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§1.1 Expanding Brackets
Arithmetic with Letters
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Slide 1:
Diapositive
Wiskunde
Middelbare school
vwo
Leerjaar 2
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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…
… simplify products with letter variables.
… simplify additions and subtractions with letter variables.
… collect like terms to simplify letter variables.
… 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…
… simplify an expression with the following rule: a(b + c) = ab + ac
… 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
=
A
B
⋅
A
E
=
A
B
⋅
B
E
=
A
B
⋅
A
E
+
A
B
⋅
B
E
Slide 7 - Diapositive
Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=
a
⋅
b
=
a
b
=
a
⋅
c
=
a
c
=
a
⋅
b
+
a
⋅
c
=
a
b
+
a
c
Slide 8 - Diapositive
Farmer Edward - Area of the land and the barn
Area I
Area II
Total Area
=
a
⋅
b
=
a
b
=
a
⋅
c
=
a
c
=
a
⋅
(
b
+
c
)
=
a
b
+
a
c
Slide 9 - Diapositive
More examples
2
b
(
5
a
−
7
)
=
=
1
0
a
b
−
1
4
b
=
2
b
⋅
5
a
+
(
2
b
⋅
−
7
)
=
1
0
a
b
+
(
−
1
4
b
)
Slide 10 - Diapositive
More examples
−
(
3
p
−
2
q
)
=
=
−
3
p
+
2
q
=
−
1
⋅
3
p
+
(
−
1
⋅
−
2
q
)
=
−
3
p
+
(
2
q
)
Slide 11 - Diapositive
More examples
8
−
3
(
2
a
−
b
)
=
8
+
(
−
3
⋅
2
a
)
+
(
−
3
⋅
−
b
)
=
=
8
+
(
−
6
a
)
+
(
3
b
)
=
8
−
6
a
+
3
b
=
8
+
(
−
3
⋅
2
a
)
+
(
−
3
⋅
−
b
)
Slide 12 - Diapositive
According to the book
2
b
(
5
a
−
7
)
=
1
0
a
b
−
1
4
b
−
(
3
p
−
2
q
)
=
−
3
p
+
2
q
8
−
3
(
2
a
−
b
)
=
8
−
6
a
+
3
b
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
=
a
⋅
b
=
a
b
=
a
⋅
2
=
2
a
=
a
b
+
2
a
+
3
b
+
6
=
3
⋅
b
=
3
b
=
3
⋅
2
=
6
=
(
a
+
3
)
(
b
+
2
)
Slide 15 - Diapositive
More examples
(
a
+
2
)
(
b
+
5
)
=
=
(
a
⋅
b
)
+
(
a
⋅
5
)
+
(
2
⋅
b
)
+
(
2
⋅
5
)
=
(
a
b
)
+
(
5
a
)
+
(
2
b
)
+
(
1
0
)
=
a
b
+
5
a
+
2
b
+
1
0
Slide 16 - Diapositive
More examples
(
c
+
2
)
(
d
−
4
)
=
=
(
c
⋅
d
)
+
(
c
⋅
−
4
)
+
(
2
⋅
d
)
+
(
2
⋅
−
4
)
=
(
c
d
)
+
(
−
4
c
)
+
(
2
d
)
+
(
−
8
)
=
c
d
−
4
c
+
2
d
−
8
Slide 17 - Diapositive
More examples
(
x
+
2
)
(
x
−
3
)
=
=
(
x
⋅
x
)
+
(
x
⋅
−
3
)
+
(
2
⋅
x
)
+
(
2
⋅
−
3
)
=
(
x
2
)
+
(
−
3
x
)
+
(
2
x
)
+
(
−
6
)
=
x
2
−
3
x
+
2
x
−
6
=
x
2
−
x
−
6
Slide 18 - Diapositive
According to the book
(
x
+
2
)
(
x
−
3
)
=
x
2
−
3
x
+
2
x
−
6
=
x
2
−
x
−
6
(
c
+
2
)
(
d
−
4
)
=
c
d
−
4
c
+
2
d
−
8
(
a
+
2
)
(
b
+
5
)
=
a
b
+
5
a
+
2
b
+
1
0
Slide 19 - Diapositive
Worktime
You work neatly by…
… reading the
theory
(again) before asking a question to your classmate.
…
raising a hand
before asking a question to the teacher.
… 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...
… simplify an expression with the following rule: a(b + c) = ab + ac
… simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
Reflection
Slide 21 - Diapositive
I can already…
… simplify an expression with the following rule: a(b + c) = ab + ac
… 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
)
(
x
−
3
)
=
3
x
2
+
x
−
6
(
c
+
2
)
(
d
−
4
)
=
−
c
d
−
4
c
−
2
d
−
8
(
a
+
2
)
(
b
+
5
)
=
a
b
+
1
0
a
b
+
1
0
Slide 23 - Diapositive
After this lesson, I can…
… 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.
(
6
a
+
1
)
(
4
a
+
2
)
−
(
5
a
−
4
)
(
a
+
3
)
=
=
2
4
a
2
+
1
2
a
+
4
a
+
2
−
(
5
a
2
+
1
5
a
−
4
a
−
1
2
)
=
2
4
a
2
+
1
2
a
+
4
a
+
2
−
5
a
2
−
1
5
a
+
4
a
+
1
2
=
1
9
a
2
+
5
a
+
1
4
Slide 27 - Diapositive
Conclusion after this week
Slide 28 - Diapositive
Worktime
You work neatly by…
… reading the
theory
(again) before asking a question to your classmate.
…
raising a hand
before asking a question to the teacher.
… 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...
… simplify an expression with the following rule: a(b + c) = ab + ac
… simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
Reflection
Slide 30 - Diapositive
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