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Schemes of Work

Number of lessons (between 6&8)

Content of the unit

Assumed prior learning (tested at the beginning of the unit)

7 weeks Quadratic equations

Linear Graphs

Simultaneous Equations

Inequalities

Students should understand the ≥ and ≤ symbols.

• Students can substitute into, solve and rearrange linear equations. • Students should be able to factorise simple quadratic expressions. • Students should be able to recognise the equation of a circle.

Assessment points and tasks

Written feedback points

Learning Outcomes (tested at the end and related to subject competences)

Pre test Post test (half term exams/ mock exams)

Diagnostic marking (TF)-( green sticker)-(PF)/(SF) yellow and orange stickers Traffic lighting of exam papers

• N1 order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥ • N8 calculate exactly with … surds; … simplify surd expressions involving squares • (e.g. √12 = √(4 × 3) = √4 × √3 = 2√3) • A3 understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors • A4 simplify and manipulate algebraic expressions (including those involving surds …) by: … factorising quadratic expressions of the form ax2 + bx + c • A5 understand and use standard mathematical formulae; rearrange formulae to change the subject • A9 … find the equation of the line through two given points, or through one point with a given gradient • A11 identify and interpret roots … of quadratic functions algebraically … • A18 solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; … • A19 solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically;


Schemes of Work

Lesson

Clear learning intentions

Clear success criteria

Hook

Presentation of content

Guided practice

New GCSE higher text book page number 165

Closure

1. Lesson plan

Solving quadratic equations of the form ax2+bx+c , where a=1, using factorisation.

Factorising quadratics expressions with

Solving a quadratic equation means finding the values for the unknown that fit.

Find the roots of quadratic functions using Factorisation.

Power point on starter question Pool question The sum of two numbers is 15 and the product of the two numbers is 56, find two numbers. For higher ability pupils use negative numbers. Algebra fluency page 280 Prior knowledge check numerical

Active teach page number 280 – 281 Video on how to factorise quadratic equations Marking technique

New GCSE higher text book page number 281 questions 1-8. 97 q1-3 Page 298- q1-5

Questions 5-11.

Write any function that will give the roots x=4 and x=-6. Compare your functions with other people’s. What do you notice about them all?

find approximate solutions using a graph • A21 … derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution.

A22 solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

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Schemes of Work

positive terms.

To be able to find the factors of a number which multiply to give the last term and add together to give the middle term of a quadratic expression.

fluency page 280.

Which factor pairs of 12 have a sum of 7?

Flip charts on solving quadratic equations using factorisation. Board works slides, maths watch clip number 161a,b

Use page 300 extend exercise for the higher ability pupils. New GCSE higher text book questions 1-6 and 10. Page 46-47 Page 53, q13,15

The factors of x^2 +5x+6 are -1 and 6, Is that correct justify your answer

2. Lesson plan: Use only factorisation

Solving quadratic equations of the form ax2+bx+c , where a=/ 1, using factorisation

Factorising quadratics

Solving a quadratic equation with coefficient of ‘a’ not equal to one. Find the roots of quadratic functions using Factorisation.

Mix and match questions on factorising quadratics. Fluency question Warm up exercise page 282

Active teach page number Page 283 question 5-12 Maths watch clip

New GCSE higher text book page number 283 questions 7-11. Page 298

Exam question on solving quadratics using factorisation Make up your own questions and swap with your partners,






https://www.activeteachonline.com/product/view/id/405/page/282/mode/dps?modal=/player/image/id/451053/product/405













Schemes of Work

with last term positive.

Find the solution of differences of two squares. To be able to find the factors of a number which multiply to give the last term and add together to give the middle term of a quadratic expression with last terms positive

q5-9 Use page 300 q5 extend exercise for the higher ability pupils. Collins GCSE higher text book questions 1-21 page 285

identify any common errors. Peer mark and feedback.

3. lesson plan

Solving quadratic equations of the form ax2+bx+c , where a=1, using completing the square • Factorising quadratics with terms with different signs.

Understand what a perfect square means. To be able to write expressions in the form (x+a)^2+b To be able to solve quadratic

Starter fluency questions Warm up activity question 1 -3 page 285

Active teach modelling the question Video on completing the square FSMP RESOURCES FROM

New GCSE higher text book page number 285 questions 4,5,6,7,8,9 Page 299

*Question Discuss which method is more accurate, giving the answer in exact form or two d.p, why explain your answer. X^2+6x-5 =0





















Schemes of Work

equations using completing the square. To write the solution using exact form and using decimal number. To be able to find the factors of a number which multiply to give the last term and add together to give the middle term of a quadratic expression with last term negative .

INTEGRAL MATHS

q13-14 Use page 300 q13 extend exercise for the higher ability pupils. Collins GCSE higher text book questions22-40 page 285

Consolidation video on solving quadratics, always,sometimes, never true. Use only the first few minutes, pause and use it for assessment. Make up your own questions and swap with your partners, identify any common errors. Peer mark and feedback.

4. lesson plan

Solving quadratic equations of the form ax2+bx+c , where a=/ 1, using completing the square. Factorising

To be able to understand that completing the square can be used to find the minimum and

FSMP RESOURCES FROM INTEGRAL MATHS

Active teach Model answer. Maths watch clip number

New GCSE higher text book page number 286 questions

11 -14 is extended learning

Consolidation video on solving quadratics, always,sometimes, never true.





















Schemes of Work

quadratics involving all three types mentioned above.

maximum points of a curve. To be able to factorise expression by taking the common factor out and complete the square. To be able to write the expressions in the form a(x+a)^2+b To solve equations using completing the square, giving the answer in surd form and to dp. To be able to find the factors of a number which multiply to give the last term and add together to give the middle term of a quadratic

11-15. Page 299 q12-14 Use page 300 q14 extend exercise for the higher ability pupils. New GCSE higher text Page 47 q10,11,12

Use the clip where it refers to expressions with a>/<1 Page 57 questions 13 on factorisation






Schemes of Work

expression involving negative and positive terms.

5. Lesson plan

Solving quadratic equations of the form ax2+bx+c , where using the formula. Difference of two squares

To solve quadratic equations using the formula. To be able to substitute in the formula To be able to round the numbers to appropriate degree of accuracy. To be able to factorise expressions of the form x^2-y^2

Starter questions on factorising quadratics Page 46 warm up questions

Video on solving quadratic equation using the formula. Solving quadratics example active teach page 284 Match watch clip number

New GCSE higher text book page number 284 questions 13-15 Page 297 q4 Page 298- q10,11 Use page 300 extend exercise for the higher ability pupils. Collins GCSE higher text book page 286

Exam style questions: Solve a quadratic expression using a formula. Factorise 2x^2-50 Can you use difference of two squares ? yes/no Explain




















Schemes of Work

exercise 12f

6. HW lesson on QUADRATIC EQUATIONS Hw on factorising quadratic expressions

To be able to go through the HW and clarify any misconceptions.

To give constructive feedback/ peer /self or TF/ both written and verbal

Hw corrections/ragging if needed, it can be peer, self or computer generated corrections.

Do few questions on the HW corrections. Can use active teach text book Chapter 9 any of the questions on extend, strengthen or check- up depending on their ability

End of unit test for chapter 9 on quadratics Check up Strengthen /extend use quadratic equations only End of unit test on factorisation question 13

New GCSE Foundation text book Questions 1-9.

Pupils to identify one main misconception and then work on the feedback, use it as a learning tool, can plan a session to present it as a starter for the next lesson.

















Schemes of Work

7. lesson plan

● Find the gradient and

y-intercept

from a linear equation.

● Rearrange an equation into the form

y = mx + c.

● Compare two graphs from their equations.

Plot graphs with

equations ax + by

= c.

● Students may use equations in different forms to compare graphs or find gradient

and y-

intercept values. Remind students to always use

the y = mx +

c form of the

equation.

Plotting x and y in the wrong directions. Discuss ways of remembering

that x always goes on the horizontal axis

and y on the vertical axis.

Video on how to find the gradient

Active Teach p.g 161-163

New GCSE higher text book page number 161 questions 1-4. *Questions 5 -8 is extended learning.

New GCSE higher text book page number 165

Display a sketch graph with only the

y-intercept

labelled. Ask students to write down what the gradient could be (on mini whiteboards, if possible).

Display a sketch graph

of y = x. Tell

students that this graph meets the axes at 45° (assuming the scales are the same for both axes). Use the

graph of y = x to check students’ suggested gradients for the first graph. Is the

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Schemes of Work

gradient less than 1? Equal to 1? More than 1?

Repeat with further sketch graphs. Use students’ answers to highlight any misconceptions, reiterating how you can tell if a gradient is positive or negative and including some graphs with

negative y-intercepts.

8. lesson plan

● Find the gradient and

y-intercept

from a linear equation.

● Rearrange an equation into the form

y = mx + c.

● Compare two

● Students may use equations in different forms to compare graphs or find gradient

and y-

intercept values.

Video on how to find the gradient

Active Teach p.g 161-163 Flip charts on solving Linear equations. Board works slides, maths

New GCSE higher text book page number 161 questions 1-4. *Question

Questions 5-11.

Display a sketch graph with only the

y-intercept

labelled. Ask students to write down what the gradient could be (on mini

https://activeteach-prod.resource.pearson-intl.com/r00/r0044/r004485/r00448589/current/ks4_maths_tg_h_6_1.doc





Schemes of Work

graphs from their equations.

Plot graphs with

equations ax + by

= c. Plot straight line graphs from a table of values

Remind students to always use

the y = mx +

c form of the

equation.

Plotting x and y in the wrong directions. Discuss ways of remembering

that x always goes on the horizontal axis

and y on the vertical axis.

To work out the rules of two functions machines

Active Teach

s 5 -8 is extended learning. New GCSE Foundation text book questions 1-5 Extended learning 6-11

whiteboards, if possible).

Display a sketch graph

of y = x. Tell

students that this graph meets the axes at 45° (assuming the scales are the same for both axes). Use the

graph of y = x to check students’ suggested gradients for the first graph. Is the gradient less than 1? Equal to 1? More than 1?

Repeat with further sketch graphs. Use students’ answers to highlight any misconception













Schemes of Work

s, reiterating how you can tell if a gradient is positive or negative and including some graphs with

negative y-intercepts. Draw and label the graphs of y=-3x+2

9. Lesson plan

● Sketch graphs using the gradient and intercepts.

● Find the equation of a line, given its gradient and one point on the line.

Find the gradient of a line through two points.

● Students

may use x-

and y-

coordinates in different orders when substituting values into formulae for gradients. Encourage them to label the points A and B to avoid confusion.

Pick two points

What types of lines will never intersect and why?

Video example Flip charts on Find a gradient. Board works slides, maths Active Teach

New GCSE higher text book page number 164 questions 1-10. *Question 11 -15 is extended learning New GCSE Foundatio

Ask students to write down three things they learned today, and one thing they still want to improve to refer to in future. Draw the graph of y=x+1






Schemes of Work

from a line and find the difference in y and x axis than divide to find the gradient.

n text book Questions 1-4. *Question 5 -11 is extended learning

10. Lesson plan

Equation of lines Can I draw equation of a line? Can I draw and interpret graphs from real data?

● Draw and interpret distance-time graphs.

● Calculate average speed from a distance-time graph.

● Understand velocity-time graphs.

Find acceleration and distance from velocity-time graphs.

Write the values of each arrow pointing to

Video Example Flip charts on Drawing real graphs Active Teach

New GCSE higher text book page number 166 questions 1-9. *Question 10 -12 is extended learning New GCSE Foundation text book questions 1-7. *Question

*Question Display a distance–time graph and ask students to write a story to describe the journey. You can use nursery rhymes as an example, such as Red Riding Hood’s journey through the woods. They must include reference to all sections of the graph and use words to describe the relative speed




https://www.mathswatchvle.com/video/mw-clip.php












Schemes of Work


from one part of the graph to another. Draw a real life graph against the number of hours worked and the amount paid.

11. Lesson plan

● Find the coordinates of the midpoint of a line segment.

● Find the gradient and length of a line segment.

Find the equations of lines parallel or perpendicular to a given line



Understand what is y=mx+c

Which of these equations give parallel lines?

Video Example Flip charts on Gradient and intercept Active Teach

New GCSE higher text book page number 174 questions 1-4. New GCSE Foundation text book questions 1-12.


In pairs, students should make a list of the key points from this lesson.

Ask them to then refer back to the lesson objectives.

Which questions did you feel confident answering? Which questions did










Schemes of Work

you find difficult? What does the gradient represent? And what does the y intercept represent?

12. Lesson plan

Equation of perpendicular Lines



Find the equations of lines parallel or perpendicular to a given line.

Find the equations of perpendicular to a given line What is a parallel and perpendicular line draw one in your book?

Copy and fill the table of values and what type of line is it? https://www.activeteachonline.com/product/view/id/384/page/266/mode/dps

Video Example Flip charts on Gradient and intercept Active Teach

New GCSE higher text book page number 165 Questions 5-11. *Question 11 -14 is extended learning New GCSE Foundation text book Questions 1-9. *Question

In pairs, students should make a list of the key points from this lesson.

Ask them to then refer back to the lesson objectives.

Which questions did you feel confident answering? Which questions did you find difficult?





https://www.mathswatchvle.com/video/mwclip.php



Schemes of Work


Find the equation of the line, the gradient and the y intercept

12. HW lesson on equation of lines.




Do few questions on the HW corrections. Can use active teach text book for reference.

End of unit test q2 and 8



14. Simultaneous Equations: both linear equations

Can you solve linear simultaneous

What do you mean by simultaneous equation? How can you solve simultaneous equation using elimination method?

Using a venn diagram find as many solutions for the two

video New GCSE higher text book

New GCSE higher text book page number 287-288

Reflection on elimination method Which method










Schemes of Work

equations with same coefficients using elimination method.

Foundation students solve equations with both + signs for the elimination variable.

Can you substitute value of one unknown in one of the equation to find the other?

equations x+y 5 x-y 7 hels to reinforce the idea of Venn diagram. Foundation starter

page number 287-288

questions 1- 7

do you refer and why? http://activetea.ch/1NSbCfI

15. Simultaneous Equations :both linear equations

• Can you solve linear simultaneous equations with different coefficients using elimination method. • Foundation students solve equations with

How can you eliminate variables with different coefficients? Can you construct equations in a real life context?

Write a real life example/ story with two unknowns. Give a real life situation like two chicken wings and 2

video New GCSE higher text book page number 288-289 Questions 10-14. Questions -290

Exam question to construct and solve equations Go through different methods and justify the answers/methods



http://activetea.ch/1NSbCfI

http://activetea.ch/1NSbCfI
















Schemes of Work

both ‘–‘signs for the elimination variable.

fries cost £1:30 and 3 fries and 4 wings cost £1:80, which one is cheaper, why? Justify mathematically.

*Question 2 -9

16. Simultaneous Equations :linear and quadratic

Understand the difference between linear and quadratic equations.

Understand and justify that there are 4 solutions to the equations.

To be able to

Reasoning question which shows a graphical representation of simultaneous equations Students to justify the answer. Foundation students continue with linear simultaneous equations

video Active teach age 292-93

New GCSE higher text book page number 292-293 questions 3-

Exam style question
















Schemes of Work

solve equations using substitution method..

To understand that one equation represent a curve and the other represent a line.

Use real life context to construct and solve simultaneous equations

17. Simultaneous equations: Linear and quadratic

• Understand that x^2+ y^2 r^2 represent a circle.

Reasoning • An equation of a curve or line given and find out as many points as possible which satisfies that equation.

video Foundation students continue

New GCSE higher text book page

Exam question Exam question 2






Schemes of Work

• Understand and justify that there are 4 solutions to the equations.

Understand that the symmetrical nature of the circle may lead to same answers with different signs, but not always the case.

• To be able to solve equations using substitution Method. • To understand that one equation represent a circle

• Discuss their findings? What shape can you see?

with linear simultaneous equations, more practise from Collins foundation book

number 293 Question 12




Schemes of Work

and the other represent a line.

18. Simultaneous Equation: graphical method

To be able to draw lines when two linear equation are given.

To understand that the crossing point of the two lines gives the solution of the simultaneous equations

To know that the solution has only one set of points which lies

• An equation of two lines given and find out as many points as possible which satisfies that equations. • Discuss their findings? What shape can you see?

video Foundation students continue with linear simultaneous equations, more practise from Collins foundation book

New GCSE higher text book page number questions

Exam style question




Schemes of Work

on both lines.

To be able to justify and notice the equation of parallel and perpendicular lines.

19. Simultaneous Equation: linear and quadratics; graphical method.

• To be able to draw curves/ circles when linear and quadratic equation are given. • To understand that the crossing point of the curve and a line gives the solution of the simultaneous equations • To know that the solution

An equation of a circle given and find out as many points as possible which satisfies that equation.

An equation of a curve or line given and find out as many points as possible which satisfies that equation.

Discuss their findings? What shape can you see?

video Foundation students continue with linear simultaneous equations, more practise from Collins foundation book

New GCSE higher text book page number questions

Exam question Show that question geometrically and check the solution by doing algebraic method.



Schemes of Work

have two sets of points which lies on both curve and the line. • To be able to justify and notice the equation of parallel and perpendicular lines.

20. HW lesson on simultaneous equation




Do few questions on the HW corrections. Can use active teach text book for reference.

End of unit test q2 and 8







Schemes of Work

21. Rearranging

the formulae

Re-arrange the subject of the formulae

Make t ths subject S=d/t Make x the subject Y= ax + b /c Make v the subject t=v+3

Display a rectangle with sides labelled 5 m and 7 m. Find the perimeter (answer: 24 m). How did you work it out? Elicit the general formula for the perimeter of a rectangle of width

w and length l. Explain that the formula can be written with or

without brackets: P = 2w + 2l or

P = 2(w + l). Check that it works

by substituting w = 5 and l = 7.

Write down 3 example in real life where you substitute

Video Example Clip 107 maths watch

New GCSE higher text book page number 38 Questions 1-15. maths watch worksheet

Ask students to suggest formulae they have seen previously in maths and other subjects. Pick one of these and illustrate its use by substituting in values or demonstrating a rearrangement.

Write down 3 key words and explain to the class

22. Change the subject of a formula where the power of the subject appears

Find the values of x. Y=5x-2 y=2 Make a the subject of the formulae v=u+at Make y the

Display the following information.

Temperature is often

Video Example Video Example

New GCSE higher text book page number 532 questions 1-12.

Ask students to list the key steps needed to solve Q9a.

Encourage them to use formulae to





Schemes of Work

Change the subject of a formula.

subject H= xy –ty Make 5 the subject 8=5+3

measured in Celsius (°C) or Fahrenheit (°F).

The freezing point of water is 0 °C or 32 °F.

The boiling point of water is 100 °C or 212 °F.

Ask students if there is a temperature at which the Celsius and Fahrenheit readings are the same.

New GCSE Foundation text book page number 134 questions 13-14.

form and solve an equation. For example,

2l + 2w = lw.

Suppose l =

3. 6 + 2w =

3w, leading

to w = 3. Encourage students to check their answers.

23. Solve

inequalities and show the solution on a number line and using set notation.

Solve simple linear inequalities.

Write down 4 integers that satisfy the inequality

Solve the inequalities

What do the following mean as ‘greater than’,

Display the following two lists, with the entries in random order.

> greater than


New GCSE higher text book page number 294 questions 1-7. New GCSE Foundation text book page number

Ask students to write down one thing they have learned in the lesson that they didn’t know before and share it with the person sitting next to them.

Display a number line spanning





Schemes of Work

‘greater than or equal to’, ‘less than’, ‘less than or equal to’ and ‘equals’.

≥ greater than or equal to

< less than

≤ less than or equal to

= equal to

Ask students to match the symbols to the correct meaning.

294 questions 1-6.

from –5 to 5.

Ask students to draw the solutions to the following inequalities on the number line.

2x > 4

2x 4

2x < 4

2x 4 24. Solving

Inequalities:

Write down whole numbers which satisfy an inequality.

What happens when you multiply and divide an inequality by a negative What is an integer and write it down

What are the possible interger values of x -5 <x<4


New GCSE higher text book page number 294 questions 8-15. New GCSE foundation text book page number 131

Swap books and write down a question from today’s lesson Write the new words you have learned this lesson and what they mean in mathematics





Schemes of Work

questions 1-6

(also alternative meanings in other curriculum areas)

25. Interpret graphs of inequalities and regions

Represent inequalities on a number line.

Solve the inequality and show its region

y < 2x + 5 and display a coordinate grid. Ask a student to come to the board and mark on points that satisfy this inequality What do the symbols mean on the inequality signs? What does a hollow and solid circles represent

M is at least 55 and at most 63 represent this on a number line.


New GCSE higher text book page number 475 questions 1-14. New GCSE foundation text book page number 130 questions 6-10.

Suggest the inequality if the solution is

: 4 4x x x

.

Is there more than one possible solution? Where can you use/apply this skill in other areas of mathematics or in other subjects?





Schemes of Work

26 Solving quadratic inequalities.

Solve two-sided inequalities.

Two-variable

equation, y = –x2 + 4, and

consider where its graph is below

the x-axis.

Solve 2x2 +

4x > x2 – x – 6.

Explain the term parabola. List integer values that satisfy an inequality

On mini whiteboards or paper, ask students to write an inequality for each of the following real-life events.

More than 30 mm of rain fell yesterday.

The film was an 18 certificate.

My steak weighs between 100 and 200 g.

The number of students in a class is between 18 and 27.

Matthew never arrives at school later than 8.30 am.

Chloe never arrives at school before 8.30 am.

Sasha takes between 3 and 4 minutes to iron a


New GCSE higher text book page number 478 questions 1-10. New GCSE foundation text book page number 131 questions 1-12.

Solve x2 +

2x – 8 < 0.

Write your answers in your books and sketch the graph

Solve the

inequality 2x – 3 ≥ 12 and represent the solution on a number line.

Write down all the integer values that satisfy the inequality 7 ≤

3x < 24.





Schemes of Work

blouse.

Every student scored above 70% in a test.

27. Solve quadratic equations using an iterative process.

Substitute values into equations and then solve.

y = x2 – 3x – 1 Ask pupils to sketch this graph. Write the set of values that satisfy

Find the value of y = s+2 S=4

What is the inverse of each operation X9, -3, +6


New GCSE higher text book page number 484 questions 11-14. New GCSE Foundation text book page number 133 questions 1-10.

Ask each student to write one mathematical word they have used in the lesson on a piece of paper. Ask them to swap with a partner, who must then explain its meaning. Self-assessment record what you’ve learnt, any difficulties you have had and set your personal targets

20. HW lesson on Inequalities and re-

To be able to

Hw corrections/ragging if needed, it can be peer, self or

Do few questions on

End of unit test

Pupils to identify one

https://www.activeteachonline.com/product/view/id/405/pagehttps:/www.activeteachonline.com/product/view/id/405/page/480/mode/dps/476/mode/dps






Schemes of Work

arraging the formulae.

go through the HW and clarify any misconceptions.


computer generated corrections. the HW corrections. Can use active teach text book for reference.

q2 and 8 main misconception and then work on the feedback, use it as a learning tool, can plan a session to present it as a starter for the next lesson.

29, 30,31

Revision 1 To be able to revise and clarify all the misconceptions regarding the topic. Time given for the students to ask any questions.

Teachers to produce the past exam paper on equations, lines and inequalities on three different days. Can use the



Schemes of Work

resources and the end of unit tests available in the book

32. Assessment 1

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