G6 m5-a-lesson 1-t

Lesson 1: The Area ofParallelograms Through Rectangle Facts
Date: 5/11/15 13
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 1
Lesson 1: The Area of Parallelograms Through Rectangle
Facts
Student Outcomes
 Students show the area formula for the region bounded by a parallelogramby composing it into rectangles.
They understand that the area of a parallelogram is thearea of the region bounded by the parallelogram.
Lesson Notes
For students to participatein the discussions,each will need the parallelogramtemplates attached to this lesson, along
with the following: scissors,glue,ruler,and paper on which to glue their shapes.
FluencyExercise (5 minutes)
Multiplication of FractionsSprint
Classwork
OpeningExercise (4 minutes)
Students name the given shapes.
Opening Exercise
Name each shape.
 Identify the shapethat is commonly referred to as a parallelogram. How do you know it’s a parallelogram?
NOTE: A rectangle is considered a parallelogram,butis commonly called a rectanglebecauseit is a more specific name.
 The shape is a quadrilateral (4-sided) and has two sets of parallel lines.
Right Triangle
Parallelogram
Rectangle
AcuteTriangle
Trapezoid
Scaffolding:
Some students may not know
this vocabulary yet, so creating
a poster or chartfor student
desks may help them to
remember these terms.

Date: 5/11/15 14
 What aresome quadrilateralsthatyou know?
 Answers will vary.
 Today we are going to find the area of one of these quadrilaterals: the parallelogram. Weare going to use our
knowledge of the area of rectangles to help us. Who can remind us what we mean by area?
 The number of square units that make up the inside of the shape.
NOTE: Students with limited English would benefit from a further discussion of area thatrelates to things they have
personal connections to.
 Talk to your neighbor about how to calculatearea of a rectangle.
Once students have had time for discussion,teachers should pick someonewho can clearly explain howto find the area
of a rectangle.
 Count the number of square units inside the shape (if that is given) or multiply the base by the height.
Discussion(10 minutes)
Provideeach student with the picture of a parallelogramprovided as an attachment to this lesson.
 What shapedo you have in front of you?
 A parallelogram.
 Work with a partner to make a prediction of how we would calculatethe area of the shape.
 Answers will vary.
 Cut out the parallelogram.
 Sincewe know how to find the area of a rectangle, how can we change the parallelograminto a rectangle?
 Cut off a triangle on one side of the parallelogram and glue it to the other side.
 Draw a dotted perpendicular lineto show the triangleyou will cut. Fold your paper alongthis line.

Check to make sureall students have drawn the dotted linein the correct placebefore instructingthem to cut.
Explain thatthe fold on the lineshows that the two right angles form a 180° angle.
 Could the dotted linebe drawn in a different location? If so,where?
 The dotted line can be drawn in a different location. It could be drawn on the other side of the
parallelogram, displayed below.
 The baseand height of a parallelogramform a rightangle.
MP.7

Date: 5/11/15 15
 Measure (inches) the baseand height of the parallelogramusingthecorrect mathematical tools.
 The base is 7 inches, and the height is 3 inches.
 Cut alongthe dotted line.
 Glue both parts of the parallelogramonto a piece of paper to make a rectangle.

 What shapedid you create?
 A rectangle.
 Use the correctmathematical tool to measure (inches) and label each sideof the rectanglecreated from the
original parallelogram.

 How does this compare to the base and height of the parallelogram?
 They are the same.
 When we moved the triangle,did the area insidethe shapechange? Explain.
 The area did not change because it is the same size. It just looks different.
 What is the area of the rectangle?
 21 square inches or 21 inches squared or 21 in2.
NOTE: English learners would benefit from a discussion on why all three of these answers represent the same value.
 If the area of the rectangle is 21 squareinches,whatis the area of the original parallelogram? Why?
 The area of the original parallelogram is also 21 square inches because both shapes have the same
amount of space inside.
 We know the formula for the area of a rectangle is 𝐴𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡,or 𝐴 = 𝑏ℎ. What is the formula to
calculatethe area of a parallelogram?
 The formula to calculate the area of a parallelogram would be the same as a rectangle, 𝐴 = 𝑏ℎ.
 Examine the given parallelogram,label thebaseand height.

MP.7
7 inches
3 inches

Date: 5/11/15 16
 Why is the height the vertical lineand not the slanted edge?
NOTE: English learners may need a further explanation of the meaning of the slanted edge.
 If we look back to the rectangle we created, the base and height of both the rectangle and the original
parallelogram are perpendicular to each other. Therefore, the height of a parallelogram is the
perpendicular line drawn from the top base to the bottom base.
Exercise 1 (5 minutes)
Students work individually to complete the followingproblems.
Exercises
1. Find the areaofeach parallelogram below. Each figure isnot drawn toscale.
a.
b.
c.
Discussion(8 minutes)
 How could we constructa rectangle from this parallelogram?
 Students will try to draw the height of the parallelogram differently.
 Why can’t we use the same method we used previously?
 The vertical dotted line does not go through the entire parallelogram.
Students will struggledrawingthe height becausethey will notbe surewhether part of the height can be outsideof the
parallelogram.
𝑨 = 𝒃𝒉
= 𝟔 𝒄𝒎( 𝟒 𝒄𝒎)
= 𝟐𝟒 𝒄𝒎 𝟐
𝑨 = 𝒃𝒉
= 𝟐𝟓 𝒎( 𝟖 𝒎)
= 𝟐𝟎𝟎 𝒎 𝟐
𝑨 = 𝒃𝒉
= 𝟏𝟐 𝒇𝒕.( 𝟕 𝒇𝒕. )
= 𝟖𝟒 𝒇𝒕. 𝟐
𝟓cm
𝟔cm
𝟒cm
𝟕ft. 𝟏𝟏.𝟓ft.
𝟏𝟐ft.
𝟏𝟎m
𝟐𝟓m
𝟖m
Scaffolding:
English learners may need
some clarification aboutwhat
it means to not be drawn to
scaleand why this may be the
case.
MP.7

Date: 5/11/15 17
 Cut out the shape.
 To solvethis problem, we are actually goingto cut the parallelogramhorizontally into four equal pieces. Use
the appropriatemeasurement tool to determine where to make the cuts.
Allowtime for students to think about how to approach this problem. If time allows,havestudents sharetheir thoughts
before the teacher demonstrates how to move forward.
Teacher should demonstrate these cuts before allowingstudents to make the cuts.
 We have four parallelograms. Howcan we use them to calculatethe area of the parallelogram?
 Turn each of the parallelograms into rectangles.
 How can we make these parallelogramsinto rectangles?
 Cut a right triangle off of every parallelogram and move the right triangle to the other side of the
parallelogram.
 How can we show that the original parallelogramforms a rectangle?
 If we push all the rectangles together, they will form one rectangle.
 Therefore, it does not matter how tilted a parallelogramis. Theformula to calculatethe area will always be
the same as the area formula of a rectangle.
 Draw and label the height of the parallelogrambelow.
base
height

Date: 5/11/15 18
Exercise 2 (5 minutes)
Students complete the exercises individually.
2. Draw and label the height ofeach parallelogram. Use thecorrect mathematical tool to measure (in inches)the base
and height, and calculatetheareaofeach parallelogram.
a.
𝑨 = 𝒃𝒉 = ( 𝟎.𝟓 𝒊𝒏. )( 𝟐 𝒊𝒏. ) = 𝟏 𝒊𝒏 𝟐
b.
𝑨 = 𝒃𝒉 = ( 𝟏.𝟓 𝒊𝒏. )( 𝟐 𝒊𝒏. ) = 𝟑 𝒊𝒏 𝟐
c.
𝑨 = 𝒃𝒉 = ( 𝟏 𝒊𝒏. )( 𝟏 𝒊𝒏. )= 𝟏 𝒊𝒏 𝟐
base
base
height
height
height
base

Date: 5/11/15 19
3. If the areaofaparallelogram is
𝟑𝟓
𝟒𝟐
cm2 and theheight is
𝟏
𝟕
cm, writean equation that relatestheheight, base, and
areaof the parallelogram. Solvetheequation.
𝟑𝟓
𝟒𝟐
𝒄𝒎 𝟐
= 𝒃(
𝟏
𝟕
𝒄𝒎)
𝟑𝟓
𝟒𝟐
𝒄𝒎 𝟐
÷
𝟏
𝟕
𝒄𝒎 = 𝒃(
𝟏
𝟕
𝒄𝒎)÷
𝟏
𝟕
𝒄𝒎
𝟑𝟓
𝟔
𝒄𝒎 = 𝒃
𝟓
𝟓
𝟔
𝒄𝒎 = 𝒃
Closing(3 minutes)
 Why are the area formulas for rectangles and parallelograms thesame?
Exit Ticket (5 minutes)
Scaffolding:
English learners may benefit
from a sentence starter, such
as “The formulas arethe same
because …”
Lesson Summary
The formulato calculate theareaofaparallelogram is 𝑨 = 𝒃𝒉, where 𝒃representsthebase and 𝒉 representsthe
height ofthe parallelogram.
The height ofaparallelogram isthe line segmentperpendicular tothe base. The heightisdrawn from avertex that
isopposite the base.

Date: 5/11/15 20
Name Date
Lesson 1: The Area of Parallelograms Through Rectangle Facts
Exit Ticket
Calculatethe area of each parallelogram. The figures arenot drawn to scale.
1.
2.
3.
35 cm
5 cm 15 cm
42 cm
12 ft.
20 ft.
10 ft.

Date: 5/11/15 21
Exit Ticket Sample Solutions
Calculate the areaofeach parallelogram. The figuresare not drawn to scale.
1.
𝑨 = 𝒃𝒉 = 𝟐𝟎 𝒇𝒕.( 𝟏𝟎 𝒇𝒕. )= 𝟐𝟎𝟎 𝒇𝒕 𝟐
2.
𝑨 = 𝒃𝒉 = 𝟓 𝒄𝒎( 𝟑𝟓 𝒄𝒎)= 𝟏𝟕𝟓 𝒄𝒎 𝟐
3.
𝑨 = 𝒃𝒉 = 𝟕 𝒎( 𝟐 𝒎) = 𝟏𝟒 𝒎 𝟐
Problem Set Sample Solutions
Draw and label the height ofeach parallelogram.
1.
2.
base
height
base
height

Date: 5/11/15 22
Calculate the areaofeach parallelogram. The figuresare not drawn to scale.
3.
𝑨 = 𝒃𝒉
= 𝟏𝟑 𝒄𝒎( 𝟔 𝒄𝒎)
= 𝟕𝟖 𝒄𝒎 𝟐
4.
𝑨 = 𝒃𝒉
= 𝟏.𝟐 𝒇𝒕.( 𝟏𝟐.𝟖 𝒇𝒕. )
= 𝟏𝟓.𝟑𝟔 𝒇𝒕 𝟐
5.
𝑨 = 𝒃𝒉
= 𝟐
𝟏
𝟐
𝒊𝒏.( 𝟓
𝟏
𝟒
𝒊𝒏. )
=
𝟓
𝟐
𝒊𝒏. (
𝟐𝟏
𝟒
𝒊𝒏. )
=
𝟏𝟎𝟓
𝟖
𝒊𝒏 𝟐
= 𝟏𝟑
𝟏
𝟖
𝒊𝒏 𝟐
6.
𝑨 = 𝒃𝒉
= 𝟒
𝟏
𝟑
𝒎( 𝟑
𝟏
𝟐
𝒎)
=
𝟏𝟑
𝟑
𝒎 (
𝟕
𝟐
𝒎)
=
𝟗𝟏
𝟔
𝒎 𝟐
= 𝟏𝟓
𝟏
𝟔
𝒎 𝟐
𝟓
𝟏
𝟒
in.
𝟑
𝟓
𝟔
in.
𝟕
𝟐
𝟑
in.
𝟐
𝟏
𝟐
in.
𝟏.𝟐 ft.
𝟏𝟑.𝟒ft. 𝟏𝟐.𝟖ft.
𝟔cm
𝟏𝟑cm
𝟖cm
𝟑
𝟏
𝟐
m
𝟑
𝟓
𝟔
m𝟒
𝟏
𝟑
m

Date: 5/11/15 23
7. Brittany and Sid were both asked to draw theheight ofaparallelogram. Their answersare below.
Brittany Sid
Are both Brittany and Sid correct? Ifnot, who iscorrect? Explain your answer.
Both Brittany and Sidarecorrect becauseboth oftheir heights represent a linesegment that is perpendicular to the
baseand whoseendpoint is theoppositesideoftheparallelogram.
8. Do the rectangleand parallelogram below havethe same area? Explain why or why not.
Yes, therectangleand parallelogram havethesamearea becauseifwe cut ofthetriangleon theleft sideofthe
parallelogram, wecanmoveit over to theright and maketheparallelogramintoa rectangle. At this time, both
rectangles would havethesamedimensions; therefore, theirareas would bethesame.
9. A parallelogram hasan areaof 𝟐𝟎.𝟑sq. cm and a base of 𝟐.𝟓 cm. Write an equation that relatestheareato the
base and height, 𝒉. Solve the equation todeterminethelength ofthe height.
𝟐𝟎.𝟑 𝒄𝒎 𝟐
= 𝟐. 𝟓 𝒄𝒎( 𝒉)
𝟐𝟎.𝟑 𝒄𝒎 𝟐
÷ 𝟐. 𝟓 𝒄𝒎 = 𝟐.𝟓 𝒄𝒎( 𝒉)÷ 𝟐. 𝟓 𝒄𝒎
𝟖.𝟏𝟐 𝒄𝒎 = 𝒉
base
height
base
height
𝟏𝟓ft.
𝟖ft.
𝟖ft
𝟏𝟓ft.
𝟏𝟎ft.

Date: 5/11/15 24
Multiplication of Fractions – Round 1
Directions: Determine the product of the fractions.
1.
1
2
×
3
4
16.
8
9
×
3
4
2.
5
6
×
5
7
17.
3
4
×
4
7
3.
3
4
×
7
8
18.
1
4
×
8
9
4.
4
5
×
8
9
19.
3
5
×
10
11
5.
1
4
×
3
7
20.
8
13
×
7
24
6.
5
7
×
4
9
21. 2
1
2
× 3
3
4
7.
3
5
×
1
8
22. 1
4
5
× 6
1
3
8.
2
9
×
7
9
23. 8
2
7
× 4
5
6
9.
1
3
×
2
5
24. 5
2
5
× 2
1
8
10.
3
7
×
5
8
25. 4
6
7
× 1
1
4
11.
2
3
×
9
10
26. 2
2
3
× 4
2
5
12.
3
5
×
1
6
27. 6
9
10
× 7
1
3
13.
2
7
×
3
4
28. 1
3
8
× 4
2
5
14.
5
8
×
3
10
29. 3
5
6
× 2
4
15
15.
4
5
×
7
8
30. 4
1
3
× 5
NumberCorrect:______

Date: 5/11/15 25
Multiplication of Fractions – Round 1 [KEY]
1.
1
2
×
3
4
𝟑
𝟖
16.
8
9
×
3
4
𝟐𝟒
𝟑𝟔
=
𝟐
𝟑
2.
5
6
×
5
7
𝟐𝟓
𝟒𝟐
17.
3
4
×
4
7
𝟏𝟐
𝟐𝟖
=
𝟑
𝟕
3.
3
4
×
7
8
𝟐𝟏
𝟑𝟐
18.
1
4
×
8
9
𝟖
𝟑𝟔
=
𝟐
𝟗
4.
4
5
×
8
9
𝟑𝟐
𝟒𝟓
19.
3
5
×
10
11
𝟑𝟎
𝟓𝟓
=
𝟔
𝟏𝟏
5.
1
4
×
3
7
𝟑
𝟐𝟖
20.
8
13
×
7
24
𝟓𝟔
𝟑𝟏𝟐
=
𝟕
𝟑𝟗
6.
5
7
×
4
9
𝟐𝟎
𝟔𝟑
21. 2
1
2
× 3
3
4
𝟕𝟓
𝟖
= 𝟗
𝟑
𝟖
7.
3
5
×
1
8
𝟑
𝟒𝟎
22. 1
4
5
× 6
1
3
𝟏𝟕𝟏
𝟏𝟓
= 𝟏𝟏
𝟐
𝟓
8.
2
9
×
7
9
𝟏𝟒
𝟖𝟏
23. 8
2
7
× 4
5
6
𝟏𝟔𝟖𝟐
𝟒𝟐
= 𝟒𝟎
𝟏
𝟐𝟏
9.
1
3
×
2
5
𝟐
𝟏𝟓
24. 5
2
5
× 2
1
8
𝟒𝟓𝟗
𝟒𝟎
= 𝟏𝟏
𝟏𝟗
𝟒𝟎
10.
3
7
×
5
8
𝟏𝟓
𝟓𝟔
25. 4
6
7
× 1
1
4
𝟏𝟕𝟎
𝟐𝟖
= 𝟔
𝟏
𝟏𝟒
11.
2
3
×
9
10
𝟏𝟖
𝟑𝟎
=
𝟑
𝟓
26. 2
2
3
× 4
2
5
𝟏𝟕𝟔
𝟏𝟓
= 𝟏𝟏
𝟏𝟏
𝟏𝟓
12.
3
5
×
1
6
𝟑
𝟑𝟎
=
𝟏
𝟏𝟎
27. 6
9
10
× 7
1
3
𝟏𝟓𝟏𝟖
𝟑𝟎
= 𝟓𝟎
𝟑
𝟓
13.
2
7
×
3
4
𝟔
𝟐𝟖
=
𝟑
𝟏𝟒
28. 1
3
8
× 4
2
5
𝟐𝟒𝟐
𝟒𝟎
= 𝟔
𝟏
𝟐𝟎
14.
5
8
×
3
10
𝟏𝟓
𝟖𝟎
=
𝟑
𝟏𝟔
29. 3
5
6
× 2
4
15
𝟕𝟖𝟐
𝟗𝟎
= 𝟖
𝟑𝟏
𝟒𝟓
15.
4
5
×
7
8
𝟐𝟖
𝟒𝟎
=
𝟕
𝟏𝟎
30. 4
1
3
× 5
𝟔𝟓
𝟑
= 𝟐𝟏
𝟐
𝟑

Date: 5/11/15 26
Multiplication of Fractions – Round 2
1.
5
6
×
1
4
16.
3
7
×
2
9
2.
2
3
×
5
7
17.
4
5
×
10
13
3.
1
3
×
2
5
18.
2
9
×
3
8
4.
5
7
×
5
8
19.
1
8
×
4
5
5.
3
8
×
7
9
20.
3
7
×
2
15
6.
3
4
×
5
6
21. 1
1
2
× 4
3
4
7.
2
7
×
3
8
22. 2
5
6
× 3
3
8
8.
1
4
×
3
4
23. 1
7
8
× 5
1
5
9.
5
8
×
3
10
24. 6
2
3
× 2
3
8
10.
6
11
×
1
2
25. 7
1
2
× 3
6
7
11.
6
7
×
5
8
26. 3 × 4
1
3
12.
1
6
×
9
10
27. 2
3
5
× 5
1
6
13.
3
4
×
8
9
28. 4
2
5
× 7
14.
5
6
×
2
3
29. 1
4
7
× 2
1
2
15.
1
4
×
8
11
30. 3
5
6
×
3
10
NumberCorrect:______
Improvement:______

Date: 5/11/15 27
Multiplication of Fractions – Round 2 [KEY]
1.
5
6
×
1
4
𝟓
𝟐𝟒
16.
3
7
×
2
9
𝟔
𝟔𝟑
=
𝟐
𝟐𝟏
2.
2
3
×
5
7
𝟏𝟎
𝟐𝟏
17.
4
5
×
10
13
𝟒𝟎
𝟔𝟓
=
𝟖
𝟏𝟑
3.
1
3
×
2
5
𝟐
𝟏𝟓
18.
2
9
×
3
8
𝟔
𝟕𝟐
=
𝟏
𝟏𝟐
4.
5
7
×
5
8
𝟐𝟓
𝟓𝟔
19.
1
8
×
4
5
𝟒
𝟒𝟎
=
𝟏
𝟏𝟎
5.
3
8
×
7
9
𝟐𝟏
𝟕𝟐
=
𝟕
𝟐𝟒
20.
3
7
×
2
15
𝟔
𝟏𝟎𝟓
=
𝟐
𝟑𝟓
6.
3
4
×
5
6
𝟏𝟓
𝟐𝟒
=
𝟓
𝟖
21. 1
1
2
× 4
3
4
𝟓𝟕
𝟖
7.
2
7
×
3
8
𝟔
𝟓𝟔
=
𝟑
𝟐𝟖
22. 2
5
6
× 3
3
8
𝟒𝟓𝟗
𝟒𝟖
= 𝟗
𝟗
𝟏𝟔
8.
1
4
×
3
4
𝟑
𝟏𝟔
23. 1
7
8
× 5
1
5
𝟑𝟗𝟎
𝟒𝟎
= 𝟗
𝟑
𝟒
9.
5
8
×
3
10
𝟏𝟓
𝟖𝟎
=
𝟑
𝟏𝟔
24. 6
2
3
× 2
3
8
𝟑𝟖𝟎
𝟐𝟒
= 𝟏𝟓
𝟓
𝟔
10.
6
11
×
1
2
𝟔
𝟐𝟐
=
𝟑
𝟏𝟏
25. 7
1
2
× 3
6
7
𝟒𝟎𝟓
𝟏𝟒
= 𝟐𝟖
𝟏𝟑
𝟏𝟒
11.
6
7
×
5
8
𝟑𝟎
𝟓𝟔
=
𝟏𝟓
𝟐𝟖
26. 3 × 4
1
3
𝟑𝟗
𝟑
= 𝟏𝟑
12.
1
6
×
9
10
𝟗
𝟔𝟎
=
𝟑
𝟐𝟎
27. 2
3
5
× 5
1
6
𝟒𝟎𝟑
𝟑𝟎
= 𝟏𝟑
𝟏𝟑
𝟑𝟎
13.
3
4
×
8
9
𝟐𝟒
𝟑𝟔
=
𝟐
𝟑
28. 4
2
5
× 7
𝟏𝟓𝟒
𝟓
= 𝟑𝟎
𝟒
𝟓
14.
5
6
×
2
3
𝟏𝟎
𝟏𝟖
=
𝟓
𝟗
29. 1
4
7
× 2
1
2
𝟓𝟓
𝟏𝟒
= 𝟑
𝟏𝟑
𝟏𝟒
15.
1
4
×
8
11
𝟖
𝟒𝟒
=
𝟐
𝟏𝟏
30. 3
5
6
×
3
10
𝟔𝟗
𝟔𝟎
= 𝟏
𝟑
𝟐𝟎

G6 m5-a-lesson 1-t

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G6 m5-a-lesson 1-t