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Warm Up: On the back of your lab sheet, answer the following questions.
Agenda
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3) Which of the following shapes are parallelograms? Explain how you know.
A. B. C. D.
1) What is the area of this shape?
2) What is the area of this rectangle?
A = 6 sq unitsA = 24 sq units
Shape A, B and D are all parallelograms!
Agenda:
OBJECTIVE: As a result of this lesson you will be able to find the area of any parallelogram.
1) Warm Up 2) Launch – Building Blocks A, B & C
3) Explore – Partners: Area of Parallelogram
4) Summary – Formula for Area of Parallelogram
5) Practice – Interleaving
6) Assessment – Exit Ticket
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Launch A
Agenda
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What is the definition of a parallelogram?
A parallelogram is a quadrilateral that has 2 pairs of parallel sides. Opposite sides have the same length and opposite angles have equal measurements.
Vocabulary
Launch B
Agenda
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Can you quickly find the area of this parallelogram by counting the unit squares?
Area = 12 square units
1 2 3 4 56 7 8 9 10
11
12
(Wait time: 30 seconds)
Launch B
Agenda
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Can you quickly find the area of this parallelogram by counting the unit squares?
Launch B
Agenda
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Your challenge:Develop a more efficient method to determine the area of the parallelogram.
“I don’t have all day. Counting takes way too long!”
Launch C
Agenda
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Did you have to count squares to find the area of the rectangle?
NO!
Multiplying length x width is a more efficient method for finding the area of a rectangle than counting squares.
A = 6 sq unitsA = 24 sq units
What does it mean to find an efficient method?
Remember the warm up problems?
Launch C
Agenda
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Let’s consider the first shape in the Warm Up.
How could decomposing (cutting) and composing (putting back together) into another shape help you find the area of this shape?
Explore
Agenda
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Part 1 - (10 Min)
Work with your PARTNER to find an efficient method of finding the area of a parallelogram.
You will get a parallelogram and a pair of scissors. You can:
- Write on the shape- Draw on it- Use scissors on it
1-Partners2-Share Out
3-Worksheet
In 10 minutes you will be asked to stop and think about it!
HINT
Explore – Student Share Out
Agenda
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Part 2 - (3 Min)
Complete #1-5 on Classwork.
Classwork Questions
Explore – Complete top half of worksheet Part 3 - (5 Min)
Agenda
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Fill out the top half of your worksheet.
Summary – Sharing Questions #1-5
Agenda
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#1) Explain what you did to find a quicker way to find the area of the parallelogram.
Summary – Sharing Questions #1-5
Agenda
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#2) Draw the shapes you decomposed (cut apart) your parallelogram into. Do you know the names of these shapes?
#3) Did you create any new shape or shapes by composing (putting back together in a different way)?
Summary – Sharing Questions #1-5
Agenda
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#4) What dimensions does your new shape (rectangle) have?
original parallelogram
12 cm
8 cm
The base is
The base is 12 cm. The height is 8 cm.#5) Can you identify those dimensions on the original parallelogram?
also 8 cm.also 12 cm. ...? The height is ...?
rectangle
12 cm
8 cm
Summary – Interactive Worksheet
Agenda
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We are going to complete the rest of the worksheet together. You will fill in the boxes at the bottom of the first side as we go.
Summary
Agenda
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original parallelogram rectangle
12 cm12 cm
8 cm8 cm
96 sq cm = 12 cm x 8 cmArea = base x height
A = b x h
#6)
The base and the height in the rectangle match the base and height in the parallelogram!
Summary
Agenda
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Let’s look at the example from earlier today…
6 cm
2 cm
6 cm
2 cm
A = b x h = 6 x 2 = 12 cm2
Okay, so that worked with one parallelogram. But can any parallelogram be decomposed and composed into a rectangle with the same base and height?
Summary
Agenda
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So…. could we find the area of this rectangle without cutting and changing it to a rectangle?
Write the formula in your summary in #7.
Summary
Agenda
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A = b x h #7) Now that you know this is the formula for area of a
parallelogram, what dimensions must you always know in order to find area?
base and height#8) If we don’t rearrange the shape into a rectangle, could we
still find the height? Yes, the height is the perpendicular distance from the top to the base. Copy this in #8. H
eigh
t Base
Summary
Agenda
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#10) Answer this question: Do you need to know this length in order to find the area of the parallelogram?
No, you only need the base and height.#11) Answer this question: When would you need to know this length? You would need to know the slant height to measure perimeter.
#9) Answer this question: Can you tell what the length of the other side (the slant height) of the parallelogram is? No, not exactly
12 cm
8 cm
slant height?
Summary
Agenda
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#12) Oops! Your sleepy friend slept through the last 20 minutes of class! Can you help her out?
• In the space for #12, write her a note explaining what you learned so far today.
• Use complete sentences.
(2 minutes)
Scaffolding
Practice – Interleaving Worksheet
Agenda
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Many kids learn better when the alternate solving problems with their teacher. Watch me solve one, and then you’ll do one, then I’ll do one…
Practice
Agenda
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#1)
16 cm
8 cm10 cm
base = _____
height = ____
16 cm
8 cm
#2)
20 in
14 in 17 in
height = ______
base = _____ 20 in
14 in
Practice
Agenda
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#3)
20 ft
14 ft18 ft
base = _____
height = ____
20 ft
14 ft
#4)
48 m
27 m 32 m
height = ______
base = _____ 48 m
27 m
Practice
Agenda
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#5)
16 in
22 in28 in
base = _____
height = ____
16 in
22 in
#6)
30 m
45 m 55 m
height = ______
base = _____ 30 m
45 m
Practice
Agenda
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#7)
10 ft
8 ft
12 ft
base = _____
height = ____
12 ft
8 ft
#8)
18 cm
20 cm
25 cm
height = ______
base = _____ 25 cm
18 cm
Practice: Which rectangle has the same area as the green parallelogram?
Agenda
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#9)
13 m
7 m9 m
A.9 m
13 m
B.7 m
13 m
#10)
30 in
35 in 40 in
A.35 in
30 in
B.40 in
30 in
Practice: Which rectangle has the same area as the blue parallelogram?
Agenda
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#11)
23 ft
16 ft19 ft
A.16 ft
23 ft
B.19 ft
23 ft
#12)
32 cm
16 cm
20 cm
B.
16 cm
32 cm
A.
20 cm
32 cm
Practice: What is the area of the parallelogram?
Agenda
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#13)
8 in
4 in
#14)
7 ft
9 ft
A = b x hA = 8 in x 4 inA = 32 in2
A = b x hA = 7 in x 9 inA = 63 ft2
Practice: What is the area of the parallelogram?
Agenda
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#15)
12 m
6 m
A = b x hA = 12 m x 6 mA = 72 sq. m
#16)
15 cm
3 cm
A = b x hA = 15 cm x 3 cmA = 45 sq. cm
6.7 m 5.4 cm
Practice: What is the area of the parallelogram?
Agenda
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#17)
9 in
13 in
A = b x hA = 9 in x 13 inA = 117 in2
A = b x hA = 14 cm x 5 cmA = 70 cm2
15 in
#18)
14 cm
5 cm7 cm
Practice: What is the area of the parallelogram?
Agenda
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A = b x hA = 6 ft x 3.2 ftA = 19.2 ft2
A = b x hA = 9 m x 4.5 mA = 40.5 m2
6 ft
#19)
3.2 ft
5.8 ft
6 ft
#20)4.5 m
6.1 m
9 m
