Mathematics Scheme of Work Year 7 New Mathematics Framework 1
YEAR 7: Overview of year 7 scheme of work YEAR 7 Topics Assessment Tests Term 1 Algebra 1 Number 1 Geometry and Measures 1 Test 1 Sequences and functions (6 hours) Place values, integers, calculations (6 hours) Mensuration (perimeter and area) Number 2 Statistics 1 Algebra 2 Test 2 Fractions, decimals, percentages, ratio and proportion Statistics including probability Equations and formulae Term 2 Geometry and Measures 2 Statistics 2 Number and Measures 3 Test 3 Coordinates, geometrical reasoning: lines, angles and shapes Statistics Place value, calculations, calculator methods, measures (7 hours) Algebra 3 Geometry and Measures 3 Number 4 Test 4 Integers, powers and roots. Sequences, functions and graphs Geometrical reasoning: lines, angles and shapes. Construction Fractions, decimals, percentages, ratio and proportion Term 3 Algebra 4 Geometry and Measures 4 Statistics 3 Test 5 Equations and formulae Transformations Statistics, including probability Number 5 Algebra 5 Geometry and Measures 5 End of year test Place value, calculations including calculator methods, fractions, decimals, percentages, ratio and proportion, solving problems (6 hours) Sequences, functions and graphs, equations and formulae Geometrical reasoning: lines, angles and shapes; construction 2
YEAR 7: AUTUMN TERM Algebra 1 (6 hours) OVERVIEW FRAMEWORK OBJECTIVES 1.1 Sequences and rules 1.2 Finding missing terms 1.3 Functions and mappings 1.4 Using letter symbols to represent functions 1.5 The general term (nth term) 1.6 An nth term investigation 1.1 Describe integer sequences. 1.2 Generate terms of a simple sequence given a rule (for example, finding a term from the previous term; finding a term given its position in the sequence). 1.3 Express simple functions in words, then using symbols; represent them in mappings. 1.4 Use letter symbols to represent unknown numbers or variables. 1.5 Generate sequences from patterns or practical contents and describe the general term in simple cases. 1.6 Identify the necessary information to understand or simplify a context or problem; represent problems, making correct use of symbols, words, diagrams, tables and graphs; use appropriate procedures. Classify and visualise properties and patterns; generalise in simple cases by working logically. Number 1 (6 hours) Geometry & Measures 1 Number 2 Statistics 1 2.1 Decimals 2.2 Ordering decimals 2.3 Directed numbers 2.4 Estimates 2.5 Column method for addition and subtraction 2.6 Solving problems 3.1 Length, perimeter and area 3.2 Areas of some 2-D shapes 3.3 3-D shapes 3.4 Surface area and volume of cuboids 4.1 Fractions 4.2 Fractions and decimals 4.3 Adding and subtracting fractions 4.4 Equivalences 4.5 Solving problems 5.1 Mode, median and range 5.2 The mean 5.3 Statistical diagrams 5.4 Probability 5.5 Experimental probability 2.1 Understand and use decimal notation and place value. Multiply and divide integers and decimals by 10, 100, 1000, and explain the effect. 2.2 Compare and order decimals in different contexts. Know that when comparing measurements, the units must be the same. 2.3 Understand negative numbers as positions on a number line. Order, add and subtract integers in context. 2.4 Make and justify estimates and approximations of calculations. 2.5 Use efficient written methods to add and subtract whole numbers and decimals with up to two places. 2.6 Represent problems, making correct use of symbols, words and diagrams; use appropriate procedures and tools. 3.1 Choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts. 3.2 Choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts. Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles. 3.3 Use 2-D representations to visualise 3-D shapes and deduce some of their properties. Make accurate mathematical diagrams, graphs and constructions on paper and on screen. 3.4 Know and use the formula for the area of a rectangle. Calculate the perimeter and area of shapes made from rectangles. Calculate the surface area of cubes and cuboids. 4.1 Express a smaller whole number as a fraction of a larger one. Simplify fractions by cancelling all common factors and identify equivalent fractions. 23 4.2 Convert terminating decimals to fractions: for example, 0.23 = 100. Use a diagram to compare two or more simple fractions. 4.3 Add and subtract simple fractions and those with common denominators. 4.4 Calculate simple fractions of quantities and measurements (whole-number answers). Multiply a fraction by an integer. Understand percentage as the number of parts per 100. Calculate simple percentages and use percentages to compare simple proportions. Recognise the equivalence of percentages, fractions and decimals. 4.5 Check results by considering whether they are of the right order of magnitude and by working the problem backwards. 5.1 Calculate statistics for small sets of discrete data. Find the mode, median and range, and the modal class for grouped data. Explain and justify methods and conclusions; compare and evaluate approaches. 5.2 Calculate statistics for small sets of discrete data. Calculate the mean, including from a simple frequency table, using a calculator for a larger number of items. 5.3 Interpret diagrams and graphs (including pie charts), and draw conclusions based on the shape of graphs and simple statistics for a single distribution. Interpret information from a mathematical representations or context. 5.4 Use vocabulary and ideas of probability, drawing on experience. Understand and use the probability scale from 0 to 1. Find and justify probabilities based on equally likely outcomes in simple contexts. Identify all the possible mutually exclusive outcomes of a single event. 5.5 Estimate probabilities by collecting data from a simple experiment and recording it in a frequency table. Compare experimental and theoretical probabilities in simple contexts. 3
YEAR 7: AUTUMN TERM Algebra 2 OVERVIEW Teacher Pack 2 6.1 Algebraic terms and expressions 6.2 Rules of algebra 6.3 Simplifying expressions 6.4 Formulae 6.5 Equations FRAMEWORK OBJECTIVES 6.1 Use letter symbols to represent unknown numbers or variables. Know the meanings of the words term, expression and equation. 6.2 Understand that algebraic operations follow the rules of arithmetic. 6.3 Simplify linear algebraic expressions by collecting like terms. Multiply a single term over a bracket (integer coefficients). 6.4 Use simple formulae from mathematics and other subjects. Substitute positive whole numbers into linear expressions and formulae and, in simple cases, derive a formula. 6.5 Give simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (for example, inverse operations). 31 Hours Teaching 4
YEAR 7: SPRING TERM Measures 2 OVERVIEW Teacher Pack 2 FRAMEWORK OBJECTIVES Teacher Pack 2 7.1 Lines and angles 7.2 Calculating angles 7.3 Coordinates 7.1 Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes. Identify parallel and perpendicular lines. Identify and use angle, side and symmetry properties of triangles and quadrilaterals. Distinguish between and estimate the size of acute, obtuse and reflex angles. Represent problems, making correct use of symbols, words and diagrams. 7.2 Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes. Know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles. 7.3 Use conventions and notation for 2-D coordinates in all four quadrants. Find coordinates of points determined by geometric information. Statistics 2 Numbers & Measures 3 (7 hours) Algebra 3 Measures 3 Number 4 8.1 Using a tally chart 8.2 Using the correct data 8.3 Grouped frequencies 8.4 Data collection 9.1 Rounding 9.2 The four operations 9.3 BODMAS 9.4 Long multiplication and long division 9.5 Efficient calculations 9.6 Calculating with measurements 9.7 Solving problems 10.1 Square numbers and square roots 10.2 Triangle numbers 10.3 From mappings to graphs 10.4 Naming graphs 10.5 Naming sloping lines 11.1 Measuring and drawing angles 11.2 Constructions 11.3 Solving geometrical problems 12.1 Percentages 12.2 Ratio and proportion 12.3 Calculating ratios and proportions 12.4 Solving problems 8.1 Suggest possible answers given a problem that can be addressed by statistical methods. 8.2 Decide which data would be relevant to an enquiry and possible sources. Plan how to collect and organise small sets of data; design a data collection sheet or questionnaire to use in a simple survey. 8.3 Construct frequency tables for discrete data, grouped where appropriate in equal class intervals. 8.4 Collect small sets of data from surveys and experiments, as planned. 9.1 Round positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one decimal place. 9.2 Understand and use the rule of arithmetic and inverse operations in the context of positive integers and decimals. 9.3 Use the order of operations, including brackets. 9.4 Multiply and divide three-digit by two-digit whole numbers. 9.5 Check results by considering if they are of the right order of magnitude and by working problems backwards. Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys. 9.6 Choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts. Convert one metric unit to another (for example grams to kilograms); read and interpret scales on a range of measuring instruments. 9.7 Draw simple conclusions and explain reasoning, communicate own findings effectively in writing. 10.1 Recognise and use multiples, factors, primes (less than 100), common factors, highest common factors and lowest common multiples in simple cases. Recognise the squares of numbers to at least 12 12, and the corresponding roots. 10.2 Recognise the first few triangle numbers. 10.3 Generate terms of a simple sequence, given a rule. (For example, find a term from the previous term; find a term given its position in the sequence). 10.4 Generate coordinate pairs that satisfy a simple linear rule. Recognise straight-line graphs parallel to the x-axis or y-axis. 10.5 Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT. 11.1 Use a ruler and protractor to: measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree. 11.2 Use a ruler and protractor to: measure and draw lines to the nearest millimetre and angles to the nearest degree; construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA). Explore these constructions using ICT. Make accurate mathematical diagrams and constructions on paper and screen. 11.3 Identify and use angle, side and symmetry properties of triangles and quadrilaterals. Explore geometrical problems involving these properties, using step-by-step deduction supported by diagrams. Make accurate mathematical diagrams and constructions on paper. Classify and visualize in patterns. 12.1 Recognise the equivalence of percentages, fractions and decimals. Calculate simple percentages and use percentages to compare simple proportions. 12.2 Recognise the equivalence of percentages, fractions and decimals. Calculate simple percentages and use percentages to compare simple proportions. 12.3 Understand the relationship between ratio and proportion; use ratio notation, simplify ratios and divide a quantity into two parts in a given ratio. 12.4 Solve simple problems about ratio and proportion using informal strategies. 26 Hours Teaching 5
YEAR 7: SUMMER TERM Algebra 4 OVERVIEW FRAMEWORK OBJECTIVES 13.1 Solving brick wall problems 13.2 Solving square-andcircle problems 13.3 Triangle-and-circle problems 13.1 Use letter symbols to represent unknown numbers or variables. Simplify linear algebraic expressions by collecting like terms. Construct and solve linear equations with integer coefficients (unknown on one side only) using an appropriate method (for example, inverse operations). 13.2 Use letter symbols to represent unknown numbers or variables. Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (for example, inverse operations). 13.3 Use letter symbols to represent unknown numbers. Understand the significance of a counter-example. Measures 4 Statistics 3 Number 5 (6 hours) Algebra 5 14.1 Line symmetry 14.2 Rotational symmetry 14.3 Reflections 14.4 Rotations 14.5 Translations 15.1 Pie charts 15.2 Comparing data 15.3 and 15.4 Statistical surveys 15.5 Probabilities from two way tables 16.1 Adding and subtracting decimals 16.2 Multiplying and dividing decimals 16.3 Using a calculator 16.4 Fractions of quantities 16.5 Percentages of quantities 16.6 Solving problems 17.1 Solving equations 17.2 Formulae 17.3 Dotty investigations 17.4 Graphs from the real world 14.1 Understand and use the language and notation associated with reflections, translations and rotations. Recognise and visualise the symmetries of a 2-D shape. 14.2 Understand and use the language and notation associated with rotations. Recognise and visualise the symmetries of a 2-D shape. Transform 2-D shapes by rotating about a given point. 14.3 Understand and use the language and notation associated with reflections. Recognise and visualise the symmetries of a 2-D shape. Transform 2-D shapes by reflecting in given mirror lines. Explore these transformations and symmetries using ICT. 14.4 Understand and use the language and notation associated with rotations. Recognise and visualise the transformation and symmetry of a 2-D shape. Transform 2-D shapes by rotating about a given point. Explore these transformations and symmetries using ICT. 14.5 Understand and use the language and notation associated with translations. Recognise and visualise the transformation and symmetry of a 2- D shape. Transform 2-D shapes by translating. Explore the transformations and symmetries using ICT. 15.1 Construct, on paper and using ICT, graphs and diagrams to represent data, including simple pie charts. Use ICT to generate pie charts. Interpret diagrams and graphs (including pie charts). 15.2 Compare two simple distributions using the range and one of the modes, median or mean. Interpret information from a mathematical representation or context; relate findings to the original context; check the accuracy of the solution; explain and justify methods and conclusions; compare and evaluate approaches. 15.3 & 15.4 Decide which data would be relevant to an enquiry and possible sources. Plan how to collect and organise small sets of data from surveys and experiments. Design data collection sheets or questionnaires to use in a simple survey. Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of presentation. 15.5 Understand and use the probability scale from 0 to1; find and justify probabilities based on equally likely outcomes in simple contexts; identify all the possible mutually exclusive outcomes of a single event. 16.1 Use efficient written methods to add and subtract whole numbers and decimals with up to two places. 16.2 Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers. 16.3 Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys. 16.4 Calculate simple fractions of quantities and measurements (whole-number answers); multiply a fraction by an integer. 16.5 Calculate simple percentages and use percentages to compare simple proportions. Recognise the equivalence of percentages, fractions and decimals. 16.6 Draw simple conclusions and explain reasoning. Communicate own findings effectively, orally and in writing. 17.1 Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (for example, inverse operations). 17.2 Use simple formulae from mathematics and other subjects; substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula. 17.3 Generate sequences from patterns or practical contexts and describe the general term in simple cases. 17.4 Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x. 6
YEAR 7: SUMMER TERM Measures 5 OVERVIEW FRAMEWORK OBJECTIVES 18.1 Polygons 18.2 and 18.3 Tessellations 18.4 and 18.5 Constructing 3-D shapes 18.1 Identify and use angle, side and symmetry properties of triangles and quadrilaterals; explore geometrical problems involving these properties, explaining reasoning orally, using step-by-step deduction supported by diagrams. Explore these transformations and symmetries using ICT. 18.2 and 18.3 Identify and use angle, side and symmetry properties of triangles and quadrilaterals; explore geometrical problems involving these properties explaining reasoning orally, using step-by-step deduction supported by diagrams. 18.4 and 18.5 Make accurate mathematical diagrams and constructions on paper. Use a ruler and protractor to construct simple nets of 3-D shapes; for example, cuboid, regular tetrahedron, square-based pyramid, triangular prism. 26 Hours Teaching 7