Year 8 Scheme of Work C Course
Topic / Links to NC / PLTs / Learning Objectives / Learning Outcomes/Success Criteria/Assessment / Resources / Cross curricular links/Key words/Points to note1. Quadrilaterals (3 lessons) / 2 – 25 Solve word problems and
investigate in a range of contexts:
number, algebra, shape, space and
measure, and handling data,
compare and evaluate solutions.
26 – 27 Identify the necessary to solve a problem; represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
28 – 29 Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
30 – 31 Present and interpret solutions in the context of the original problem; and justify methods and conclusions, orally and in writing.
32 – 35 Suggest extensions to problems by asking “what if …?, begin generalise and to understand the significance of a counter-example.
FG Reasoning about quadrilateral properties.
184 – 189 Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals; solve geometric problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text.
ABFGProperties of special quadrilaterals.
C Angle sum of quadrilateral.
184 – 189 Solve geometrical problems using side and angle proportions of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometric properties.
DE Special quadrilaterals. / TW
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EP / Recognise and name quadrilaterals.
Draw them.
Learn about their properties.
Recognise that some quadrilaterals are special types of other quadrilaterals.
MPA Communicating and reflecting
Making connections between deduced properties and definitions of shapes / ALL will:
Name and describe, using appropriate language, quadrilaterals.
MOST will:
Work out angles in quadrilaterals.
SOME will:
Accurately draw quadrilaterals.
Assessment criteria:
(S) Level 3 ~ classify 2D shapes in various ways
(S) Level 4 ~ use the properties of 2D shapes
Level 4 ~ draw common 2D shapes in different orientations
(S) Level 5 ~ use a wider range of properties of 2D shapes and identify all the symmetries of 2D shapes
(S) Level 6 ~ classify quadrilaterals by their geometric properties
(S) Level 6 ~ solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons / C1 chapter 17, 7C chapter 33.
10 Ticks, Level 6 pack 5 pages 39-42.
NRICH tasks
Quadrilaterals Game
Property Chart / Parallel, rotation symmetry, reflection symmetry, bisect, quadrilateral, square, rectangle, trapezium, rhombus, parallelogram, arrowhead, kite
2. Negative numbers (2 lessons) / 48 – 51 Understand negative numbers as positions on a number line; order, add and subtract positive and negative integers in context.
A Add, subtract positive and negative whole numbers.
48 – 51 Add, subtract, multiply and divide integers.
BC Multiply and divide negative numbers.
82 – 85 Understand addition and subtraction of fractions and integers, and multiplication and division of integers; use the laws of arithmetic and inverse operations.
D Inverse operations. / TW
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EP / Multiply and divide negative numbers.
Understand positive and negative square roots.
MPA Communicating and reflecting
Linking mental methods with jottings and representations, for example, on a number line / ALL will:
Add and subtract negative whole numbers
MOST will:
Use all four operations with negative numbers.
SOME will:
Understand positive and negative squares, square roots, cubes and cube roots
Assessment criteria:
(C) Level 5 ~ solve simple problems involving ordering, adding and subtracting negative numbers in context
(N) Level 5 ~ order negative numbers / C1 chapter 18, 7C chapter 34.
10 Ticks, Level 5 page 4 pages 7–12 and 17–18. / Positive numbers, negative numbers, number line
3. Fair to all (4 lessons) / 2 – 25 Solve word problems and
investigate in a range of contexts:
number, algebra, shape, space and
measure, and handling data,
compare and evaluate solutions.
26 – 27 Identify the necessary to solve a problem; represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
28 – 29 Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
30 – 31 Present and interpret solutions in the context of the original problem; and justify methods and conclusions, orally and in writing.
32 – 35 Suggest extensions to problems by asking “what if …?, begin generalise and to understand the significance of a counter-example.
C Word count investigations.
110 – 111 Check results by considering whether it is of the right order of magnitude and by working the problem backwards.
C Word count investigations.
256 – 261 Calculate statistics for small sets of discrete data; find the mode, median and range, and the modal class for grouped data; calculate the mean, including from a simple frequency table, using a calculator for a larger number of items.
AB Mean, including from frequency tables.
D Median, mean, mode. / TW
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EP / Calculate the mean of a set of data.
Choose a suitable average to represent a set of data.
MPA ~ use appropriate mathematical procedures
Calculate summary statistics, for example, measures of average and spread
MPA Interpreting and evaluating
Considering the effects of changes to the data / ALL will: Calculate the mean of a set of data
MOST will:
Can calculate the mean from a frequency table
SOME will:
I know what is meant by mean, mode and median and which “is better” in a given situation
Assessment criteria:
(H) Level 4 ~ understand the mode and range to describe sets of data
(H) Level 5 ~ understand and use the mean of discrete data and compare two simple distributions, using the range and one of mode, median and mean
(U) Level 5 ~ check results, considering whether they are reasonable
(U) Level 5 ~ draw simple conclusions of their own and give an explanation of their reasoning / C1 chapter 19, 7C chapter 35?
10 Ticks. Level 5 pack 6 pages 3-6
NRICH Task
Searching for Mean(ing) / Frequency table, mean, mode, median, range
4. Know your calculator (3 lessons) / 56 – 59 Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
E Square.
F Square root.
86 – 87 Know and use the order of operations, including brackets.
ABCDE Order of operations, brackets.
108 – 109 Carry out calculations with more than one step using brackets and the memory, use the square root and sign change keys.
B Brackets
C Bracketing effect of horizontal line for division.
D Memory.
EMulti-step calculations involving squaring.
F Square root.
G Sign change key. / TW
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EP / Use a calculator effectively, including the bracket, square, square root, memory and sign-change keys.
Evaluate expressions with more than one operation.
Substitute into formulae.
MPA Representing
Breaking more complex problems into a sequence of steps
MPA Analysisng ~ use mathematical reasoning
Use different techniques to analyse a situation, evalute an approach or check a calculation
MPA ~ use appropriate mathematical procedures
Developing efficient use of calculators and spreadsheets / ALL will:
Evaluate expressions involving more than one operation without a calculator.
MOST will:
Use a calculator to evaluate expressions involving more than one operation.
SOME will:
Use square and square root keys.
Deal with negative numbers on a calculator.
Assessment criteria:
(N) Level 4 ~ recognise square numbers
(C) Level 7 ~ use a calculator efficiently and appropriately to perform complex calculations with numbers of any size / C1 chapter 20, 7C chapter 36.
10 Ticks, Level 5 pack 5 pages 3-7
Also need Sheet 179 / BODMAS, square, square root, memory, brackets,
Assessment 1 / Formal assessment based on quadrilaterals, negative numbers, fair to all and know your calculator.
5. Finding Formulas (3 lessons) / 56 – 59 Recognise the first few triangular numbers, squares of numbers to at least 12x12 and the corresponding root.
C Triangular numbers.
138 – 143 Using simple formulae from mathematics and other subjects, substitute positive integers in simple linear expressions and formulae and, in simple cases, derive a formula.
B Derive formulae from spatial pattern.
144 – 147 Generate and describe integer sequences.
C Describe integer sequence.
D Use nth term of a sequence.
148 – 151 Generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence).
A Find term from its position
C Use term to term rule.
154 – 157 Generate sequences from practical contexts and describe the general term in simple cases.
A Generate sequence from a context.
BEF Find nth term.
154 – 157 Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated.
D nth term of a sequence.
EF Find nth term. / TW
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EP / Find and use patterns and formulas from geometric patterns.
MPA Analysisng ~ use mathematical reasoning
Identifying and describing numerical patterns and relationships symbolically
Making connections between sequences and functions and exploring the effects of varying values
MPA Interpreting and evaluating
Interpreting general statements expressed in algebraic form and consider their significance / ALL will:
Work out a formula from a design.
MOST will:
Use a rule for the nth term of a sequence.
Find an expression for the nth term of an increasing linear sequence.
SOME will:
Find an expression for the nth term of a decreasing linear sequence.
Assessment criteria:
(N) Level 4 ~ recognise and describe number patterns
(A) Level 6 ~ generate terms of a sequence using term to term and position to term definitions of the sequence
(A) Level 6 ~ write an expression to describe the nth term of an arithmetic sequence / C1 chapter 22, 7C chapter 38.
10 Ticks, Level 7/8 pack 1 pages 37-38.
/ Expression, equation, formula, nth term.
6. Ratio (3 lesosns) / 78 – 81 Understand the relationship between ratio and proportion; use direct and indirect proportion in simple contexts; use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio; solve simple problems about ratio and proportion using informal strategies.
ABC Introducing ratio, ratio notation.
DFG Ratio problems including comparing ratios.
E Divide in a given ratio.
H Ratio written as a single number.
78 – 81 Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.
D Ratio in simplest form.
E Divide in a given ratio. / TW
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EP / Use the notation for ratio
Understand equal ratios
Share a quantity in a given ratio
Compare ratio.
MPA Interpreting and evaluating
Consider the effectiveness of different strategies, for example, when completing a mental calculation / ALL will:
Understand the way in which ratios are written.
Change a ratio in its simplest form.
MOST will:
Share a quantity in a given ratio.
SOME will:
Compare ratio.
Calculate a ratio as a single number.
Assessment criteria:
(N) Level 4 ~ Begin to understand simple ratio
(N) Level 5 ~ understand simple ratio
(C) Level 5 ~ solve simple problems involving ratio and direct proportion
(C) Level 6 ~ divide a quantity into tow or more parts in a given ratio
(C) Level 6 ~ solve problems involving ratio and direct proportion / C1 chapter 23, 7C chapter 39
10 Ticks Level 5 Pack 2 41-42, Level 6 Pack 4 3-6
/ Ratio, equivalent ratio.
7. Functions and graphs (4 lessons) / 112 –113 Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the meaning of the words formula and function.
B Use of function.
164 – 167 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, on paper and using ICT, recognising straight-line graphs parallel to the x-axis or y-axis.
B Generate pairs and plot.
C Recognise function represented by graph parallel to axis.
172 – 177 Begin to plot and interpret the graphs of simple linear functions arising from real-life situations.
A Plot linear graph from situation.
160 – 163 Express simple functions in symbols, represent mappings expressed algebraically.
C Spot rule.
164 – 167 Generate points in all four quadrants and 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.
B Generate pairs and plot in all four quadrants. / TW
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EP / Draw the graph of a function like y=2x + 3.
Find the equation of a straight line graph.
MPA Representing
Developing understanding of algebraic conventions…coordinate points and equations of lines / ALL will:
Draw the graph of a function like y=2x+3.
MOST will:
SOME will:
Find the equation of a straight line graph
Assessment criteria:
(A) Level 5 ~ use and interpret coordinates in all four quadrants
(A) Level 6 ~ plot the graphs of linear functions
(A) Level 6 ~ recognise that equations of the form y = mx + c correspond to straight line graphs / C1 chapter 25, 7C chapter 41
10 Ticks Level 4 Pack 6 21-22; Level 6 Pack 1 27-28;
Level 7-8 Pack 121-30
NRICH Task
Parallel Lines
Surprising Transformations (need knowledge of transformations) / Gradient, intercept.
9. 3D (4 lessons) / 198 – 201 Use 2-D representations to visualise 3-D shapes and deduce some of their properties.
A Drawing on triangular dotty paper.
B Views.
F Nets.
228 – 231 Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts, involving length, area, mass, capacity, time and angle; convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring instruments.
CE Volume.
238 – 241 Calculate the surface area of cubes and cuboids.
G Surface area.
238 – 241 Know and use the formula for the volume of a cuboid. Calculate volumes and surface areas of cuboids and shapes made from cuboids.
C Volume of cuboid.
E Volume of prism. / TW
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EP / Describe, make and draw 3-D objects.
Find the volumes of cuboids and prisms.
Draw nets and find surface area of 3-D objects.
MPA Representing
Sketching different representations
MPA ~ use appropriate mathematical procedures
Sketching solids, including nets of solids and the use of geometric convections / ALL will:
Draw three-dimensional objects.
Find the volume of a cuboid.
MOST will:
Calculate the volume of a prism.
Draw the nets of solid.
SOME will:
Calculate the length of a prism given the volume and cross-sectional area.
Find the surface area of a cuboid.
Assessment criteria:
(S) Level 3 ~ classify 3D shapes in various ways
(S) Level 4 ~ use the properties of 3D shapes
(S) Level 4 ~ make 3D models by linking given faces or edges
(S) Level 5 ~ use a wider range of properties of 3D shapes
(S) Level 6 ~ deduce and use formulae for the volume of a cuboid; calculate volumes and surface area of cuboids
(S) Level 7 ~ calculate lengths, areas and volumes in plane shapes and right prisms / C1 chapter 21, 7C chapter 37.
10 Ticks, Level 4 pack 8 pages 21–28; Level 5 pack 4 pages 41–42; Level 5 pack 6 pages 30–38; Level 6 pack 2 pages 40–42; Level 6 pack 5 pages 23–26; Level 7/8 pack 6 pages 15–18.
Also need: Multilink cubes, triangular dotty paper
NRICH Task
Boxed In
Cuboids / Net, view, plan view, side view, top view, cube, cuboid, prism, volume, cross-sectional area, capacity, surface area.
Investigation (Polyhedron) / Polyhedron activity
Teachernotes
And more notes
Need straws and pipe cleaners, available in office.
Assessment 2 / Formal assessment based on finding formulae, ratio, 3D and functions and graphs.
8. Scaling (3 lessons) / 212 – 215 Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor; explore enlargement using ICT.
AB Enlargement on grid.
78 – 81 Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.
E Scale as ratio. / TW
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EP / Understand enlargement and scale factors.
Use map scales.
Work with ratios where different units are used for example 5cm:2m.
MPA Interpreting and evaluating
Interpret information from a mathematicalrepresentation; relate findings to the original context / ALL will:
Draw an enlargement with a given scale factor.
Work out the scale factor of an enlargement.
MOST will:
Find a distance from a scale drawing.
Work out lengths for scale drawings.
SOME will:
Find the ratios of two quantities expressed in different units.
Assessment criteria:
(N) Level 5 ~ understand simple ratio
(C) Level 6 ~ solve problems involving ratio
(S) Level 6 ~ enlarge 2D shapes, given a centre of enlargement and a positive whole number scale factor
Level ??? enlarge without a centre of enlargement / C2/8C chapter 2
10 Ticks Level 5 Pack 3 9-11;
Level 6 Pack 2 19-22; Level 7-8 Pack 434-36; Level 9-10 Pack 3 pages 3-5 / Scale factor, centre of enlargement.
10. Graphs that tell stories (1 lesson) / 172 – 177 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations.
A Sketch and interpret linear graph from real situation.
BC Linear and non-linear graphs. / TW
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EP / Interpret graphs.
Sketch graphs describing real situations.
MPA Communicating and reflecting
MPA Communicating and reflecting
Communicate own findings effectively / ALL will:
Sketch simple real-life graphs.
MOST will:
Interpret simple real-life graphs.
Interpret and sketch more complex real-life graphs.
SOME will:
Assessment criteria:
(H) Level 5 ~ interpret graphs and diagrams and draw conclusions / C2/8C chapter 1
10 Ticks Level 4 Pack 6 17-22 / Axis, origin, scales, coordinates, speed.
11. Solids (2 lessons) / 198 – 201 Know and use geometric properties of cuboids and shapes made from cuboids; begin to use plans and elevations.
A Identify cross sections of solids. / TW
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EP / Identify cross-sections of solids.
Draw cross-sections.
Identify the planes of symmetry of a solid.
MPA ~ use appropriate mathematical procedures
Make accurate mathematical diagrams / ALL will:
Identify cross-sections of a solid.
MOST will:
Draw cross-sections of a solid.
SOME will:
Identify the planes of symmetry of a solid.