year 7 mathematics mastery programme ... - hilbre high school
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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
Year 8 Mathematics Mastery Programme of Study
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).
Year 9 Mathematics Mastery Programme of Study
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
MW Learning Objectives: Students will be able to:-
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
MODULE 4 PARENT INFORMATION
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MODULE 5 PARENT INFORMATION
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MODULE 6 PARENT INFORMATION
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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
MODULE 7 PARENT INFORMATION
MW Learning Objectives: Students will be able to:-
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
MW Learning Objectives: Students will be able to:-
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