1. Algebra using brackets
Grade 7
Algebra using brackets
Expand brackets, including multiplication of binomial expressions.
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Expand brackets, including multiplication of binomial expressions.
Grade 7
Prior Knowledge
Multiplication and simplification of of algebraic terms (eg 2x + 5x = 7x, x × x = x2).
Duration
60 minutes (variable).
Resources
Slides 16 onwards are printable versions of some of the earlier slides.
Equipment
May choose to use scissors for SLIDE 19
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Starter; Basic simplification.
Teacher led activity. Of the sixteen statements, half are true and half are false, etc; could be run as a “wipeout” game, or similar. The false statements should be corrected by students. FIRST CLICK REMOVES THE INSTRUCTIONS AND REVEALS THE BOARD; CLICK ON A TILE TO TURN IT GREEN (TRUE) OR RED (FALSE). A PRINTED VERSION OF THIS SLIDE IS PROVIDED AS SLIDE 16. 10
Recap of multiplying a bracket by a single term.
Introduction using slides that adapt the “grid” method for multiplying a single by a two digit number. Followed by differentiated slide of practice questions. PRINT SLIDE 17
Mini-plenary
Pairs of brackets added together – introduces idea of simplification.
Multiplying two binomial expressions together.
Tell me three ways in which these two expressions differ; comparing expressions of the form
5( x + 1 ) + 2 ( x + 3 ) with those of the form ( x + 1 )( x + 3 )
Slides that adapt the “grid” method for multiplying two two digit numbers. Followed by differentiated slide of practice questions. PRINT SLIDE 18
15-20
Reasoning; spotting which factors expand to become which expressions. Slide 15 is actually factorising. Both slides include at least one expression of the form (x + c)2 and one of the form x2 − y2
Can you make the expressions from the factors? Is there only one pair of brackets that produces a given answer? Why is it impossible to get some of the answers? (May choose to cut out and use slide 19 as a card sort activity.) ON SLIDE 15, CLICK ON A TILE TO TURN IT GREEN (POSSIBLE) OR RED (IMPOSSIBLE).
PRINT SLIDES 19 AND 20
10-15
Next Steps
Factorising x2 + bx + c
Assessment

3. x × x = x2 y ÷ y = y g3 × g5 = g8 5a × 3b = 15ab 2x × 2x = 2x2
There are sixteen statements on the slide.
Half are true (these turn green when you click them).
Half are false (these turn red).
Find the true statements.
Explain what is wrong with each of the others.
x × x = x2
y ÷ y = y
g3 × g5 = g8
5a × 3b
= 15ab
2x × 2x
= 2x2
5p − 4p = p
y × y = 2y
x × x2 = x3
−3n × −2n
= −6n2
6a + 2b
= 8ab
6q ÷ 2q = 3
3f − 5f
= −2f
3a × b
= 4ab
m2 × m4
= m8
−m × −2m
= 2m2
z + z = z2
Skip this activity

4. Key Vocabulary
Expand Factor/factorise Simplify

5. Expanding brackets 3 × 34 3 × 30 3 × 4 34cm 3cm 30cm 4cm 3cm
Click on a box to learn more about it. Click anywhere else to advance the slide

6. Expanding brackets 2 × (x + 5) 2(x + 5) 2 × x 2x 2 × 5 10 x + 5 2 x 5
Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide

7. Expanding brackets BRONZE SILVER GOLD SILVER GOLD 3 ( x + 4 )
5 ( y + 2 )
2 ( x − 6 )
x ( x + 8 )
y ( y + 3 )
n ( n − 5 )
5 ( 2x + 1 )
3 ( 4y + z )
2 ( p − 4q )
x ( x + y )
p ( 4p + 3q )
m ( 2m − 3n )
4x ( x + y )
2y ( y + z )
2x ( x − 3w )
3x ( 2x + z )
4y ( 2y + 3z )
5m ( 2m − 7n )
SILVER
GOLD
5 ( x + 1 ) + 2 ( x + 3 )
5 ( y + 3 ) + 7 ( y + 1 )
3 ( x − 6 ) + 5 ( x − 6 )
5 ( x + 2 ) + 2 ( x − 7 )
4 ( y + 6 ) − 3 ( y − 1 )
3 ( n − 4 ) − 5 ( n − 7 )
6 ( 2x + 3 ) − 2 ( 3x + 3 )
8 ( y + 4 ) − 3 ( 2y + 1 )
x ( 5x − 6 ) + x ( x + 4 )
x ( x + 8 ) + x ( 3x + 7 )
y ( y + 1 ) + y ( y − 2 )
m ( m − 6 ) + m ( m − 7 )

8. Expanding brackets
3( x + 5 ) + +
2( x + 4 )
3x + 15
2x + 8
5x + 23

9. Expanding brackets BRONZE SILVER GOLD SILVER GOLD 3 ( x + 4 )
5 ( y + 2 )
2 ( x − 6 )
x ( x + 8 )
y ( y + 3 )
n ( n − 5 )
5 ( 2x + 1 )
3 ( 4y + 3 )
2 ( 3x − 4 )
x ( 3x + 1 )
p ( 4p + 3 )
m ( 2m − 3 )
4x ( x + y )
2y ( y + z )
2x ( x − 3w )
3x ( 2x + z )
4y ( 2y + 3z )
5m ( 2m − 7n )
SILVER
GOLD
5 ( x + 1 ) + 2 ( x + 3 )
5 ( y + 3 ) + 7 ( y + 1 )
3 ( x − 6 ) + 5 ( x − 6 )
5 ( x + 2 ) + 2 ( x − 7 )
4 ( y + 6 ) − 3 ( y − 1 )
3 ( n − 4 ) − 5 ( n − 7 )
6 ( x + 3 ) − 2 ( x + 3 )
8 ( y + 4 ) − 3 ( y + 1 )
x ( x − 6 ) + x ( x + 4 )
x ( x + 8 ) + x ( x + 7 )
y ( y + 1 ) + y ( y − 2 )
m ( m − 6 ) + m ( m − 7 )

10. Tell me three ways in which these two expressions differ
Expanding brackets
3( x + 5 ) +
2( x + 4 )
(x + 5) ×
(x + 8)
Tell me three ways in which these two expressions differ

11. Expanding brackets; binomials49
20 × 40
800
20 × 9
180 20 27
7 × 40
280
7 × 9 63 7 40 9
1323
Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide

12. Expanding brackets; binomials
x × x x2
8 × x 8x x
x + 5
x × 5 5x
8 × 5 40 5 x 8
x2 + 5x + 8x + 40
x2 + 13x + 40
Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide

13. Expanding brackets; binomials
BRONZE
SILVER
GOLD
( x + 4 )( x + 2 )
( x + 6 )( x + 9 )
( x + 7 )( x + 3 )
( x + 1 )( x + 6 )
( x + 6 )( x + 1 )
( x + 8 )( x + 5 )
( x − 3 )( x + 7 )
( x + 6 )( x − 5 )
( x + 2 )( x − 4 )
( x − 6 )( x + 2 )
( x − 3 )( x − 4 )
( x − 6 )( x − 2 )
( y − 1 )( y + 4 )
( p + 2 )( p − 6 )
( n + 1 )( n − 7 )
( g + 6 )2
( z − 3 )2
( a − 9)2
( 2y + 3 )( y + 1 )
( n + 6 )( 3n − 5 )
( 3a − b )( 2a − b )
( x − 6 )( x + 6 )
( m + 3 )( m − 3 )
( a − b )( a + b )
SILVER
GOLD
Take extra care here with negative signs.
What does ( g + 6 )2 mean? – think how to start this question. Have you made sure you have fully simplified all your answers?
Finished? Now look at your answers to questions 22, 23 and 24. They all have something in common – in fact they are linked by a rule. Can you see what it is?

14. Expanding brackets; binomials
Can you make the expressions from the factors? (Actually, no you can’t – there are 8 expressions but only 12 factors, where you would need to have 16 altogether.) When you have sorted them, there will be two expressions left over that can’t be made from any brackets. Can you work out why not?
x2 + 6x + 8
x2 + x − 20
x2 + 3x − 18
( x + 3 )
( x − 6 )
( x + 2 )
x2 + 2x + 5
( x − 4 )
( x − 3 )
( x + 4 )
x2 − 2x − 8
( x + 5 )
( x + 2 )
( x − 4 )
x2 + 4
x2 − 16
( x + 6 )
( x + 4 )
( x − 4 )
x2 − 3x − 18

15. Expanding brackets; binomials
If this is the answer, what is the question? All but two of these can be made by multiplying together a pair of brackets. Can you find a pair of brackets for those that can be done – and how about explaining why the other two don’t work? (What you are actually doing is called factorising. This is the opposite of expanding – instead of taking the brackets out, you are putting them in).
x2 + 8x + 15
x2 + 6x + 12
x2 + 7x − 18
x2 + x − 30
x2 + 6x + 9
x2 + x
x2 + 9
x2 − 25
x2 − 2x
Click on a box to see if it will factorise. If it turns red, it won’t. If it turns green, you know what to do…

16. x × x = x2
y ÷ y = y
g3 × g5 = g8
5a × 3b
= 15ab
2x × 2x
= 2x2
5p − 4p = p
y × y = 2y
x × x2 = x3
−3n × −2n
= −6n2
6a + 2b
= 8ab
6q ÷ 2q = 3
3f − 5f
= −2f
3a × b
= 4ab
m2 × m4
= m8
−m × −2m
= 2m2
z + z = z2

17. Expanding brackets 3 ( x + 4 ) 5 ( y + 2 ) 2 ( x − 6 ) x ( x + 8 )
BRONZE
SILVER
GOLD
3 ( x + 4 )
5 ( y + 2 )
2 ( x − 6 )
x ( x + 8 )
y ( y + 3 )
n ( n − 5 )
5 ( 2x + 1 )
3 ( 4y + z )
2 ( p − 4q )
x ( x + y )
p ( 4p + 3q )
m ( 2m − 3n )
4x ( x + y )
2y ( y + z )
2x ( x − 3w )
3x ( 2x + z )
4y ( 2y + 3z )
5m ( 2m − 7n )
SILVER
GOLD
5 ( x + 1 ) + 2 ( x + 3 )
5 ( y + 3 ) + 7 ( y + 1 )
3 ( x − 6 ) + 5 ( x − 6 )
5 ( x + 2 ) + 2 ( x − 7 )
4 ( y + 6 ) − 3 ( y − 1 )
3 ( n − 4 ) − 5 ( n − 7 )
6 ( x + 3 ) − 2 ( x + 3 )
8 ( y + 4 ) − 3 ( y + 1 )
x ( x − 6 ) + x ( x + 4 )
x ( x + 8 ) + x ( x + 7 )
y ( y + 1 ) + y ( y − 2 )
m ( m − 6 ) + m ( m − 7 )

18. Expanding brackets; binomials
BRONZE
SILVER
GOLD
( x + 4 )( x + 2 )
( x + 6 )( x + 9 )
( x + 7 )( x + 3 )
( x + 1 )( x + 6 )
( x + 6 )( x + 1 )
( x + 8 )( x + 5 )
( x − 3 )( x + 7 )
( x + 6 )( x − 5 )
( x + 2 )( x − 4 )
( x − 6 )( x + 2 )
( x − 3 )( x − 4 )
( x − 6 )( x − 2 )
( y − 1 )( y + 4 )
( p + 2 )( p − 6 )
( n + 1 )( n − 7 )
( g + 6 )2
( z − 3 )2
( a − 9)2
( 2y + 3 )( y + 1 )
( n + 6 )( 3n − 5 )
( 3a − b )( 2a − b )
( x − 6 )( x + 6 )
( m + 3 )( m − 3 )
( a − b )( a + b )
SILVER
GOLD
Take extra care here with negative signs.
What does ( g + 6 )2 mean? – think how to start this question. Have you made sure you have fully simplified all your answers?
Finished? Now look at your answers to questions 22, 23 and 24. They all have something in common – in fact they are linked by a rule. Can you see what it is?

19. Expanding brackets; binomials
Can you make the expressions from the factors? (Actually, no you can’t – there are 8 expressions but only 12 factors, where you would need to have 16 altogether.) When you have sorted them, there will be two expressions left over that can’t be made from any brackets. Can you work out why not?
x2 + 6x + 8
x2 + x − 20
x2 + 3x − 18
( x + 3 )
( x − 6 )
( x + 2 )
x2 + 2x + 5
( x − 4 )
( x − 3 )
( x + 4 )
x2 − 2x − 8
( x + 5 )
( x + 2 )
( x − 4 )
x2 + 4
x2 − 16
( x + 6 )
( x + 4 )
( x − 4 )
x2 − 3x − 18

20. Expanding brackets; binomials
If this is the answer, what is the question? All but two of these can be made by multiplying together a pair of brackets. Can you find a pair of brackets for those that can be done – and how about explaining why the other two don’t work? (What you are actually doing is called factorising. This is the opposite of expanding – instead of taking the brackets out, you are putting them in).
x2 + 8x + 15
x2 + 6x + 12
x2 + 7x − 18
x2 + x − 30
x2 + 6x + 9
x2 + x
x2 + 9
x2 − 25
x2 − 2x
On the screen, the ones that factorise change colour and become green; the ones that don’t become red. If you have a coloured crayon…