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Stratford School Academy Schemes of Work Number of lessons (between 6&8) Content of the unit Assumed prior learning (tested at the beginning of the unit) 27 Direct and Indirect Proportion (2 weeks) Similarity and congruence (2 weeks) Pythagoras and Basic Trigonometry ( 2 weeks) (Edexcel Scheme of Work Unit 12: Similarity and congruence in 2D and 3D) Students should be able to find a percentage of an amount and relate percentages to decimals. Students should be able to rearrange equations and use these to solve problems. Knowledge of speed = distance/time, density = mass/volume. Students should be able to convert between metric units. Students should be able to solve simple direct and indirect proportion problems, including currency conversion. 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 R10 solve problems involving direct and inverse proportion, including graphical and algebraic representations 18. R11 use compound units such as speed, rates of pay, unit pricing, density and pressure 19. R13 understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportion 20. R14 … recognise and interpret graphs that illustrate direct and inverse proportion 21. R16 set up, solve and interpret the
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Stratford School Academy Stratford School Academy
Schemes of Work
Number of lessons (between 6&8)
Content of the unit
Assumed prior learning (tested at the beginning of the unit)
27 Direct and Indirect Proportion (2 weeks)
Similarity and congruence (2 weeks)
Pythagoras and Basic Trigonometry ( 2 weeks)
(Edexcel Scheme of Work Unit 12: Similarity and congruence in 2D and 3D)
Students should be able to find a percentage of an amount and relate percentages to decimals.
Students should be able to rearrange equations and use these to solve problems.
Knowledge of speed = distance/time, density = mass/volume.
Students should be able to convert between metric units.
Students should be able to solve simple direct and indirect proportion problems, including currency conversion.
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
R10 solve problems involving direct and inverse proportion, including graphical and algebraic representations 18. R11 use compound units such as speed, rates of pay, unit pricing, density and pressure 19. R13 understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportion 20. R14 … recognise and interpret graphs that illustrate direct and inverse proportion 21. R16 set up, solve and interpret the
Stratford School Academy Stratford School Academy
Schemes of Work
answers in growth and decay problems, including compound interest. R6 express a multiplicative relationship between two quantities as a ratio or a fraction • R12 compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors • G5 use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) G6 apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including … the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs • G7 identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors) • G17 … calculate: surface area and volume of spheres, pyramids, cones and composite solids • G19 apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures
Stratford School Academy Stratford School Academy
Schemes of Work
Lesson
Clear learning intentions
Clear success criteria
Hook
Presentation of content
Guided practice
Independent practice (homework)
Closure
1. Use relationship involving ratios.
Lesson plan
Convert between currencies and measures.
Which of these ratios are equivalent 1:3, 2:5, 4:7, 6:15 5:7.5
Video Example
New GCSE higher text book page number 103 Questions 1-8.
List three
things you
have learned
today
2. Unit proportion
Lesson plan
Recognise and use direct proportion.
Are these pairs of quantities in direct proportion?
a. 10 bread rolls cost £1.60, 15 rolls cost £2.24
Play snap with ratios. Ask students to write three different ratios in their books and stand up. Call out a ratio. If the student has that ratio (or an equivalent ratio) in their book, they can sit down. Do not always call out a ratio in its simplest form. With the final few students, ask them to simplify or find an equivalent ratio to a given example before sitting down. Alternative starter
Video Example
New GCSE higher text book page number 104 Questions 9-15.
Discuss quantities that have a linear relationship but are not in direct proportion (such as the number of miles travelled in a taxi and cost of the taxi fare) to develop understanding
Stratford School Academy Stratford School Academy
Schemes of Work
of direct proportion. What is different about these kinds of relationships? Use graphs to illustrate if desired.
3. Direct proportion Lesson plan
To write and use equations to solve problems involving direct proportion.
A wildlife sanctuary has 7 adult tigers and 2 tiger cubs. What proportion of the tigers are cubs?
If 5 apples cost £1.25 how much would 7 cost?
Video Example
Mathswatch Worksheet Questions 1-3 Active teach page 588-591
Pixl resources homework Grade A/A* WORK ratio and proportion 1
Write the
new words
you have
learned this
lesson and
what they
mean in
mathematics
(also
alternative
meanings in
other
curriculum
areas)
Exam
question
Stratford School Academy Stratford School Academy
Schemes of Work
4. Direct proportion with squares and square roots Lesson plan
Solve problems involving square and cube proportionality
Able to understand the use of proportionality statements to write equations with different variables.
Understand the algebraic method to solve proportionality problems.
example Page 590-592 Question 1-13
Exam
question
5. Inverse proportion
Lesson plan
Solving inverse proportion using a constant
P is inversely proportional to V When v=8 p=6
a. Find a formula for P in terms of V
M is directly Proportional to L3 When L=2, M=160 Find M when L = 3
Video Example
Mathswatch Worksheet Questions 4-5 and next page down on
Students
write their
own
questions
based on the
objective of
the lesson
Stratford School Academy Stratford School Academy
Schemes of Work
b. Calculate value for P when V=2
the worksheet. Active teach page 592- 593 Pixl resources on proportionality 2
(these
questions can
then be
selected
randomly and
used with
the rest of
the class)
Exam question
6. Inverse proportion
Solving inverse proportion using a constant
P is inversely proportional to V2
When v=8 p=6 c. Find a
formula for P in terms of V
d. Calculate value for P when V=2
Justify your answer : hook activity
Video Example
Mathswatch Worksheet Questions 4-5 and next page down on the worksheet Active teach page 594-595
Students
write their
own
questions
based on the
objective of
the lesson
(these
questions can
then be
selected
randomly and
used with
the rest of
the class)
Stratford School Academy Stratford School Academy
Schemes of Work
Exam
question
7.hw HW lesson on proportionality
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 for reference.
Use the text
book on
extend ,
strength and
check
Page-611-619
Stratford School Academy Stratford School Academy
Schemes of Work
8. Geometric proof and congruence Lesson plan
Show that 2 triangles are congruent
Which triangles are congruent and draw some triangles.
Video Example
New GCSE higher text book page number 364 -366 Questions 1-11
List three
things you
have learned
today
Exam
question
9. Geometric proof and congruence
Lesson plan
What are the conditions for congruence in triangles? How can you prove two triangles are congruent? Understand SSS,SSA,SAA,RHS
Fgh is an equilateral triangle. Point e lies on fh eg is perpendicular to fh. Prove that triangle fge is congruent to triangle ghe.
Video Example
New GCSE higher text book page number 367-69 Questions 1-12
Pixl resources grade a/a* congruence homework 1 and 2
List three
things your
neighbour
has learned
today
Exam
question
10.Similarity proofs
How can you prove that two triangles are similar?
To be able to identify the corresponding sides and angles.
Wxyz is a rectangle
Video Example Use only the first part of the video.
Past exam questions on the proof Old higher GCSE books page 128 q 3-5
Write the
new words
you have
learned this
lesson and
what they
mean in
mathematics
(also
Stratford School Academy Stratford School Academy
Schemes of Work
Prove that wxy is similar to triangle xyz.
Page 130 q8
alternative
meanings in
other
curriculum
areas)
Exam
question 6
11.similarity with lengths Lesson plan
Use the ratio of corresponding sides to work out scale factors
To be able to understand about the scale factors. Identify the corresponding sides Able to calculate the missing sides of similar shapes using the linear scale factor. State if this rectangle is similar 24 by 9 And 8 by 3
Video Example
New GCSE higher text book page number 368 Questions 9-13. Old higher book page 126-127
Exam
questions
Take one
minute to
compose two
sentences in
your head to
explain what
we have
learnt and
how we have
learnt it,
using the key
words from
the lesson
Stratford School Academy Stratford School Academy
Schemes of Work
12. Similarity with areas Lesson plan
Use the link between linear scale factor and area scale factor to solve problems
What do you mean by k2.
How can you find the new area when corresponding lengths are given.
How can you find length when the corresponding area are given.
Video Example
New GCSE higher text book page number 375 Questions 7-16 Old higher GCSE books page 506-507
Where can
you
use/apply
this skill in
other areas
of
mathematics
or in other
subjects?
Exam
question
13. Similarity with volumes. Lesson plan
Use the link between linear scale factor and volume scale factor to solve problems
What is the enlargement that maps from triangle y on to z Which has length
a. 48mm by 62
A. 9.3cm by 7.2cm
Video Example
New GCSE higher text book page number 374 Questions 1-8. Old higher GCSE books page 509-510
Pixl resources grade B Similar shapes homework 1 and 2
In pairs,
answer this
question on a
post-
it/sheet,
stick it on
the board
and review.
Does
everyone
agree?
Exam
questions
Stratford School Academy Stratford School Academy
Schemes of Work
16. More similarity
Use the link between volume scale factor and area scale factors to solve problems
a. Us the links between scale factors for length, area to solve problems.
Example New GCSE higher text book page number 378 Questions 1-15. Old higher GCSE books page 510-511
Show your
work to your
neighbour,
work in pairs
to set
targets
Exam question
19. HW lesson HW lesson on similar shapes
To be able to go through the HW and clarify any misconceptions.
To give constructive feedback/ peer /self or TF/ both
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 for reference.
Unit test lesson plan
Stratford School Academy Stratford School Academy
Schemes of Work
written and verbal
20.Pythagoras theorem Lesson plan
Calculate the length of the longer side in a right angle triangle.
Calculate the length of the missing hypotenuse in a right angle triangle with base 7cm and height 6cm
Example Video
New GCSE higher text book page number 132 Questions 4-12.
Self
assessment –
record what
you’ve learnt,
any
difficulties
you have had
and set your
personal
targets
Exam
questions
21. .Pythagoras theorem Lesson plan
Calculate the length of the shorter side in a right angle triangle.
Find the square root of 16
b. 100 c. 25
To be able to square root numb
Example Video
New GCSE higher text book page number 134 Questions 1-8.
Predic
tion -
what
do
you
think
will
happe
n
next?
Stratford School Academy Stratford School Academy
Schemes of Work
ers
Find the shortest side of a triangle when the hypotenuse id given.
Exam
questi
ons
22.Trigonometry Lesson plan
To be able to find the missing sides of a triangle To solve problems involving trig ratios.
Find sin , cos, tan of the given value• To be able to identify which formula to use • understand and use SOHCAHTOA. Find the missing sides of a triangle using trig ratios.
Video example
New GCSE higher text book page number 136-139 Questions 1-11
Self assessment – record what you’ve learnt, any difficulties you have had and set your personal targets Exam question 4 Exam question
Stratford School Academy Stratford School Academy
Schemes of Work
23. Trigonometry Lesson plan
To be able to find the missing anglesof a triangle To solve problems involving trig ratios.
To be able to calculate the inverse trig functions.
Find the missing angles in a triangle using trig ratios.
Calculate the angle of elevation and depression
Video example
New GCSE higher text book page number 140 -141 Questions 1-11
Pixl resources grade B trig and Pythagoras homework 1 and 2
Self assessment – record what you’ve learnt, any difficulties you have had and set your personal targets Exam questions Exam question 2
24. Trigonometry
To be able to find the exact value of trigonometric ratios.
Understand what do you mean by the exact value
Use trigonometric functions
Use question 12 on page 142 to explain the work. Maths watch clip
New GCSE higher text book page number 142 -143 Questions 12-14
Pixl resources grade B trig and Pythagoras homework 1 and 2
question
Stratford School Academy Stratford School Academy
Schemes of Work
without a calculator
Find the relationship between the exact values for eg; sin 30= cos 60
25. HW lesson on Pythagoras and Trig.
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 for reference.
Stratford School Academy Stratford School Academy
Schemes of Work
26,27 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 resources and the end of unit tests available in the book.
28. Assessment
