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# Unit of work - Bedfordshire Schools

By Tony Reynolds,2014-12-08 10:56
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Unit of work - Bedfordshire Schools

Unit Algebra 3 (112113, 122125, 132137) Year Group Year 9

Time Level 5 out of 6 hours Support/Core

Teaching objectives

; Distinguish the different roles played by letter symbols in equations, identities, formulae and

functions.

; Construct and solve linear equations with integer coefficients (with and without brackets,

negative signs anywhere in the equation, positive or negative solution) using an appropriate

method.

; Represent problems and synthesise information in algebraic, geometric or graphical form; move

from one to another to gain a different perspective on the problem.

Key vocabulary

Expressions, like terms, simplify, equation

Resources

‘Constructing and solving linear equations’ Year 7 Booklet (0083 -2004G)

‘Constructing and solving linear equations’ Year 8 Booklet (0084 -2004G)

Arithmagon OHT and worksheet (attached)

Algebraic magic squares - resource (attached)

What’s missing? OHT (attached)

Pyramids and equations - OHT (attached)

Solving linear equations using a number line - OHT (attached)

Solving linear equations using a number line - worksheet (attached)

Oral and mental Main teaching Plenary

Lesson 1

Pg124 Framework: Number Magic square arrange the digits 1 to What’s missing? (OHT) Arithmagons 9 in a 3 by 3 array so that the total of the 3 ; 3x is the same as x + x (OHT/worksheet) rows, 3 columns and 2 diagonals are all the + ?

What numbers could same. ; a + 2b = 2a - ? + b + ? A, B, C, D be?’ ; 3x + 2y = 4x + y - ? + ?

‘How did you start? How did you continue?’ ; p + ? = 3p - ? + 3q q Are there any etc relationships between Draw out some useful strategies which will help A, B, C and D? to solve the problem. For example: ; All the digits will be used in the 3 rows (columns) and each row must have the same total. So the sum of 1 to 9 divided by 3 will give the magic number (15). ; The mean/median/’middle’ number (5) will go in the centre to leave 4 pairs of numbers which sum to 10. Algebraic Magic square use the strategies as above to solve the algebraic magic square (see resource sheet.) Lesson 2 Introduce the idea of Extend the laws of arithmetic to algebra and Invite pupils to demonstrate solving pyramids using solve pyramids by collecting like terms: Pg 22 how they have been solving 1 laws of arithmetic: Pg Yr 7 booklet. or 2 selected problems. 21 Yr 7 booklet Pyramids (1) Draw the pyramid on board: ‘What strategies have you n 6 8 been using for solving the

? ? equations?’ ?

Oral and mental Main teaching Plenary

I want the bottom number to be 34, what ‘Pyramids and equations’

should n be? (OHT).

‘How did you work the number out?’

‘Can I write an equation using n?’ ‘Will the same strategy help

us to solve this pyramid?’

Pg 19 Yr 7 booklet: ‘Pyramids and equations

(1)’ Q1 to 7. Link back to objectives:

Constructing and solving

linear equations. Explain that

we are going to be working

on a strategy that will help us

to solve equations of this type

as well.

Lesson 3: Model ‘Solving linear equations using a number Invite pupils to share their Pg 18 Yr 8 booklet line’ (OHT) responses to the questions

starter activity: Provide pupils with similar problems: ‘Solving (at the front or on plastic equation from a pie linear equations using a number line’ wallets they have been chart, solved on a (worksheet.) working on) from the

number line. extension problem.

Extension: Pg 21Yr 8 booklet (Double pyramid)

‘Can you derive an equation to help solve the Review the objectives and

problem?’ explain that we have been

‘What do you notice about the equation?’ using a number line to solve

(variables on both sides.) linear equations with a

‘How could you work out the value of t? variable on one side. Next

time, however, we are going

to use it to see if we can

solve equations with

variables on both sides as we

generated in this problem.

Lesson 4 ‘Was the number line useful Model the use of the number line to solve

in solving these equations?’ Ask pupils to generate equations of this type with variables on both

the linear equation sides (Pg 19 Year 8 booklet.) Ask pupils to use which would help this method to solve the double pyramid from Take feedback and ask one solve the double the previous lesson (or to verify their answer.) or two pupils to share their pyramid: solutions.

Pupils solve similar linear equations, for

n n 4 example: Present the following three

? ? 1. 5x + 3 = 2x + 15 equations:

? 2. 6x + 5 = 3x + 14 1. 4x + 7 = 2x + 13

? ? 3. 10x + 3 = 4x + 21 2. 2x + 3 = 2x + 7

n 10 6 4. 9x + 1 = 5x + 9 3. 2x 1 = x + 9

5. 4x + 7 = 2x + 13

Can anyone work out Ask pupils to use a number the value of n? There are more problems of increasing difficulty line to solve Q1 and spend a

on Pg 20 Year 8 booklet. few minutes on Q2 and Q3.

for homework.

Lesson 5

(As Pgs 23 25 in (As Pgs 23 25 in the Year 8 booklet) (As Pgs 23 25 in the Year the Year 8 booklet) 8 booklet)

Complicating the Introducing the matching method.

expression.

K Wallis 10/04

OHT/Worksheet

Arithmagons

B A 7

14

2

D 9 C

Some results Some relationships A B C D

OHT/Worksheet

Arithmagons

7

1 4

2

9

Some results Some relationships A B C D

Resource

Algebraic magic squares

a + 4b 2a + b 8a + 3b

5a + 2b 7a + 6b 7b

6a + 9b 4a + 5b 3a + 8b

Teacher note:

The sum of the expressions is 36a + 45b.

The magic number is (36a + 45b) ? 3 = 12a + 15b

The middle expression when put in order of ascending a terms is 4a + 5b

The other expressions can then be paired off e.g. 7b with 8a +

3b and a + 4b with 7a + 6b, which when added to the middle expression will give the magic number.

OHT

What’s missing?

E.g. 3x + y is the same as x + + +

1. a + 2b = 2a + b +

2. 3x + 2y = 4x + y +

3. p + = 3p + 3q q

4. 2a + = 3a + b + 3c b c

5. + q r = 3q + 4p q + 4r 2p

OHT

Pyramids and equations

8 n 3n

= 10 + 4n

OHT

Solving Linear equations using a number line

180 = 64 + 4x

180

x x x x 64

180 =

Name:______________________ Worksheet

Solving Linear equations using a number line

180 = 4x + 64 180 = x + x + x + x + 64

180 116 = x + x + x + x

29 = x

x x x x 64

Now try these the same way. i.e. Draw a number line. Show all your working. Underline your answer.

1. 3x + 5 = 17

2. 4x + 16 = 28

3. 13 + 3x = 37

4. 360 = 51 + 3x

5. 4x + 76 = 180

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