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MATHS DEPARTMENT YEAR 9 SCHEME OF WORK SET 4: IMPACT 3G SEPT 2004 3G PLAN AUTUMN TERM – FIRST HALF Topic 1 Place Value + Number Additional Unit + 3G Ch. 1 Topic 2 Angles 3G Ch. 2 Topic 3 Working with Algebra 3G Ch. 3 Topic 4 Multiplication & Division 3G Ch. 4 Topic 5 Graphs 3G Ch. 6 TEST 1 AUTUMN TERM – SECOND HALF Topic 6 Problem Solving Additional Unit Topic 7 Averages 3G Ch. 5 Topic 8 Fractions & Ratio 3G Ch. 8 Topic 9 Shape, Space & Measure 3G Ch. 7 Topic 10 Using a Calculator Additional Unit TEST 2 SPRING TERM – FIRST HALF Topic 11 Geometrical Reasoning Additional Unit Topic 12 Proportional Reasoning Additional Unit Topic 13 Number Patterns 3G Ch. 10 Topic 14 Probability 3G Ch. 13 TEST 3 SPRING TERM – SECOND HALF Topic 15 Handling Data + unit 3G Ch. 9 + Additional Unit Topic 16 Decimals 3G Ch. 11 Topic 17 Perimeter, Area & Volume 3G Ch. 15 Topic 18 Percentages 3G Ch. 12 TEST 4 SUMMER TERM – FIRST HALF Topic 19 Positive & Negative Numbers 3G Ch. 16 Topic 20 Formulae & Equations 3G Ch. 14 Topic 21 Revision for SATs CGP Packs & Past Papers SAT’s WEEK SUMMER TERM – SECOND HALF Start KS4 Foundation Tier Scheme of Work immediately after SATs have taken place. AUTUMN TERM A ADDITIONAL LESSON TOPIC 1 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: Other references: This links closely to ch.1 Booster lesson 1 Mental & Oral Starters: SEE LESSON PLAN 1 FOR DETAILED INFORMATION Time: 1 lesson AUTUMN TERM A TOPIC 1+ Topic: Number NC Level: 3-5 NC Programme of Study: Ref2a: Use previous understanding of integers and place value to deal with large positive numbers and round them to a given power of 10. Ref3aij: Add and subtract integers. Develop a range of strategies for mental calculation. Use standard column procedures for addition and subtraction of integers. Ref4c: Use a variety of checking procedures including working the problem backwards and considering whether a result is of the right order of magnitude. Learning Objectives: Order integers Extend mental methods of calculation – addition and subtraction Written methods for addition and subtraction Round numbers to powers of 10. Make and justify estimates and approximations of calculations Check results using appropriate methods Key Vocabulary: PLACE VALUE ORDER ADD SUBTRACT ROUND ESTIMATE CHECK MENTAL MATHS Impact Reference: Other references: Book 3G – ch. 1 Booster L1 Mental & Oral Starters: 3G folder: pg. 4-7 101 Starters: pg. 2-18 Discussion opportunities: Pair / Group Work: Discuss different methods for calculations Set each other problems to solve, time each Are answers sensible? other ICT Links: “Balloon” (Outware) Spiritual/Moral/Citizenship Links: We should all respect each others‟ methods and ideas Investigation: Investigate the quickest way of solving different types of questions Time: 6-7 lessons AUTUMN TERM A TOPIC 2 Topic: Angles NC Level: 5&6 NC Programme of Study: Ref2abcd: 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 different triangles; understand congruence; explain why angle sum of any quadrilateral is 360. Ref4b: Understand angle measure using the associated language. Learning Objectives: Recognise acute, obtuse and reflex angles 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 Solve geometrical problems using side and angle properties of equilateral, isosceles and right- angled triangles and special quadrilaterals Solve problems using properties of angles, of parallel and intersecting lines Justify inferences and explain reasoning with diagrams and text Key Vocabulary: ACUTE OBTUSE REFLEX OPPOSITE PRALLEL TRIANGLE ISOSCELES CORRESPONDING ALTERNATE RIGHT ANGLE AT A POINT STRAIGHT Impact Reference: Other references: Book 3G – ch. 2 Booster L8 V5 – ch17, 19, 21 V6 – ch12-14 Mental & Oral Starters: 3G folder: pg. 28-31 101 Starters: pg. 73,80 Discussion opportunities: Pair / Group Work: Discuss angles rule Proof, derive angle rules ICT Links: LOGO Spiritual/Moral/Citizenship Links: All things have their own rules to follow – even shapes Investigation: Investigate the different angle rules, rather than being taught them straight away Time: 6 lessons AUTUMN TERM A TOPIC 3 Topic: Working with Algebra NC Level: 5 NC Programme of Study: Ref5bc: 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‟. Use index notation for simple integer powers and simple instances of index laws; substitute positive and negative numbers into expressions. Learning Objectives: Use letters to represent unknowns Simplify or transform linear expressions by collecting like terms; multiply terms together; multiply a single term over a bracket Simplify or transform algebraic expressions by taking out single-term common factors Understand the order of precedence and effect of powers Key Vocabulary: LETTER COLLECT SIMPLIFY EXPRESSION MULTIPLY TERM BRACKET POWER EXPAND Impact Reference: Other references: Book 3G – ch.3 Booster L6 V5 – ch9 V6 – ch7 Mental & Oral Starters: 3G folder: pg.52-54 101 Starters: pg. 62-71 Discussion opportunities: Pair / Group Work: Discuss what the letters can represent Create problems for real life circumstances ICT Links: EXCEL can be used to substitute different values into different expressions. Spiritual/Moral/Citizenship Links: Variables can be used to represent real life objects or situations. Each letter can take many different values; symbolises different numbers – in life things change, objects symbolise significant meanings. Investigation: Investigate what happens as the numbers change in each expression Time: 4-5 lessons AUTUMN TERM A TOPIC 4 Topic: Multiplication & Division NC Level: 4&5 NC Programme of Study: Ref2ab: Use the concepts and vocab of factor, multiple, HCF, LCM, prime number and prime factor decomposition. Use the terms square, positive and negative square root, cube, cube root; use index notation for small integer powers and index laws for multiplication and division of positive integer powers. Ref3ahk: Multiply and divide integers by powers of 10 and then by any number; find the prime factor decomposition of positive integers. Round to the nearest integer and to 1 sig. fig. Use standard column procedures for multiplication and division. Ref4c: Use a variety of checking procedures. Learning Objectives: Use place value to multiply and divide by powers of 10 Use standard column procedures for multiplication and division of integers Understand and identify multiples, factors and primes Use the prime decomposition of a number Find the HCF and LCM Read and write positive integer powers of 10 Use squares, positive and negative square roots, cubes and cube roots Use index notation for integer powers and simple instances of the index laws Check answers by approximation; round to significant figures Use inverse operations Key Vocabulary: MULITPLE FACTOR PRIME CHECK APPROXIMATE POWER ROOT PLACE VALUE INVERSE OPERATION HCF LCM Impact Reference: Other references: Book 3G – ch.4 V5 – ch4 & 7 Mental & Oral Starters: 3G folder: pg.72-74 101 Starters: pg. 24-35 Discussion opportunities: Pair / Group Work: It is important to discuss methods Create problems, test/time each other ICT Links: “Balloon” (Outware) C4 Video “Primes & Powers” Spiritual/Moral/Citizenship Links: We should all respect each other‟s different methods and ideas Investigation: Investiagate the HCF and LCM of pairs of numbers – quick ways for finding them? Time: 8-10 lessons AUTUMN TERM A TOPIC 5 Topic: Graphs NC Level: 5&6 NC Programme of Study: Ref6ef(algebra): 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. Learning Objectives: Use fractions in co-ordinates 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 Interpret graphs arising from real situations, including distance-time graphs Construct functions arising from real-life problems and plot their corresponding graphs Key Vocabulary: COORDINATE QUADRANT LINE GRAPH EQUATION SLOPING LINE Impact Reference: Other references: Book 3G – ch.6 V5 – ch11 V6 – ch8-9 V7 – ch9 Mental & Oral Starters: 3G folder: pg. 110-112 101 Starters: pg. 72 Discussion opportunities: Pair / Group Work: Discuss the relationship between different Investigate the significance of m and c in graphs – leading to y=mx+c y=mx+c ICT Links: Autograph, Omnigraph, graphical calculators. “Carpark” (Outware) Spiritual/Moral/Citizenship Links: Use graphs from current issues Investigation: See above Time: 8 lessons AUTUMN TERM B TOPIC 6 Topic: Problem Solving NC Level: Learning Objectives: Identify the necessary information to solve a problem Solve more complex problems by breaking them down into smaller tasks/steps Interpret the numbers on a calculator display in different contexts Carry out more difficult calculations effectively and efficiently Solve problems and investigate in a range of contexts Explain and justify methods and conclusions Identify exceptional cases or counter-examples Additional Notes: Booster lessons 12 and 16 should be used as a stand-alone Problem Solving unit Key Vocabulary: EXPLAIN REASONS JUSTIFY Impact Reference: Other references: Booster lesson 12 & 16 Mental & Oral Starters: SEE LESSON PLAN 12 & 16 FOR DETAILED INFORMATION Time: 2 lessons AUTUMN TERM B TOPIC 7 Topic: Averages NC Level: 4–6 NC Programme of Study: Ref4ab: Draw and produce pie charts for categorical data and diagrams for continuous data, including line graphs for time series, scatter graphs, frequency diagrams and stem-and-leaf diagrams. Calculate mean, range and median of small data sets with discrete then continuous data; identify the modal class for grouped data. Learning Objectives: Calculate statistics, including with a calculator Recognise when it is appropriate to use the range, mean, median and mode Find the mean and median from a frequency table Construct and use stem-and-leaf diagrams Key Vocabulary: MEAN MEDIAN MODE RAMGE CUMULATIVE FREQUENCY STEM-AND-LEAF DIAGRAM DATA Impact Reference: Other references: Book 3G – ch. 5 Booster L14 V7 – ch19 Mental & Oral Starters: 3G folder: pg. 93-93 101 Starters: pg. 96-97 Discussion opportunities: Pair / Group Work: What do the results mean? Collect results from the class Which is the most useful average? ICT Links: EXCEL, data can be taken from the internet Spiritual/Moral/Citizenship Links: Data to be analysed should be taken from current issues Investigation: There is much scope here – try to keep it relevant to the students Time: 6 lessons AUTUMN TERM B TOPIC 8 Topic: Fractions & Ratio NC Level: 5&6 NC Programme of Study: Ref2cfg: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting then with a common denominator. Use ratio notation, including reduction to its simplest form and its various links to fraction notation. Recognise where fractions are needed to compare proportions. Ref3cd: 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 by writing them with a common denominator; perform short division to convert a simple fraction to a decimal. Understand and use unit fractions as multiplicative inverses; multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction. Learning Objectives: Add and subtract fractions by writing then with a common denominator Calculate fractions of quantities Multiply and divide an integer by a fraction 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 Consolidate understanding of the relationship between ratio and proportion Use the unitary method to solve simple word problems involving ratio and direct proportion Key Vocabulary: MIXED NUMBER IMPROPER EQUIVALENT DENOMINATOR NUMERATOR RATIO PROPORTION Impact Reference: Other references: Book 3G – ch. 8 Booster L5 & 15 V5 – ch2-3 V6 – ch2 & 4 Mental & Oral Starters: 3G folder: pg.174-178 101 Starters: pg. 36-38 Discussion opportunities: Pair / Group Work: Relationship between fractions and ratio Convert a recipe Where are ratios used in life? ICT Links: C4 Video “Scaling the Heights” Spiritual/Moral/Citizenship Links: We are all made up of different „parts‟ – e.g. creative, logical, academic, sporty – our ratios are all different Investigation: What happens to the ratio as the quantities change and vice versa? Time: 8-10 lessons AUTUMN TERM B TOPIC 9 Topic: Shape, Space & Measure NC Level: 4&5 NC Programme of Study: Ref2dk: Use angle properties of triangles; understand congruence, recognising when 2 triangles are congruent. Use 2D representation of 3D shapes and analyse 3D shapes through 2D projections and cross-sections, including plan and elevation. Ref3abe: Understand that rotation are specified by a centre and an angle; use right angles, fractions of turn or degrees to measure the angle of rotation; understand that reflections are specified by a mirror line, translations by a distance and direction, and enlargements by a centre and positive scale factor. Recognise and visualise rotations, reflections and translations; recognise that these transformations preserve length and angle. Learning Objectives: Know and identify solids – cubes, cuboids, pyramids, prisms, sphere, hemisphere Recognise and construct nets of 3D shapes Form tessellations Understand congruence Transform 2D shapes by combinations of translations, rotations and reflections, on paper and using ICT Know that translations, rotations and reflections preserve length and angle and map objects on to congruent images Draw plans and elevations of solids Know rough metric equivalents of imperial measures in daily use – feet, miles, pounds, pints, gallons Key Vocabulary: POINT LINE SHAPE NET SOLID TESSELLATION TRANSFORMATION TRANSLATION REFLECTION ROTATION CONGRUENCE PLAN ELEVATION METRIC IMPERIAL UNIT Impact Reference: Other references: Book 3G – ch. 7 V5 – ch19-21 V6 – ch12-16 Mental & Oral Starters: 3G folder: pg. 139-146 101 Starters: pg. 74-86 Discussion opportunities: Pair / Group Work: Identify the transformations that have taken Create nets of different solids place ICT Links: LOGO. OHT‟s are very useful here Spiritual/Moral/Citizenship Links: People can be transformed or reformed Investigation: Investigate the effects of the order of transformations on different shapes Time: 8-10 lessons AUTUMN TERM B TOPIC 10 Topic: Using a Calculator NC Level: Learning Objectives: Make and justify estimates and approximations of calculations Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size Use sign change keys and function keys for powers, roots, brackets and memory Additional Notes: This should be used as a stand-alone lesson Key Vocabulary: ESTIMATE SIGNIFICANT UNITS DIGIT SQUARE SQUARE ROOT CUBE FRACTION BRACKETS Impact Reference: Other references: Booster lesson 4 Mental & Oral Starters: 101 Starters: pg. SEE LESSON PLAN 4 FOR DETAILED INFORMATION Time: 1 lesson SPRING TERM A TOPIC 11 Topic: Geometrical Reasoning Unit Learning Objectives: Distinguish between conventions, definitions and derived properties Distinguish between practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them. 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 Solve problems using properties of angles, parallel and intersecting lines, and triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. Visualise and use 2D representation so of 3D objects; analyse 3D shapes through 2D projections, including plans and elevations Transform 2D shapes by combinations of translations and rotations Know that translations and rotations preserve length and angle and map objects on to congruent images Present a concise, reasoned argument, using symbols, diagrams and related explanatory text Give reasons for choice of presentation, explaining selected features and showing insight into the problem‟s 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. Additional Notes: Should be used as a stand-alone unit. Key Vocabulary: CONVENTION DEFINITION JUSTIFY DEDUCE GENERALISE PROVE PROOF VERTICALLY OPPOSITE ALTERNATE CORRESPONDING INTERIOR EXTERIOR SUPPLEMENTARY PLAN ELEVATION PROJECTION Impact Reference: Other references: Ch.7 Year 9 Geometrical Reasoning mini-pack SEE MINI-PACK FOR FURTHER GUIDANCE Time: 6-7 lessons SPRING TERM A TOPIC 12 Topic: Proportional Reasoning Unit Learning Objectives: Understand the effects of multiplying and dividing numbers between 0 and 1 Use the laws of arithmetic and inverse operation Recognise and use reciprocals Enter numbers into a calculator and interpret the display in context Recognise when fractions or percentages are needed to compare proportions Solve problems involving percentage changes Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100% or as a whole Understand and use proportionality and calculate the result of any proportional change using multiplicative methods Understand the implications of enlargement for area and volume Compare 2 ratios Interpret and use ratio in a range of contexts, including solving word problems Enlarge 2D shapes; recognise the similarity of the resulting shapes; identify the scale factor of an enlargement as the ratio of the lengths of any 2 corresponding line segments; recognise that enlargements preserve angle but not length Solve increasingly demanding problems and evaluate solutions Explore connections in maths across a range of contexts Represent problems and synthesise information in algebraic, geometric or graphical form 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 Additional Notes: Should be used as a stand-alone unit. Can relate back to topic 9 Key Vocabulary: SCALE MULTIPLIER INVERSE OPERATION RECIPROCAL RATIO PROPORTION RATE UNITARY ENLARGE CENTRE SIMILAR Impact Reference: Other references: Ch.8 Year 9 Proportional Reasoning mini-pack Securing L5 lessons 9N4.3, 9P1.2 & 9P1.3 SEE MINI-PACK FOR FURTHER GUIDANCE Time: 9 lessons SPRING TERM A TOPIC 13 Topic: Number Patterns NC Level: 4-6 NC Programme of Study: Ref5d: Set up simple equations; solve simple equations by using inverse operations or by transforming both sides in the same way. Ref6ac:Generate common integer sequences. Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence; use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or context from which it was generated. Learning Objectives: Generate and describe picture and integer sequences Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence on paper and using ICT Use one-step, two-step and inverse number machines Use the difference method to find the general rule of a linear sequence Key Vocabulary: SEQUENCE NUMBER MACHINE INVERSE DIFFERENCE GENERAL RULE Impact Reference: Other references: Book 3G – ch. 10 Booster L7 V5 – ch8 V6 – ch6 V7 – ch5 Mental & Oral Starters: 3G folder: pg. 228-229 Discussion opportunities: Pair / Group Work: The rules for the next value Create number patterns, test each other on the rules ICT Links: Use EXCEL to create patterns C4 Video “Primes & Powers” Spiritual/Moral/Citizenship Links: Patterns / sequences that occur in nature. The terms follow the same rule – like the rules we all have to follow in school/life Investigation: Investigate patterns that occur in real life Time: 5 lessons SPRING TERM A TOPIC 14 Topic: Probability NC Level: 5&6 NC Programme of Study: Ref4cdf: Understand and use the probability scale. Understand and use estimates or measures of probability from theoretical models, including equally likely outcomes, or from relative frequency. Identify different mutually exclusive outcomes and know that the sum of the probabilities of these outcomes is 1. Learning Objectives: Understand and use the probability scale Use the vocabulary of probability in interpreting results involving uncertainty and prediction Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems Know that is the probability of an event occurring is p, then the probability of it not occurring is 1 – p Find and record all possible mutually exclusive outcomes for combined events using diagrams and tables Key Vocabulary: PROBABILITY SCALE EVENT OUTCOME SAMPLE SPACE Impact Reference: Other references: Book 3G – ch. 13 Booster L11 V5 – ch28-29 V6 – ch20 V7 – ch22-23 Mental & Oral Starters: 3G folder: pg. 286-290 101 Starters: pg. 99-101 Discussion opportunities: Pair / Group Work: Discuss the probability of real life events Experimental probability occurring ICT Links: Random number generators Spiritual/Moral/Citizenship Links: Probability of real life events; gambling; the lottery Investigation: Experimental probability – e.g. dice, coins, cards Time: 6 lessons SPRING TERM B TOPIC 15 Topic: Handling Data NC Level: 3–5 NC Programme of Study: Ref3a: Design and use data collection sheets for grouped discrete and continuous data; collect data using various methods including observation, controlled experiment, data logging, questionnaires and surveys. Ref4a: Draw and produce using paper and ICT, pie charts for categorical data and diagrams for continuous data including scatter graphs, frequency diagrams and stem-and-leaf diagrams. Learning Objectives: Design questionnaires Decide which data to collect to answer a question, and the degree of accuracy needed Construct on paper and using ICT: - pie charts for categorical data - bar charts and frequency diagrams for discrete data Identify which are most useful in the context of a problem Identify key features present in the data Interpret graphs and diagrams and draw inferences to support or cast doubt on initial conjectures Have a basic understanding of correlation Key Vocabulary: TALLY BAR CHART PICTOGRAMS HISTOGRAMS SCATTER GRAPHS. DISCRETE CONTINUOUS DATA COMPARE Impact Reference: Other references: Book 3G – ch. 9 Booster L14 V5 – ch24-26 V6 – ch18-19 V7 – ch18 Mental & Oral Starters: 3G folder: pg.200-203 101 Starters: pg. 98 Discussion opportunities: Pair / Group Work: It is very important to discuss which method of Collect information and select how best to presentation is most appropriate and to compare present it. different sets of results. INFERENCES ICT Links: EXCEL, Autograph (Statistics) Spiritual/Moral/Citizenship Links: Use data from current issues – draw inferences Investigation: There is plenty of scope here Time: 8-10 lessons ADDITIONAL UNIT Topic: Handling Data NC Level: Learning Objectives: Find the mode, median, mean and range Interpret graphs, diagrams and tables for discrete and continuous data Draw inferences that relate to the problem being discussed Relate summarised data to the questions being explored Compare two distributions using the range and one or more of the mode, median and mean Additional Notes: This should be used alongside chapter 9 Key Vocabulary: MODE MEDIAN MEAN RANGE COMPARE GREATER LESS SLIGHTLY SIGNIFICANTLY Impact Reference: Other references: Ch.9 Booster lesson 14 Mental & Oral Starters: SEE LESSON PLAN 14 FOR DETAILED INFORMATION Time: 1 lesson SPRING TERM B TOPIC 16 Topic: Decimals NC Level: 4-7 NC Programme of Study: Ref2d: Use decimal notation and recognise that each terminating decimal is a fraction. Ref3achijk:Add, subtract, multiply and divide integers and then any number; multiply a number by a number between 0 and 1. Perform short division to convert a simple fraction to a decimal. Round to the nearest integer and to 1 sig fig; estimate answers to problems involving decimals. Add and subtract mentally numbers with up to 2 decimal places; multiply and divide numbers with no more than 1 decimal digit. Use standard column procedures and understand where to position the decimal point. Ref4c: Use a variety of checking procedures. Learning Objectives: use rounding to make estimates Round decimals to the nearest whole number and 1 or 2 decimal places Extend mental methods of calculation – including decimals Know that a recurring decimal is an exact fraction Use standard column procedures to add and subtract integers and decimals of any size Use standard column procedures for multiplication of integers and decimals, inc. decimals such as 0.6 and 0.06 Divide decimals by transforming to division by an integer Understand where to position the decimal point by considering equivalent calculations Key Vocabulary: ORDER CONVERT ROUND NEAREST DECIMAL PLACE APPROXIMATE Impact Reference: Other references: Book 3G – ch. 11 V6 – ch2 V7 – ch2 Mental & Oral Starters: 3G folder: pg. 250-253 101 Starters: pg. 53 Discussion opportunities: Pair / Group Work: Discuss place value, methods When are decimals used? ICT Links: Spiritual/Moral/Citizenship Links: Significance – the numbers after the decimal point are equally as important as the numbers before the point – we are all equally significant Investigation: Which are more useful, decimals or fractions? Time: 6-7 lessons SPRING TERM B TOPIC 17 Topic: Perimeter, Area & Volume NC Level: 5&6 NC Programme of Study: Ref4fgh: 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. Learning Objectives: Use units of measurement to calculate, estimate, measure and solve problems in a variety of contexts Know and use the formulae for finding the area and perimeter of rectangles Use methods to estimate area 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 Key Vocabulary: FORMULA LENGTH WIDTH HEIGHT PERPENDICULAR COMPOSITE ESTIMATE CIRCUMFERENCE SURFACE AREA Impact Reference: Other references: Book 3G – ch. 15 Booster L9 & 10 V6 – ch11 V7 – ch15 Mental & Oral Starters: 3G folder: pg. 330-337 Discussion opportunities: Pair / Group Work: Estimations Derive formulae for circle/surface areas ICT Links: LOGO Spiritual/Moral/Citizenship Links: Real life shapes and areas Investigation: The Fencing Problem Time: 8-10 lessons SPRING TERM B TOPIC 18 Topic: Percentages NC Level: 5&6 NC Programme of Study: Ref3cem: Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. Solve simple percentage problems, including increase and decrease. Learning Objectives: Interpret percentage as the operator „so many hundredths of‟ Converting between fractions, decimals and percentages Express one given number as a percentage of another Recognise when fractions or percentages are needed to compare proportions Solve problems involving percentage change Key Vocabulary: CONVERT FRACTION DECIMAL PERCENTAGE AMOUNT INCREASE DECREASE COMPARE Impact Reference: Other references: Book 3G – ch. 12 Booster L2 & 3 Securing L5 lessons 9N1.3 & 9N1.4 V5 – ch2 V6 – ch3 Mental & Oral Starters: 3G folder: pg. 272-273 101 Starters: pg. 36-38 Discussion opportunities: Pair / Group Work: Conversions between fractions, decimals, Investigate interest rates – bank accounts percentages. ICT Links: EXCEL C4 Video “Not all There” Spiritual/Moral/Citizenship Links: Tax, interest rates, the Budget Investigation: As above Time: 4 lessons SUMMER TERM A TOPIC 19 Topic: Positive & Negative Numbers NC Level: 4&5 NC Programme of Study: Ref2a: Understand and use negative numbers, both as positions and translations on a number line. Ref3a: Add, subtract, multiply and divide integers and then any number. Ref6a: Generate common integer sequences. Learning Objectives: Order positive and negative integers Use a horizontal number line to add and subtract positive and negative integers Complete, generate and describe number sequences involving negative numbers Use two-way number tables for addition and subtraction Key Vocabulary: ORDER NUMBER LINE SEQUENCES INTEGER POSITIVE NEGATIVE Impact Reference: Other references: Book 3G – ch. 16 V5 – ch5 Mental & Oral Starters: 3G folder: pg. 360-361 101 Starters: pg. 19-23 Discussion opportunities: Pair / Group Work: Discuss where negative numbers occur in real Human number line life ICT Links: C4 Video “Walking Backwards” Spiritual/Moral/Citizenship Links: Positive qualities can balance out the negative Investigation: When do we use negative numbers? Collect temperatures over a period of time, discuss the changes Time: 3 lessons SUMMER TERM A TOPIC 20 Topic: Formulae & Equations NC Level: 5&6 NC Programme of Study: Ref5bdefi: 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. 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: Know the meanings of the words „formula‟ and „function‟ Construct and solve linear equations with integer coefficients (unknown on either or both sides) using appropriate methods – inverse operations, transforming both sides in the same way Solve equations involving brackets Substitute into formulae Use the correct order of operations – BIDMAS Use inequalities Key Vocabulary: SUBSTITUTE WORD FORMULAE BIDMAS SOLVE EQUATION OPERATION BRACKETS INEQUALITIES BALANCE LINEAR Impact Reference: Other references: Book 3G – ch. 14 Booster L13 Securing L5 lessons 9A2.1 & 9A2.1 V5 – ch9-10 V6 – ch7 V7 – ch7 Mental & Oral Starters: 3G folder: pg. 308-312 101 Starters: pg. 62-71 Discussion opportunities: Pair / Group Work: Think of a situation that can be represented by Create a formula „story‟ explaining what the a given formula variables mean ICT Links: EXCEL for trial and improvement C4 Video “Orders Please” Spiritual/Moral/Citizenship Links: Real life situations can be represented by formulae. Investigation: What happens as the variables change? Time: 6-7 lessons Time should now be spent revising for the SATs exams – use past papers and CGP packs. After the SATs, the KS4 Foundation Tier Scheme of Work should be started.

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