Chapter 8 – Measurement
Section 1 – Estimating Perimeter and Area
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To estimate length, perimeter and area.
Content Standard:
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
Video Tutor.
Lesson Procedure:
1. Bell Ringer – Coach Connected book
2. Discuss concepts to be learned in the new chapter.
3. Introduce the new topic and practice
1. Discuss Chapter terms p. 373
2. Review p. 374 Example 1 – online book

7-3 = 1/(73)
(-5)-2 = 1/(-5)2
3. Discuss area and perimeter.
4. Example 2 and Example 3 – use PHschool.com Video Tutor

Students complete Examples with the handout – see attachment
5. Example 4 – Review book example.
4. Assign homework: pg. 377 #6 – 23 all.
Chapter 8 – Measurement
Section 2 – Area of a Parallelogram
Class time: - 90 minutes (double period)
Grade Level: - 7th grade Math
Objectives: To find the area and perimeter of a parallelogram.
Content Standard: 6.G.1
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard.
Lesson Procedure:
1. Bell Ringer – draw a rectangle, show where the area and perimeter are.
2. Review homework and check for understanding.
3. Introduce the new topic and practice

Review
1. Area is number of square units a figure encloses (the inside)
2. Perimeter is a distance abound the figure
3. Parallelogram is a figure with two pairs of parallel sides

Draw a parallelogram, then have the students find the area formula on the
Reference Sheet

Show the students transparency with a transformation from a rectangle to a
parallelogram to prove the area formula.

Review Example 1 from the book and then do additional problem on the board:
1. Ex. 1 Find the area (measured in unites squared)
24 ft
9ft
A = bh
1. Write the formula
A = (24)(9)
2. Substitute
A = 216 ft2

3. Simplify
How would we find a perimeter of this parallelogram?
1. Is there a formula on the reference sheet? (no) So how do we find it?
Perimeter is a sum of the lengths of all sides.

Review Example 2 from the book, then do an additional problem on the board:
1. Ex. 2 – A backyard rectangular pool has a perimeter of 90ft and area of 500ft2.
What are the lengths and widths?
A = 500ft2
P = 90ft = sum of all sides = 2l + 2w
P = 90 ft
A = 500ft2 = lw
Guess and check:
Do area first: Find factors of 500
Perimeter
A = lw
P = 2l + 2w
5(100)
P = 2(5) + 2(50) ≠ 90
(10)(50)
P = 2(10) + 2(50) ≠ 90
(20)(25)
P = 2(20) + 2(25) = 90
Therefore, the length is 25ft and the width is 20ft.
4. Assign homework: pg. 382 #6 – 19 all, 22 & 23.
5. Work on Coach Connected to prepare for NJASK exam.
Chapter 8 – Measurement
Section 3 – Perimeter and Area of a Triangle
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To find the area and perimeter of a triangle.
Content Standard: 6.G.1
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard.
Lesson Procedure:
5. Bell Ringer – Coach Connected book.
6. Review homework and check for understanding.
7. Introduce the new topic and practice
1. Draw a triangle, then have the students find the perimeter formula on the
Reference Sheet (not there) so the perimeter is defined as the sum of all sides.
2. Review Example 1 from the book and then do additional problem on the board:
1. Ex. 1 Find the perimeter:
P = sum of sides
1. Write the formula
P = 7 + 10 + 14
2. Substitute
P = 31 ft
3. Simplify
3. Find an area formula on the Reference Sheet --> A = 0.5bh
4. Show the students transparency with a transformation from a parallelogram to a
triangle to prove the area formula.
5. Ex. 2 Find the Area:
a.
12m
36m
b.
A = 0.5bh
1. Write the formula
A = 0.5(36)(12)
2. Substitute
A = 216 m2
3. Simplify
A = 0.5bh
6cm
A = 0.5(16)(6)
16cm
A = 48 cm2
c. A school is creating a triangular playground. Find the area if the base is 80yd
and the height is 40yd.
A = 0.5bh
A = 0.5(80)(40)
A = 1600yd2
8. Assign homework: pg. 386 #2 – 26 even, 25.
Chapter 8 – Measurement
Section 4 – Area of other Figures – Day 1
Class time: - 90 minutes (double period)
Grade Level: - 7th grade Math
Objectives: To find an area of a trapezoid.
Content Standard: 4.2.7.E.1, 4.5.A.2
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator.
Lesson Procedure:
1. Bell Ringer – Coach Connected book.
2. Review homework and check for understanding.
3. Introduce the new topic and practice
1. Draw a trapezoid, and then have the students define the figure and identify the
height and bases of the trapezoid.
2. Find formula for an area of a trapezoid on the reference sheet.
3. Write the formula on the board and identify the parts of it:
A = 0.5h(b1 + b2) where h is height (distance from top base to the bottom base), b1
– top or bottom base, b2 – the other base
4. Perimeter of the trapezoid – Sum of all sides.
5. Show the students transparency with a transformation from a parallelogram to a
trapezoid to prove the area formula.
6. Ex. 1 – Find the Area
6cm
6cm
16cm
A = 0.5h(b1 + b2)
1. Write the formula
A = 0.5(6)(6 + 10)
2. Substitute
A = (3)(16) = 48 cm2 3. Simplify
7. Ex. 2 – Estimate the area of a piece of metal by using the trapezoid shown:
A = 0.5h(b1 + b2)
1. Write the formula
h = 9cm
A = 0.5(9)(10 + 18)
2. Substitute
b1 = 10cm
A = 126 cm2
3. Simplify
b2 = 8 + 10 = 18
4. Assign homework: pg. 391 #1 – 8 all, 12 – 17 all.
5. Work on Coach Connected books to prepare for NJASK.
Section 4 – Area of other Figures – Day 2
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To find an area of an irregular figure.
Content Standard: 4.2.7.E.1, 4.5.A.2
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator.
Lesson Procedure:
1. Bell Ringer – Coach Connected book.
2. Review homework and check for understanding.
3. Introduce the new topic and practice
1. Review page 390 in the textbook. Look at the figure and decide what kind of a
shape it is. The students will identify that the figure doesn’t have an actual name
2. Show the students how to take a part the figure to find shapes that we know how
to find areas of.
3. Write the data and formulas on the board and find areas of each figure as done in
Ryan’s method on page 390.
4. Ex. 1 – Find the Area
1. Divide into known polygons
3
6
2
2. Identify the dimensions
6
3. Find area of each part
16
4. Add the three areas together.
Rectangle #1
Rectangle #2
Triangle
L=6
l=6
b = 16 – 6 – 6 = 4
W=3
w=3–2=1
h=2+1=3
A = lw
A = lw
A=
1
bh
2
A = (6)(3)
A = (6)(1)
A=
1
( 4)(3)
2
A = 18m2
A = 6m2
A = 6m2
A = 18 + 6 + 6 = 30m2
4. Assign homework: pg. 391 #l0, 11, 18, 19, 21.
Chapter 8 – Measurement
Section 5 – Circumference and Area of a Circle – Day 1
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To find an area and perimeter of a circle.
Content Standard: 7.G.4, 7.G.6
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator, Brain Pop Video, YouTube.
Lesson Procedure:
1. Bell Ringer – Coach Connected book.
2. Review homework and check for understanding.
3. Show Brain Pop Video or Pi Day video on YouTube.com
4. Introduce the new topic and practice
5. Circumference – the distance around the circle (equivalent to perimeter)
6. Pi = the ratio of a circle’s circumference (C) to its diameter (d). Symbol π
7. Review π =
C
22
.π=
We use 3.14 not the π key on the calculator
7
d
1. What’s today’s date? 3/14 reminds you of π? Today is called a Pi day for that
reason. What a great coincidence to learn about circumference and area of a
circle on a Pi day!
8. We start with the circumference. Ask students to find the formulas on the
reference sheet.
1. C = πd
or
C = 2πr
Use the first when you have the diameter (d) given, for π use 3.14
Use the second formula when you have radius (r) given. 2 is always there and
never changes (ASK the students why they think we need that 2 there – radius
is half of a diameter), use 3.14 for π and r is the radius.
9. Ex. 1 – Find the circumference to the nearest tenth.
a)
9yd
b)
40cm
C = 2πr
1. Write the formula
C = (2)(3.14)(9)
2. Substitute
C = 56.52
3. Simplify
C = 56.5 yd
4. Round if necessary
C = πd
1. Write formula
C = (3.14)(40)
2. Substitute
C = 125.6 cm
3. Simplify and round if necessary
10. Area – the inside of the circle. Ask the students to find the formula on their
reference sheets.
1. A = πr2 where r is the radius and π = 3.14
11. Ex. 2 – Find the area to the nearest unit
a)
8.5m
b)
A = πr2
1. Write the formula
A = (3.14)(8.5)2
2. Substitute
A = 226.865
3. Simplify
A = 227m2
4. Round to the nearest unit
d = 15
7.5km
r = 15 ÷ 2 = 7.5
A = πr2
1. Write the formula
A = (3.14)(7.5)
2. Substitute
A = 176.625
3. Simplify
A = 177km2
4. Round to the nearest unit
9. Assign homework: pg. 396 #7 – 27 odd.
Section 5 – Shaded and Unshaded Circles – Area – Day 2
Class time: - 90 minutes
Grade Level: - 7th grade Math
Objectives: To find an area and circumference of a circle.
Content Standard: 7.G.4, 7.G.6
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator, transparencies.
Lesson Procedure:
1. Bell Ringer – Coach Connected book.
2. Review homework and check for understanding.
3. Introduce the new topic and practice
a. Review area and perimeter formulas for circles. Remind the shape they saw
yesterday, with the shaded circle with missing small circles form the inside.
b. Ex. 1 – Find the area of the shaded region to the nearest tenth. The radius of the
large circle is 8in. The radius of each small circle is 2in.

Talk about how to do it (remind them about a problem from few days ago
about the kitchen island that doesn’t need tile)

Show the transparency with the visual of the drawn figure with the shaded
and unshaded region.
1. Find the area of the shaded region.
Area of the large circle. A = πR2
A = (3.14)(8)2
A = 200.96in2
A = (3.14)(64)
(use all decimal places)
2. Find the area of the unshaded region. First find the area of one
small circle:
A = πr2
A = (3.14)(2)2
A = 12.56in2
Now this is only one small circle, and we have three of them so we
need to multiply the area of one small circle by 3: (12.56)(3) =
37.68in2
3. Subtract the area of the 3 unshaded circles from the area of the
large circle:
A = 200.96 – 37.68 = 163.28 in2 = 163.3in2 – round to one decimal
place.
c. Give the students a worksheet – Enrichment 8.5 to work in class and then finish fr
homework. They can work in pairs if they want to, but each person has to have all
the work.
4. Assign homework: Finish Enrichment 8.5 worksheet.
5. If time work in Coach Connected books to prepare for NJ ASK.
Chapter 8 – Measurement
Section 6 – Square Roots and Irrational Numbers – Day 1
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To .
Content Standard:
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator, square root table.
Lesson Procedure:
1. Bell Ringer – Coach Connected book.
2. Review homework and check for understanding.
3. Introduce the new topic and practice
4. In chapter 2 we simplified expressions with exponents.
Recall: 42
Means: 4(4) or “4 squared”
4 is the base and 2 is the exponent
In the square each side is 4 in. A = side2
5.
(find on reference sheet). A = s2 A = 42 = 16 in2
There are 16 square inches inside this square. The number 4 is the square root.
6. Terms:
Perfect Square: a number that is the square of an integer. Ex. The square of 4 is
16. 42 = 16, so 16 is a perfect square.
Square root: the inverse of squaring a number. Symbol
(radical sign).
7. Pass out square root table and have the students highlight the perfect squares.
8. Pass out calculators.
9. Ex. 1 – Find the square root: (ask the students to use both calculators and tables)
a)
49
72 = 49,
49 = 7
b)
81
92 = 81,
81 = 9
10. Show on the SMARTboard and review bottom of page 400.
11. Ex. 2 – Estimate the square root.
60 - check the table – not a perfect square.
49 = 7
60 is closer to
64 = 8
64 so
1. Check if perfect square
2. Find 2 perfect squares it is between
60 ≈ 8 3. Choose closest perfect square
12. Assign homework: pg. 402, #6 – 21 all, 30, 31, 41, 44, 47.
Section 6 – Square Roots and Irrational Numbers – Day 2
Class time: - 45 minutes
Grade Level: - 7th grade Math
Objectives: To .
Content Standard:
Materials: Textbook – Prentice Hall Course 2 hard copy and online version, SMARTboard,
calculator.
Lesson Procedure:
10. Bell Ringer – Coach Connected book.
11. Review homework and check for understanding.
12. Introduce the new topic and practice
1.
Recall: Rational numbers can be written as the ratio of 2 integers terminate or
repeat in decimal form. Ex.
4 , 0.125, 6, 0.3
2. Irrational numbers cannot be written as the ratio of 2 integers. They neither repeat
nor terminate. Ex.
2 , 3 , π, 5.196152423…
3.
Real Numbers
Rational #s
Irrational #s
Integers
Whole #s
Natural #s
4. Ex. 3 – Classify numbers as rational or irrational ( R or I)
a)
121 = 11 R
1. Find equivalent decimal
b)
30 = 5.477225575… I
2. Identify
c) – 0.5167 R
d) 29.2992999…
e) 0.6
f) 1
I
R
6
= 1.2857142857 - ask the students to do this one on a calculator, hit F -->
7
D 2 times (show on SB calculator – it shows that it repeats).
13. Assign homework: pg 402 # 22 -29 all, 34 – 39 all – read directions!