

125

• calculate experimental probabilities and relative frequencies from experiments • recognise different methods for estimating probabilities. • predict the likely number of successful outcomes, given the number of trials and the probability of any one outcome.

58 • apply systematic listing and counting strategies to identify all outcomes for a variety of problems.

UNIT 4B HOMEWORK

UNIT 4A and 4B TEST


Unit 4C – Geometry: Volume and Surface Area

43 • use the correct terms when working with 3D shapes.

114a 115

• calculate the surface area and volume of a cuboid.

114b • calculate the volume and surface area of a prism.

119 • calculate the volume and surface area of a cylinder.

UNIT 4C HOMEWORK

Unit 4D – Algebra: Equations

135 • solve equations where you have to first expand brackets. • solve equations where the variable appears on both sides of the equals sign.

157 • factorise a quadratic expression of the form x2 + ax + b into two linear brackets.

137 Forming and Solving Equations

UNIT 4D HOMEWORK

UNIT 4C and 4D TEST


Unit 4E – Ratio and Proportion

85 • convert percentages to fractions and decimals and vice versa..

89 • calculate a percentage of a quantity.

86 • increase and decrease quantities by a percentage.

89 • express one quantity as a percentage of another • work out percentage change.

142 • recognise and solve problems involving the compound measures of rates of pay, density and pressure.

UNIT 4E HOMEWORK

Unit 4F – Ratio and Proportion: Percentage and Variation

164 • calculate simple interest • calculate compound interest • solve problems involving repeated percentage change.

110 • calculate the original amount, given the final amount, after a known percentage increase or decrease.

42

• solve problems in which two variables have a directly proportional relationship (direct variation) • work out the constant of proportionality • recognise graphs that show direct variation.

199 • solve problems in which two variables have an inversely proportional relationship (inverse variation) • work out the constant of proportionality.

UNIT 4F HOMEWORK

UNIT 4E and 4F TEST


Unit 4E – Geometry and Measures: Pythagoras and Contruction

150a 150b 150c

• Know what Pythagoras' theorem is • calculate the length of the hypotenuse in a right-angled triangle.

• calculate the length of a shorter side in a right-angled triangle.

• Solve problems using Pythagoras’ theorem.

• use Pythagoras’ theorem in isosceles triangles.

147 • construct accurate drawings of triangles, using a pair of compasses, a protractor and a straight edge.

145 146

• construct the bisectors of lines and angles • construct angles of 60° and 90°.

165 • draw a locus for a given rule.

• solve practical problems using loci.

UNIT 4G HOMEWORK

UNIT 4G



Unit 5A – Geometry and Measures: Right-Angled Triangles

120 • calculate angles in parallel lines.

123 • calculate the exterior angles and the interior angles of a regular polygon.

168

• define, understand and use the three trigonometric ratios.

• use trigonometric ratios to calculate a length in a right-angled triangle.

• use the trigonometric ratios to calculate an angle.

173 • work out and remember trigonometric values for angles of 30°, 45°, 60° and 90°.

168 • solve practical problems using trigonometry • solve problems using an angle of elevation or an angle of depression.

124 • solve bearing problems using trigonometry.

168 • use trigonometry to solve problems involving isosceles triangles.

UNIT 5A HOMEWORK

Unit 5B – Geometry and Measures: Congruence/Similarity and Vectors

166 • demonstrate that two triangles are congruent.

144 • recognise similarity in any two shapes • show that two shapes are similar • work out the scale factor between similar shapes.

174 • Add and subtract vectors. • Draw Vectors

UNIT 5B HOMEWORK

UNIT 5A and 5B TEST


Unit 5C – Algebra: Number and Sequences

102 • recognise patterns in number sequences.

• recognise how number sequences are built up • generate sequences, given the nth term.

103 • find the nth term of a linear sequence.

104 • recognise and continue some special number sequences • understand how prime, odd and even numbers interact in addition, subtraction and multiplication problems.

141 • find the nth term from practical problems involving sequences.

UNIT 4C HOMEWORK

Unit 5D – Probability: Combined Events

59 • work out the probabilities when two or more events occur at the same time.

61 • read two-way tables and use them to work out probabilities.

127 • use Venn diagrams to solve probability questions.

104 141

• understand frequency tree diagrams and probability tree diagrams • use probability tree diagrams to work out the probabilities involved in combined events.

UNIT 5D HOMEWORK

UNIT 5C and 5D TEST


Unit 5E – Number: Powers and Standard Form

82 131 154

• write a number as a power of another number • use powers (also known as indices) • multiply and divide by powers of 10.

• use rules for multiplying and dividing powers • multiply and divide numbers by powers of 10.

83 • write a number in standard form • calculate with numbers in standard form.

155 • Find the error interval or limits of accuracy of numbers that have been rounded to different degrees of accuracy.

UNIT 5E HOMEWORK

Unit 5F – Algebra: Simultaneous Equations and Linear Inequalities

162

• solve simultaneous linear equations in two variables using the elimination method.

• solve simultaneous linear equations in two variables using the substitution method.

• solve simultaneous linear equations using graphs.

• solve simultaneous linear equations by balancing coefficients.

• solve problems using simultaneous linear equations.

139 • solve a simple linear inequality and represent it on a number line.

UNIT 5F HOMEWORK

UNIT 5E and 5F TEST


Unit 5G – Algebra: Non Linear Graphs

143 • interpret distance–time graphs • draw a graph of the depth of liquid as a container is filled.

216 • read information from a velocity-time graph • work out the acceleration from a velocity-time graph

98 • draw and read values from quadratic graphs.

157 • solve a quadratic equation by factorisation.

160

• identify the significant points of a quadratic function graphically • identify the roots of a quadratic function by solving a quadratic equation • identify the turning point of a quadratic function.

161 • recognise and plot cubic and reciprocal graphs.

UNIT 5G HOMEWORK

Unit 5H – Geometry: Sectors, Pyramids, Cones and Spheres

167 • calculate the length of an arc • calculate the area and angle of a sector.

170 • calculate the volume and surface area of a pyramid.

171 • calculate the volume and surface area of a cone.

169 • calculate the volume and surface area of a sphere.

UNIT 5H HOMEWORK

UNIT 5G and 5H TEST



Unit 6A – Number: Counting, accuracy and Surds

177 189

Recognise rational numbers, reciprocals, terminating decimals and recurring decimals. Convert terminal decimals to fractions. Convert fractions to recurring decimals. Find reciprocals of numbers or fractions.

131 154 188

How to estimate powers and roots of any given positive number.

Apply the rules of powers to negative and fractional power

207 Simplify surds. Calculate and manipulate surds, including rationalising a denominator.

206

Find the error interval or limits of accuracy of numbers that have been rounded to different degrees of accuracy.

Combine limits of two or more variables together to solve problems.

Work out the number of choices, arrangements or outcomes when choosing from lists or sets.

42 199

Solve problems in which two variables have a directly proportional relationship (direct variation) Work out the constant of proportionality Recognise graphs that show direct variation."

Solve problems in which two variables have an inversely proportional relationship (inverse variation) Work out the constant of proportionality.

UNIT 6A HOMEWORK


Unit 6B – Statistics: Sampling and More Complex Diagrams

186 Draw and interpret cumulative frequency graphs.

187 Draw and interpret box plots.

205

Draw and interpret histograms where the bars are of equal width. Draw and interpret histograms where the bars are of unequal width. Calculate the median, quartiles and interquartile range from a histogram.

152 176

Peterson Capture/Recapture / Stratified Sampling

UNIT 6B HOMEWORK

UNIT 6A and 6B TEST


Unit 6C – Statistics: Combined Events

60 Work out the probability of different outcomes of combined events.

Work out the probability of two outcomes or events occurring at the same time.

175 Use tree diagrams to work out the probability of combined events.

204

Use the connectors ‘and’ and ‘or’ to work out the probabilities for combined events.

Work out the probability of combined events when the probabilities change after each event.

185 Use Venn diagrams to solve probability questions.

UNIT 6C HOMEWORK

Unit 6D – Geometry: Properties of Circles

183 184

Work out the size of angles in circles.

Find the size of angles in cyclic quadrilaterals.

Use tangents and chords to find the size of angles in circles.

Use the alternate segment theorem to find the size of angles in circles.

UNIT 6D HOMEWORK

UNIT 6C and 6D TEST


Unit 6E – Algebra: Quadratics

98 Draw and read values from quadratic graphs

157 Solve a quadratic equation by factorisation. Rearrange a quadratic equation so that it can be factorised.

191 Solve a quadratic equation by using the quadratic formula. Recognise why some quadratic equations cannot be solved.

209 Solve a quadratic equation by completing the square.

160

Identify the significant points of a quadratic function graphically. Identify the roots of a quadratic function by solving a quadratic equation. Identify the turning point of a quadratic function by using symmetry or completing the square.

140 Solve a pair of simultaneous equations where one is linear and one is non-linear, using graphs.

Solve equations by the method of intersecting graphs.

211 Solve simultaneous equations where one equation is linear and the other is non-linear.

212 Solve quadratic inequalities.

UNIT 6E HOMEWORK

UNIT 6E TEST



Unit 7A - Graphs

216

Use areas of rectangles, triangles and trapeziums to estimate the area under a curve. Interpret the meaning of the area under a curve.

Draw a tangent at a point on a curve and use it to work out the gradient at a point on a curve Interpret the gradient at a point on a curve.

208 Draw linear graphs parallel or perpendicular to other lines and passing through a specific point.

197 Find the equation of a tangent to a circle.

161 Recognise and plot cubic, exponential and reciprocal graphs.

196 Transform a graph.

UNIT 7A HOMEWORK

UNIT 7A TEST

Unit 7B - Triangles

181 Enlarge a shape by a negative/fractional scale factor

217 218

Use trigonometric ratios and Pythagoras’ theorem to solve more complex two-dimensional problems.

Use trigonometric ratios and Pythagoras’ theorem to solve more complex three-dimensional problems.

173 Find the sine, cosine and tangent of any angle from 0° to 360°.

201 202

Use the sine rule and the cosine rule to find sides and angles in any triangle.

203 Work out the area of a triangle if you know two sides and the included angle.

UNIT 7B HOMEWORK

UNIT 7B TEST


Unit 7C – Algebraic Fractions and Functions

210 Simplify algebraic fractions Solve equations containing algebraic fractions.

190 Change the subject of a formula where the subject occurs more than once.

214 Find the output of a function. Find the inverse function.

213 Generate the terms of a quadratic sequence from the nth term.

Work out the nth term of a quadratic sequence.

215 Find the composite of two functions.

180 Find an approximate solution for an equation using the process of iteration.

193 use algebra to support and construct arguments and proofs

UNIT 7C HOMEWORK

UNIT 7C TEST

Unit 7D - Vectors

219 Add and subtract vectors.

Use vectors to solve geometric problems.

UNIT 7D HOMEWORK

UNIT 7D TEST

Key Stage 5

Term Year 12 Year 13

Autumn

Core: Unit 1: Algebra and Functions Unit 2: Coordinate Geometry Unit 3: Further Algebra Stats and Mechanics: Unit 1: Statistical Sampling Unit 2a: Data presentation and interpretation Unit 6: Quantities and Units in Mechanics Unit 7a: Kinematics 1 Unit 2b: Data Presentation and Interperation Unit 7b: Kinematics

Core: Unit 3: Functions and Modelling Unit 4: Series and Sequences Unit 5: The binomial theorem Unit 6: Trigonometry Unit 7: Parametric Equations Stats and Mechanics: Unit 1: Regression and Correlation Unit 4: Moments Unit 2: Probability Unit 5: Forces at any angle

Spring

Core: Unit 4: Trigonometry Unit 5: Vectors Unit 6: Differentiation Unit 7: Integration Stats and Mechanics: Unit 3: Probability Unit 4: Statistical Distributions Unit 8a: Forces & Newton’s Laws Unit 5a: Statistical Hypothesis Unit 8b: Forces & Newton’s Laws

Core: Unit 8: Differentiation Unit 9: Numerical Methods Unit 10: Integration Stats and Mechanics: Unit 3a: The normal distribution Unit 6: Applications of Kinematics Unit 3b: The normal distribution Unit 7: Applications of Forces

Summer

Core: Unit 8: Exponentials and Logs A2: Unit 1: Proof A2: Unit 2 Algebraic and Partial Fractions Stats and Mechanics: Unit 5b: Statistical and Hyptheisis Testing Unit 9: Kinematics 2

Core: Unit 12: Vectors (3D) Stats and Mechanics: Unit 3c: The normal distribution Unit 8: Further Kinematics

Documents

Year 7 Mathematics Mastery Programme ... - Hilbre High School