MATHS DEPARTMENT

YEAR 9

SCHEME OF WORK

SET 1: IMPACT 3R

3R PLAN

AUTUMN TERM – FIRST HALF

Topic 1 / Number + Place Value / 3R Ch. 1 + Additional Unit
Topic 2 / Working with Algebra / 3R Ch. 2
Topic 3 / Area, Volume & Measure / 3R Ch. 3
Topic 4 / Averages & Spread / 3R Ch. 4
Topic 5 / Formulae, Equations & Inequalities / 3R Ch. 5

TEST 1

AUTUMN TERM – SECOND HALF

Topic 6 / Angles / 3R Ch. 6
Topic 7 / Fractions, Ratio & Proportion / 3R Ch. 8
Topic 8 / Graphs / 3R Ch. 7
Topic 9 / Number Sequences / 3R Ch. 16
Topic 10 / Problem Solving / Additional Unit

TEST 2

SPRING TERM – FIRST HALF

Topic 11 / Geometrical Reasoning + unit / 3R Ch. 10 + Additional Unit
Topic 12 / Proportional Reasoning / Additional Unit
Topic 13 / Decimals / 3R Ch. 11
Topic 14 / Probability / 3R Ch. 14

TEST 3

SPRING TERM – SECOND HALF

Topic 15 / Handling Data + unit / 3R Ch. 9 + Additional Unit
Topic 16 / Using a Calculator / Additional Unit
Topic 17 / Percentages / 3R Ch. 12
Topic 18 / Pythagoras’ Theorem / 3R Ch. 13

TEST 4

SUMMER TERM – FIRST HALF

Topic 19 / Transformations / 3R Ch. 15
Topic 20 / Trigonometry / 3R Ch. 17
Topic 21 / Revision for SATs / CGP Packs & Past Papers

SAT’s WEEK

SUMMER TERM – SECOND HALF

Start KS4 Higher Tier Scheme of Work immediately after SATs have taken place.

AUTUMN TERM A TOPIC 1

Topic: Number

/ NC Level: 6 - 8
NC Programme of Study:
Ref2ab: Use previous understanding of integers and place value to deal with large numbers and round to given powers of 10. Use the terms square, positive and negative square root, cube, cube root; use index notation and index laws.
Ref3gh: Recall all positive integer complements to 100, all multiplication facts to 10 x 10 and use to quickly derive division facts; recall cubes of 2, 3, 4, 5, 10.Round to the nearest integer and to 1 sig. fig.
Ref4c: Use a variety of checking procedures including working through the problem backwards.
Ref5c: Use index notation for simple integer powers and simple instances of index laws.
Learning Objectives:
  • Use laws of arithmetic and inverse operations
  • Make and justify estimates and approximations of calculations
  • Check results using appropriate methods
  • Round positive numbers to any given power of 10, and significant figures
  • Move from one form to another to gain a different perspective on the problem
  • Use ICT to estimate square roots and cube roots
  • Use index notation for integer powers and simple instances of the index laws
  • Give solutions to problems to an appropriate degree of accuracy
EXT – Estimate calculations by rounding numbers to 1 sig. fig. and multiplying or dividing mentally; know and use index laws for multiplication and division of positive integer powers; recognise that index laws can be applied to negative and fractional powers; recognise limitations on the accuracy of data and measurements
Additional Notes: The Place Value lesson should be used as part of this chapter (Booster Lesson 1)
Key Vocabulary:

INDICES INDEX SIGNIFICANT BOUNDS INVERSE SQUARE CUBE ROOT

Impact Reference:

Book 3R – ch.1

/ Other references: Booster L1

V8 – ch4

Mental & Oral Starters:

3R folder: pg. 4-7

101 Starters: pg. 11-13, 33-35, 46, 57

Discussion opportunities:
Explain methods; discuss whether an answer is ‘sensible’ / Pair / Group Work:
Give each other questions to calculate or estimate.
ICT Links:

EXCEL – trial and improvement for square / cube roots

C4 Video “Primes & Powers”
Spiritual/Moral/Citizenship Links:
We should all respect each other’s different methods and ideas
Investigation:

Why do we need to round numbers?

Time: 4-5 lessons

ADDITIONAL LESSON

Topic: Place Value

/ NC Level: 5 & 6
Learning Objectives:
  • Understand and use decimal notation and place value
  • Multiply and divide integers and decimals by 10, 100, 1000
  • Explain the effects of the above multiplication and division
  • Extend knowledge of integer powers of 10
  • Multiply and divide integers and decimals by 0.1, 0.01 etc.

Additional Notes: Booster lesson 1 should be covered as a stand-alone lesson here
Key Vocabulary:
PLACE VALUE TENTHS HUNDREDTHS THOUSANDTHS EQUIVALENT POWER INDEX MULTIPLY DIVIDE
Impact Reference:

This links closely to ch.1

/ Other references:

Booster lesson 1

Mental & Oral Starters:
SEE LESSON PLAN 1 FOR DETAILED INFORMATION
Time: 1 lesson

AUTUMN TERM A TOPIC 2

Topic: Working with Algebra

/ NC Level: 6 - 8
NC Programme of Study:
Ref5bc: Understand the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms, by multiplying a single term over a bracket, by taking out single term common factors, by expanding the product of 2 linear expressions, including squaring a linear expression. Use index notation for simple integer powers and simple instances of index laws; substitute positive and negative numbers into expressions.
Learning Objectives:
  • Simplify or transform algebraic expressions by taking out single term common factors
  • Multiply and divide powers
  • Add and subtract expressions involving brackets
  • Combine simple algebraic fractions
EXT – Square a linear expressions, expand the product of 2 linear expressions of the form xn; establish identities such as a2-b2 = (a+b)(a-b)
Key Vocabulary:

INDICES POWERS FACTORISE EXPAND ALGEBRAIC FRACTIONS

COMMON FACTOR
Impact Reference:

Book 3R – ch.2

/ Other references: Booster L6
V8 – ch6
Mental & Oral Starters:

3R folder: pg. 24-26

101 Starters: pg. 69 - 71

Discussion opportunities:
What expressions can represent, relate to real life. / Pair / Group Work:
Develop expressions to represent real life situations
ICT Links:

EXCEL – input formulae, substitute values into expressions

Spiritual/Moral/Citizenship Links:
Each letter can take many different values; symbolises different numbers – in life things change, objects symbolise significant meanings.
Investigation:

What happens as the variables change?

Time: 4 lessons

AUTUMN TERM A TOPIC 3

Topic: Area, Volume & Measure

/ NC Level: 5 - 8
NC Programme of Study:
Ref4fghi:Find areas of rectangles, recalling the formula, understanding the connection to counting squares and how it extends this approach; recall and use the formulae for the area of a parallelogram and a triangle; find the surface area and perimeter of simple shapes. Find volumes of cuboids; calculate volumes of right prisms and of shapes made from cubes and cuboids. Find circumferences of circles and areas enclosed by circles, recalling relevant formulae. Convert between area measures and volume measures.
Learning Objectives:
  • Use units of measure to calculate, estimate, measure and solve problems in a variety of contexts
  • Convert between area measures (mm2 to cm2, cm2 to m2 and vice versa) and between volume measures (mm3 to cm3, cm3 to m3 and vice versa)
  • Deduce and use formulae for the area of a triangle, parallelogram and trapezium
  • Calculate areas of compound shapes made from rectangles and triangles
  • Know and use the formulae for the circumference and area of a circle
  • Know and use the formula for the volume of a cuboid
  • Calculate volumes and surface areas of cuboids and shapes made from cuboids
  • Calculate the surface area and volume of right prisms
EXT – Recognise that measurements given to the nearest whole unit may be inaccurate by up to ½ unit in either direction; understand and use compound measures to solve problems; know and use formulae for lengths of arc and area of sectors; calculate lengths, areas and volumes in right prisms
Key Vocabulary:
AREA VOLUME CIRCUMFERENCE CONVERSION SURFACE AREA CAPACITY ACCURACY COMPOUND UNITS
Impact Reference:

Book 3R – ch.3

/ Other references: Booster L9 & 10

V6 – ch11 V7 – ch15 V8 – ch12

Mental & Oral Starters:

3R folder: pg. 40-44

101 Starters: pg. 83 - 86

Discussion opportunities:
Discuss known formulae / Pair / Group Work:
Find areas of complicated composite shapes
ICT Links:

EXCEL – finding max area of different shapes

Spiritual/Moral/Citizenship Links:
Some countries have a larger surface area – does that mean they are better off?
Investigation:

Discover the formulae for circles.

Compare surface area of shapes with same volume. The ‘Fencing Problem’
Time: 5 lessons

AUTUMN TERM A TOPIC 4

Topic: Averages & Spread

/ NC Level: 6 - 8
NC Programme of Study:
Ref4bg: Calculate mean, range and median of small data sets with discrete then continuous data; identify modal class for grouped data. Find the median for large data sets and calculate an estimate of the mean for large data sets with grouped data.
Learning Objectives:
  • Calculate statistics including with a calculator
  • Recognise when it is appropriate to use the range, mean, median and mode
  • Recognise when it is appropriate to use the modal class for grouped data
  • Find summary values that represent the raw data and select the statistics most appropriate to the problem
  • Construct and use stem-and-leaf diagrams
  • Find the mean and median of grouped or continuous data
EXT – Find the median and quartiles for large data sets; estimate the mean, median and IQR of a large set of grouped data; generate fuller solutions to increasingly demanding problems
Key Vocabulary:
MEAN MODE MEDIAN RANGE CONTINUOUS GROUPED DATA QUARTILES CUMULATUVE FREQUENCY
Impact Reference:

Book 3R – ch. 4

/ Other references: Booster L14

V7 – ch19

Mental & Oral Starters:

3R folder: pg. 64-66

101 Starters: pg. 96

Discussion opportunities:
Discuss which measure is most appropriate.
Interpretation of results / Pair / Group Work:
Compare averages, draw inferences
ICT Links:

EXCEL for representing data, analysis of statistics – pupils can then focus on inferences

Spiritual/Moral/Citizenship Links:
Pupils can draw inferences from data which relates to the class as a whole; use statistics from current affairs
Investigation:

Plenty of real life topics/statistics can be investigated here

Time: 5 lessons

AUTUMN TERM A TOPIC 5

Topic: Formulae, Equations

& Inequalities

/ NC Level: 6 - 8
NC Programme of Study:
Ref5defhij: Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms and by expanding the product of 2 linear expressions; distinguish in meaning between the words ‘equation’ ‘formula’ ‘identity’ ‘expression’. Set up simple equations; solve simple equations by using inverse operations or by transforming both sides in the same way. Solve linear equations with integer coefficients in which the unknown appear on either side or on both sides of the equation; solve linear equations that require prior simplification of brackets. Link a graphical representation of an equation to is algebraic solution; find an approx. solution of a pair of linear simultaneous equations by graphical methods, then find the exact solution by eliminating one variable; consider the graphs of cases with no solution or an infinite number of solutions. Use formulae from maths and other subjects; substitute numbers into formulae; derive a formula and change its subject. Solve simple linear inequalities in one variable and represent the solution on a number line.
Learning Objectives:
  • Distinguish the different roles played by letter symbols in equations, identities, formulae and functions
  • Construct and solve linear equations with integer coefficients (unknown on either or both sides) using appropriate methods
  • Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20
  • Use formulae from maths and other subjects
  • Substitute numbers into expressions and formulae
  • Derive a formula, and in simple cases, change its subject
  • Simplify non-linear equations
EXT – Solve a pair of simultaneous linear equations by eliminating 1 variable; link a graphical representation of an equation or pair of equations to the algebraic solution; solve linear inequalities in 1 and 2 variables; derive and use more complex formulae, and change the subject of a formula
Key Vocabulary:
SOLVE LINEAR EQUATION VARIABLE UNKNOWN REARRANGE SUBSTITUTE TRIAL AND IMPROVEMENT
Impact Reference:

Book 3R – ch. 5

/ Other references: Booster L13

V6 – ch7 V7 – ch6-8 V8 – ch6 & 8

Mental & Oral Starters:

3R folder: pg. 86-91

101 Starters: pg. 69-72

Discussion opportunities:
Discuss different methods / Pair / Group Work:
Can set each other equations to solve
ICT Links:

EXCEL for trial and improvement. Graphical equations for solving equations graphically?

C4 Video “Orders please”
Spiritual/Moral/Citizenship Links:
Treat both sides equally. Can set up formulae that model real life issues.
Investigation:

Investigate what happens as the values change

Time: 6-8 lessons

AUTUMN TERM B TOPIC 6

Topic: Angles

/ NC Level: 5 - 7
NC Programme of Study:
Ref2abcdg:Recall and use properties of angles at a point, on a straight line, perpendicular lines and opposite angles at a vertex. Distinguish between acute, obtuse, reflex and right angles; estimate the size in degrees. Use parallel line rules; understand properties of parallelograms and proof that the angle sum of a triangle is 180; understand proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other 2 vertices. Use angle properties of equilateral, isosceles and right-angled triangles; understand congruence, recognising when 2 triangles are congruent; explain why the angle sum of any quadrilateral is 360. Calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons.
Learning Objectives:
  • Solve problems using properties of angles, of parallel and intersecting lines
  • Justify inferences and explain reasoning with diagrams and text
  • Identify alternate angles and corresponding angles
  • Understand the proof that:
-the sum of the angles of a triangle is 180 and of a quadrilateral is 360
-the exterior angle of a triangle is equal to the sum of the 2 interior opposite angles
  • Explain how to find, calculate and use:
-the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons
-the interior and exterior angles of regular polygons
  • Distinguish between conventions, definitions and properties
  • Recognise and use three figure bearings
EXT – Distinguish between practical demonstration and proof
Key Vocabulary:
STRAIGHT INTERSECTING LINE PARALLEL SUPPLEMENTARY ALTERNATE CORRESPONDING VERTICALLY OPPOSITE INTERIOR EXTERIOR BEARING
Impact Reference:

Book 3R – ch. 6

/ Other references: Booster L8

V6 – ch12-14

Mental & Oral Starters:

3R folder: pg. 110-113

101 Starters: pg. 82-83

Discussion opportunities:

Explain angle rules

/ Pair / Group Work:
Proof of angle facts
ICT Links:
Spiritual/Moral/Citizenship Links:
Everything has its own rules to follow
Investigation:

Investigate angle rules by measurement

Time: 3-4 lessons

AUTUMN TERM B TOPIC 7

Topic: Fractions, Ratio & Proportion

/ NC Level: 6 & 8+
NC Programme of Study:
Ref2fg: Use ratio notation, including reduction to its simplest form and its various links to fraction notation. Recognise where fractions are needed to compare proportions.
Ref3cfn: Calculate a given fraction of a given quantity, expressing the answer as a fraction; express a given number as a fraction of another; add and subtract fractions; perform short division to convert a simple fraction to a decimal. Divide a quantity in a given ratio. Solve word problems about ratio and proportion, including using informal strategies and the unitary method.
Ref5fg: Use formulae from maths and other subjects; substitute numbers into a formula; derive a formula and change its subject. Set up and use equations to solve word and other problems involving direct proportion and relate their algebraic solutions to graphical representations of the equations.
Ref3d(shape): recognise that enlargements preserve angle and not length; identify the scale factor of an enlargement as the ratio of the lengths of any 2 corresponding line segments and apply this to triangles; understand the implications of enlargement for perimeter; use and interpret maps and scale drawings.
Learning Objectives:
  • Calculate fractions of quantities
  • Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse
  • Cancel common factors before multiplying or dividing
  • Reduce a ratio to its simplest form, including a ratio expressed in different units
  • Divide a quantity into 2 or more parts in a given ratio
  • Use the unitary method to solve simple word problems involving ratio and direct proportion
  • Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100% or as a whole
  • Compare 2 ratios; interpret and use ratio in a range of contexts, involving solving word problems
  • Solve problems involving direct proportion using algebraic methods, relating algebraic methods, relating algebraic solutions to graphical representations of the equations
  • Use and interpret maps and scale drawings
  • Consolidate understanding of the relationship between ratio and proportion
EXT – Understand and use proportionality and calculate the result of any proportional change using only multiplicative methods
Additional Notes: THIS CHAPTER SHOULD BE USED TO PREPARE FOR THE PROPORTIONAL REASONING UNIT IN THE SPRING TERM.
Key Vocabulary:

FRACTION RATIO DIRECT PROPORTION CONSTANT SIMPLIFY

Impact Reference:

Book 3R – ch. 8

/ Other references: Booster L5 & 15

V6 – ch2 & 4 V8 – ch1 & 10

Mental & Oral Starters:

3R folder: pg.158-162

Discussion opportunities:

Dividing quantities

/ Pair / Group Work:
e.g Adapt a recipe using ratio
ICT Links:

C4 Video “Scaling the Heights”

Spiritual/Moral/Citizenship Links:

Can keep the problems relevant to pupils/ current issues

Investigation:

What happens to quantities as the ratio changes and vice versa?

Time: 3- 4 lessons

AUTUMN TERM B TOPIC 8

Topic: Graphs

/ NC Level: 7 & 8
NC Programme of Study:
Ref5d: Set up simple equations.
Ref6efgh:Use the conventions for co-ordinates in the plane; plot points in all 4 quadrants; recognise that equations of the form y=mx+c correspond to straight line graphs; plot graphs of functions in which y is given explicitly in terms of x. Construct linear functions arising from real life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Generate points and plot graphs of simple quadratic and cubic functions. Find the gradient of lines given by equations of the form y=mx+c; investigate the gradients of parallel lines and lines perpendicular to these lines.
Learning Objectives:
  • Find the inverse of a linear function
  • Plot the graphs of linear functions where y is given explicitly in terms of x, on paper and using ICT
  • Recognise that equations of the form y=mx+c correspond to straight line graphs
  • Given values for m and c, find the gradient of lines given by equations of the form y=mx+c
  • Construct functions arising from real-life problems and plot their corresponding graphs
  • Interpret graphs arising from real situations including distance-time graphs
  • Represent problems and synthesise information in algebraic, geometric or graphical form
  • Communicate interpretations and results of a statistical enquiry using selected tables, graphs and diagrams in support, using ICT as appropriate
  • Analyse 3D shapes through 2D projections, including plans and elevations
EXT – Plot the graph of the inverse of a linear function; consider cases that have no solution or an infinite no. of solutions; investigate the gradients of parallel and perpendicular lines; plot graphs of simple quadratic and cubic functions
Key Vocabulary:

GRADIENT INTERCEPT COORDINATE AXES