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21 st 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.

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Presentation Transcript
slide1

21st Century Lessons

Trapezoids Lesson

Mrs. Thompson

Level 1

warm up

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.

Warm Up

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

warm up 1
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

warm up 2
Warm Up #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?

Average = Mean

80% = B-

80

65

+95

240

65% = D

95% = A

÷ 3 = 80

Agenda

Scaffolding

Questions

agenda
Agenda:

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

slide6

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

slide7

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

slide8

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

slide9

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

launch
Launch

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

launch1
Launch

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

explore
Explore

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

summary when you counted the unit squares
Summary When you counted the unit squares…

12

11

1

2

3

4

5

6

7

8

9

10

Area = 12 square units

Agenda

slide14

Did anyone decompose and (re)compose like this?

height

= 2

base = 6

Area = 12 square units

Agenda

slide15

Did anyone decompose and (re)compose like this?

height = 2

base = 6

Area = 12 square units

Agenda

slide16

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

when you used the formula area base x height did you get the same answer of 12
When you used the formula Area = base x height did you get the same answer of 12?

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

slide18

Summary When you counted the unit squares…

1

2

3

4

5

6

?

Area = 24 square units

Agenda

slide19

Did anyone decompose and (re)compose like this?

height = 3

base = 8

Area = 24 square units

Agenda

slide20

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

when you used the formula area base x height did you get the same answer of 24
When you used the formula Area = base x height did you get the same answer of 24?

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

mini lesson
Mini-Lesson

The formula for the Area of a Trapezoid is…

A = (b1+b2) x h

2

b2

height or h

b1

Agenda

slide23

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

slide24

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

slide25

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

slide26

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

slide27

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

practice 1
Practice #1

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

practice 2
Practice #2

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

practice 3
Practice #3

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

practice 4
Practice #4

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

independent practice
Independent Practice

Continue practicing on your own…

Agenda

slide34

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