FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 1
INTEGERS – FOUR RULES, ROUNDING, ORDERING
SPECIFICATION REFERENCE
Using place value diagrams
Using place value to read, write and order whole numbers
Representing number, additions and subtractions on a number line
Mental and written column methods
Mental and written methods including short division
Order of operations not including powers
Rounding to powers of 10
Identifying factors and multiple of numbers
Writing numbers in prime factor form and using this to identify HCF;
find LCM by writing lists of multiples
Using a number line to calculate with negative numbers
Using the four rules with negative numbers
Time: 8 – 11 hours
NA2a
NA2a
NA2a
NA3a/g/i/j/4a/b/c
NA3a/g/i/k/4b/c
NA 3b/i
NA2a/3h
NA2a
NA2a/3a
NA2a
NA3a
Prior Knowledge
The ability to order numbers.
Use a number line to show how numbers are related to each other.
Experience of the 4 operations using whole numbers
Knowledge of integer complements to 10 and multiplication facts to 10  10
Objectives
By the end of the chapter the student should be able to:
Understand place value and order positive and negative integers
Write numbers in words and visa versa
Add, subtract, multiply and divide positive and negative integers
Understand simple instances of BIDMAS, e.g. work out 12  5 – 24  8
Round whole numbers to the nearest, 10, 100, 1000, …
Identify factors and multiples of numbers
Find the HCF and LCM of number
Write a number as a product of primes, e.g. 108 = 2  2  3  3  3
Understand and use negative numbers in context, e.g. temperature.
Differentiation & Extension
More work on long multiplication and division without using a calculator
Estimating answers to calculations involving combinations of the four rules
Directed number work with two or more operations, or with decimals
Use a number square to find primes (sieve of Eratosthenes).
Use prime factors to find LCM.
Calculator/ spreadsheet exercise to find factors of large numbers.
Resources
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 1.1 – 1.11
See the Teaching and Learning Software for the activities linking to this chapter.
Assessment Issues
Written testing to assess knowledge of content
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 working clearly with numbers in line; emphasising that all working is to be shown.
For non-calculator methods make sure that remainders and carrying are shown.
Factor trees should not contain the number 1.
Use Exercises 1A – 1K for practice. Use Mixed Exercise 1 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 2 (Part A) FRACTIONS, DECIMALS AND PERCENTAGES
Time: 5 – 7 hours
SPECIFICATION REFERENCE
Converting improper fractions to mixed numbers and vice versa
Finding equivalent fractions in their simplest form
Ordering fractions by converting them to equivalent fractions with the same number
NA2c
NA2c
NA2c
PRIOR KNOWLEDGE
Multiplication facts
Ability to find common factors
A basic understanding of fractions as being ‘parts of a whole unit’
Use of a calculator with fractions
OBJECTIVES
By the end of the chapter the student should be able to:
Understand a fraction as part of a whole
Recognise and write fractions in everyday situations
Write a fraction in its simplest form and recognise equivalent fractions
Compare the sizes of fractions using a common denominator
Write an improper fraction as a mixed fraction.
DIFFERENTIATION & EXTENSION
Careful differentiation is essential for this topic dependent upon the student’s ability.
Relating simple fractions to remembered percentages and vice-versa
Using a calculator to change fractions into decimals and looking for patterns.
Working with improper fractions and mixed numbers
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 2.1 – 2.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Testing ability to simplify fractions without a calculator
Mental arithmetic test involving simple fractions such as ½, ¼...
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.
Equivalent fractions worksheet
Worksheet for comparing fractions, ordering fractions, and adding and subtracting fractions
Extra examples on a regular basis for revision purposes
HINTS AND TIPS
Understanding of equivalent fractions is the key issue in order to be able to tackle the other content.
Weaker students will need to visualise fractions.
Calculators should only be used when appropriate.
All work needs to be presented clearly with the relevant stages of working shown.
Use Exercises 2A – 2C for practice.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
Time: 7 – 9 hours
FOUNDATION CHAPTER 2 (Part B) FRACTIONS, DECIMALS AND PERCENTAGES
SPECIFICATION REFERENCE
Using a place value table for decimal numbers
Using place value to order decimal numbers
Adding and subtracting decimals- written column methods
Multiplying and dividing decimals by 10, 100 or 1000
Multiplying and dividing decimal numbers
Converting between fractions and decimals
Rounding whole numbers and decimals to 1s.f.
Estimating by rounding all numbers in a calculation to 1s.f.
Rounding up or down in the context of the problem
Using trial and improvement where there is no obvious simple method
NA2d
NA2d
NA3j
NA3a/i
NA3a/i/k
NA2d/3g/i
NA3h
NA3h/o/p/4c
NA3q/4a/d
NA4b
PRIOR KNOWLEDGE
The concepts of a fraction and a decimal
OBJECTIVES
By the end of the chapter the student should be able to:
Understand place value in decimal numbers and write decimals in ascending order of size
Add and subtract decimal numbers (including practical examples)
Multiply and decimals by 10, 100 and 1000
Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 d.p.), e.g. 5.95  0.35
Know that e.g. 13.5  0.5 = 135  5
Convert a fraction to a decimal (including recurring numbers); convert a decimal to a fraction (not including recurring decimals)
Round whole numbers and decimal numbers to 1s.f. and calculate an estimate (including practical examples) to check their
calculations
Solve problems by trial and improvement to solve practical problems.
DIFFERENTIATION & EXTENSION
Use harder decimal numbers in real-life problems.
Use standard form for vary large/small numbers.
Money calculations that require rounding answers to the nearest penny
Multiply and divide decimals by decimals (more than 2 d.p.).
Research the earliest use of decimals in the history of mathematics.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 2.4 – 2.13
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
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 working clearly with decimal points in line; emphasising that all working is to be shown.
For non-calculator methods make sure that remainders and carrying are shown.
Amounts of money should always be rounded to the nearest penny where necessary.
Use Exercises 2D – 2M for practice.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 2 (Part C) FRACTIONS, DECIMALS AND PERCENTAGES
Time: 3 – 5 hours
SPECIFICATION REFERENCE
Understanding percentages- percentages as parts per 100
Ordering fractions by converting to percentages
Percentages of quantities
NA2e
NA2e
NA2e
PRIOR KNOWLEDGE
4 operations of number
The concepts of a fraction and a decimal
Number complements to 10 and multiplication tables to 10  10
Awareness that percentages are used in everyday life
OBJECTIVES
By the end of the chapter the student should be able to:
Understand that a percentage is a fraction in hundredths
Convert percentages into fractions or decimals (including practical examples)
Compare proportions of quantities
Write one number as a percentage of another number
Calculate the percentage of a given amount.
DIFFERENTIATION & EXTENSION
Fractional percentages of amounts
-
Percentages which convert to recurring decimals (e.g. 33 13 %), and situations which lead to percentages of more than 100%.
-
Simple interest calculations
Discuss why reducing a quantity by 10%, and than by 10% again, is not the same as reducing a quantity by 20%.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 2.14 – 2.16
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Reinforce equivalence and the connection between percentage, fraction and decimal.
Mental methods of calculating common percentages (e.g. 17.5% using 10%, 5%, 2.5%)
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.
Independent research into the many uses made of percentages, particularly in the media.
HINTS AND TIPS
For non-calculator methods make sure that remainders and carrying are shown.
In preparation for this unit students should be reminded of basic percentages and recognise their fraction and decimal equivalents.
Use Exercises 2N – 2P for practice. Use Mixed Exercise 2 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 3
Time: 5 – 7 hours
PAWES, INDICES AND CALCULATIONS
SPECIFICATION REFERENCE
Squares and cubes; square roots and cube roots, using a calculator
Squares, cubes and roots to memorise
Using index notation; solving equations involving indices
The order of operations - BIDMAS
Using a calculator for complex calculations
The rules for multiplying powers of the same number
Using standard form in written calculations and on a calculator
NA2b/3o
NA3g/i
NA2b
NA3b
NA3h/o/p/p
NA2b
NA2b
PRIOR KNOWLEDGE
Ability to multiply numbers up to 2 d.p.
Experience of multiplying/dividing by 10, 100 or 1000
OBJECTIVES
By the end of the chapter the student should be able to:
Work out squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and
improvement)
Calculate with numbers expressed in index form, e.g. work out 30  24
Solve equations involving indices, e.g. solve 6x = 216, find x
4  3  15
3
-
Use a calculator to work out expression involving powers, e.g. work out
-
Appreciate that when you multiply/divide powers of the same number you add/subtract the indices
Convert a number to a number in standard form, and vice versa
Interpret and represent numbers expressed in standard form on a calculator display (using the correct notation).
25
DIFFERENTIATION & EXTENSION
(For the most able) Further work on indices to include negative and/or fractional indices
Calculator/ spreadsheet exercise to find squares, cubes and square roots of larger numbers (using trial and improvement)
Harder examples using the calculator to work out expressions involving powers of numbers
Introduce the index rule for the power of a power of a number.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 3.1 – 3.7
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Regular oral work – e.g. a five-minute assessment at the beginning or end of a lesson
Mental test to check knowledge of squares and cubes
Test on performance using a calculator to find squares, cubes and square roots.
Test without a calculator on knowledge of squares, cubes and square numbers (keeping the numbers small).
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.
Investigational tasks leading to number patterns involving powers of numbers
GCSE past paper questions
HINTS AND TIPS
All of the work in this unit is easily reinforced by starter and end activities.
Calculators should be used only when appropriate.
Use Exercises 3A – 3G for practice. Use Mixed Exercise 3 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 4 (Part A) COORDINATES AND ESSENTIAL ALGEBRA
Time: 3 – 5 hours
SPECIFICATION REFERENCE
Reading and plotting coordinates
Reading and plotting positive and negative coordinates
Finding the coordinates of the final point to make a shape
Using the formula to find the coordinates of the mid-point
Identifying 2-D and 3-D shapes; using 3-D coordinates
NA6b
NA6b/ SSM3e
SSM3e
SSM2c/ 3e
SSM3e
PRIOR KNOWLEDGE
Using positive and negative integers on a number line
Experience of drawing simple 2-D shapes, e.g. triangles, squares, parallelograms, etc
OBJECTIVES
By the end of the chapter the student should be able to:
Plot and read coordinates on a coordinate grid (in all four quadrants)
Understand that one coordinate identifies a point on a line, two coordinates identify a point in a plane and three coordinates identify
a point in space, and use the terms ‘1-D’, ‘2-D’ and ‘3-D’
Find the coordinates of a third point to complete an isosceles triangle
Find the coordinates of the fourth vertex of a parallelogram, trapezium, rhombus and kite
Use the mid-point formula to work out the coordinates of the mid-point of the line connecting two point with given coordinates
Identify the coordinates of the vertex of a cuboid on a 3-D grid.
DIFFERENTIATION & EXTENSION
Use non-integer coordinates.
Find the coordinates of the point of intersection of the medians of a triangle.
Identify the coordinates of the mid-point of a line segment in 3-D.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 4.1 – 4.5
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
5 minutes mini-test at the start/end of each lesson
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.
Drawing shapes using coordinates, e.g. Christmas tree
HINTS AND TIPS
Clear presentation with axes labelled correctly is vital.
Students often have difficulty visualising 3-D coordinates; 3-D models are useful.
Use Exercises 4A – 4E for practice.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 4 (Part B) COORDINATES AND ESSENTIAL ALGEBRA
SPECIFICATION REFERENCE
Using letters to represent numbers
Simplifying expressions by collecting like terms
Multiplying expressions and simplifying the result
Order of operations in calculations with brackets
Multiplying a single term over a bracket
Simplifying expressions with brackets
Write a common factor outside the bracket
The product of two brackets
Cancelling common factors in algebraic fractions
Time: 6 – 8 hours
NA5a
NA5b
NA5a
NA5b
NA5b
NA5b
NA5b
NA5b
NA5a
PRIOR KNOWLEDGE
Know that a letter can be used to represent a number
Ability to use negative numbers with the four operations
Experience of using BIDMAS in calculations without a calculator
OBJECTIVES
By the end of the chapter the student should be able to:
Write simple algebraic expressions, e.g. 5 less than x
Simplify algebraic expressions in one, or more like terms, by adding and subtracting, e.g. simplify 2x + 3 + 3x – 1
Multiply letters and numbers, e.g. simplify 3x  4y
Simplify expressions involving one, or two, pairs of brackets, e.g. 4(a + 3b) + 2(a – b) and (x + 3)(x – 2)
Factorise expressions involving one pair of brackets, e.g. ap +4a
Simplify algebraic fractions, e.g. 4ab/b.
DIFFERENTIATION & EXTENSION
Further work on collecting like terms, involving negative terms
Simplify expressions involving fractions, e.g. ab/3 + 4ab
Expand brackets with non-unitary coefficients, e.g. (2x + 1)(3x + 2)
Harder factorisation, e.g. x2 + 3x + 2
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 4.6 – 4.14
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
5 minutes mini-test at the start/end of each lesson
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 4F – 4N for practice. Use Mixed Exercise 4 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 5
Sequences
SPECIFICATION REFERENCE
Generating sequences and finding rules
Number sequences from shapes
Generating number sequences and finding the nth term
Finding the number of matchsticks in pattern number n
Time: 3 – 5 hours
NA6a
NA6a
NA6a
NA6a
PRIOR KNOWLEDGE
Know about odd and even numbers
Recognise simple number patterns, e.g. 1, 3, 5, ...
Writing simple rules algebraically
OBJECTIVES
By the end of the chapter the student should be able to:
Generate a sequence from a rule, e.g. given first term = 25, and rule = subtract 5
Find the rule and continue the number pattern or sequence
Relate the term in a sequence to its position, e.g. multiply term number by 2 and add 1
Continue a sequence when the sequence is a pattern of shapes
Find and use the nth term of a sequence of numbers/shapes
Find whether a number is part of a given sequence
Use a calculator to produce a sequence of numbers.
DIFFERENTIATION & EXTENSION
Investigate the number patterns in Pascal’s triangle.
Investigate sequences of triangle numbers, Fibonacci numbers, etc.
Generate sequences on a spreadsheet.
Use algebra to describe real situation, e.g. n quadrilaterals have 4n sides.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 5.1 – 5.5
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Simple investigation of a sequence, using diagrams and number patterns
Use of mental maths in the substitution of simple numbers into expressions
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
Emphasis on good use of notation 3n means 3  n
When investigating linear sequences, students should be clear on the description of the pattern in words, the difference between
the terms and the algebraic description of the nth term.
Calculators may be used to generate simple sequences, e.g. using the “ans” function (or similar).
Use Exercises 5A – 5E for practice. Use Mixed Exercise 5 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 6
LINEAR GRAPHS
Time: 3 – 5 hours
SPECIFICATION REFERENCE
Straight line parallel to the axes
Straight line passing through the origin
Graphs of linear functions
Straight line graphs in real life
NA6b
NA6b
NA6b
NA6c
PRIOR KNOWLEDGE
Experience at plotting points in all quadrants
OBJECTIVES
By the end of the chapter the student should be able to:
Draw a line parallel to the axis from given coordinates
Write down the equation of a line parallel to the coordinate axes, e.g. y = 5
Find the value of a in y = ax from the graph of in y = ax (by considering number pattern in the coordinates)
Produce a table of values for a linear relation and plot the points on a grid (including fractional coefficients of x)
Identify and use linear relations in real-life contexts, e.g. conversion graphs.
DIFFERENTIATION & EXTENSION
Find the gradient of a line formally.
Identifying regions defined by lines, e.g. shade y > x +1
Draw quadratic graphs.
Use a graphic calculator to draw graphs of straight lines.
Find the coordinates of the point of intersection of two lines.
Relate the intercept of y = mx + c to (0, c).
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 6.1 – 6.4
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
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.
Use data collected by students to draw linear graphs.
HINTS AND TIPS
Coordinate axes should be labelled.
Recognise linear graphs and see when data may be incorrect.
Link linear graphs to other subject areas, e.g. science, geography, etc.
Use Exercises 6A – 6D for practice. Use Mixed Exercise 6 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 7
PROPERTIES OF SHAPES
SPECIFICATION REFERENCE
Definitions and names of polygons
Definitions and notation for parallel and perpendicular lines
Properties of triangles
Properties of quadrilaterals
Properties of circles
Exploring cubes and cuboids
Drawing on isometric grids
Time: 6 – 8 hours
S2a/c
S2d
S2f
S2i
S2j
S2j
PRIOR KNOWLEDGE
The concept of parallel lines
The concept of vertical and horizontal
The concept of an angle between two lines
Experience in drawing triangles, quadrilaterals and circles
OBJECTIVES
By the end of the chapter the student should be able to:
Name a polygon with 3, 4..., 10 sides
Use the notation and identify parallel and perpendicular lines in diagrams
Identify and name the different types of triangles and use appropriate notation to label sides of equal length
Identify and name the different types of quadrilateral
Use squared paper to draw shapes from their descriptions, e.g. draw a trapezium with parallel sides 2cm and 4cm
Use the angle the properties of triangles to find missing angles
Identify and name the parts of a circle
Identify, name and count the faces, edges and vertices of 3-D shapes (including the use of Euler’s formula)
Use isometric paper to draw shapes based on the combination of cuboids.
DIFFERENTIATION & EXTENSION
Use triangles to find the angle sums of polygons.
Use the angle properties of triangles to find missing angles in combinations of triangles.
Construct nets of 3-D shapes.
Investigate Euler’s formula in more complicated 3-D shapes.
Draw 2-D and 3-D shapes using software, e.g. Word.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 7.1 – 7.8
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Incorporate this work in regular mini-tests.
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, and accurately.
Draw lines using an HB pencil.
A sturdy pair of compasses are essential – spare equipment is advisable.
Use Exercises 7A – 7H for practice. Use Mixed Exercise 7 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 8
Time: 4 – 6 hours
ANGLES AND BEARINGS
SPECIFICATION REFERENCE
Acute, obtuse and reflex angles
Angles on a straight line
Angles meeting at a point
Angles in parallel lines
Proofs of angle properties of parallelogram and triangle
Bearings
S2b
S2a
S2a
S2e
S2e
S4b
PRIOR KNOWLEDGE
An understanding of angle as a measure of turning
The ability to use a protractor to measure angles.
OBJECTIVES
By the end of the chapter the student should be able to:
Distinguish between acute, obtuse and reflex angles
Use letters to define an angle, e.g. angle ABC
Know that the angle on a straight line = 180, and use this to find missing angles
Recognise and use vertically opposite angles
Know that angles meeting at a point add to 360, and use this to find missing angles
Recognise and use corresponding and alternate angles to find missing angles
Show that: the opposite angles in a parallelogram are equal; angles in a triangle add to 180; the exterior angle of a triangle is equal
to the sum of the interior and opposite angles.
Know that a bearing is an angle measured clockwise from North
Work out the bearing of B from A given the bearing of A from B.
DIFFERENTIATION & EXTENSION
Investigate the angle sum of polygons.
Investigate cyclic quadrilaterals.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 8.1 – 8.6
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Regular quick tests on angle properties of various shapes
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
Make sure that all pencils are sharp and drawings are neat and accurate – a ruler is essential.
Diagrams should be clearly labelled.
Use Exercises 8A – 8F for practice. Use Mixed Exercise 8 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 9
MEASURE
Time: 8 – 11 hours
SPECIFICATION REFERENCE
Reading clock times from analogue and digital displays
Reading scales
Choosing appropriate units for quantities and estimating measurements
Converting metric units of length, weight and capacity
Approximate metric to imperial conversions
Accuracy in measurements
Calculating speed and density
Converting between units of speed
Comparing measurements
NA3p/ S4a
S4a
S4a
S4a
S4a
NA4d/ S4a
Na4c/ S4c
NA4a/ S4a/c
S4a/c
PRIOR KNOWLEDGE
Know that: 1 hour = 60 minutes; 1 day = 24 hours
Some experience of metric/imperial measures
OBJECTIVES
By the end of the chapter the student should be able to:
Write down the time from a clock display (analogue and digital; 12-hour and 24-hour)
Convert minutes into fractions of an hour
Read the value from a linear scale
Choose suitable units to measure real-life situations
Use a known amount to estimate quantities, e.g. their hand-span to estimate their height.
Convert metric to metric units, e.g. 0.05m to cm
Use approximate metric/imperial measurements to convert units, e.g. 8km  5 miles
Write down the maximum/minimum possible value of a measurement
Use speed = distance/time to work out speed, distance or time
Change the units of speed between metric/metric units or metric/imperial units
Use density = mass/volume to work out density, mass or volume.
DIFFERENTIATION & EXTENSION
Use ICT and reference books to find the weights, volumes and heights of large structures such as buildings, aeroplanes and ships.
Work with more difficult examples.
Work with “real” timetables and “real” holiday brochures for working out holiday dates.
Use combinations of timetables for multi-stage trips.
Measure the solar system using Astronomical Units.
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 9.1 – 9.11
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental testing to check for knowledge of everyday measures, and estimation
Mental test questions on changing units, changing between metric and imperial units
Mental questions to test knowledge of common conversion factors
Aural questions on dates, times and timetables
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.
Plan a foreign holiday with dates/timetables to arrive at the airport, etc.
HINTS AND TIPS
Measurement is essentially a practical activity.
Use a range of everyday objects to make the lesson more real.
All working should be shown with multiplication or division by powers of 10.
Use a distance/speed/time triangle and a density/mass/volume triangle to assist calculations.
Use Exercises 9A – 9J for practice. Use Mixed Exercise 9 for consolidation.
FOUNDATION UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
FOUNDATION CHAPTER 10
PERIMETER, AREA AND VOLUME
SPECIFICATION REFERENCE
Finding the area and perimeters of 2-D shapes
Using formulae to find the area of triangles, parallelograms, and trapeziums
Calculating the surface area and volume of cuboids
Using the formula to calculate the volume of a prism
Time: 6 – 8 hours
S4f
S2f/4g
S4f/4g
S4g
PRIOR KNOWLEDGE
The names of quadrilaterals
Ability to substitute numbers into a formula
Some notion of the difference between length, area and volume
OBJECTIVES
By the end of the chapter the student should be able to:
Work out the perimeter of a shape drawn on a centimetre grid
Estimate the area of a shape drawn on a centimetre grid
Use area = length  width to work out the area, length or width of a rectangular shape
Use the area formulae for triangles, parallelograms and trapeziums
Work out the surface area of a cuboid (by working out the area of each face)
Find the volume of a cuboid by counting centimetre cubes, and by formula (including shapes made from cuboids)
Use volume = cross-section  length to find the volume of a regular prism
Work out how many small boxes fit into a large box.
DIFFERENTIATION & EXTENSION
Further problems involving combinations of shapes
Using compound shape methods to investigate the area of other standard shapes, e.g. kites
Practical activities e.g. using estimation and accurate measuring to calculate perimeters and areas of classroom/corridor floors
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Foundation Chapter/section: 10.1 – 10.8
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Regular quick tests on perimeters, areas and volumes of standard shapes
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.
Find the perimeter and area of the floor of a room at home.
A fencing problem – find the smallest/largest area with a fixed perimeter.
HINTS AND TIPS
Discuss the correct use of language and units.
Ensure that pupils can distinguish between perimeter, area and volume.
Many students have little real understanding of perimeter, area and volume. Practical experience is essential to clarify these
concepts.
Use Exercises 10A – 10I for practice. Use Mixed Exercise 10 for consolidation.