KS3 Maths Now Scheme of Work – Year 7

YEAR 7 Practice Topic session Year 7 Autumn term Practice Topic 1 session 1 Factors and multiples

Subtopic

1.1 Factors and highest common factors 1.2 Multiples and lowest common multiples 1.3 Prime factors Practice Topic 2 2.1 Sequences session 2 Sequence and rules s

National Curriculum link

Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property Generate terms of a sequence from Recognise arithmetic sequences and Recognise geometric sequences and either a term-to-term or a position-to- find the n th term appreciate other sequences that term rule arise

2.2 Working out missing terms 2.3 Other sequences Practice 2.4 The n th session 3 tern of a sequence 2.5 Finding the n th term Practice Topic 3 3.1 Perimeter session 4 Perimeter, and area of a area and rectangle volume

Recognise geometric sequences and appreciate other sequences that Appreciate the infinite nature of the sets of integers, real and rational numbers

Understand and use standard mathematical formulae; rearrange formulae to change the subject

3.2 Compound Change freely between related shapes standard units [for example time, length, area, volume/capacity, mass] Derive and apply formulae to 3.3 Area of a calculate and solve problems triangle Practice 3.4 Area of a involving: perimeter and area of session 5 parallelogram triangles, parallelograms, trapezia, 3.5 Area of a volume of cuboids (including cubes) trapezium and other prisms (including cylinders) Year 7 Autumn half term Practice Topic 4 4.1 The number Understand and use place value for decimals, measures and integers of session 6 Negative line numbers 4.2 Arithmetic any size with negative numbers 4.3 Subtraction with negative numbers

Derive and apply formulae to Change freely between related calculate and solve problems standard units [for example time, length, area, volume/capacity, mass] involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes

Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, â&#x2030; , <, >, â&#x2030;¤, â&#x2030;Ľ

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

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Practice session 7

4.4 Multiplication with negative numbers

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and Practice Topic 5 Describe, interpret and compare 5.1 Mode, session 8 Averages median, range observed distributions of a single 5.2 The mean variable through: appropriate 5.3 Statistical Construct and interpret appropriate diagrams tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and Practice Topic 6 6.1 Equivalent Use the four operations, including session 9 Equivalent fractions formal written methods, applied to fractions integers, decimals, proper and improper fractions, and mixed numbers, all both positive and 6.2 Adding and Order positive and negative integers, decimals and fractions; use the subtracting number line as a model for ordering fractions of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

4.5 Division with negative numbers

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and 6.4 Adding and Use the concepts and vocabulary of prime numbers, factors (or divisors), subtracting mixed numbers multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property 6.3 Mixed numbers and improper fractions

Practice session 10

Practice session 11

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Topic 7 Algebraic expressio ns

7.1 Order of operations 7.2 Expressions and substitution

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Understand and use the concepts Substitute numerical values into formulae and expressions, including and vocabulary of expressions, equations, inequalities, terms and scientific formulae factors

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Practice session 12

7.3 Simplifying expressions

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

7.4 Using formulae

Substitute numerical values into Understand and use standard formulae and expressions, including mathematical formulae; rearrange scientific formulae formulae to change the subject

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Interpret mathematical relationships both algebraically and graphically

7.5 Writing formulae Progress assessment opportunity 1

End of term session Practice Topic session Year 7 Spring term Practice Topic 8 Angles session 13

Practice session 14

Practice session 15

Practice session 16

Subtopic

National Curriculum link

8.1 Calculating Apply the properties of angles at a angles point, angles at a point on a straight line, vertically opposite angles 8.2 Angles in a Derive and illustrate properties of triangles, quadrilaterals, circles, and triangle 8.3 Angles in a other plane figures [for example, quadrilateral equal lengths and angles] using 8.4 Angles with Describe, sketch and draw using parallel lines conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric 8.5 Derive and use the standard ruler Constructions and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagorasâ&#x20AC;&#x2122; Theorem, and use known results to obtain simple proofs Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

Understand and use the relationship between parallel lines and alternate and corresponding angles

Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

9.1 Rounding Topic 9 Decimals numbers

Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures] 9.2 Multiplying Use the four operations, including and dividing by formal written methods, applied to powers of ten integers, decimals, proper and improper fractions, and mixed numbers, all both positive and Understand and use place value for 9.3 Putting decimals, measures and integers of decimals in any size order 9.4 Estimates Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x â&#x2030;¤ b

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Practice session 17

Practice session 18

Topic 10 Linear graphs

9.5 Adding and subtracting decimals 9.6 Multiplying and dividing decimals 10.1 Coordinates 10.2 Graphs from formulae 10.3 Some simple graphs

10.4 Graphs of the form x + y = a

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative Revision of KS2 material Interpret mathematical relationships Recognise, sketch and produce both algebraically and graphically graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Reduce a given linear equation in two variables to the standard form y = mx + c ; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Reduce a given linear equation in two variables to the standard form y = mx + c ; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

10.5 Conversion graphs Year 7 Spring half term Practice Topic 11 11.1 Fractions, Define percentage as ‘number of Percentag decimals and session parts per hundred’, interpret es 19 percentages and percentage percentages changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages and 11.2 Fractions Interpret fractions and percentages of a quantity as operators Define percentage as ‘number of Practice Interpret fractions and percentages 11.3 session as operators Percentages of parts per hundred’, interpret percentages and percentage 20 a quantity 11.4 changes as a fraction or a decimal, Use a calculator and other technologies to calculate results Percentages interpret these multiplicatively, accurately and then interpret them with a express one quantity as a calculator percentage of another, compare two appropriately quantities using percentages, and work with percentages greater than Use the properties of faces, surfaces, Practice Topic 12 12.1 Naming and drawing 3D edges and vertices of cubes, 3D session cuboids, prisms, cylinders, pyramids, shapes shapes 21 cones and spheres to solve problems

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Practice session 22

12.2 Using nets Describe, sketch and draw using to construct 3D conventional terms and notations: points, lines, parallel lines, shapes perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally Derive and apply formulae to Change freely between related 12.3 Volumes Understand and use standard calculate and solve problems standard units [for example time, of a cuboid mathematical formulae; rearrange length, area, volume/capacity, mass] involving: perimeter and area of formulae to change the subject triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

12.4 Surface Derive and apply formulae to area of a cuboid calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) Practice session 23

Topic 13 13.1 Probability Introductio words n to probability 13.2 Probability scales

Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0â&#x20AC;&#x201C;1 probability scale

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D

Understand that the probabilities of all possible outcomes sum to 1

13.3 Experimental probability Progress assessment opportunity 2

End of term session National Curriculum link Practice Topic Subtopic session Year 7 Summer term Use ratio notation, including Practice Topic 14 14.1 Ratio Introduction to reduction to simplest form session ratio 24 14.2 Simplifying ratios

Practice session 25 Practice session 26

14.3 Ratios and sharing 14.4 Solving problems Topic 15 15.1 Reflection Symmetry symmetry 15.2 Rotation symmetry

Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

Express one quantity as a fraction of Use ratio notation, including reduction to simplest form another, where the fraction is less than 1 and greater than 1 Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles,

Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

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15.3 Properties Use the standard conventions for of triangles and labelling the sides and angles of quadrilaterals triangle ABC, and know and use the criteria for congruence of triangles

Practice session 27

Practice session 28

Topic 16 16.1 Finding unknown Solving equations numbers

16.2 Solving equations 16.3 Solving more complex equations

Use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions rather than as decimals Recognise and use relationships between operations including inverse operations

16.4 Setting up Use and interpret algebraic notation, including: and solving • ab in place of a × b equations • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions rather than as decimals • brackets Year 7 Summer half term Construct and interpret appropriate Practice Topic 17 17.1 Interpreting pie tables, charts, and diagrams, Using session charts data including frequency tables, bar 29 17.2 Drawing charts, pie charts, and pictograms for pie charts categorical data, and vertical line (or Practice 17.3 Grouped bar) charts for ungrouped and session frequencies grouped numerical data 17.4 Collecting Construct and interpret appropriate 30 continuous data tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

Interpret mathematical relationships Apply angle facts, triangle congruence, similarity and properties both algebraically and geometrically of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Simplify and manipulate algebraic expressions to maintain equivalence Use and interpret algebraic notation, by: including: • collecting like terms • ab in place of a × b • multiplying a single term over a • 3y in place of y + y + y and 3 × y bracket • a ² in place of a × a , a ³ in place of • taking out common factors a × a × a ; a ²b in place of a × a × b • expanding products of two or more • a /b in place of a ÷ b binomials.

• coefficients written as fractions rather than as decimals • brackets

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

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Practice session 31

Practice session 32

Practice session 33 Practice session 34 Practice session 35

Practice session 36

End of term session

Topic 18 18.1 Short and Pencillong and-paper multiplication calculatio ns 18.2 Short and long division 18.3 Calculations with measurements 18.4 Multiplication with large and small numbers 18.5 Division with large and small numbers Topic 19 19.1 Transform Reflections 19.2 Rotations ations 19.3 Translations 19.4 Tessellations Topic 20 20.1 Powers Working and roots with numbers

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and Use conventional notation for the priority of operations, including brackets, powers, roots and Use standard units of mass, length, time, money and other measures, including with decimal quantities Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their 20.2 Powers of Interpret and compare numbers in 10 standard form A × 10ⁿ 1≤A<10, where n is a positive or negative 20.3 Rounding Interpret and compare numbers in large numbers standard form A × 10ⁿ 1≤A<10, where n is a positive or negative integer or zero

Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

20.4 Significant Round numbers and measures to an figures appropriate degree of accuracy [for example, to a number of decimal places or significant figures] Interpret and compare numbers in 20.5 Large standard form A × 10ⁿ 1≤A<10, numbers in standard form where n is a positive or negative Progress assessment opportunity 3

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