WORKING PAPER SERIES

WORKING PAPER SERIES

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Institutional Members: CEPR, NBER and Università Bocconi WORKING PAPER SERIES Understanding the Income Gradient in College Attendance in Mexico: The Role of Heterogeneity in Expected Returns Katja Maria Kaufmann Working Paper n. 362 This Version: March 2010 IGIER – Università Bocconi, Via Guglielmo Röntgen 1, 20136 Milano –Italy The opinions expressed in the working papers are those of the authors alone, and not those of the Institute, which takes non institutional policy position, nor those of CEPR, NBER or Università Bocconi.
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Maths lesson plan 



This lesson plan is aimed for a Year 11 Foundation class
It is a revision lesson on algebraic expressions, equations and simple factorizing.

It is common practice that for a revision lesson, the teachers usually prepares a mixed set
of examples and exam questions on one or more topics; students then work
independently; later they discuss answers with the rest of the class and the teacher.
Although this always tends to be a useful exercise, it sometimes happens that not all
students are engaged in their learning and progress.
Also, students are often not given the opportunity to be analytical and reflect on their
working and answers.

Hence, this revision lesson, not only gives the students the opportunity to revise key skills
in algebra, but also makes them become critical thinkers and instructional resources for
one another. In this lesson, the teacher takes on the role of a facilitator rather than the
usual role of an instructor.

DETAILS OF LESSON  
Context:  Technical  Resources: 
In view of the forthcoming mocks, today’s lesson is the  Vocabulary:   PowerPoint slides 
first out of three that revises key algebraic skills.   Simplify  Starter activity  
  Expand  Carousel  worksheets  +  answer 
  Factorize  sheets  
Solve  Hw worksheet  
Substitute  Plenary exam questions  
   
Learning Objective(s):  Success Criteria /Learning Outcomes ‐ By the end of 
the lesson: 
1. Recall what are the 5 basic skills of algebra   All students must be able to simplify simple 
2. Revise  expressions,  equations  and  simple  expressions and solve 2 – step equations  level 
factorizing   D 
3. Become more analytical – aware of what the   Majority of students should also be able to 
examiner is looking for; giving more attention  expand  brackets  and  factorize  expressions 
to working and marks; providing feedback that  level C 
helps them reflect on their work; more aware   Some students could accurately identify what 
of time.  they are expected to do to against the amount 
  of marks given level C 
 
Personal Learning and Thinking Skills  Programmes  of  Citizenship/PHSE/ECM 
study/specification 
Independent Enquirer: Students work independently as  Specification –   ECM:  
they  try  to   recall  and  practice  the  5  algebraic  skills  Foundation GCSE –  All  students  participate  in  a 
(starter)  Ma2 – 5b and 5e  range of engaging approaches 
Creative Thinker: The 5 tasks during the main activity    to  learn  and  revise  the 
will give the students an opportunity to think critically  algebraic  skills,  which  are 
and  constructively  otherwise regarded as boring, 
Reflective Learning: Students are given the opportunity  useless and difficult.  
to evaluate their work and that of their peers   
Team  workers:  Students  work  in  pairs  during  main 
activity and plenary – the carousel activity ensures that          
each pair is working on different tasks at the same time 
and must rely on each other to complete the questions. 

 
Independent Timing  Teaching and Learning activities: 
enquirers   Starter activity: 
5  +  5  5 S’s: Students come in class to find the starter activity on their desk – 
mins  the 5Ss of algebra – helps them to recall and practice the 5 algebraic 
Afl: skills. 
Setting Teacher explains the big picture and aims of lesson and success criteria. 
learning targets  
and   Main activities of lesson: 
expectations to 40 mins  In pairs, students complete 5 tasks. (attached)  
demonstrateTask A highlights the importance of working and checking out answers. 
Task B involves a ranking exercise which makes the students aware of 
what the examiner is looking for. 
Task  C  and  D  use  the  ‘find  and  fix’  technique  which  helps  students 
Carousel activity
become analytical by spotting mistakes, justify their answers and reflect  gives students
upon them.  opportunity to be
Task E is about factorizing which students find most difficult. So in this  team workers,
task  part  of  the  solution  is  given  which  activates  the  students  to  critical thinkers
complete the solution and consequently, are able to complete the other  and reflective
examples.   learners.
 
The 5 tasks rotate between 5 pairs of students.  
The tasks are timed – 5 minutes each to create that sense of exigency 
when working within a given timescale.  
The tasks are rotated so that every pair is working on a different task 
and cannot discuss with other groups and have to rely on each other for 
help.  Afl:
At the end, students are given the answers to assess their work.    Self-assessment
  Plenary: 
10 mins  Two exam questions are placed repeatedly around the room.  
This plenary gives Each pair of students will stand in front of one question and complete 
the opportunity to the task. 
students to be They then move to the next question and evaluate their peer’s working 
critical thinkers and and answers. They also write 1 star and 1 wish comment on their peers’ 
reflective learners. work. Students then go back in front of their original question to view 
There is also peer-the corrections and the comments written by their peers.  
assessment.

Key questions:  Assessment opportunities: 
What are the 5 skills of algebra?  Students  are  given  opportunities  for  self‐
How can you check your work using the answer?  assessment and peer‐assessment.  
How  can  you  make  sure  you  achieve  the  full  Teacher  will  assess  pupils’  learning  by 
marks?  observation,  questioning,  the  plenary  task  and 
  through the HW task. 
Homework: 
The students complete a mixed exercise on algebra.  


submitted by Etienne Ebejer 
         



Resources follow below:
Starter

Name:
The 5 Ss of Algebra
Fill in the blanks 
What are the 5Ss of and complete the 5 
algebra?tasks. 
2a +3b + 5a ‐b=
submitted by Etienne Ebejer SI______
         




Carousel questions
Task A

Solve the equation 3x + 2 = 17

Answer: 5.



1. How many marks do you think you will get if you only wrote the
answer?

2. Why?


3. How can you use the answer to check if it is correct? Show what
you would do.



4. Now complete the question to ensure you will get all the full 3
marks.




5. Similarly solve:
a. 5x – 3 = 2 b. 12x – 7 = 11









submitted by Etienne Ebejer 
         





Task B


Solve the equation 5x + 2 = 2x +11
(3 marks)


1. Three students got the same answer but completed the question in
different ways.
Put the 3 solutions in order, starting with the one which you think is the
least favourable way of showing the solution.

Solution A Solution B Solution C.
3x = 9 5x – 2x = 11 – 2 5x – 2x= 3x = 11-2
x = 3 3x = 9 x = 9 = 3
x = 9 3
3
x = 3

Write answer here: ________ _________ _______________

2. How many marks do you think each solution got?
Solution A: __________
Solution B: __________
Solution C: __________

3. Following the model of the best solution, now solve:
a. 7x – 3 = 5x + 28 b. 3x + 4 = 6x - 1







submitted by Etienne Ebejer 
         








Task C


Solve the equation 9(x - 6) = 2x - 5

.


1. Three students solved the equation and got three different answers.
Which solution gives the right answer? __________________

Solution A Solution B Solution C.
9x – 6 = 2x - 5 9x – 54 = 2x - 5 9x – 54 = 2x - 5
7x = 1 9x – 2x = 54 - 5 7x = 59
x = 1 7x = 49 x = 59/7
7 x = 7

2. What was wrong with the other 2 solutions?



3. How many marks do you think a question like this will have?


4. Using the right solution as your model, now solve the following
equations:
a. 8 (x + 3) = -12 – 4x b. 16x – 4 = 2(5x – 5)







submitted by Etienne Ebejer 
         









Task D


Simplify the following expressions:
a. 5c – 2d + 3c – 8d
b. 3a x 4b x 5c
c. 3(4h – 2)
2 3 d. 5a b x 3ab
.


A student wrote the following answers. They are all wrong.
For each one, circle what is the mistake and write the correct answer.

a. 5c – 2d + 3c – 8d = 2cd ____________________
b. 3a x 4b x 5c = 12ab x 5c ____________________
c. 3(4h – 2) = 12h – 2 ________________________
2 3 3 3d. 5a b x 3ab = 8a b _______________________

By avoiding the mistakes above, work out:

a. 7b – 4c – 3b + c ________________
b. 4c x 5c x d ____________________
c. 5(3h + 3) _____________________
2 2d. 10a x 3ab x 2ab ___________
submitted by Etienne Ebejer 
         









Task E


Factorize the following expressions:
2a. 15a – 10ac
2b. 20ab – 15a b
2c. x + x
2 4 d. 3a + 15a
.


1. A student dropped tippex on her answer sheet. She forgot what she had
written!
Can you help her out by filling in the blanks.

2a. 15a – 10ac = 5a (3a – __)
2b. 20ab – 15a b = __(4 – 3a)
2c. x + x = x( __ + 1)
2 4 __ __d. 3a + 15a = 3a (__ + 5a )

2. Now factorize the following completely:

a. 5ac – 10cd __________________
3b. 10a – 15a __________________
submitted by Etienne Ebejer 
         
3 4c. x + x _____________________
3 2d. 24d + 16df _________________








ANSWERS

Task A


Solve the equation 3x + 2 = 17

Answer: 5.



6. 1 mark

7. No working is shown. Just 1 mark for the answer.


8. Substitute 5 instead of x – (3 x 5) + 2 = 17.



9. 3x + 2 = 17
3x = 15
x = 5


10. Similarly solve:
b. 5x – 3 = 2 b. 12x – 7 = 11
submitted by Etienne Ebejer 
         
5x = 5 12x = 18
x =1 x = 18/12 = 1 ½


If you got all answers right or up to one wrong, then you answered a Grade D
question correctly.












Task B


Solve the equation 5x + 2 = 2x +11
(3 marks)


1. A, C, B

2. Solution A: 2
Solution B: 3
Solution C: 3

3. Following the model of the best solution, now solve:
b. 7x – 3 = 5x + 28 b. 3x + 4 = 6x – 1
2x = 31 -3x = -5
x = 31/2 = 15 ½ x = 5/3
x = 1 2/3

If you got question 3a and 3b right, then you are able to answer a Grade C question.
If you got one wrong, than that means you are not confident enough and need to practice.



submitted by Etienne Ebejer