§1.1 Expanding Brackets

Arithmetic with Letters
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Arithmetic with Letters

Slide 1 - Diapositive

Date
Thursday august 29th
Paragraph
§1.1 Expanding Brackets
Pages from the handbook
Pag. 12-14
Subject
Rules:
a(b + c) = ab + ac
(a + b)(c + d) = ac + ad + bc + bd
Today is the day...

Slide 2 - Diapositive

I can already…
  1. … simplify products with letter variables.
  2. … simplify additions and subtractions with letter variables.
  3. … collect like terms to simplify letter variables.
  4. … simplify letter variables by applying the order of operations.

Prior Knowledge

Slide 3 - Diapositive

Examples of letter variables

Slide 4 - Diapositive

After this lesson, I can…
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd

Goals

Slide 5 - Diapositive

Farmer Edward - Area of the land and the barn

Slide 6 - Diapositive

Farmer Edward - Area of the land and the barn
Area I
Area II 
Total Area
=ABAE
=ABBE
=ABAE+ABBE

Slide 7 - Diapositive

Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=ab=ab
=ac=ac
=ab+ac=ab+ac

Slide 8 - Diapositive

Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=ab=ab
=ac=ac
=a(b+c)=ab+ac

Slide 9 - Diapositive

More examples
2b(5a7)=
=10ab14b
=2b5a+(2b7)
=10ab+(14b)

Slide 10 - Diapositive

More examples
(3p2q)=
=3p+2q
=13p+(12q)
=3p+(2q)

Slide 11 - Diapositive

More examples
83(2ab)=8+(32a)+(3b)=
=8+(6a)+(3b)
=86a+3b
=8+(32a)+(3b)

Slide 12 - Diapositive

According to the book
2b(5a7)=10ab14b
(3p2q)=3p+2q
83(2ab)=86a+3b

Slide 13 - Diapositive

Farmer Charles - Area of the land and the barn

Slide 14 - Diapositive

Farmer Charles - Area of the land and the barn
Total Area

Area I
Area II
Area III
Area IV
Total Area

=ab=ab
=a2=2a
=ab+2a+3b+6
=3b=3b
=32=6
=(a+3)(b+2)

Slide 15 - Diapositive

More examples
(a+2)(b+5)=
=(ab)+(a5)+(2b)+(25)
=(ab)+(5a)+(2b)+(10)
=ab+5a+2b+10

Slide 16 - Diapositive

More examples
(c+2)(d4)=
=(cd)+(c4)+(2d)+(24)
=(cd)+(4c)+(2d)+(8)
=cd4c+2d8

Slide 17 - Diapositive

More examples
(x+2)(x3)=
=(xx)+(x3)+(2x)+(23)
=(x2)+(3x)+(2x)+(6)
=x23x+2x6
=x2x6

Slide 18 - Diapositive

According to the book
(x+2)(x3)=
x23x+2x6
=x2x6
(c+2)(d4)=
cd4c+2d8
(a+2)(b+5)=
ab+5a+2b+10

Slide 19 - Diapositive

Worktime
You work neatly by…
  1. … reading the theory (again) before asking a question to your classmate.
  2. raising a hand before asking a question to the teacher.
  3. … if the teacher is busy, remember your question and move on.
Help:
Exercises: 9,15
Assignments:
Pages: 14-16
Exercises:  10, 11, 12, 13, 16, 17, 19, 20
Assignments from the planning of WEEK 3:
Extra:
Exercises: L3

Slide 20 - Diapositive

Now I can...
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
Reflection

Slide 21 - Diapositive

I can already…
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd

Prior Knowledge

Slide 22 - Diapositive

Prior Knowledge - What mistake was made?
(x+2)(x3)=
3x2+x6
(c+2)(d4)=
cd4c2d8
(a+2)(b+5)=
ab+10ab+10

Slide 23 - Diapositive

After this lesson, I can…
  1. … simplify expressions that contain brackets.

Goals

Slide 24 - Diapositive

Simplify expressions

Slide 25 - Diapositive

Exercise 17 (Homework)
Determine the area of the blue shape.


Slide 26 - Diapositive

Exercise 17 (Homework)
Determine the area of the blue shape.



(6a+1)(4a+2)(5a4)(a+3)=
=24a2+12a+4a+2(5a2+15a4a12)
=24a2+12a+4a+25a215a+4a+12
=19a2+5a+14

Slide 27 - Diapositive

Conclusion after this week

Slide 28 - Diapositive

Worktime
You work neatly by…
  1. … reading the theory (again) before asking a question to your classmate.
  2. raising a hand before asking a question to the teacher.
  3. … if the teacher is busy, remember your question and move on.
Help:
Exercises: 2, 4, 5, 8, 9, 11, 13, 15, 17, 18 and 19.
Assignments:
Pages: 12-16
Exercises: 4, 5, 6, 9, 11, 13, 15, 17, 18 and 19.
Assignments from the planning of WEEK 2:
Extra:
Exercises: 7 and 20.

Slide 29 - Diapositive

Now I can...
  1. … simplify an expression with the following rule: a(b + c) = ab + ac
  2. … simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
Reflection

Slide 30 - Diapositive