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21 st Century Lessons

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21st Century Lessons

Trapezoids Lesson

Mrs. Thompson

Level 1

OBJECTIVE 1:SWBAT prove whether the area formula for a parallelogram

(A = b x h) can also be used to find the area of a trapezoid

OBJECTIVE 2:Students will practice finding the area of trapezoids using the correct formula.

1) Greg and his sister, Laura, have a snack everyday after school. Yesterday, Greg put these cookies on the table and Laura began crying “that’s not fair! Mamaaaaa!”

To even out the piles, how many cookies

should each kid have? How would you do this?

2) José got back 3 quizzes today at school with the following grades: 80, 65, 95. What is the average grade for all 3 quizzes?

Laura Greg

(6 cookies) (10 cookies)

Agenda

video

Warm up 2

Warm up 1

.

To even out the piles, how many cookies should each kid have?

How would you do this?

Laura

Greg

8 cookies 8 cookies

Finally, Laura stopped crying!

Agenda

Scaffolding

Questions

José got back 3 quizzes today at school with the following grades: 80, 65, 95. What is the average grade for all 3 quizzes?

Average = Mean

80% = B-

80

65

+95

240

65% = D

95% = A

÷ 3 = 80

Agenda

Scaffolding

Questions

OBJECTIVE:SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid

- Warm Up – Cookies!

2) Launch– Can we just do base x height ???

3) Explore – Partners

4) Summary – Yes or No?

5) Mini-Lesson

6) Practice– with Interleaving

7) Assessment

Agenda

Quadrilateral … 4-sided shape

Launch

RECTANGLE

What kind of quadrilateral is shown here?

h = 4

b = 10

How would you find the AREA of this 4-sided shape?

Area = base x height

Agenda

Quadrilateral … 4-sided shape

Launch

SQUARE

What kind of quadrilateral is shown here?

h = 5

b = 5

How would you find the AREA of this 4-sided shape?

Area = base x height

Agenda

Quadrilateral … 4-sided shape

Launch

PARALLELOGRAM

How would you find the AREA of this 4-sided shape?

Area = base x height

What kind of quadrilateral is shown here?

h = 8

b = 12

Agenda

Quadrilateral … 4-sided shape

Launch

TRAPEZOID

What kind of quadrilateral is shown here?

How would you find the AREA of this 4-sided shape?

Can I use Area = base x height???

Agenda

Remember the objective:

OBJECTIVE:SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid

Agenda

Before you test the formula, what are strategies for finding area that always work?

- Count the unit squares

- Decompose (cut into pieces)
- & compose (put back together)
- into a different shape

With your partner, you will use these strategies FIRST,

and THEN test the formula A = b x h !

Agenda

KEY QUESTION:

Can the formula A = base x height be used to find the area of a trapezoid???

You will provewhether the formula works by…

- Counting the unit squares of your trapezoid
- Decomposing (cutting into pieces) & composing (putting back together) your trapezoid into a different shape
- Using A = base x height

…and comparing your results!

Agenda

12

11

1

2

3

4

5

6

7

8

9

10

Area = 12 square units

Agenda

Did anyone decompose and (re)compose like this?

height

= 2

base = 6

Area = 12 square units

Agenda

Did anyone decompose and (re)compose like this?

height = 2

base = 6

Area = 12 square units

Agenda

Did anyone decompose and (re)compose like this?

height = 2

Area = ½ b h

Area = ½ x 8 x 2

Area = 8

base = 4

Area = 4 + 8

Area = ½ b h

Area = 12 square units

Area = ½ x 4 x 2

Area = 4

height

= 2

base = 8

Agenda

NO!!

A = base x height

A = 8 x 2

A = 16

TOO BIG!

A = base x height

A = 4 x 2

A = 8

TOO SMALL!

Agenda

Summary When you counted the unit squares…

1

2

3

4

5

6

?

Area = 24 square units

Agenda

Did anyone decompose and (re)compose like this?

height = 3

base = 8

Area = 24 square units

Agenda

Did anyone decompose and (re)compose like this?

height= 3

height= 3

base= 6

base= 4

Area = ½ b x h

½ x 4 x 3

½ x 12

6

Area = b x h

6 x 3

18

Area = 24 square units

Agenda

NO!!

A = base x height

A = 10 x 3

A = 30

TOO BIG!

A = base x height

A = 6 x 3

A = 18

TOO SMALL!

Agenda

The formula for the Area of a Trapezoid is…

A = (b1+b2) x h

2

b2

height or h

b1

Agenda

A = (b1+b2) x h

2

Let’s Test it out using the Trapezoids from the Explore…

A = (8+4) x 2

2

A = (12) x 2

2

It works!

A = 6 x 2 = 12 sq. units

b2 = 4

Trapezoid A

h = 2

b1 = 8

Agenda

A = (b1+b2) x h

2

Let’s try the

formula again…

A = (10+6) x 3

2

A = (16) x 3

2

Trapezoid B

A = 8 x 3

A = 24 sq. units

b2 = 6

h = 3

It works!

b1 = 10

Agenda

HOLD UP! I feel like I’ve seen this trapezoid somewhere

before… it reminds me of something… wait for it…

b2 = 6

h = 3

h = 3

b1 = 10

Agenda

YES! Greg and Laura’s cookies! See what I mean? The piles of cookies had to even out just like the trapezoid’s bases!!!

b = 8

h = 3

Agenda

So, this part of the formula means….

we take the AVERAGE of the base lengths,

then multiply by the height to get the Area of a Trapezoid!

Agenda

Now that we know the formula for the area of a trapezoid, let’s try to use it together!

A = (b1+b2) x h

2

A = (9+5) x 4

2

b2 = 5

A = (14) x 4

2

h = 4

A = 7 x 4 = 28 sq. units

b1 = 9

Agenda

Now you try one…

A = (b1+b2) x h

2

b2 = 3

A = (9+3) x 10

2

A = (12) x 10

2

h = 10

A = 6 x 10 = 60 sq. units

b1 = 9

Agenda

Let’s try another one together, but make it a little more interesting!

A = (b1+b2) x h

2

Edward wants make a curtain for his living room window so he can sit in the dark and think of ways to get rid of Jacob! Calculate the area so that she knows how much fabric to buy.

b2 = 4 ft

A = (2+4) x 7

2

A = (6) x 7

2

h = 7 ft

A = 3 x 7 = 21 ft2

b1 = 2 ft

Agenda

Now you try another one…

A = (b1+b2) x h

2

Brian is getting a custom sticker to completely cover the back of his guitar. How much space will it take up?

A =(18+12) x 40

2

A = (30) x 40

2

b2 = 12 in

A = 15 x 40 = 600 in2

h =

40 in

Agenda

b1 = 18 in

Continue practicing on your own…

Agenda

Independent Practice Answers

5. a) 6 ft2

b) 11 cm2

c) 27.6 sq. units

d) 20 yd2

6. Juan’s Area: 90 m2

Cheyanne’s Area: 50 m2

Agenda

Agenda