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§1.1 Expanding Brackets
C1 Arithmetic with Letters
Mr. Fintelman (FNL)
Wednesday September 4th
2024
1 / 31
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Slide 1:
Tekstslide
Wiskunde
Middelbare school
vwo
Leerjaar 2
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31 slides
, met
tekstslides
.
Lesduur is:
90 min
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C1 Arithmetic with Letters
Mr. Fintelman (FNL)
Wednesday September 4th
2024
Slide 1 - Tekstslide
Date
Wednesday September 4th 2024
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 - Tekstslide
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 - Tekstslide
Examples of letter variables
Slide 4 - Tekstslide
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 - Tekstslide
Farmer Edward - Area of the land and the barn
Slide 6 - Tekstslide
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 - Tekstslide
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 - Tekstslide
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 - Tekstslide
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
)
Explain
In this rule we multiply the factor outside the brackets with
both
factors in the brackets.
So in this example we multiply 2b with 5a and 2b with -7.
If you find it difficult, it might help to 'split' the parts with brackets, this often helps with the rule of 'two negatives makes it positive'.
Slide 10 - Tekstslide
More examples
−
(
3
p
−
2
q
)
=
=
−
3
p
+
2
q
=
−
1
⋅
3
p
+
(
−
1
⋅
−
2
q
)
=
−
3
p
+
(
2
q
)
Explain
Again you multiply factors, but in this case we see an 'invisible -1'.
This is another example in which it might help to 'split' the parts with brackets, because negative numbers often lead to mistakes for starters.
Slide 11 - Tekstslide
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
)
Explain
Here we see a longer example, in which I 'split' the (-3) to make sure that I won't make mistakes later.
This is a tricky example.
Slide 12 - Tekstslide
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
Explain
So if we go by the steps the book tells you, you'll see that the book doesn't show most steps.
I don't like that, this is one of the reasons why students often feel lost in this particular paragraph.
Slide 13 - Tekstslide
Farmer Charles - Area of the land and the barn
Slide 14 - Tekstslide
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 - Tekstslide
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
Explain
This distribution is a little more, but not as different.
Now there are simply four factors, instead of three.
Slide 16 - Tekstslide
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
Explain
But it is such longer distributions that make me want to use brackets to make sure I won't miss negative numbers.
Slide 17 - Tekstslide
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
Explain
If these factors share variables, you will often see that you need to simplify a bit more, by either adding or subtracting like terms.
Slide 18 - Tekstslide
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
Explain
Here it is in short.
Slide 19 - Tekstslide
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 and 9
Assignments:
Pages: 10-11
Exercises: 4, 5, 6 and 9
Assignments from the planning of WEEK 1:
Extra:
Exercises: 7
Slide 20 - Tekstslide
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 - Tekstslide
Date
Monday September 9th 2024
Paragraph
§1.1 Expanding Brackets
Pages from the handbook
Pag. 15-16
Subject
Simplify expressions that contain brackets
Today is the day...
Slide 22 - Tekstslide
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 23 - Tekstslide
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 24 - Tekstslide
After this lesson, I can…
… simplify expressions that contain brackets.
Goals
Slide 25 - Tekstslide
Simplify expressions
Slide 26 - Tekstslide
Exercise 17 (Homework)
Determine the area of the blue shape.
Slide 27 - Tekstslide
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 28 - Tekstslide
Conclusion after this paragraph
Slide 29 - Tekstslide
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 30 - Tekstslide
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
… simplify expressions that contain brackets.
Reflection
Slide 31 - Tekstslide
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Lesduur is: 90 minLesduur is: 90 min
