6th Grade Unit 1 Lesson 05.notebook1 MATERIALS
Parallelograms
lesso n
UNIT 1
• geometry toolkits
tracing paper, graph  paper, colored pencils,  scissors, and an index  card to use as a  straightedge or to mark  right angles.
crudisel
2 LESSON TITLE 
Parallelograms
3 OBJECTIVE
Objective:   • I know what the terms "base" and 
"height" refer to in a parallelogram. • I can write and explain the formula for 
the area of a parallelogram. • I can identify pairs of base and height of 
a parallelogram.
Bases and Heights of  Parallelograms
6th Grade Unit 1 Lesson 05.notebook
4 WARM­UP
5 WARM­UP
Warm­up partner
Cont...link to worksheetlink to applet
How are the two strategies for finding the  area of a parallelogram the same? How  they are different?
2 students
Elena and Tyler were finding the area of  this parallelogram.
5.1: parallelogram  and its rectangles
Here is how Elena did it:
Here is how Tyler did it:
6 WARM­UP
Cont...link to worksheetlink to applet
How are the two strategies for finding the area of a parallelogram  the same? How they are different?
Though the cuts they made were in different places, were  the cuts the same length?
Was the height of the parallelograms different from the height  of the rectangles?
Does the horizontal base of the parallelogram have the  same length as the horizontal side of the rectangle?
5.1: parallelogram  and its rectangles
7 5.2 ACTIVITY
8 5.2 ACTIVITY
5.2 Activity  partner
1 of 2
Each parallelogram has a side that is labeled “base.”  Study the examples and non­examples of bases and  heights of parallelograms. Then, answer the questions that  follow.
link to worksheet
1. Only a horizontal side of a parallelogram can be a base. 2. Any side of a parallelogram can be a base. 3. A height can be drawn at any angle to the side chosen as the 
base. 4. A base and its corresponding height must be perpendicular 
to each other. 5. A height can only be drawn inside a parallelogram. 6. A height can be drawn outside of the parallelogram, as long 
as it is drawn at a 90­degree angle to the base. 7. A base cannot be extended to meet a height.
2 students
4­5 min partner talk
1. Select all statements that are true  about bases and heights in a 
parallelogram.
Examples: The dashed  segment in each  drawing represents the  corresponding height  for the given base.
Non­examples: The  dashed segment in each  drawing does not  represent the  corresponding height for  the given base.
crudisel
Text Box
false true false true false true false (a base can extend to guide the height but it can't be used as part of the measure of the base)
6th Grade Unit 1 Lesson 05.notebook
9 5.2 ACTIVITY
5.2 Activity  partner
Cont...link to worksheet
5.2 : The Right Height?
6th Grade Unit 1 Lesson 05.notebook
10 ACTIVITY SYNTHESIS
link to worksheet
1. Select all statements that are  true about bases and heights in a 
parallelogram.
5.2 : The Right Height?
Is the vertical side of a parallelogram the same as its height?
6th Grade Unit 1 Lesson 05.notebook
11 ARE YOU READY FOR MORE
Activity 5.2
link to worksheet
in the student online copy.
The applet is from a previous lesson.
link to applet
12 5.3 ACTIVITY
13 5.3 ACTIVITY
5.3 Activity  partner
Cont...link to worksheet
2 students
5 min partner talk
Identify a base and a height for each figure record them  in the table.  Record the areas in the right column.
6th Grade Unit 1 Lesson 05.notebook
14 5.3 ACTIVITY
5.3 : Finding the Formula for Area  of Parallelograms
Identify a base and a height for each figure record them in  the table.  Record the areas in the right column.
How did you choose a base? How can you be sure that  is the height?
How did you find the area? Why did you choose that  strategy for that parallelogram?
Is there another way to find the area and to check our  answer?
6th Grade Unit 1 Lesson 05.notebook
15 ACTIVITY SYNTHESIS
Cont...link to worksheet
5.3 : Finding the Formula for Area  of Parallelograms
How did you determine the expression for  the area for any parallelogram?
Do you think this expression will  always work?
Activity Synthesis
Activity 5.3
link to worksheet
17 LESSON SYNTHESIS
How do you decide the base of a  parallelogram?
Once we have chosen a base, how  can we identify a height that 
corresponds to it?
In how many ways can we identify  a base and a height for a given 
parallelogram?
What is the relationship between  the base and height of a  parallelogram and its area?
In this lesson, we identified a base and a  corresponding height in a parallelogram, and then  wrote an algebraic expression for finding the area 
of any parallelogram.
18 LESSON SUMMARY
Cont...
19 LESSON SUMMARY
Cont...
20 COOL DOWN
link to worksheet
21 PRACTICE PROBLEMS
22 PRACTICE PROBLEMS
23 PRACTICE PROBLEMS
24 PRACTICE SOLUTIONS
25 PRACTICE SOLUTIONS
PRACTICE SOLUTIONS
26 PRACTICE SOLUTIONS
27 Jun 4­1:50 PM
Attachments
m.openup.org/1/6-1-5-1
Unit 1, Lesson 5: Bases and Heights of Parallelograms Let’s investigate the area of parallelograms some more.
5.1: A Parallelogram and Its Rectangles
Elena and Tyler were finding the area of this parallelogram:
Here is how Elena did it:
Here is how Tyler did it:
How are the two strategies for finding the area of a parallelogram the same? How they are different?
GRADE 6 MATHEMATICS BY
1. Each parallelogram has a side that is labeled “base.”
Study the examples and non-examples of bases and heights of parallelograms. Then, answer the questions that follow.
Select all statements that are true about bases and heights in a parallelogram.
a. Only a horizontal side of a parallelogram can be a base.
b. Any side of a parallelogram can be a base.
c. A height can be drawn at any angle to the side chosen as the base.
d. A base and its corresponding height must be perpendicular to each other.
e. A height can only be drawn inside a parallelogram.
f. A height can be drawn outside of the parallelogram, as long as it is drawn at a 90-degree angle to the base.
Examples: The dashed segment in each drawing represents the corresponding height for the given base.
Non-examples: The dashed segment in each drawing does not represent the corresponding height for the given base.
GRADE 6 MATHEMATICS BY
g. A base cannot be extended to meet a height.
2. Five students labeled a base and a corresponding height for each of these parallelograms. Are all drawings correctly labeled? Explain how you know.
GRADE 6 MATHEMATICS BY
For each parallelogram:
Identify a base and a corresponding height, and record their lengths in the table that follows.
Find the area and record it in the right-most column.
In the last row, write an expression using and for the area of any parallelogram.
parallelogram base (units) height (units) area (sq units)
A
B
C
D
Are you ready for more?
1. What happens to the area of a parallelogram if the height doubles but the base is unchanged? If the height triples? If the height is 100 times the original?
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NAME DATE PERIOD
Lesson 5 Summary
We can choose any of the four sides of a parallelogram as the base. Both the side (the segment) and its length (the measurement) are called the base.
If we draw any perpendicular segment from a point on the base to the opposite side of the parallelogram, that segment will always have the same length. We call that value the height. There are infinitely many line segments that can represent the height!
Here are two copies of the same parallelogram. On the left, the side that is the base is 6 units long. Its corresponding height is 4 units. On the right, the side that is the base is 5 units long. Its height is 4.8 units. For both, three different segments are shown to represent the height. We could draw in many more!
No matter which side is chosen as the base, the area of the parallelogram is the product of that base and its corresponding height. We can check it:
and
NAME DATE PERIOD
We can see why this is true by decomposing and rearranging the parallelograms into rectangles.
Notice that the side lengths of each rectangle are the base and height of the parallelogram. Even though the two rectangles have different side lengths, the products of the side lengths are equal, so they have the same area! And both rectangles have the same area as the parallelogram.
We often use letters to stand for numbers. If is base of a parallelogram (in units), and is the corresponding height (in units), then the area of the parallelogram (in square units) is the product of these two numbers.
Notice that we write the multiplication symbol with a small dot instead of a symbol. This is so that we don’t get confused about whether means multiply, or whether the letter is standing in for a number.
In high school, you will be able to prove that a perpendicular segment from a point on one side of a parallelogram to the opposite side will always have the same length.
You can see this most easily when you draw a parallelogram on graph paper. For now, we will just use this as a fact.
Lesson 5 Glossary Terms
base/height of a parallelogram•
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 5: Bases and Heights of Parallelograms 7
Unit 1, Lesson 5: Bases and Heights of Parallelograms
5.1: A Parallelogram and Its Rectangles
5.2: The Right Height?
Are you ready for more?
Lesson 5 Summary
Unit 1, Lesson 5: Bases and Heights of Parallelograms
Parallelograms S and T are each labeled with a base and a corresponding height.
1. What are the values of and for each parallelogram?
Parallelogram S: = _________, = _________
Parallelogram T: = _________, = _________
2. Use the values of and to find the area of each parallelogram.
Area of Parallelogram S:
Area of Parallelogram T:
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 5: Bases and Heights of Parallelograms 1
COOL DOWN
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SMART Notebook
Unit 1, Lesson 5: Bases and Heights of Parallelograms 1. Select all parallelograms that have a correct height labeled for the given base.
2. The side labeled has been chosen as the base for this parallelogram.
3. Find the area of each parallelogram.
Draw a segment showing the height corresponding to that base.
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 5: Bases and Heights of Parallelograms 1
Practice Problems
5. Find the area of each parallelogram.
6. Do you agree with each of these statements? Explain your reasoning.
a. A parallelogram has six sides.
b. Opposite sides of a parallelogram are parallel.
c. A parallelogram can have one pair or two pairs of parallel sides.
d. All sides of a parallelogram have the same length.
e. All angles of a parallelogram have the same measure.
(from Unit 1, Lesson 4)
A. 6 units B. 4.8 units C. 4 units D. 5 units
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 5: Bases and Heights of Parallelograms 2
4. If the side that is 6 units long is the base of this parallelogram, what is its corresponding height?
(from Unit 1, Lesson 2)
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 5: Bases and Heights of Parallelograms 3
7. A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.
a. What is the area, in square meters, of 6 triangles? If you get stuck, draw a diagram.
b. How many triangles are needed to compose a region that is square meters?
Unit 1, Lesson 5: Bases and Heights of Parallelograms
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SMART Notebook
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