FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
Time: 6 – 8 hours
FOUNDATION CHAPTER 1 WORKING WITH NUMBER
SPECIFICATION REFERENCE
Multiplying and dividing whole numbers
Understanding negative numbers in context
Adding and subtracting decimals
Multiplying decimals by whole numbers and decimals
Dividing decimals by whole numbers and decimals
Multiplying and dividing for speed and Imperial/metric conversions
Using index notation with numbers
Finding reciprocals of whole numbers, fractions and decimals
NA3a
NA2a
NA3i/j
NA3k/i
NA3k/i
NA4a/SSM4a
NA5c
NA3a
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 1: Integers-four rules, rounding and ordering
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 2: Fractions, decimals and percentages
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 3: Powers, indices and calculations
OBJECTIVES
By the end of the unit the student should be able to:
-
Multiply and divide whole numbers without using a calculator, e.g. 341 28 , 782  34
Use the four rules with negative numbers
Use negative numbers in context, e.g. thermometers
Add and subtract decimals without using a calculator
Multiply a decimal by whole a number or by a decimal
Divide a decimal by a whole number or by a decimal
Calculate with speed, e.g. a car travels with an average speed of 50 km/h. How far does it travel in 2.5 hours?
Convert between Imperial and metric units
-
Use index notation and index laws in calculations, e.g. simplify
-
Find reciprocals of whole numbers, fractions and decimals.
43  42
44
DIFFERENTIATION AND EXTENSION
Use harder decimals in real-life problems.
Use standard index form in calculations.
Money calculations that require rounding to the nearest penny
Multiply and divide decimals more than 2dp.
Research the earliest use of decimals in the history of mathematics.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 1.1 – 1.8
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written tests and homework to assess knowledge of content
Mental tests using simple decimals, e.g. work out 0.5  0.35
Extra examples given regularly for revision purposes
Other work given could have decimals as a part of the process.
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Present work clearly with decimals points in line and/or 0 as a place holder.
Make sure remainders/carries are shown clearly and in the right place.
Amounts of money should be rounded to the nearest penny as necessary.
Use a distance, speed and time triangle to aid learning.
Common metric/Imperial conversions should be learned.
Use Exercises 1A – 1H for practice. Use Mixed Exercise 1 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
Time: 6 – 8 hours
FOUNDATION CHAPTER 2 FRACTIONS
SPECIFICATION REFERENCE
Multiplying fractions
Finding a fraction of a quantities
Converting between fractions and decimals
Adding and subtracting fractions
Dividing a mixed number by a whole number
Multiplying and dividing fractions and mixed numbers
NA3d/l
NA3c
NA3c
NA3c
NA3d
NA3d
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 2: Fractions, decimals and percentages
OBJECTIVES
By the end of the unit the student should be able to:
Multiply fractions by canceling common factors
Use top-heavy fractions in calculations
Find a fraction of a quantity
Write one number as a fraction of another number
Use common denominators to add and subtract fractions
Divide a fraction by a whole number (including mixed numbers)
Simplify multiplication and division of fractions by canceling common factors.
DIFFERENTIATION AND EXTENSION
Use a calculator to find fractions of a given quantity.
Use the four operations with fractions in real-life problems, e.g. find area and perimeter using fractions.
Dealing with algebraic fractions, e.g. canceling and the four rules
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 2.1 – 2.8
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written tests and homework to assess knowledge of content
Mental tests using simple fractions, e.g. work out
1 1

2 4
Extra examples given regularly for revision purposes
Other work given could have fractional answers as a part of the process.
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Constant revision of this topic is needed.
All stages of a calculation should be shown clearly.
Students often find the concept of division by a fraction difficult.
Use Exercises 2A – 2H for practice. Use Mixed Exercise 2 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
Time: 8 – 10 hours
FOUNDATION CHAPTER 3 PERCENTAGE, RATIO AND PROPORTION
SPECIFICATION REFERENCE
Converting between fractions, percentages and decimals
Using percentages in real-life situations
Finding one number as a percentage of another
Using ratio in everyday life
Using direct proportion
Sharing a quantity in a given ratio
NA3c
NA3m
NA3e
NA2f
NA3n
NA3f
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Chapters 2.1 – 2.3: Fractions, decimals and percentages
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapters 2: Fractions
OBJECTIVES
By the end of the unit the student should be able to:
Convert between percentage, ratio and proportion
Work out price increases, discounts and VAT
Work out final amounts after increases, discounts and VAT
Find one number as a percentage of another
Write a ratio in its lowest terms by canceling
Use ratio in simple practical cases
Change a ratio into a fraction
Use the unitary method to calculate proportional amounts
Increase/decrease a quantity in direct proportion
Share a quantity in a given ratio.
DIFFERENTIATION AND EXTENSION
Share quantities in a given ratio involving fractions, and decimals.
Use a map to plan a journey, e.g. how long will the journey take traveling at an average speed of 50 km/h (or mixed speed for
different roads).
Work out the lengths of corresponding sides of similar triangles.
Compare linear scale factors to area scale factors for similar rectangles.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 3.1 – 3.10
See the Teaching and Learning software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental arithmetic tests using simple ratio, e.g. divide 12 in the ratio 1 : 2
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Students often find ratios of the form a : b : c more difficult.
Practical examples/investigations will help students to understand this chapter.
Use Exercises 3A – 3J for practice. Use Mixed Exercise 3 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 4 ELEMENTS OF ALGEBRA
Time: 3 – 5 hours
SPECIFICATION REFERENCE
Using the language of algebra
Substituting numbers into expressions
Using index notation in algebra
NA5a
NA5f
NA5c
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapters 3: Powers, indices and calculations
OBJECTIVES
By the end of the unit the student should be able to:
Know the difference between equation, formula, identity, term and expression
Substitute numbers into an expression (including negative numbers)
-
Use index notation to simplify an algebraic expression, e.g.
-
Use simple cases of index laws, e.g.
y 
2 3
3 y  y  3 y2
 y6 .
DIFFERENTIATION AND EXTENSION
Further examples of substitution involving harder expressions
Use index laws for expressions with fractional indices.
Expand brackets involving the use of index laws.
Convert centigrade to Fahrenheit using the formula. Draw a graph. Discuss.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 4.1 – 4.4
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental tests using simple index laws, e.g. write down an expression for x cubed squared
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Explanations about mathematical terminology should be tailored to suit the ability of the group.
Emphasise correct use of symbolic notation, e.g. 3x rather than 3  x
Present all work neatly, writing out the questions with the answers to aid revision at a later stage.
Use Exercises 4A – 4D for practice. Use Mixed Exercise 4 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 5 EQUATIONS AND INEQUALITIES
Time: 8 – 10 hours
SPECIFICATION REFERENCE
Solving equations with one, then two, operations
Solving equations with brackets
Setting up equations and solving them
Solving quadratic equations
Solving cubic equations using trial and improvement
Solving linear inequalities
NA5e
NA5e
NA5e
NA6e
NA5m
NA5d
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 4.2: Coordinates and essential algebra
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter 4: Elements of algebra
Geometry facts, e.g. sum of angles at a point and sum of angles in a triangle
OBJECTIVES
By the end of the unit the student should be able to:
Solve simple equations involving one, then two, operations
Balance equations by applying the same change to each side
Rearrange and simplify an equation by collecting like terms
Solve equations involving one pair of brackets
Set up an equation involving given information (including geometry facts)
-
Solve simple quadratic equations, e.g. 3 x  27 and
Solve cubic equations using trial and improvement
Use a number line to show an inequality
Solve linear inequalities, e.g. 2 x 1  x  5 .
2
x 2  4  12
DIFFERENTIATION AND EXTENSION
Solve equations/inequalities where manipulation of fractions is required.
Use a spreadsheet to solve equations by trial and improvement.
Solve harder equations by trial and improvement.
Represent linear inequalities on a 2-D grid.
-
Solve simple cubic equations, e.g. 4 x
3
 32 .
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 5.1 – 5.11
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental tests using simple examples of quadratic equations, e.g. solve two x squared equals 18
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Present all work neatly, writing out the equations with the solutions to aid revision.
Use Exercises 5A – 5K for practice. Use Mixed Exercise 5 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 6 GRAPHS
SPECIFICATION REFERENCE
Understanding graphs of linear functions
Using linear graphs in practical applications
Plotting graphs of quadratic functions
Using graphs to solve quadratic equations
Time: 7 – 9 hours
NA6c
NA6c/d
NA6e
NA6e
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 6: Linear graphs
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter 4: Elements of algebra
OBJECTIVES
By the end of the unit the student should be able to:
Draw a graph of y = ax + b, where the value of a and the value of b is given
Understand the meaning of m and c in y = mx + c
Solve simultaneous equations graphically (in all four quadrants)
Find an equation for the line of best fit drawn on a scatter diagram
Use conversion graphs, and distance-time graphs to solve practical problems
Use graphs (including non-linear graphs) in a variety of real-life contexts
Use a table of values to plot a quadratic function
Solve a quadratic equation graphically, e.g. find intercepts on the x-axis.
DIFFERENTIATION AND EXTENSION
Find the equation of two linearly related variables, e.g. plot the points (0, 32) and (100, 212) and find the formula that converts
Fahrenheit to centigrade.
Solve harder simultaneous equations, e.g. a linear function and a quadratic function.
Use fractional values for m and/or c.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 6.1 – 6.8
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental tests using simple examples, e.g. sketch the distance-time graph for a sprinter
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Present all work neatly, labeling coordinate axes and functions.
Only two points are needed to draw a straight line, but three or more points will help check the working.
Stress the symmetry of quadratic functions (which may also be seen in the table of values).
Use Exercises 6A – 6H for practice. Use Mixed Exercise 6 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
Time: 4 – 6 hours
FOUNDATION CHAPTER 7 FORMULAE
SPECIFICATION REFERENCE
Using words to state the relationship between different quantities
Changing the subject of a word formula
Substituting into algebraic formulae
Changing the subject of an algebraic formula
NA5f
NA5f
NA5f
NA5f
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter 4: Elements of algebra
OBJECTIVES
By the end of the unit the student should be able to:
Use words to state the relationship between different quantities, e.g. speed = distance  time
Change the subject of a word formula, e.g. distance = speed  time
Substitute positive and negative values into an algebraic formula
Change the subject of simple algebraic formulae, e.g. v = 2a – b, make a the subject of the formula
DIFFERENTIATION AND EXTENSION
Use harder formulae, e.g. ones involving indices.
-
Change the subject of formulae involving fractions, e.g. C
-
Use a spreadsheet to evaluated formulae.

5
 F  32  , make F the subject of the formula.
9
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 7.1 – 7.5
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental tests using simple examples, e.g. area = length  width, what is length?
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Remind students about the difference between equation, formula, identity, term and expression.
Students often find substituting negative numbers difficult.
-
Some calculators evaluate 2 as 4, brackets may be required.
Use Exercises 7A – 7E for practice. Use Mixed Exercise 7 for consolidation.
2
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 8 SYMMETRY AND TRANSFORMATIONS
Time: 6 – 8 hours
SPECIFICATION REFERENCE
Finding lines of symmetry and completing shapes given their lines of symmetry
Finding the order of rotational symmetry of various shapes
Reflecting shapes in mirror lines
Understanding that rotation is a turning motion about an angle with a centre
Understanding that translation is a sliding movement with two components
Making shapes larger using centres of enlargement and scale factors
Describing the single transformation that replaces two others
Identifying and drawing planes of symmetry in 3-D shapes
SSM3a/b
SSM3a/b
SSM3b
SSM3b
SSM3b
SSM3c
SSM3a/b/c/d
SSM3b
PRIOR KNOWLEDGE
Recognition of basic shapes
An understanding of the concept of rotation, reflection and enlargement
OBJECTIVES
By the end of the unit the student should be able to:
Find lines of symmetry and complete shapes given their lines of symmetry
Find the order of rotational symmetry of various shapes, e.g. equilateral triangle, kite, parallelogram
Reflect a shape in a mirror lines (including mirror line through shape)
Reflect a shape on a coordinate grid (simple mirror lines, e.g. x = 3, y = x)
Understand that rotation is a turning motion about an angle with a centre
Understand that translation is a sliding movement with two components
Enlargement a shape using a centre of enlargement and a scale factor (including fractional scale factors)
Describe the single transformation which replaces two others
Identify and draw planes of symmetry in a 3-D shape.
DIFFERENTIATION AND EXTENSION
Investigate symmetry in nature, e.g. snow flakes, crystals, human face.
Negative scale factors.
Relate enlargement scale factors to area scale factors.
Classify 3-D shapes by their planes of symmetry.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 8.1 – 8.8
See the Teaching and Learning software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Practical work designing a poster
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Present all work neatly. Label coordinate axes and use dotted lines for mirror lines.
The use of tracing paper is allowed in the examination.
Use Exercises 8A – 8H for practice. Use Mixed Exercise 8 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 9 ANGLES, BEARINGS, DRAWINGS AND CONSTRUCTIONS
SPECIFICATION REFERENCE
Using a protractor
Measuring and calculating bearings
Drawing to scale
Constructions using a protractor
Constructions using ruler and compasses
Drawing nets from solids and recognizing solids from their nets
Drawing and interpreting plans and elevations
Recognising when shapes are congruent
Finding exterior and interior angles
Tessellating shapes
Time: 6 – 8 hours
SSM2b/4d
SSM4b
SSM3d
SSM4d/e
SSM4e/j
SSM2j/4d
SSM2k
SSM2d
SSM2d/g
SSM3b/4d
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 7: Properties of shapes
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 8: Angles and bearings
OBJECTIVES
By the end of the unit the student should be able to:
Use a protractor to measure and draw angles
Use ruler and protractor to construct triangles accurately
Measuring and calculating bearings to the nearest degree
Use scale to find the real distance from a map
Use ruler compasses to construct a triangle from given information
Use a protractor to draw a regular polygon in a circle, e.g. a pentagon
Use ruler and compasses to construct: the perpendicular bisector; the perpendicular from a point to a line; the perpendicular
from a point on a line; the bisector of an angle
Draw lines and regions using standard constructions
Draw a net for a solid and recognise a solid from its net
Draw and interpreting plans and elevations
Recognise when shapes are congruent
Use angle and side properties of equilateral and isosceles triangles
Calculate the exterior and interior angles of a regular polygon
Understand and draw a tessellation.
DIFFERENTIATION AND EXTENSION
Solve loci problems that require a combination of loci.
Construct combinations of 2-D shapes to make nets.
Investigate tessellation.
Use formal arguments to identify congruence.
Construct plans and elevations.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 9.1 – 9.13
See the Teaching and Learning Software for activities linking to this chapter.
ASSESSMENT ISSUES
Written and practical testing to assess knowledge of content
Practical work to construct a net for a 3-D object, e.g. a square base pyramid
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
All working should be presented clearly, i.e. construction lines should not be erased.
Sturdy compasses are essential.
Use Exercises 9A – 9M for practice. Use Mixed Exercise 9 for consolidation.
FOUNDATION UNIT 3 (OLD UNIT 4) SCHEMES OF WORK
FOUNDATION CHAPTER 10 MENSURATION AND PYTHAGORAS’ THEOREM
SPECIFICATION REFERENCE
Changing from one unit to another
Finding the area and circumference of circles
Calculating areas of 2-D shapes by formulae
Calculating volumes and surface areas of shapes
Using Pythagoras’ theorem to calculate the third side of a right-angled triangle
Time: 6 – 8 hours
SSM4a/i
SSM4h
SSM2e/4f
SSM4f/g
SSM2h/NA4d
PRIOR KNOWLEDGE
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter 10: Perimeter, area and volume
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter 4: Elements of algebra
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter 7: Formulae
OBJECTIVES
By the end of the unit the student should be able to:
Change from one unit to another, e.g. change 3m2 to cm2
Use πr2 and 2πr to calculate the area and the perimeter of circles (or simple parts of circles), giving the answer in terms of  if
required
Use formulae to calculate the areas of triangles and parallelograms
Calculate the volume and surface area of prisms (including cylinders)
Use Pythagoras’ theorem to calculate the length of the hypotenuse, or the shorter side, of a right-angled triangle.
DIFFERENTIATION AND EXTENSION
Find the length of the line segment between two points given as coordinates.
Use Pythagoras’ theorem in multi-step questions involving two (or more) right angles.
More complex parts of circles, e.g. 30 sectors
More complex 3-D shapes, e.g. semi-cylinders
Use 22/7 as an approximate value for  in calculations.
Harder formulae for 3-D shapes, e.g. cones and spheres
Find Pythagorian triples.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 3 (old Unit 4) Foundation Chapter/section: 10.1 – 10.7
See the Teaching and Learning software for activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental tests using simple formulae, e.g. write down the area of a circle radius 3cm. Leave your answer in terms of .
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of a similar
nature, or extension work detailed above.
HINTS AND TIPS
Students should be encouraged to learn both linguistic and mathematical statements of Pythagoras’ theorem.
Need to revise standard formulae regularly
Use Exercises 10A – 10G for practice. Use Mixed Exercise 9 for consolidation.