# YEAR 9 HIGHER TIER

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```					YEAR 9: HIGHER TIER AUTUMN TERM
Teaching objectives for the oral and mental activities
       Order, add, subtract, multiply and divide integers. Multiply and divide decimals by 10, 100, 1000, 0.1 and 0.01. Count on and back in steps of 0.4, 0.75, 3/4… Round numbers, including to one or two decimal places. Know and use squares, cubes, roots and index notation. Know or derive quickly prime numbers less than 30 and factor pairs for a given number. Convert between fractions, decimals and percentages. Know that 0.005 is half of one per cent.  Find fractions and percentages of quantities.     Know or derive complements of 0.1, 1, 10, 50, 100, 1000. Add and subtract several small numbers or several multiples of 10, e.g. 250 + 120 – 190. Use jottings to support addition and subtraction of whole numbers and decimals. Use knowledge of place value to multiply and divide, e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5, 13  1.4.  Recall multiplication and division facts to 10  10. Derive products and quotients of multiples of 10, 100, 1000.  Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15.  Multiply and divide a two-digit number by a one-digit number.  Use approximations to estimate the answers to calculations, e.g. 39  2.8.  Solve equations, e.g. n(n – 1) = 56,  +  = –46.  Visualise, describe and sketch 2-D shapes.  Recall and use formulae for the perimeter of a rectangle, and areas of rectangles and triangles.  Calculate volumes of cuboids.  Estimate and order acute, obtuse and reflex angles.  Use metric units (length, mass, capacity) and units of time for calculations.  Use metric units for estimation (length, mass, capacity).  Convert between metric units, including area, volume and capacity measures.  Discuss and interpret graphs.  Calculate a mean using an assumed mean.  Apply mental skills to solve simple problems.

Using and applying mathematics to solve problems: Teaching objectives across the modules
2 – 25 26 – 7 28 – 9 30 – 1 32 – 5 Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data; generate fuller solutions Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to gain a different perspective on the problem Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT; use trial and improvement where a more efficient method is not obvious Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text; give solutions to problems to an appropriate degree of accuracy, recognising limitations on the accuracy of data and measurements; give reasons for choice of presentation, explaining selected features and showing insight into the problems structure. Suggest extensions to problems conjecture and generalise; Identify exceptional cases or counter-examples, explaining why; Justify generalisations, arguments or solutions; pose extra constraints and investigate whether particular cases can be generalised further.

Module 1

Pythagoras’ Theorem Formulae Circles Statistics

Module 2

Accuracy Volume Number revision Algebra

MODULE 1 Pythagoras’ Theorem – Chapter 1 Topic Introducing Pythagoras Pythagorean triples Main Objectives
Distinguish between conventions, definitions and derived properties. Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and texts; understand and apply Pythagoras’ theorem. Use squares and square roots Construct a triangle, given three sides

Framework refs.
178 – 179 184 – 189

Chapter Notes

Extra Resources

Needs extra input – see framework for examples.

56 – 59 220 - 223

This is a year 8 objective

Finding the hypotenuse

Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text; understand and apply Pythagoras theorem. Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text; understand and apply Pythagoras’ theorem

Finding any side

Formulae – Chapter 2 Topic Formulas Main Objectives
Distinguish the different roles played by letter symbols in equations, identities, formulae and functions. Use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formula and, in simple cases, change its subject. Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, Generate terms of a sequence using term-to-term and position to term definitions of the sequence, on paper and using ICT Generate sequences from practical contexts and write an expression to describe the nth term of an arithmetic sequence Find the next term and the nth term of quadratic sequences and functions and explore their properties Use index notation for integer powers and simple instances of the index laws; know and use the index laws in generalised form for multiplication and division of integer powers Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x3 + x = 20

Framework refs.
112 - 113 138 – 143 108 – 109 148 – 153 154 – 159 148 – 153 56 – 59 114 - 119 132 – 135

Chapter Notes

Extra Resources

Patterns

Extension work

Trial and improvement

Circles – Chapter 3 Topic Circumference Area Main Objectives
Know the definitions of a circle and the names of its parts Know and use the formulae for the circumference and area of a circle, and arcs and sectors of circles. Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, pi and sign change keys

Framework refs.
194 – 197 234 – 237 108 - 109

Chapter Notes

Extra Resources

Statistics – Chapter 4 Topic Looking at data Main Objectives
Interpret tables, graphs and diagrams for both discrete and continuous data, and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored Compare two or more distributions and make inferences, using the shape of the distribution, the range of data and appropriate statistics. Find summary values that represent the raw data, and select the statistics most appropriate to the problem. Calculate statistics, including with a calculator; recognise when it is appropriate to use the range, mean. Median and mode and, for grouped data, the modal class; Find the median and quartiles for large data sets; estimate the mean, median and Interquartile range of a large set of grouped data. Interpret graphs and diagrams and draw inferences to support or cast doubt on initial conjecture

Framework refs.
268 – 271

Chapter Notes

Extra Resources

272 – 273 256 – 261 256 – 261 256 – 261 268 – 271

Averages and range

Cumulative frequency

MODULE 2 Accuracy – Chapter 5 Topic Rounding Main Objectives
Use rounding to make estimates; round numbers to the nearest whole number or to one, two or three decimal places, and to a given number of significant figures Check results using appropriate methods. Make and justify estimates and approximations of calculations; estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally. Understand the effects of multiplying and dividing by numbers between 0 and 1; use the laws of arithmetic and inverse operation. Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, pi and sign change keys, function keys for powers, roots and fractions, brackets and the memory Understand upper and lower bounds. Use units of measurement to calculate, estimate, measure and solve problems in a variety of contexts; recognise that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in either direction. Write numbers in standard form. Enter numbers and interpret the display in context (negative numbers, fractions, decimals, percentages, money, metric measures, time, numbers in standard form) and fractions, brackets and the memory; use the reciprocal key. Use index notation for integer powers and simple instances of the index laws; know and use the index laws for multiplication and division of positive integer powers; begin to extend understanding of index notation to negative and fractional powers, recognise that the index laws can be applied to these as well.

Framework refs.
42 – 47 110 – 111 102 – 103 82 – 85 108 – 109

Chapter Notes

Extra Resources

Error in measurement

42 – 47 228 – 231

Standard form

36 – 39 108 – 109

56 - 59

Fractional indices not covered but could be introduced as extension work.

Volume – Chapter 6 Topic Volumes of prisms and cylinders Main Objectives
Use units of measurement to calculate, estimate, measure and solve problems in a variety of contexts; convert between volume measures (mm3 to cm3 , cm3 to mm3, and vice versa); Calculate lengths, areas and volumes in right prisms, including cylinders. This is not part of KS3 programme of study, but could be covered as extension work.

Framework refs.
228 – 231

Chapter Notes

Extra Resources

238 - 241

Another dimension

Number revision – Chapter 7 Topic Replay Increase and decrease Ratio Main Objectives Framework refs. Chapter Notes Extra Resources

Algebra – Chapter 8 Topic Brackets Two brackets Equations and formulas Main Objectives Framework refs. Chapter Notes Extra Resources

YEAR 9: HIGHER TIER SPRING TERM
Teaching objectives for the oral and mental activities
    Order, add, subtract, multiply and divide integers. Find products of small integer powers. Know and use squares, cubes, roots and index notation. Know or derive quickly the prime factorisation of numbers to 30 and factor pairs for a given number.  Find highest common factors (HCF) and lowest common multiples (LCM), e.g. the HCF of 36 and 48.  Convert between improper fractions and mixed numbers. Simplify fractions by cancelling.  Find the outcome of a given percentage increase or decrease.  Know or derive complements of 0.1, 1, 10, 50, 100, 1000.  Use jottings to support addition, subtraction, multiplication and division.  Recall multiplication and division facts to 10  10. Derive products and quotients of multiples of 10, 100, 1000.  Use known facts to derive unknown facts, e.g. derive 36  24 from 36  25.  Use knowledge of place value to multiply and divide decimals by multiples of 0.1 and 0.01, e.g. 0.24  0.4, 720  0.03.  Use approximations to estimate the answers to calculations, e.g. 39  2.8.  Solve equations, e.g. n(n – 1) = 56,  +  = –46, (3 + x)2 = 25.  Visualise, describe and sketch 2-D shapes, 3-D shapes and simple loci.  Estimate bearings.      Use metric units (length, area and volume) and units of time for calculations. Use metric units for estimation (length, area and volume). Convert between metric units, including area, volume and capacity measures. Recall and use formulae for areas of rectangle, triangle, parallelogram, trapezium and circle. Calculate volumes of cuboids and prisms.

 Discuss and interpret graphs.  Solve simple problems involving probabilities.  Apply mental skills to solve simple problems.

Module 3

Statistics Trigonometry The best chapter, probably Loci: know your place

Module 4

Algebra: two at a time Graphs: on the button Transformations Get in shape

MODULE 3 Statistics – Chapter 9 Topic Scatter diagrams Pie charts Misleading diagrams Main Objectives Framework refs. Chapter Notes Extra Resources

Trigonometry – Chapter 10 Topic Introduction Finding lengths Finding an angle Main Objectives Framework refs. Chapter Notes Extra Resources

The best chapter, probably – Chapter 11 Topic Probability and relative frequency Listing outcomes Tree diagrams Main Objectives Framework refs. Chapter Notes Extra Resources

Loci: know your place – Chapter 12 Topic Locus of a point Constructions Main Objectives Framework refs. Chapter Notes Extra Resources

MODULE 4 Algebra: two at a time – Chapter 13 Topic Main Objectives Replay Simultaneous equations Inequalities

Framework refs.

Chapter Notes

Extra Resources

Graphs: on the button – Chapter 14 Topic Graphs of calculator buttons Graph sketching Main Objectives Framework refs. Chapter Notes Extra Resources

Transformations – Chapter 15 Topic Transformations Combined transformations Enlargement Similar triangles Main Objectives Framework refs. Chapter Notes Extra Resources

Get in shape – Chapter 16 Topic Polygons Symmetry Nets of solids Building a shape sorter Main Objectives Framework refs. Chapter Notes Extra Resources

YEAR 9: HIGHER TIER SUMMER TERM
Teaching objectives for the oral and mental activities
     Order, add, subtract, multiply and divide integers. Round integers and decimals. Know and use squares, cubes, roots and index notation. Find highest common factors (HCF) and lowest common multiples (LCM). Convert between fractions, decimals and percentages, and between improper fractions and mixed numbers.  Find fractions and percentages of quantities and the outcome of a given percentage increase or decrease.  Know or derive complements of 0.1, 1, 10, 50, 100, 1000.  Use jottings to support addition, subtraction, multiplication and division.  Recall multiplication and division facts to 10  10. Derive products and quotients of multiples of 10, 100, 1000.  Use knowledge of place value to multiply and divide decimals by 0.1 and 0.01, e.g. 0.24  0.4, 720  0.03.  Use approximations to estimate the answers to calculations, e.g. 0.39  2.8.  Solve equations, e.g. n(n – 1) = 56,  +  = –46, (3 + x)2 = 25, (12 – x)2 = 49,      = 0.008  Visualise, describe and sketch 2-D shapes, 3-D shapes and simple loci.  Estimate and order angles and bearings.       Use metric units (length, mass, capacity, area and volume) and units of time for calculations. Use metric units for estimation (length, mass, capacity, area and volume). Convert between metric units including area, volume and capacity measures. Recall and use formulae for the perimeter of a rectangle and the circumference of a circle. Recall and use formulae for areas of rectangle, triangle, parallelogram, trapezium and circle. Calculate volumes of cuboids and prisms.

 Discuss and interpret graphs.  Solve simple problems involving probabilities.  Apply mental skills to solve simple problems.

SATs revision SATs Assessed Investigation 1 – L-scores Assessed Investigation 2 – Average student Year 9 GCSE syllabus

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