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YEAR 7 SCHEME OF WORK AUTUMN TERM Using & Applying 1: Introductory Module – Treasure Hunt, Investigations & Calculations Handling Data 1: Questionnaires, Surveys & Charts Shape, Space & Measures 1: Symmetry & Transformations Algebra 1: Number Patterns, Factors & Multiples Number 1: Rounding, Estimating, Bodmas, Powers, Square Roots, Calculator Keys Shape, Space & Measures 2: Shapes, Tessellations & Constructions Number 2: Decimals SPRING TERM Handling Data 2: Probability Number & Algebra 3: Negative numbers & Graphs Shape, Space & Measures 3: Angles & Constructions Algebra 2: Language of Algebra, Simplifying expressions, Solving Equations Shape, Space & Measures 4: Perimeter & Area SUMMER TERM Number 4: Fractions, Decimals, Percentages, Ratio & Proportion Algebra 4: Solving Equations & Trial & Improvement Shape, Space & Measures 5: Solids, Volumes & Nets Handling Data 3: Averages Shape, Space & Measures 6: Scale Drawing, Units Reinforcement of the more difficult Y7 topics The scheme of work is differentiated into 3 levels. All students should attempt the core. The extension section is designed as extra work for the most able pupils but may be attempted by others when appropriate. The support section is aimed at helping weaker students. The success of individual students depends on careful monitoring, close teamwork and co-operative planning by staff to make sure that expections for ALL pupils are suitably high. Teaching objectives for oral and mental activities are placed at the beginning of the Scheme of Work and can be used both to support the main teaching programme in addition to providing a means of regularly revisiting important elements. Page references in each module relate to the supplement of examples in the Framework. Module tests will take place in October, December & February. The individual components of the optional Y7 National Tests will take place for all students during April & June. All of these marks will be recorded on the Department database. This is a working document and it would be helpful if colleagues could annotate it during the year with suggestions that have or have not worked well and with any additional resources that have been useful. General numeracy and mental mathematics should be covered throughout the year. Opportunities for non- calculator mathematics should be emphasised at all opportunities. Core objectives are shown in bold. 1 CITIZENSHIP, PSHE AND RELIGIOUS EDUCATION Belief and likelihood in religious education, or risk assessment in PSHE, relate well to work in mathematics. The discussion of moral and social issues is likely to lead to the use of primary and secondary data and the interpretation of graphs, charts and tables, helping pupils to make reasoned and informed decisions and to recognise biased data and misleading representations. By applying mathematics to problems set in financial and other real-life contexts pupils will develop their financial capability and awareness of the applications of mathematics in the workplace. Coursework tasks or extended investigations, particularly related to Handling Data, promote the skills of enquiry and communication. They also encourage the skill of participation and responsible action in the educational establishment and / or communication. Mathematics provides opportunities to promote: Thinking skills, through developing pupils’ problem-solving skills and deductive reasoning; Financial capability, through applying mathematics to problems set in financial contexts; Enterprise and entrepreneurial skills, through developing pupils’ abilities to apply mathematics in science and technology, in economics and in risk assessment; Work related learning, through developing pupils’ abilities to use and apply mathematics in workplace situations and in solving real life problems. LITERACY The National Curriculum statement on language suggests three areas to include in all subject teaching: General accuracy in using language – spoken, written and read; Technical terms and concepts appropriate to the subject; Awareness of patterns of language In mathematics, general accuracy in using language can be promoted through: interpreting questions posed orally or in writing; clarifying the precise meaning of words or mathematical terms; discussing the essential ideas identified in the questions and interpreting them to identify the mathematical content. Awareness of patterns of language can be developed by asking pupils to explain, argue and present their conclusions to others, and by drawing their attention to the statements involved in mathematical reasoning and proof, such as if… then, because, therefore, implies… The technical terms and concepts used in mathematics will include ideas on an inverse, of equivalence, equality, proportionality, congruence, similarity, linearity, and so on. SPIRITUAL, MORAL, ETHICAL, SOCIAL, CULTURAL AND OTHER ISSUES Mathematics provides opportunities to promote: spiritual development, through explaining the underlying mathematical principles behind some of the natural forms and patterns in the world around us; moral development, through helping pupils recognise how logical reasoning can be used to consider the consequences of particular decisions and choices helping them learn the value of mathematical truth; social development, through helping pupils work together productively on complex mathematical tasks and helping them see that the result is often better than could be achieved separately; Cultural development, through helping pupils appreciate that mathematical thought contributes to the development of our culture and is becoming increasingly central to our highly technological future, and through recognising that mathematicians from many cultures have contributed to the development of modern day mathematics. 2 YEAR 7: AUTUMN TERM Teaching objectives for the oral and mental activities Read and write whole numbers in figures and words. Add & subtract several small numbers or several multiples of 10, e.g. 50 – 40 + 80 – 100. Multiply and divide whole numbers by 10, 100, 1000. Add and subtract pairs of numbers, e.g. 76 ± 38, 760 ± 380. Count on and back in steps of 0.1, 0.2, 0.25, 1/2, 1/4… Find doubles and halves of numbers, e.g. 670, 5.6. Round whole numbers to the nearest 10 or 100. Recall multiplication facts to 10 10 and derive associated division facts. Order, add and subtract positive and negative numbers in context. Multiply and divide a two-digit number by a one-digit number. Recognise multiples and use simple tests of divisibility. Visualise, describe and sketch 2-D shapes in different orientations. Know pairs of factors of numbers to 100. Estimate and order acute and obtuse angles. Know or derive quickly prime numbers less than 30. Use metric units (length, mass, capacity) and units of time for calculations. Know or derive quickly squares to at least 12 12 and the corresponding roots. Use metric units for estimation (length, mass, capacity). Convert between fractions, decimals and percentages. Convert between m, cm and mm, km and m, kg and g, litres and ml. Find simple fractions of quantities. Know rough metric equivalents of common imperial units. Know addition and subtraction facts to 20 and whole number complements of 100. Apply mental skills to solve simple problems. Find two decimals (one decimal place) with a sum of 1. YEAR 7: SPRING TERM Teaching objectives for the oral and mental activities Read and write whole numbers in figures and words. Add several small numbers and find their mean. Multiply and divide decimals by 10, 100, 1000. Add and subtract pairs of numbers, e.g. 7.6 ± 3.8, 760 ± 380. Count on and back in steps of 0.4, 0.75, 3/4… Find doubles and halves of numbers, e.g. 6500, 0.76, 3/4. Order decimals in different contexts. Recall multiplication and division facts to 10 10. Round decimals to the nearest whole number. Derive answers to calculations, e.g. 60 80, 0.4 9. Order, add and subtract integers. Multiply and divide a two-digit number by a one-digit number. Recognise multiples and use tests of divisibility. Visualise, describe and sketch 2-D shapes. Know pairs of factors of numbers to 100. Estimate and order acute and obtuse angles. Know or derive quickly prime numbers less than 30. Use metric units (length and area) and units of time for calculations. Know or derive quickly squares to at least 12 12 and the corresponding roots. Convert between m, cm and mm, km and m. Find simple equivalent fractions. Calculate perimeter and area of rectangles. Know whole-number complements of 50 and 100. Discuss and interpret graphs. Find two decimals with a sum of 1 or 0.1 (two decimal places). Apply mental skills to solve simple problems. YEAR 7: SUMMER TERM Teaching objectives for the oral and mental activities Multiply and divide decimals by 10, 100, 1000 and small multiples of 10. Use doubling and halving to calculate, e.g. 6 4.5, 1.38 50. Round numbers, including to one or two decimal places. Recall multiplication and division facts to 10 10. Order decimals and simple fractions in different contexts. Use factors to multiply and divide mentally, e.g. 35 12, 144 36, 3.2 30. Recognise multiples and use tests of divisibility. Derive answers to calculations, e.g. 0.4 9, 0.7 0.9. Know pairs of factors of numbers to 100. Multiply and divide a two-digit number by a one-digit number. Know or derive quickly prime numbers less than 30. Use approximations to estimate the answers to calculations, e.g. 39 2.8. Squares to at least 12 12, multiples of 10, 0.1 to 0.9 and corresponding square roots. Solve equations such as 100 = x + 37. Convert between fractions, decimals and percentages. Visualise and describe 2-D and 3-D shapes. Find fractions and percentages of quantities. Estimate and order acute, obtuse and reflex angles. Know complements of 0.1, 1, 10, 50, 100. Use metric units (length, mass, capacity) and units of time for calculations. Add and subtract pairs of numbers, e.g. 0.65 + 3.8, 765 + 47. Convert between m, cm and mm, km and m, kg and g, litres and ml. Use jottings to support addition and subtraction of whole numbers and decimals. Convert between metric and common imperial units. Find doubles and halves of decimals and fractions. Discuss and interpret graphs. 3 USING & APPLYING 1: Introductory Module – Treasure Hunt, Investigations, Calculations SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) The first few lessons should be used to introduce Year 7 to all that is good and positive about Maths. The first few lessons should be used to set expectations, rules & discipline, explain equipment that is required and to ask children what they like & dislike about Maths. Number petal and white board activities should be used. Mental strategies for various sums should be shared & discussed. Stress pupils need to have a scientific calculator by next week. See Transition booklet for lesson plans. The Treasure Hunt* should build on the above positive ‘fun’ aspect of Maths in addition to helping students find their way around the school. (Liase for best timings) Investigate various buttons on the calculator, especially, squares, powers, square roots, brackets, memory. Discuss types of question that a calculator should be used for & those that can be done mentally or with jottings. Use fans & whiteboards to practise simple questions related to the 4 rules, fraction, decimal & percentages. A couple of investigations should be carried out to fulfil the objective outlined below. Some examples include Ice-Cream cones, Badges, Chessboard & Sheep pens. Decide which data would be relevant to an enquiry and possible sources. Present and interpret solutions in the context of the original problem; explain and justify methods and conclusions, orally and in writing. Identify the necessary information to solve a problem; Represent problems and interpret solutions in represent problems mathematically, making correct use of algebraic or graphical form, using correct notation. symbols, words, diagrams, tables and graphs. Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of what is presented. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Treasure Hunt Maths is boring! Investigation, powers, square roots, brackets, Mental Maths 2 Investigations Maths is hard! data Tresure Hunt Calculator activities TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Autumn Term – 1 Half st Handling Data 3: (250-273) Throughout 8 lessons *to be developed 4 HANDLING DATA 1: Questionnaires, Surveys & Charts SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Solve a problem by representing, extracting and Decide which data would be relevant to an enquiry Decide the degree of accuracy needed for the data. interpreting data in tables, graphs, charts and and possible sources. diagrams Plan how to collect and organise small sets of data; Plan how to collect the data, including sample size; design a data collection sheet or questionnaire to use construct frequency tables with given equal class in a simple survey; construct frequency tables for intervals for sets of continuous data. discrete data, grouped where appropriate in equal class intervals. Collect small sets of data from surveys and Draw scatter diagrams and analyse results, discuss the experiments, as planned. term correlation. Use co-ordinates in 1st quadrant Construct, on paper and using ICT, graphs and Construct on paper and using ICT: diagrams to represent data, including bar-line graphs; pie charts for categorical data; frequency diagrams for grouped discrete data; use simple line graphs for time series. ICT to generate pie charts. Use & plot co-ordinates in all four quadrants Draw and interpret pictograms Interpret diagrams and graphs (including pie charts), Interpret tables, graphs and diagrams for both discrete and draw conclusions based on the shape of graphs and continuous data. and simple statistics for a single distribution. Understand to read and interpret timetables. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Surveys TV survey Bar-charts or Histograms? Data, correlation, rhombus, x co-ordinate, Pie Charts Excel for various graphs Label all axes on graphs y co-ordinate, sample, statistics, angle, key, Bar-Charts Use internet to search for data Give graphs & charts titles data capture sheet Pictograms Most popular colour of staff car? (words on left under ‘topics covered’) Straight line or join the points? Tally Tables Co-ordinates Correct scales on axes Scatter Diagrams Use pencil & ruler for graphs Questionnaires Scatter Diagram through (0,0)? TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE KM: Chapter 1 Autumn Term – 1st Half Handling Data 2: FM: Sections D2, D3 8 lessons (248–255, 262–265, 268–271) 5 SHAPE, SPACE & MEASURES 1: Symmetry & Transformations SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Recognise reflection symmetry. Begin to identify & use angle, side & symmetry Solve geometrical problems using side and angle Recognise where a shape will be after reflection. properties of triangles & quadrilaterals; solve properties of equilateral, isosceles and right-angled Recognise where a shape will be after a translation geometrical problems involving these properties, triangles and special quadrilaterals. using step-by-step deduction & explaining reasoning with diagrams & text. Draw in lines of symmetry. Understand and use the language and notation Apply transformations using a co-ordinate grid, associated with reflections, translations and Complete diagrams to give desired order of rotational rotations. symmetry. Complete a diagram being given the mirror line. Recognise and visualise the transformation and Transform 2-D shapes by simple combinations of symmetry of a 2-D shape: rotations, reflections and translations, on paper and reflection in given mirror lines, and line symmetry; using ICT; identify all the symmetries of 2-D shapes. rotation about a given point, and rotation symmetry; translation; explore these transformations & symmetries using ICT Solve word problems and investigate in a range of Understand and use the language and notation contexts: shape and space. associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive whole- number scale factor. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Symmetry of Flags & Roadsigns Diagonals of rectangle not lines of symmetry Turn, degrees, order of rotational Line Symmetry Enlargement & Photos / TV’s Parallelogram has no lines of symmetry symmetry, centre of rotation, scale Rotational Symmetry Religious symbols with symmetry Use of colour with symmetry factor, symmetrical, enlargement, Enlargement Dashed line for symmetry reduction, translation. Translation All shapes have order of Rot Sym of at least 1 Diagonal lines of symmetry TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Space & Measures 3 & 4: KM: Chapter 2 Autumn Term – 1st Half Geometrical reasoning: lines, angles & shapes, transformations (Does not cover Enlargement & Translation) (184–189, 198–201, 202-212) 8 lessons FM: Section S4 Solving problems (14–17, 32–35) 6 ALGEBRA 1: Number Patterns, Factors & Multiples SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Recognise and extend number sequences formed by Generate and describe simple integer sequences and Investigate triangular & cube numbers counting from any number in steps of constant size, patterns. extending beyond zero when counting back. Know squares to at least 10 10. Generate terms of a simple sequence, given a rule Generate terms of a linear sequence using term-to- (e.g. finding a term from the previous term, finding a term and position-to-term definitions of the sequence, term given its position in the sequence). on paper and using a spreadsheet or graphical calculator. Knowledge of odd/even numbers Generate sequences from practical contexts and Begin to use linear expressions to describe the nth describe the general term in simple cases. term of an arithmetic sequence. Express simple functions in words, then using Represent mappings expressed algebraically. symbols; represent them in mappings. Recognise multiples up to 10 10; know and apply Recognise and use multiples, factors (divisors), Find the prime factor decomposition of a number. simple tests of divisibility. common factor and primes (less than 100); use Identify factors of two-digit numbers. simple tests of divisibility. Recognise the first few triangular numbers, squares of numbers to at least 12 12, and the corresponding roots. Suggest extensions to problems by asking ‘What Find the Highest Common Factor & Least Common if…?’; begin to generalise and to understand the Multiple of a pair of numbers. significance of a counter-example. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Generate rules on Excel Write 6n not n6 Multiples, factors, prime Number Sequences Investigate sides/diagonals in polygons Confusion/differences between multiples & factors numbers, square numbers, Number Machines Finding Rules Investigate machines with same output 32 does not equal 6 cube numbers, triangular Multiples & Factors Use fans for inverse machine questions 1 is not a prime number numbers, prime factor, highest common factor, least common Types of Number multiple. TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Autumn Term – 2nd Half Algebra 1: Sequences and functions (144–163) KM: Chapter 3 Solving problems (32–35) FM: Sections A1, A3 8 lessons 7 NUMBER 1: Rounding, Estimating, Bodmas, Powers, Square Roots, Calculator Keys SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Rounding to the nearest 10, 100,1000 in a range of Rounding to decimal places, units Upper and lower bounds of estimates Understand the concept of the order of operations, Use Bodmas in calculations involving multiple use BODMAS brackets and powers Use an estimate to calculate an approximate answer. Develop calculator skills and use a calculator Enter numbers and interpret the display in different effectively. contexts (decimals, money). Use a calculator to square numbers. Solve word problems and investigate in a range Use the function keys for sign change, powers and of contexts: number; compare and evaluate roots. Use the memory keys and brackets. solutions. Decide in everyday contexts if a number should be rounded up or down Find a difference by counting up through the next Check a result by considering whether it is of the Use squares, and positive and negative square roots. multiple of 10, 100 or 1000. Add & subtract right order of magnitude and by working the mentally pairs of two-digit numbers. problem backwards. Use the square root key. Consolidate mental methods: Break a complex calculation into simpler steps, Extend mental calculations to squares and square find a difference by counting up; choosing and using appropriate and efficient roots, cubes and cube roots. add or subtract a multiple of 10 then adjust. operations, methods and resources, including ICT. Add & subtract mentally pairs of two-digit numbers. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) List order of important operations in Numbers ending in 5 are rounded up! Bodmas, Powers, estimate, Rounding common contexts Lay out Bodmas calculations down the page rounding, approximation Estimation Underline operation carried out first Order of Operations (BODMAS) TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Algebra 3: Integers, powers and roots (52–59) Autumn Term – 2nd Half KM: Chapters 4 & 6 Calculator methods (108–109) 8 lessons FM: Sections N5, N3 (part) Solving problems (2–11, 28-31) 8 SHAPE, SPACE & MEASURES 2: Shapes, Tessellations & Constructions SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Recognise, draw & name different types of triangle Draw rectangle, square, rhombus, parallelogram, Recognise all of the quadrilaterals & be familiar with their Classify quadrilaterals by their geometric trapezium, kite & arrowhead. properties properties. Label sides that are parallel Understand that parallel lines never meet Understand the term regular when related to various Name all polygons up to & including 12 sides. polygons Be familiar with the terms circumference, radius & Be familiar with the terms arc, chord & segment diameter Draw circles accurately given the radius or Use a compass to accurately draw a triangle given the diameter measurements of all 3 sides Recognise properties of rectangles. Begin to identify and use angle, side and symmetry Classify triangles (isosceles, equilateral, scalene), properties of triangles and quadrilaterals. using criteria such as equal sides, equal angles, lines of symmetry. Show how various shapes can tessellate. Explain why some shapes do not tessellate TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Examples of shapes A rhombus is not just a rotated square Polygon, convex, concave, equilateral, Tessellation wall display Label parallel sides with arrows isosceles, scalene, vertex, vertices, Names & Properties of Shapes Label equal sides with lines diagonal, parallel, regular, tessellation, Using a Compass Tessellations have no gaps anywhere! congruent, quadrilateral, circumference, Circles radius, diameter, arc, semicircle, chord, Tessellations Pentagon – 5 sides, Hexagon – 6 sides Diagonals join 2 non-adjacent vertices segment, various names of shapes. TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Autumn Term – 2 Halfnd KM: Chapters 5 & 10 Shape, Space & Measures 1: Constructions (220-223) FM: Section: S5 (part) 8 lessons 9 NUMBER 2: Decimals SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Read & write whole numbers in figures & words. Understand and use decimal notation and place Use decimal notation for tenths and hundredths; value; multiply and divide integers and decimals by know what each digit represents in numbers with up 10, 100, 1000, and explain the effect. Order to two decimal places. decimals and be familiar with the use of < and >. Know squares to at least 10 x 10 Consolidate the rapid recall of number facts, Recall known facts, including fraction to decimal including positive integer complements to 100 and conversions; use known facts to derive unknown multiplication facts to 10 10, and quickly derive facts, including products such as 0.7 and 6, and 0.03 associated division facts. and 8. Approximate first & use informal pencil & paper Use standard column procedures to add and subtract methods to EXTENSION addition & subtraction. whole numbers and decimals with up to two places. Extend written methods to: Multiply and divide three-digit by two-digit whole Multiply and divide integers and decimals, ThHTU U and U.t U; numbers; extend to multiplying and dividing including by decimals such as 0.6 and. 0.06; TU TU; decimals with one or two places by single-digit understand where to position the decimal point by HTU ÷ U. whole numbers. considering equivalent calculations. Divide £.p by a two-digit number to give £.p. Carry out calculations with more than one step using Investigate recurring decimals Round up or down after division, depending on brackets and the memory; use the square root and context. sign change keys. Interpret the display of a calculator in different contexts (decimals, percentages). TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Bring in examples in sport 0.2 x 0.2 = 0.04 not 0.4 Place value, decimal point, recurring Long jump, race times 5.7 x 100 = 570 not 507 Place Value Multiply/Dividing by 10,100,1000 Ask yourself if answers are sensible Decimal Calculations Money is always rounded to 2dp’s TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Number 1: Place value (36–41) Autumn Term – 2nd Half KM: Chapter 6 Calculations (88–107, 110–111) 8 lessons FM: Section N1 (part) Calculator methods (108–109) 10 HANDLING DATA 2: Probability SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Use vocabulary and ideas of probability, drawing on experience. Give events that have a probability of 0 , 0.5 or 1. Understand and use the probability scale from 0 Know that if the probability of an event occurring is Use the terms certain, impossible, even chance, to 1; find and justify probabilities based on p, then the probability of it not occurring is 1 – p; find likely & unlikely equally likely outcomes in simple contexts; and record all possible mutually exclusive identify all the possible mutually exclusive outcomes outcomes for two successive events in a systematic of a single event. way, using diagrams and tables. Collect data from a simple experiment and record in Understand that: a frequency table; estimate probabilities based on if an experiment is repeated there may be, and usually this data. will be, different outcomes; increasing the number of times an experiment is repeated generally leads to better estimates of probability. Compare experimental and theoretical probabilities in simple contexts. Calculate simple probabilities of various events TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Play your cards right The probability Man Utd wins Premiership is not 0.5! Impossible, certain, equally likely, Horse racing game with If P(A)=0.95, P(A’) = 0.05 not 0.5 event, outcome, relative frequency. Probability Scales dice Write probability as fractions, NOT ratios, eg. 4:5 Simple Probability Is this dice fair? You cannot have a probability of over 1, eg. 1.5 Probability Experiments Probability experiments Probability washing line TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Spring Term – 1st Half KM: Chapter 8 Handling Data 1 & 3: Probability (276–283) FM: Sections D1 (part), D4 8 lessons 11 NUMBER & ALGEBRA 3: Negative Numbers & Graphs SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Calculate a temperature rise and fall across 0 C. Understand negative numbers as positions on a Add, subtract, multiply and divide positive & number line; order, add and subtract positive and negative integers. negative integers in context. Read and plot coordinates in the first quadrant. Use conventions and notation for 2-D coordinates in Square-roots of numbers have a positive and negative all four quadrants; find coordinates of points solution. determined by geometric information. Read and plot coordinates in the first quadrant. Generate coordinate pairs that satisfy a simple linear Generate points in all four quadrants and plot the Represent and interpret data in a graph (e.g. for a rule; plot the graphs of simple linear functions, graphs of linear functions; recognise that multiplication table). where y is given explicitly in terms of x, on paper equations of the form and using ICT; recognise straight-line graphs parallel y = mx + c correspond to straight-line graphs. to the x-axis or y-axis. Label graphs with their names, eg y=4, x=-3, y=x, Investigate changes to co-ordinates after a reflection y=x+3 in a given line. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Temperatues & Goal Difference Square-root of 9 is 3 AND –3 Negative, minus, quadrant, Geography – below see level All graphs need to be labelled equation, origin, y-intercept, Adding & subtracting with Negative Numbers Co-ordinates in all 4 quadrants Practise coordinate located on axes gradient Equations of lines on graphs Use lines on paper not spaces for graphs TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Spring Term – 1st Half Number 1: Integers (48–51) KM: Chapter 11 FM: Sections N1 (part), A5 8 lessons Algebra 3: Coordinates (148-167, 218–219) 12 SHAPE, SPACE & MEASURES 3: Angles & Constructions SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Recognise positions. Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes. Identify parallel and perpendicular lines; know Identify alternate and corresponding angles; the sum of angles at a point, on a straight line and understand a proof that: in a triangle and recognise vertically opposite the sum of the angles of a triangle is 180 and of a angles. quadrilateral is 360; the exterior angle of a triangle is equal to the sum of the two interior opposite angles. Understand that a right angle is 90 degrees & that Use angle measure; distinguish between and estimate Calculate angles in isosceles and equilateral triangles. there are 360 degrees in a complete turn & 180 the size of acute, obtuse and reflex angles. degrees along a line. Use a protractor to measure and draw acute and Use a protractor to: Use straight edge and compasses to construct: obtuse angles to the nearest degree. measure angles, including reflex angles, to the the mid-point and perpendicular bisector of a line nearest degree; segment; construct a triangle given two sides and the included the bisector of an angle; angle (SAS) or two angles and the included side construct a triangle given three sides (SSS). (ASA); explore these constructions using ICT. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Label angles in everyday objects Label all angles especially reflex angles Right angle, acute, obtuse, Names of Angles Cut out angles in triangle & place in line Compare angles to a right angle when estimating reflex, opposite angles, Basic Angle Calculations Left angles do not exist! isosceles, equilateral, Estimating & Drawing Angles Label all angles with a degrees symbol alternate angles, Constructions corresponding angles, proof TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Shape, Space and Measures 2: Spring Term – 1st Half Geometrical reasoning: lines, angles and shapes (178–189) KM: Chapter 10 Mensuration (232–233) FM: Sections S2, S3 (part) 8 lessons Construction (220–223) 13 ALGEBRA 2: Language of Algebra, Simplifying Expressions SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Use letter symbols to represent unknown numbers or Begin to distinguish between the different roles played by variables; know the meanings of the words term, letter symbols in equations, formulae and functions; expression and equation. know the meanings of the words formula and function. Understand and use the relationships Understand that algebraic operations follow the same Know that algebraic operations follow the same between the four operations, and the conventions & order as arithmetic operations. conventions and order as arithmetic operations; use index principles (not the names) of the arithmetic notation for small positive integer powers. laws. Use brackets. Understand that 4 times c can be written as Simplify linear algebraic expressions by collecting like Simplify or transform linear expressions by collecting 4c terms; begin to multiply a single term over a bracket like terms; multiply a single term over a bracket. (integer coefficients). Identify the necessary information to solve a problem; represent problems mathematically, making correct use of symbols, words, diagrams and tables. Use simple formulae from mathematics & other subjects, Substitute integers into simple formulae, including substitute positive integers in simple linear expressions & examples that lead to an equation to solve, and positive formulae &, in simple cases, derive a formula. integers into expressions involving small powers (e.g. 3x2 + 4 or 2x3). TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Code breaking worksheets Write 2c not c2 Term, expression, equation, Writing Rules Sponsored swim – how is money raised? Lay substitution work out down the page formula, function, powers Simplifying expressions (-3)2 = 9 not –9 or 6 Substituting into formulas 3a + 2 does not equal 5a 3a + 5a2 cannot be simplified any further a is the same as 1a not 0a TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Spring Term – 2 Halfnd Algebra 2 & 5: KM: Chapter 9 Equations, formulae and identities (112–119, 122–143) FM: Sections A2 8 lessons Solving problems (26–27) 14 SHAPE, SPACE & MEASURES 4: Perimeter & Area SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Understand that area is measured in square Know and use the formula for the area of a Deduce and use formulae for the area of a triangle, centimetres (cm2). rectangle; calculate the perimeter and area of shapes parallelogram and trapezium. Understand, measure and calculate perimeters of made from rectangles. rectangles and regular polygons. Estimate area by counting squares Calculate the surface area of cubes and cuboids. Draw shapes accurately with a given area. Be aware of the appropriate units for an area given. Calculate composite areas or areas where various shapes have been removed Calculate areas by using a ruler to measure Calculate the side of a shape having been given its accurately drawn shapes area, including squares rectangles, triangles, parallelogram and trapeziums. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Measure areas of various objects Stress the importance of units Composite, area, perimeter, Areas of Quadrilaterals Deduce formulas during a practical Layout work down the page trapezium, parallelogram Areas of Triangles Use fans to reveal areas Draw diagrams with pencil & ruler Perimeter of various shapes Use white boards to draw shapes with given area Do composite areas one at a time Composite Areas TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE KM: Chapter 14 Spring Term – 2 Half nd Shape, Space & Measures 1: (Alternate/Corresponding Angles not covered) Mensuration (198-201, 228-231, 234-241) 8 lessons Solving Problems (18-21) FM: Section S1 (part) 15 NUMBER 4: Fractions, Decimals & Percentages, Ratio & Proportion SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Change an improper fraction to a mixed number; Use fraction notation to describe parts of shapes & to express a Know that a recurring decimal is a recognise when two simple fractions are smaller whole number as a fraction of a larger one; simplify fraction; use division to convert a equivalent, including relating hundredths to tenths. fractions by cancelling all common factors & identify fraction to a decimal; order fractions by Use decimal notation for tenths and hundredths. equivalent fractions; convert terminating decimals to fractions e.g. converting them to decimals. 0.23 = 23/100 use a diagram to compare 2 or more simple fractions. Understand percentage as the ‘number of parts Begin to add & subtract simple fractions & those with common Calculate fractions of quantities and per 100’; recognise the equivalence of denominators; calculate simple fractions of quantities & measurements (fraction answers); percentages, fractions and decimals; calculate measurements (whole-number answers); multiply a fraction by an multiply and divide an integer by a simple percentages. integer. fraction. Consolidate & extend mental methods of calculation to include Find the outcome of a given decimals, fractions & percentages, accompanied where percentage increase or decrease. appropriate by suitable jottings; solve simple word problems Recall fraction to decimal conversions. mentally Calculate simple fractions of quantities and measurements (whole- number answers); multiply a fraction by an integer. Relate fractions to division. Recognise the equivalence of percentages, fractions and Express one given number as a Find simple fractions of whole-number quantities. decimals; calculate simple percentages and use percentages to percentage of another; use the Find simple percentages of whole-number compare simple proportions. equivalence of fractions, decimals and quantities. percentages to compare proportions. Solve simple problems using ideas of ratio and Understand the relationship between ratio and proportion; use Divide a quantity into 2 or more parts proportion (‘one for every…’ and ‘one in direct proportion in simple contexts; use ratio notation, reduce a in a given ratio; use the unitary every…’). ratio to its simplest form and divide a quantity into two parts in a method to solve simple word given ratio; solve simple problems about ratio and proportion using problems involving ratio & direct informal strategies. proportion. Currency conversions. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Manipulating Fractions Use various fans to improve mental sharpness 1/3 = 0.3333 not just 0.3, this is 3/10 Fraction, decimal Fraction & % of Quantities Relate work back to pie-charts ½ + ¼ is not equal to 2/6 percentage, numerator, Fraction, Decimal % Conversions Split %’s into 10%, 5%, 2.5% etc 1/5 does not equal 0.5 denominator, ratio, Ratio & Proportion Relate to work on VAT 0.5 times x, is the same as x divided by 2 proportion, equivalent Poster of magazine adverts featuring %’s fractions TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Summer Term – 1st Half KM: Chapter 15 Number 2 & 4: Fractions, decimals, percentages, ratio and proportion (60–81) (Ratio & Proportion not covered) 12 lessons Calculations (92–101, 110–111) FM: Sections N2, N4 16 ALGEBRA 4: Solving Equations and Trial & Improvement SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Construct and solve simple linear equations with Construct and solve linear equations with integer Solve equations with negative and fractional answers integer coefficients (unknown on one side only) coefficients (unknown on either or both sides, with using an appropriate method (e.g. inverse & without brackets) using appropriate methods (e.g. operations). inverse operations, transforming both sides in the same way). Form and solve equations relating to angles, areas and perimeters. Solve equations using a trial and improvement with Solve equations using a trial and improvement with integer solutions solutions to 1 decimal place. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Everyday inverse operations 0.5x = 4, x = 8, NOT 2 Inverse, equation, trial & I think of a number… x-5 = 10, x = 15, NOT 5 improvement, formula Solving Equations Algebra crosswords State the answer x = ? in T & I questions Trial & Improvement Layout questions down the page Keep equal signs in line TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE KM: Chapter 13 Summer Term – 1st Half Algebra 2 & 5: Equations, formulae and identities (112–119, 122–143) FM: Section A4 8 lessons Solving problems (26–27) 17 SHAPE, SPACE & MEASURES 5: Solids, Volumes & Nets SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Identify the names of various solids. Identify different nets for an open cube. Use 2-D representations to visualise 3-D shapes and Use isometric paper to draw various arrangements of deduce some of their properties. cubes. Discuss basic references to plane symmetry. Visualise 3-D shapes from 2-D drawings and Use a ruler and protractor to construct simple nets of identify different nets for a closed cube. 3-D shapes, e.g. cuboid, regular tetrahedron, square- based pyramid, triangular prism. Understand the differences between prisms and Draw a net of a tetrahedron pyramids Calculate volumes of cubes. Know and use the formula for the volume of a cuboid, and triangular prism. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Show pupils various solids Count space not dots on isometric paper Prism, pyramid, volume, net, cube, Construct nets & make shapes Draw in fold lines on nets cuboid, sphere, cylinder, cone. Names of Solids Nets of Solids Investigate 1cm2, 8cm3 & 64cm3. Tabs need only be drawn if a model is made! Volume of basic solids Wall display of 3D displays Include appropriate units for all answers Art & perspective, eg. railway lines TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Summer Term – 1st Half KM: Chapter 7 Shape, space and measures 1: Mensuration (198-201, 228-231, 234-241) 8 lessons FM: Sections S3 (part), S5 (part) 18 HANDLING DATA 3: Averages SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Find the mode and range of a set of data. Calculate statistics for small sets of discrete data: Recognise when it is appropriate to use the range, Begin to find the median and the mean of a set of find the mode, median and range, and the modal mean, median and mode; calculate a mean using an data. class for grouped data; assumed mean. Calculate the mean, including from a simple Calculate median, range & mode from a frequency frequency table, using a calculator for a larger table number of items. Compare two simple distributions using the range Calculate a data value having been told the mean. and one of the mode, median or mean. Understand that statistics can also be misleading if not interpreted with an element of caution TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Use everyday examples Mean, median & mode are all averages Mean, median, mode, range, Mean Relate misleading statistics to government statistics, frequency table, Median Don’t just add up values & divide to misleading data Mode find mean in a frequency table! Range Misleading Statistics TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Summer Term – 2 Halfnd KM: Chapter 16 Handling Data 1 Handling data (256–261, 268–271) FM: Section D1 (part) 8 lessons 19 SHAPE, SPACE & MEASURES 6: Scale Drawing & Units SUPPORT CORE EXTENSION (from Y5/6 teaching programme) (from Y7 teaching programme) (from Y8 teaching programme) Measure and draw lines to the nearest millimetre. Use names and abbreviations of units of Record estimates and readings from scales to a measurement to measure, estimate, calculate and suitable degree of accuracy. solve problems in everyday contexts involving length, area. Reading basic scales Convert between metric units, eg, mm to cm, etc Conversions between metric & imperial 30cm = 1 foot, 4.5 litres = 1 gallon, 1kg = 2.2 pounds, measurements 5 miles = 8km Understand how a scale is used to make accurate drawings Solve a problem by representing, extracting and Interpret diagrams and graphs (including pie charts), interpreting data in tables, graphs, charts and and draw conclusions based on the shape of graphs diagrams, for example: and simple statistics for a single distribution. line graphs; frequency tables and bar charts. TOPICS COVERED RESOURCES MISCONCEPTIONS TO ADDRESS KEY WORDS (at a glance) (Worksheets, Activities, ICT) (common errors) (use & definition necessary) Relate conversions to work on ratio. Use a sharp pencil to increase accuracy Metric, imperial, conversion, Use distances, speeds in Europe Ask yourself, is a conversion sensible? scales, scale drawing. Metric & Imperial Conversions Scale Drawing Draw a scale diagram of their bedroom A standard (long) ruler is 30cm or 1 foot Reading Scale TIMING NATIONAL FRAMEWORK REFERENCE TEXTBOOK REFERENCE Summer Term – 2 Halfnd KM: Chapter 12 Shape, Space & Measures 1: Mensuration (198–201, 228–231, 234–241) FM: Sections S1 (part), N3 (part) 8 lessons Any spare time should be used to reinforce areas of the curriculum that pupils have found particularly difficult. The sharpening of mental skills and strategies could also be emphasised. 20