Year 10

AUTUMN TERM A TOPIC 1

Topic: Integers and Powers

/ Target Grade: E/D/C
Edexcel Content:
NA2a: Understanding place value in whole numbers
NA3a: Long multiplication and long division without using a calculator
NA3a: 4-rules using negative numbers
NA2a: Rounding off to a given power of ten
NA2b: Use the terms square, positive square root, negative square root, cube and cube root
NA3b: Use brackets and the hierarchy of operations
NA3a: Find the prime factor decomposition of positive integers
Prior Knowledge:
Knowledge of times tables and strategies for multiplying and dividing whole numbers by 10.
Learning Objectives:
Write integers in words and digits
Do long multiplication and long division without using a calculator
Work confidently without the aid of a calculator, including the four rules with negative numbers
Estimating answers by rounding to 1 significant figure
Use the terms square, positive square root, negative square root, cube and cube root
Use BIDMAS to work out answers
Use prime factor decomposition to find the HCF of integers. Find the LCM using multiples.
Differentiation & Extension:
Non-calculator maths: 3 (or more) digit numbers multiplied/divided by 3 (or more) digit numbers.
Use prime factors to find LCM.
Notes:

All of this topic should be revision, but these are things that need to be revised regularly.

All working should be presented clearly.

Non-calculator methods should show remainders and carries as evidence.
London Reference:

Book 1 Chapter 1 p.1 - 12

/ Other references:
Discussion opportunities:
Which is the best method for long multiplication/division? Show various methods and let the students decide.
Pair / Group Work:
Students could write non-calculator questions (or a mental test) for a partner to answer.
Factors/multiple board game in pairs.
ICT Links:
- for Mental arithmetic practice (see ICT folder).
Investigation:

Investigate why the grid method works for long multiplication.

When you multiply a number does it always increase?

Spiritual, Moral, Citizenship and Literacy links:
Numbers can be positive or negative – so can humans.
Writing numbers in words helps literacy.
Time: 6 - 7 lessons

AUTUMN TERM A TOPIC 2

Topic: Fractions and Decimals

/ Target Grade: E/D/C/B
Edexcel Content:
NA2c: Using diagrams to find equivalent fractions
NA2c: Cancelling fractions
NA3d: Interchanging improper fractions and mixed numbers
NA2d & NA3c: Interchanging fractions and decimals and using recurring decimals
NA2c: Ordering fractions using common denominators
NA3c: Adding and subtracting fractions using common denominators
NA3d: Multiplying and dividing fractions
NA3d: Using fractions in problems involving multiplication and division
NA3c: Calculating a fraction of a quantity
NA3c: Writing a given number as a fraction of another
NA3a: Place value, multiplication and division of decimal numbers by powers of ten
Prior Knowledge:
A basic understanding of fractions as being ‘parts of a whole unit’.
Use of a calculator with fractions.
Learning Objectives:
Equate one fraction with another, and simplify fractions to their lowest terms
Understand and change between improper fractions and mixed numbers
Perform the four basic operations with fractions
Place value, multiplication and division of decimal numbers by powers of ten
Put decimals in order of size
Multiply and divide decimals
Convert fractions into decimals and vice-versa, including recurring decimals
Order decimals and fractions
Convert between metric and imperial units
Differentiation & Extension:
Mental maths problems with negative powers of 10, e.g. 2.5 x 0.01, 0.001.
Relating the basic fractions to readily remembered percentages and vice-versa.
For very able students cancelling down of algebraic expressions could be considered.
Notes:
Constant revision of this topic is needed. All work needs to be presented clearly with the relevant stages of working shown.
London Reference:

Book 1 Chapter 2 p.13 - 24

/ Other references:
Discussion opportunities:
Why does the division rule work?
Pair / Group Work:
Students could write questions for a partner to solve. Revision can be done as some kind of group quiz.
Domino/Bingo/Snap games – match equivalent fractions
ICT Links:
Calculator Tennis (see ICT folder, Graphical Calculator section) to understand multiplying and dividing by numbers between 0 and 1.

Calculators can be used to check answers.

Number Foundations (Outware Education on laptop).
Investigation:
Some four rules work (e.g. division) could be approached investigatively.

Patterns with Fractions.

Spiritual, Moral, Citizenship and Literacy links:

What fraction of the House of Commons does each political party occupy?

Fractions can be equivalent, simplified, improper and mixed – can humans?

Time: 8 - 9 lessons

AUTUMN TERM A TOPIC 3

Topic: Percentages

/ Target Grade: E/D/C
Edexcel Content:
NA2e: Understanding percentages
NA3e: Interchanging between percentages, fractions and decimals
NA3j: Finding percentages, and percentage changes
NA3j: Calculating percentage profit or loss
Prior Knowledge:
Topic 2.
Learning Objectives:
Change between percentages, fractions and decimals
Find percentages of quantities, by both mental mathematics and calculator methods
Increase and decrease quantities by a percentage, including within contexts of VAT, profit and loss
Find one quantity as a percentage of another, and calculate the percentage when an actual profit or loss is given
Differentiation & Extension:
Include percentages with recurring decimals (e.g. 33 %), and percentages over 100%
Combine multipliers to simplify a series of percentage changes.
Notes:
Amounts of money should be rounded to the nearest penny (but only at the end of the question).
Working out should always be shown.
London Reference:

Book 1 Chapter 3 p.27 - 33

/ Other references:
Discussion opportunities:
Plenty of opportunity, especially when dealing with real-life situations.
Pair / Group Work:
Domino/Bingo/Snap games – match equivalent fractions, decimals and percentages.
ICT Links:
Use of Excel for budgeting.
Investigation:

VAT, credit, interest, mortgages – the students can research all these applications of percentages.

Spiritual, Moral, Citizenship and Literacy links:

How much should we be taxed? Facts relating to the third world often involve percentages.

What percentage of 18 year olds voted in the last general election? Discuss.
Time: 4 - 5 lessons

AUTUMN TERM A TOPIC 4

Topic: Coordinates and the Elements

of Algebra

/ Target Grade: E/D/C/B
Edexcel Content:
NA6b: Plot points in all four quadrants
NA5a: Using letters to represent numbers
NA5b: Collecting like terms
NA5b: Removing a single pair of brackets
NA5b: Multiplying with letters and numbers
NA5b: Factorising with a single pair of brackets
NA5g: Using word formulae
NA5g: Using algebraic formulae
NA5d: Substituting into expressions involving squares or cubes
Prior Knowledge:
Negative numbers and indices. Experience of using a letter to represent a number.
Learning Objectives:
Plot coordinates in all four quadrants
Simplify algebra by collecting like terms – answers may involve negative coefficients.
Simplify expressions by expanding single brackets
Factorise expressions (single brackets)
Understand the terms; equation, formula, identity and expression
Substitute numbers into algebraic formulae
Differentiation & Extension:
Further work on simplifying, e.g. three variables
Factorising with three or more terms
Substitution into more difficult formulae (Algebra crossword)
Notes:
Emphasise the need to show working out and correct use of symbolic notation (e.g. 3x rather than 3 x x). Encourage students to check their factorising by expanding the brackets.
London Reference:

Book 1 Chapter 4 p.34 – 40

/ Other references:
Discussion opportunities:
What is the point of coordinates and algebra? Discuss real life examples.
Pair / Group Work:

Battleship – to practice coordinates

Domino/Bingo/Snap games – match expressions with their factorised equivalent
Algebra crossword
ICT Links:

Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.

Autograph or graphics calculators could be used to show the equivalence of expressions.
Excel work on substitution (see ICT folder)
Investigation:

Beyond Pythagoras involves a lot of rearranging equations, as does Opposite Corners.

Factorisation could be approached investigatively.
Spiritual, Moral, Citizenship and Literacy links:
Literacy: It is important to arrange variables in alphabetical order e.g. ‘abc’ rather than ‘cab’
Time: 5 - 6 lessons

AUTUMN TERM B TOPIC 5

Topic: Algebraic Equations

/ Target Grade: E/D/C/B
Edexcel Content:
NA5f: Inverse operations
NA5e: Simple linear equations
NA5e: Equations combining operations
NA5f: Solving equations with the unknown on both sides
NA5f: Solving equations with brackets and negative solutions
NA5e: Set up simple equations
NA5e: Using algebraic equations to solve problems
NA5f: Linear equations with fractional coefficients
NA5e: Solve equations with the unknown as the denominator
Prior Knowledge:
Topic 4. An understanding of balancing methods. Squares and square roots.
Learning Objectives:
Solve equations using inverse operations.
Solve linear equations including those with an unknown on both sides, those that require prior simplification (e.g. brackets), fractional equations, and those where the answers are either negative or a fraction.
Derive algebraic expressions from information given and extend this to derive equations.
Solve simple quadratic equations
Solve equations with the unknown as the denominator
Differentiation & Extension:
The work can be extended to include more complex algebraic manipulation and equations.
Notes:
Students need to realise that not all linear equations can easily be solved by observation or trial and improvement, so use of a formal method is vital.
Answers can be left as fractions where appropriate.
London Reference:

Book 1 Chapter 5 p.41 - 51

/ Other references:
Discussion opportunities:
Discuss the ‘best’ way to solve an equation.
Why do quadratic equations have two solutions (usually)?
Pair / Group Work:
Equation loop cards could be played as a class. Equation dominoes could be played in groups.
ICT Links:
Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.
Investigation:

Investigate the history of algebra.

Spiritual, Moral, Citizenship and Literacy links:
How can equations be used to solve real life problems?
Time: 6 - 7 lessons

AUTUMN TERM B TOPIC 6

Topic: Sequences

/ Target Grade: E/D/C/B
Edexcel Content:
NA6a: Extending diagrammatic sequences
NA6a: Extending number sequences
NA6a: Generating common number sequences
NA6a: Finding the nth term (linear expressions)
Prior Knowledge:
The ability to follow a series of instructions and appreciate that symbols can represent numbers.
Learning Objectives:
Continue linear and non-linear sequences of numbers and find term to term rules
Find and use the nth term for linear sequences
Continue sequences of shapes and find associated rules
Differentiation & Extension:
Try to emphasise the difference between a term-to-term rule and a position-to-term rule.
Recurrance sequences e.g. Fibonacci (especially if you are planning to do the Flagging coursework). Pascal’s triangle.
Notes:
Try to emphasise the difference between a term-to-term rule and a position-to-term rule.
London Reference:

Book 1 Chapter 6 p.52 - 63

/ Other references:
Discussion opportunities:
Describe in words what is happening in each sequence. What is the best way to represent this in algebra?
Pair / Group Work:
Some pattern spotting could be done in pairs. Students could make up sequences for a partner to find the rule.
ICT Links:

Use of Excel to generate sequences (see ICT folder).

Powerpoint – students put each number in their own sequence on a different slide (see ICT folder).

Graphics calculators

Investigation:
You could bring in some short investigations which lead to simple number sequences – see Rayner p.48-51

Flagging and The Pay Phone Problem involve recurrence sequences.

Spiritual, Moral, Citizenship and Literacy links:

Fibonacci’s “Golden Ratio”.

The numbers in sequences all follow the same rule – this is an excellent example of teamwork.
Time: 4 - 5 lessons

AUTUMN TERM B TOPIC 7

Topic: Properties of Shapes

/ Target Grade: E/D/C
Edexcel Content:
SSM2d: Angles of regular polygons
SSM2b: Angle properties of triangles
SSM2c: Classify quadrilaterals by their geometric properties
SSM2h: Definition of a circle and the meaning of related terms
Prior Knowledge:
Experience of measuring and drawing angles with a protractor.
Learning Objectives:
Name polygons with up to ten sides
Understand the names and properties of triangles
Understand the names and properties of quadrilaterals
Identify the parts of a circle and its properties
Differentiation & Extension:
Inscribe regular polygons in circles
Notes:
Emphasise the need for accurate drawings using a pencil and ruler (and protractor).
London Reference:

Book 1 Chapter 7 p.64 - 70

/ Other references:
Discussion opportunities:
“What is the largest angle you can have in a triangle?” – this should set off a lively debate.
Encourage the use of proper vocabulary here, particularly with circles.
Pair / Group Work:
Match up pictures of polygons with the description of their properties.
ICT Links:

Cabri Geometry (see ICT folder)

LOGO (see ICT folder).
Investigation:

Investigate whether a rule exists between the number of vertices and the number of lines of symmetry.

Spiritual, Moral, Citizenship and Literacy links:
Literacy: Use a dictionary to look up the terms used to describe polygons.
Time: 3 - 4 lessons

Note: If students are unsure how to complete an investigation, use Edexcel Int.(new) chapter 9A to introduce the coursework.

COURSEWORK 1: Choose a task from the Edexcel coursework folder (in the maths staff room)

All groups will do this piece at the same time.

Time: 2 weeks + half term.

SPRING TERM A TOPIC 8

Topic: Line and Rotational

Symmetry

/ Target Grade: E/D/C
Edexcel Content:
SSM3a: Specifying transformations
SSM3b: Line symmetry
SSM3b: Rotational symmetry
SSM3b: Planes of symmetry
SSM3b: Transforming 2D shapes by reflection, rotation and translation
Prior Knowledge:
Co-ordinates, sketching 3D shapes, angles.
Learning Objectives:
Identify lines of symmetry or the order of rotational symmetry in 2-D shapes
Sketch planes of symmetry on 3D shapes
Reflect a 2D shape in a vertical, horizontal or diagonal line and state the equation of the line.
Rotate a 2D shape about the origin or a point other than the origin, stating the angle, direction and centre of rotation.
Translate a 2D shape using a vector
Differentiation & Extension:
Attempt to draw up to 3 shapes each which have exactly 1, 2, 3, …8 lines of symmetry.
Mirrors could be used to make the topic easier.
Notes:
Emphasise the need for accurate drawings using a pencil and ruler (and protractor).
Students can lose marks in their GSCE for neglecting to mention one part of a transformation, e.g. the centre of rotation.
London Reference:

Book 1 Chapter 8 p.71 - 83

/ Other references:
Discussion opportunities:
What real life objects in the classroom are symmetrical?
Discuss how to find the centre of a rotation.
Pair / Group Work:
Display work could be done in groups or pairs.
The ICT work below could be done in pairs.
ICT Links:

Geometry Transformations (Outware Education) on department laptop.

Powerpoint presentation on laptop. Cabri Geometry (see ICT folder).
Transformation Golf on the internet –
Investigation:

Investigation into different ways of transforming an object onto a particular image.

Spiritual, Moral, Citizenship and Literacy links:
Many wonderful works of art are symmetrical.
Time: 5 - 6 lessons

SPRING TERM A TOPIC 9

Topic: Angles, Constructions and

Bearings

/ Target Grade: E/D/C
Edexcel Content:
SSM4b: Draw approximate constructions of triangles and other 2D shapes
SSM4b: Construct specified 3D shapes
SSM2a: Use parallel lines, alternate and corresponding angles
SSM2d: Calculate and use the angles of regular polygons
SSM4a: Use bearings to specify direction
Prior Knowledge:
Estimating angles, use of a protractor.
Learning Objectives:
Construct triangles and other 2D shapes
Use nets to construct 3D shapes
Calculate angles on parallel lines, and a point and on a straight line
Calculate the angle sum of a polygon and the interior and exterior angles of a regular polygon
Draw and measure three figure bearings accurately
Differentiation & Extension:

Find all possible nets of a cube.

Draw shapes made from multi-link on isometric paper.
Build shapes from cubes, which are represented in 2D.
Notes:
Students are often confused about the position from where a bearing is measured. Emphasise the fact that bearings are given in three figures.
London Reference:

Book 1 Chapter 9 p.84 - 94

/ Other references:
Discussion opportunities:
Which nets will work? Discuss why or why not.
Where are bearings used in real life? Why use three digits e.g. 045º ?
Pair / Group Work:
Could use multi-link cubes in pairs or groups.
ICT Links:
Cabri Geometry (see ICT folder). LOGO (see ICT folder).
Powerpoint presentation on angles in polygons (on laptop).
Investigation:

Angles in polygons could be approached investigatively, as could the work on nets

Spiritual, Moral, Citizenship and Literacy links:
People can be described as 2-dimensional or 3-dimensional. Is there such a thing as the 4th dimension?
Time: 6 – 7 lessons

SPRING TERM A TOPIC 10

Topic: Handling Data

/ Target Grade: E/D
Edexcel Content:
HD3a: Collect data using various methods
HD3b: Gather data from secondary sources
HD3c: Design and use two-way tables for discrete and grouped data
HD3d: Deal with practical problems such as non-response or missing data
Prior Knowledge:
An understanding of why data needs to be collected. Simple inequalities (for grouped tables)
Learning Objectives:
Understand the difference between primary and secondary data
Design a simple questionnaire and appreciate deficiencies in a question.
Undertake steps to eliminate bias.
Sort and collect data in a tally table and grouped frequency table.
Design and use two-way tables.
Differentiation & Extension:
Stratified random sampling could be introduced here as it is important in the Data Handling coursework.
You could use data from newspapers, censusatschool, class experiments (reaction times) etc.
Notes:
This chapter is quite straightforward and should be revision. Try to make it as practical as possible.
London Reference:

Book 1 Chapter 10 p.95 - 98

/ Other references:
Discussion opportunities:
What makes a good questionnaire? Discuss bias in questionnaires.
Pair / Group Work:
Questionnaires can be done in pairs and then presented to a group or the whole class for constructive criticism.
ICT Links:

Excel – collect data in tables and draw different types of graphs.

- provides interesting raw data to take samples from and analyse
Investigation:

Students could carry out a statistical investigation of their own, including designing an appropriate means of gathering the data.