Nonsuch High School For Girls: Lesson Plan Outline
| Teacher: Gavin Wilson for Elly Cook
| Room:
| Date: 28th January 2010
| Lesson Start-time: 9.40
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| Module/Topic: Algebra: The roles of letter symbols in equations, functions, formulae and identities
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| Number of Girls: about 30
| Lesson Duration: 60 minutes
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| National Curriculum Reference: N5a
| National Curriculum Level Range: 7C to 8A
| Class/Set: Year 8 Ma2
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Lesson Objectives
- Explain the distinction between the words equation, formula, identity, function and expression.
- Know the meaning of an identity and use the ≡ sign.
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Possible Pupil Misconceptions:
- Avoid interpreting the equals sign as 'makes' -- i.e. it is merely the answer to a calculation. The symbol = denotes equality.
- Avoid misuse of the equals sign in a chain of steps -- e.g. 56 + 30 = 86 + 7 = 93
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Vocabulary:
- equation, expression, function, identity, formula, variable, algebra
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Lesson Context:
- This is a one-off lessons to demonstrate my suitability for the school to Elly Cook (potentially my mentor) and Philip Sides.
| Prior Pupil Knowledge:
- Experience of using a letter to represent a number.
- Know how multiplication and division are represented in algebraic expressions, e.g. 2 x n is written as 2n.
- Manipulate algebraic expressions by:
- collecting like terms,
- multiplying a single term over a bracket,
- taking out common factors, and
- cancelling common factors.
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Resources/Equipment/ICT:
- Interactive Whiteboard
- PC with PowerPoint
- Boardmarkers
- 33 copies of worksheet
- USB memory stick
- Textbook: 9B Maths Links (Oxford)
- Textbook: Koll and Mills: Y9 Algebra (A&C Black)
- Box for 'Professor Layton' game.
| Extensions
- Can you prove that the sum of three consecutive numbers is always a multiple of three?
- Difference of two consecutive squares:
- Pick any two consecutive numbers.
- Square each, and find the difference, ignoring the sign.
- Add the two original numbers together.
- Why are the answers in steps 2 and 3 the same?
- Prove or disprove this conjecture: 'The square of every even number is a multiple of 4.'
- And this: 'The square of every odd number is odd.'
- And this: 'A square number with a units digit of 1 is the square of a number with a units digit of 1.'
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Health and Safety:
- No particular concerns, due to resources.
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| Cross-curricular links (Literacy, Numeracy, Citizenship, Spirituality, ICT):
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| Homework
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| Section
| Duration
| Key Learning Points and/or Resource Instructions
| Assessment (methods and exercises)
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| Pre-Entry
| 2 mins
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- Introduce myself to Mrs Cook.
- Sign on to PC.
- Check I know how to load and display PowerPoint slides.
- Write the lesson title and date on the board.
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| Entry
| 2 mins
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- As per normal Nonsuch procedure.
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| Registration / Introduction
| 2 mins
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- (Assume Mrs Cook will either perform this or give me instructions.)
- Introduce myself as Mr. Wilson. "I'm your maths teacher for today."
- Today's lesson title is: Letter symbols in equations, functions, formulae and identities. Do you write the title down in your exercise books?
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| Starter A
| 5-10 mins
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- My daughter Erika was here but left two years ago, a year before most of you arrived, I believe. We can make a puzzle out of this:
- Two years ago, I was three times older than Erika.
- 14 years from today, I will be twice her age.
- How old is she today?
- Let's give you three minutes to solve it. If, rather than work alone, you'd prefer to work on this puzzle with the girl sitting next to you, that's fine.
- (Demonstrate solution -- she's 18 now -- on whiteboard.)
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- Put your hands up if you got the correct answer.
- For those of you who didn't get there, where did you get stuck?
- Rather than set up an equation, did you take a completely different approach? Perhaps trial and error? Perhaps you guessed her age from the photograph and tested whether it worked?
- Did you get stuck setting up the right expressions for our ages?
- Or did you go astray in manipulating the equations?
- If you'd like more practice with hundreds of puzzles, some like this and many that are completely different, I'd recommend this game for the Nintendo DS: 'Professor Layton'.
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| Starter B (if A is too difficult, or if it was too easy)
| 5-10 mins
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- Rectangle length equation
- Rectangle Perimeter equation
- Cross equation
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- Put your hands up if you got these right.
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| Main
| 35 mins
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- Write up the 'equation' 4(x + 1) - 3(x - 1) = x + 7
- How many of you think you can solve this one?
- So what does x equal?
- This relationship isn't an equation. It's what we call an identity, because it is always true, no matter what the value of x.
- So we add a third bar to the equals sign, to create ≡.
- (Hand out the worksheet.) Can you have a go at exercise B on the left-hand side of this worksheet? It shouldn't take you very long. I'll give you four minutes for this exercise.
- Check they get the answers correct. So is everyone happy they now understand what an identity is?
- Write the words 'function', 'equation', 'expression', 'formula' and 'identity' on the board.
- Ask them to discuss in pairs/groups what they mean.
- List some of the suggestions on the board to see if the class can pick out the characteristics of each.
- Using these suggestions, ask if they can match the word to the algebraic expression:
- 4x + 3 = 47 (equation)
- 6x + 7 (expression)
- V = IR (formula)
- y = 3x - 4 (function)
- 4(a + 1) ≡ 4a + 4
- Display a Powerpoint slide: Letter symbols represent:
- particular unknown numbers in equations—for example, in the equation 5x + 5 = 2x + 31, x is a particular unknown number. There is only one value of x that can satisfy this equation.
- variables and constants in algebraic expressions—for example, in the expression 5x2 + 4.
- variables in formulae—in the formula v = u + at, v, u , a and t are variable quantities related by the formula. Once the values of three of them are known, the fourth value can be calculated.
- identities are always true, no matter what the value of the letter symbols—for example, 4(a + 1) ≡ 4a + 4
- in functions such as y = 8x + 11, y can be calculated given any chosen value of x.
- Ask them to do questions from Exercise 4a on the worksheet, subject to time remaining.
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| Plenary
| 10 mins
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- Ask the children to take it in turns to give an example of an identity, formula, equation and function. (They can make them up if they wish.) Go round the class asking the pupils to come to the board, write one up, and then ask the other pupils to state what it is and explain why.
- Algebra Pairs (two Pelmanism games) on www.mymaths.co.uk
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| Dismiss
| 2 mins
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| TOTAL
| 60 mins
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