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2TH §5.1 Removing single brackets
1. Calculate the perimeter of the figure. Write your answer as short as possible.
2. Calculate the area of the figure. Write your answer as a single square root.
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Wiskunde
Middelbare school
havo, vwo
Leerjaar 2
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Lesson duration is:
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Items in this lesson
1. Calculate the perimeter of the figure. Write your answer as short as possible.
2. Calculate the area of the figure. Write your answer as a single square root.
Entry Ticket
timer
6:00
Slide 1 - Slide
Starting with something new
Removing single brackets
Something like this ..... 5(2+4) =
Slide 2 - Slide
Removing single brackets
5(2+4)=
11 -1
30 something else
Slide 3 - Slide
Rectangles
You can think of the calculation 5(2+4) as working out the area of this rectangle.
Slide 4 - Slide
Rectangles
The area of the rectangle is
length x width =
5 x (2+4) =
5(2+4)
Slide 5 - Slide
Rectangles
area rectangle = 5(2+4) = 5 x 6 = 30
You could also calculate the area of the
blue rectangle and red rectangle first
and then add those up.
area rectangle = 5 x 2 + 5 x 4 =
10 + 20 = 30
Slide 6 - Slide
Rectangles with variables
If at least one of the sides of the rectangle is given as a variable, you can make a formula for the area of the rectangle.
Slide 7 - Slide
Rectangles with variables
You can make a formula with brackets and one without.
Area rectangle = 5 x (t+4) = 5(t+4)
OR
Area rectangle = 5 x t + 5 x 4 =
5t + 20
Slide 8 - Slide
Rectangles with variables
Because both formulas give the same area, we now now that
5(t+4) = 5t + 20
We can use this to rewrite formulas
with brackets as formulas without
brackets.
Slide 9 - Slide
Removing brackets
Write the formula y = 2(3t + 4) without brackets.
Slide 10 - Slide
Removing brackets
Write the formula y = 2(3t + 4) without brackets.
Think of a rectangle with a side of 2 and a side of 3t + 4
Slide 11 - Slide
Removing brackets
Write the formula y = 2(3t + 4) without brackets.
Think of a rectangle with a side of 2 and a side of 3t + 4
Area blue rectangle = 2 x 3t = 6t
Area red rectangle = 2 x 4 = 8
y = 6t + 8
Slide 12 - Slide
Removing brackets
Instead of a rectangle, you can also use a
multiplication table
.
y = 2(3t + 4) = 6t + 8
Slide 13 - Slide
More variables, negative numbers
If you want to write 2t(5t - 3) without brackets, it is hard to imagine a rectangle, because a lenght of -3 is not possible.
We can still use a multiplication table!
Slide 14 - Slide
More variables, negative numbers
Write y = 2t(5t - 3) without brackets.
What should be written over here?
7
t
1
0
t
7
t
2
1
0
t
2
Slide 15 - Slide
More variables, negative numbers
Write y = 2t(5t - 3) without brackets.
What should be written over here?
−
t
6
t
−
6
t
2
t
−
3
Slide 16 - Slide
More variables, negative numbers
Write y = 2t(5t - 3) without brackets.
Slide 17 - Slide
Notation
If a 1 is written in front of a variable or bracket, you do not write down the 1.
Instead of
1p
, you write
p
Instead of
-1t
, you write
-t
Instead of
-1(5t+2)
, you write
-(5t+2)
Slide 18 - Slide
Homework Tuesday
§5.1 Do exercises S4, 4, 5, S6 and 6
Don't forget to check and correct your answers with the solutions book!
Slide 19 - Slide
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