21st Century Lessons

Area of Parallelogram Lesson

Primary Lesson Designers:Sarah Cook

Nicola Larcombe

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This project is funded by the American Federation of Teachers.

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*1st Time Users of 21st Century Lesson:Click HERE for a detailed description of our project.

21st Century Lessons – Teacher Preparation

• Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets.

• Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly.

Please do the following as you prepare to deliver this lesson:

• Feel free to customize this file to match the language and routines in your classroom.

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Lesson Objective Lesson Objective: SWBAT demonstrate that any parallelogram can be decomposed and recomposed into a rectangle, and as such to calculate the area of a parallelogram multiply the base times the height (and not slant height/side length).Student- Friendly Objective: SWBAT use an efficient method to find the area of any parallelogram and explain why it makes sense.

Lesson Description The overarching design of this lesson is to launch students on a brief and somewhat directed explore time on how to decompose and compose a parallelogram in order to find an efficient way to find area. Following that exploration, a succinct summary will make the key connections between a parallelogram and a rectangle, revealing that the same area formula can be used for parallelograms as is used for rectangles.The remainder of the lesson involves interleaving practice for students to identify base and height on parallelograms and calculate area using the formula. An exit ticket will be used to assess both student understanding of the concept and accuracy at calculating area of a parallelogram.

Lesson Overview (1 of 3)

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Lesson Vocabulary

Base – A side of a figure that a height can be drawn from.Height – The distance of a line, perpendicular to the base, measured from the

base to the opposite side or vertex.Area – The number of square units that cover a closed figureSquare Unit – Units used to measure area (in2, cm2, ft2, etc.)Parallelogram – Four-sided figure with opposite sides equal and parallelCompose – Combining shapes to construct new ones.Decompose – Breaking shapes apart into familiar pieces.Perimeter – Distance around the outside of a figure.

Materials Parallelogram Lab Sheet, Scissors, Area of Parallelogram Class Work handout, Lesson 1 Homework

Scaffolding Throughout the Explore, Summary, and Practice portions, a handout will be used by students to organize their notes.Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections.

Enrichment Advanced Objective: SWBAT prove two other methods for decomposing and composing parallelograms that help find the area.

To support students in doing this, give students multiple copies of the lab sheet during the Explore time, and challenge them to come up with additional methods of decomposing and composing.

Online Resources for Absent Students

http://www.mathexpression.com/area-of-a-parallelogram.html

Lesson Overview (2 of 3)

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Lesson Overview (3 of 3)Common Core State Standard

Common Core State Standard: 6.G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problem

Before and After

Before: Many of the concepts in this lesson build on learning that has taken place over the past 8 years of the students’ schooling.

v Introduction to Concept of Area – PK.MD.MA1 (pre-k)v Composing Shapes – 1.G.2 (first grade)v Square units – 3.MD.5 (third grade) v Perpendicular and Parallel Lines – 4.G.1 (fourth grade)

After: The objectives of this lesson build the foundation for students’ future learning in middle and high school

v Solving real-life math problems with area, surface area, and volume – 7.G.4v Shape orientation (transformations) – 8.G.4v Solving equations with one variable – 8.EE.7

Topic Background

Ancient Egyptian mathematicians have had a significant influence on the development of geometric concepts. Sources such as the Rhind Papyrus and the Moscow Papyrus demonstrate that the Ancient Egyptians knew how to compute areas of several geometric shapes (triangles, rectangles, circles, etc.) and the volumes of cylinders and pyramids – the pyramids being one of the world’s wonders for which they are famous. Greek mathematicians were also fundamental contributors to the development of geometric concepts. Euclid, often referred to as the “Father of Geometry,” produced “Elements,” a series of books that covered various geometry concepts (including area) as well as much of what is now known as algebra, trigonometry, and advanced arithmetic. “The Pythagorean Theorem,” one of the most famous geometric concepts, has been attributed to the Greek philosopher and mathematician Pythagoras. While the Theorem is not directly related to this lesson or unit, a strong understanding of triangles and special quadrilaterals will lay the foundation for later learning.This lesson incorporates the research-based practice of interleaving repeated teacher-guided problems with individual student practice.

Warm UpOBJECTIVE: SWBAT use an efficient method to find the area of any parallelogram, and explain why it makes sense.

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: SWBAT use an efficient method to find the area of any parallelogram, and explain why it makes sense.

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

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(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

Click on the timer!

Explore – Student Share Out

Agenda

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Part 2 - (3 Min)

Students share out work.

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?

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.

Hei

ght

Base

Summary

Agenda

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#10) 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) When would you need to know this length? You would need to know the slant height to measure perimeter.

#9) 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

Assessment – Exit Ticket!

Agenda

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Complete and hand in the Exit Ticket before you leave!

The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to:

•Support an increase in student achievement; •Engage teachers and students; •Align to the National Common Core Standards and the Massachusetts curriculum frameworks;•Embed best teaching practices, such as differentiated instruction; •Incorporate high-quality multi-media and design (e.g., PowerPoint); •Be delivered by exemplary teachers for videotaping to be used for professional

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21st Century LessonsThe goal…

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Directors:Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues CommitteeTed Chambers - Co-director of 21st Century LessonsTracy Young - Staffing Director of 21st Century LessonsLeslie Ryan Miller - Director of the Boston Public Schools Office of

Teacher Development and AdvancementKevin Qazilbash - Co-director of 21st Century Lessons

21st Century Lessons

The people…

Lesson Designers:Nicola LarcombeSarah CookMeghan McGoldrickBrian ConnorTracy Young

Technology Coordinator:Shane Ulrich

PowerPoint Designers:Alex RobinsonLaQueena Williams

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