Download Complementary and Supplementary Angles

A Unit on 6th Grade Geometry
Danielle Cancelli
Education 352
Professor Schilling
December 6, 2010
TEXTBOOK/ COURSE INFORMATION
NAME OF COURSE/GRADE LEVEL:
6th Grade Mathematics
DESCRIPTION OF COURSE:
This course will help students to develop and improve their mathematical concepts and
problem solving skills.
NAME OF CHAPTER/UNIT:
Unit 4: Measurement and Geometry
DESCRIPTION OF CHAPTER/UNIT:
Students will explore measurements while applying it to geometry. They will study the
metric system, measures of length, mass, time and temperature. They will also study the
measures of angles and polygons. Students will find areas of parallelograms and
triangles. They will explore both two-dimensional and three-dimensional figures.
TITLE OF TEXTBOOK:
Indiana Math Connects: Concepts, Skills, and Problem Solving
NAME(S) OF AUTHOR(S)/EDITOR(S):
Day, Frey, Howard, Hutchens, Luchin, McClain, Molix-Bailey, Ott, Pelfrey, Price,
Vielhaber, Willard.
NAME OF PUBLISHING COMPANY:
The McGraw-Hill Companies, Inc
COPYRIGHT DATE:
2011
READING LEVEL OF TEXTBOOK:
6th Grade
PHILOSOPHY OF READING IN THE CONTENT AREA
STANDARDS:
6.5.1 Select and apply appropriate standard units and tools to measure length, area,
volume, weight, time, temperature, and the size of angles.
6.4.1 Identify complementary and supplementary angles and describe the angle
relationships.
6.4.4 Understand that the sum of the interior angles of any triangle is 180º and the sum
of the interior angles of any quadrilateral is 360º. Use this information to solve
problems.
6.4.3 Draw quadrilaterals and triangles from given information about them.
6.4.5 Identify and draw two-dimensional shapes that are similar.
6.4.6 Draw the translation (slide) and reflection (flip) of shapes.
6.5.7 Construct a cube and rectangular box from two-dimensional patterns and use
these patterns to compute the surface area of the objects.
6.5.8 Use strategies to find the surface area and volume of right prisms and cylinders
using appropriate units (Core Standard).
6.5.10 Add, subtract, multiply, and divide with money in decimal notation (Core
Standard).
IMPORTANCE:
The importance of this unit is to allow the students to explore the world through
measurements and geometry. They will learn the metric system, how to measure time
and how to measure temperature. All of which will be used throughout their lives after
they move on from this class. They are a part of our everyday lives in one way or
another, so students will be able to carry all of this information on with them.
PHILOSOPHY:
Reading is important in every subject, including mathematics. Most students do not
completely understand or believe that to be true, but it most definitely is.
Readability Test
You have already learned to compare fractions. A rational number is a number that can
be expressed as a fraction. Fractions, terminating and repeating decimals, percents, and
integers are all rational numbers. An irrational number is a number that cannot be
expressed as a fraction. Decimals that are both nonterminating and nonrepeating are
irrational numbers. Some common irrational numbers are π, √2, and √3. Together,
rational numbers and irrational numbers make up the set of real numbers. Every real
number is always a certain distance away from zero on the number line. The number line
below shows that –2.5 and
Excerpt One (p. IN3) Number of syllables: 181
Number of sentences: 8.8
The diameter of a music CD is 12 centimeters. Find the circumference of a CD to the
nearest tenth. The Belknap shield volcano is located in Oregon. The volcano is circular
and has a diameter of 5 miles. What is the circumference of this volcano to the nearest
tenth? The largest tree in the world by volume is The General Sherman Tree in Sequoia
National Park. The diameter at the base is 36 feet. If a person with outstretched arms can
reach 6 feet, how many people would it take to reach around the base of the tree? At a
Excerpt Two (p. 532) Number of syllables: 150
Number of sentences: 8.2
A jewelry store is selling a set of 4 pairs of gemstone earrings for $58, including tax.
Neva and three of her friends bought the gift set so each could have one pair of earrings.
Write and solve a multiplication equation to find how much each person should pay. In
the winter of 2004, Pen Hadow and Simon Murray walked 680 miles to the South Pole.
The trip took 58 days. Write and solve a multiplication equation to find about how many
miles they traveled each day. The total time to burn a CD is 18 minutes. Last weekend,
Josiah
Excerpt Three (p.659) Number of syllables: 149
Number of sentences: 7.3
Average # of syllables: 160 Average # of sentences: 8.1
I do not necessarily agree with the readability of the test. I do not think the reading level
is as high as it indicates. I suspected the test would be a little off just because it is a math
book. Math books are harder to do readability tests on, compared to all of the other
subjects, because most of the texts consist of math problems, not necessarily reading.
That is why I don’t think these types of tests are as accurate for math textbooks
Annotate List of Trade Books for Math
1. Burns, M. (1994). The Greedy Triangle. New York. Scholastic, Inc.
The Greedy Triangle is a book about a triangle that can take the shape of many
things, like a piece of pie. It sets out to become many other geometric shapes along
its journey. By becoming the many different geometric shapes, the triangle was able
to take the shape of many more things, like a television or parts of a house. The book
explains the many different types of geometric shapes there are.
2. Neuschwanter, C. (1997). Sir Circumference and the First Round Table: A
Math Adventure. Watertown, MA. Charlesbridge Publishing.
Sir Circumference and the First Round Table: A Math Adventure is about a man and
his knight who set out on an adventure. They were on a mission to find the perfect
shape for his table. It talks about the many geometric shapes that there are and which
one is the most suitable for a table. Sir Circumference and his knight end up finding
the perfect shape.
3. Axelrod, A. (1994). Pigs Will Be Pigs: Fun With Math and Money. New York.
Four Winds Press.
Pigs Will Be Pigs: Fun With Math and Money is a story about a family of pigs. They
get really hungry and eat all of the groceries in their home. They decide that they
want to go out and get more groceries, but they don’t have enough money. They
search around their home for change. Throughout the story they keep track of how
much money is found. This is a good book for teaching children how to add money
and decimals.
4. Schwartz, D. (1985). How Much is a Million. New York, New York. Lee and
Shepard Books.
How Much is a Million is about a magician who shows his friends what a million
looks like in size and thought. For example, he shows them that a fishbowl large
enough to hold a million goldfish would be big enough to hold a whale. He portrays
a million in many ways to show the reader how large it really is.
5. Murphy, S. (1997). Lemonade For Sale. New York, New York. Harper
Collins.
Lemonade For Sale is a book about a group of friends that set up a lemonade stand
that attracts many different neighbors. The friends create bar graphs to look at the
success of their sales. It is a good book to show children how to create bar graphs.
I believe that trade books can enhance my classroom’s content by helping my students
relate to what they are learning. They put math concepts into real-life situations so that
students can better understand how and why those concepts are used. If they can relate
Lesson Plan #1
Danielle Cancelli
Lesson: Fun With Angles
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.5.1 Select and apply appropriate standard units and tools to measure length, area,
volume, weight, time, temperature, and the size of angles.
Performance Objective(s):
The sixth graders will measure angles of different objects in the classroom when given a
corresponding worksheet with six out of eight correct.
Assessment:
Students will be assessed by the completion and correction of the worksheet that they are
given. They will be evaluated by the amount of problems that are answered correctly.
There will be eight cutouts and shapes placed around the classroom. Students will walk
around the classroom and use a protractor to measure the indicated angles of each cutout
or shape. If the student correctly measures the angle, full credit will be given. Students
will be able to partner up with their “math mate” to measure the angles and complete the
worksheet. They will be expected to answer six of the eight problems correctly.
Advance Preparation by Teacher:
Materials:
Worksheets
Cutouts
Protractors
Dry Erase Board
Dry Erase Markers
Preparation:
To prepare for the lesson, make sure that there are enough copies of the worksheet for
each student (worksheet is attached). Make sure that there are enough protractors for
each student, as well. Place the eight cutouts in different areas of the classroom.
Procedure:
Introduction/Motivation:
Pass out the protractors to each student. Allow them to draw and experiment with them
for a short amount of time. See if they can figure out how to use them to draw interesting
shapes. Since the students might not know how to use a protractor to measure angles,
draw a few angles on the board and demonstrate how to do it. Then let the students
experiment for a few minutes by making their own angles on paper and measuring them.
Walk around to make sure the students understand.
Step-by-Step Plan:
1. Pass out protractors to each student in the class.
2. Allow the students to draw and experiment with the protractors for a while so that
they get a hang out how to use them.
3. Allow the students to share their designs that they made with the class (Gardner
Interpersonal).
4. Draw a few angles on the board and show the students how to use the protractor
to measure those angles. (Bloom Level II Comprehension)(Gardner
Visual/Spatial).
5. Allow the students to draw their own angles on paper and experiment measuring
those angles with their protractors. (Bloom Level III Application)(Gardner
Logical/Mathematical).
6. Pass out the worksheets to the students. (Attached).
7. Tell the students to partner up with their “math mates” (Gardner Interpersonal).
Allow them to walk around the room to each different cutout and use their
protractors to measure the indicated angles. Tell them to fill out the worksheet as
they measure the indicated angle of each cutout (Bloom Level III Application)
(Gardner Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with any of
the measurements. If they do need help, spend the last amount of class time working
with them. If they do not need help, review what the students learned throughout the
class by asking them questions (Bloom Level II Comprehension).
1. What is a protractor used for?
2. How do you use the protractor?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand how to properly use a protractor to measure angles?
Name __________________________
FUN WITH ANGLES
Directions: On each cutout there is an arrow pointing to an angle. Use your protractor to
measure the angle and record your measurements.
WHAT IS THE ANGLE MEASURE OF:
CUTOUT 1: _____________
CUTOUT 2: _____________
CUTOUT 3: _____________
CUTOUT 4: _____________
CUTOUT 5: _____________
CUTOUT 6: _____________
CUTOUT 7: _____________
CUTOUT 8: _____________
Lesson Plan #2
Danielle Cancelli
Lesson: Complementary and Supplementary Angles
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.4.1 Identify complementary and supplementary angles and describe the angle
relationships.
Performance Objective(s):
The sixth graders will correctly identify eight out of ten complementary and
supplementary angles when given a corresponding worksheet.
The sixth graders will correctly create eight out of ten complementary and supplementary
angles when given a corresponding worksheet.
Assessment:
Students will be given two worksheets each with ten math problems. They will be
assessed by the completion and correction of each problem on the worksheet. They will
be evaluated by the amount of problems that are answered correctly. If the student
correctly answers the problems on the worksheet, full credit will be given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry Erase Board
Dry Erase Markers
Note cards
Angle Cards
Preparation:
To prepare for the lesson, make sure that there are enough copies of the worksheet for
each student (worksheet is attached). Make sure there are enough angle cards. Also
make sure there are enough note cards for each student to use as language cards for the
definitions of complementary and supplementary angles. Before the students arrive,
write some sample problems on the board (attached) that you will discuss with the
students before the worksheet is given to them.
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about measuring angles. Refresh the
students’ memories on how to use a protractor to measure angles. Then allow the
students to partner up with their “math mates” and ask them to discuss what they think
complementary and supplementary angles are. Once they have had time to discuss, ask
them what they think. Then explain to them what the actual definitions are.
Complementary angles: two angles that have a sum of 90º.
Supplementary angles: two angles that have a sum of 180º.
Step-by-Step Plan:
8. Draw the example problems on the dry erase board.
9. Let the students discuss with their “math mates” what they think complementary
and supplementary angles are. (Bloom Level I Knowledge) (Gardner
Interpersonal).
10. Pass out two note cards to each student. Define both types of angles with the
students so that they can distinguish between the two (Bloom Level II
Comprehension). Let the students write the definitions on one side and the word
on the other. They can use these cards as references for homework and studying.
Complementary angles: two angles that have a sum of 90º.
Supplementary angles: two angles that have a sum of 180º.
11. Put the students into groups of 2 or 3. Pass out a handful of angle cards (each
containing and angle measurement) to each group. Let the groups sort out the
cards into pairs of complementary and supplementary angles (Gardner
Interpersonal) (Bloom Level III Application).
12. Pass out the worksheets to the students. (Attached).
13. Have the students independently complete (Gardner Intrapersonal) the
worksheet problems based on what they have learned and assist those who need
help (Bloom Level III Application) (Gardner Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding the different types of angles. If they do need help, spend the last amount
of class time working with them. If they do not need help, review what the students
learned throughout the class by asking them questions (Bloom Level II
Comprehension).
3. What do complementary angles add up to?
4. What do supplementary angles add up to?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the difference between complementary and supplementary
angles?
Name __________________________
Complementary and Supplementary Angles
Directions: Identify each pair of angles as complementary, supplementary or neither.
1. 65º, 25º
_______________
2. 72º, 108º _______________
3. 124º, 16º
_______________
4. 130º, 50º
_______________
5. 16º, 74º
_______________
6. 60º, 40º
_______________
7. 43º, 47º
_______________
8. 156º, 24º
_______________
9. 5º, 155º
_______________
10. 95º, 85º
_______________
Directions: Given is the measure of one angle. Give the correct measure of the second
angle in order to make the two angles complementary or supplementary to each other.
Complementary Angles:
1. 45º, ________
2. 77º, ________
3. 32º, ________
4. 80º, ________
5. 24º, ________
Supplementary Angles:
1. 126º, ________
2. 75º, ________
3. 164º, ________
4. 88º, ________
5. 145º, ________
SAMPLE PROBLEMS
Complementary, Supplementary, Neither:
55º, 35º Complementary
115º, 65º Supplementary
40º, 70º Neither
Make into complementary angles:
24º, 66º
80º, 10º
Make into supplementary angles:
142º, 38º
70º, 110º
Lesson Plan #3
Danielle Cancelli
Lesson: Angles Within Triangles
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.4.4 Understand that the sum of the interior angles of any triangle is 180º and the sum
of the interior angles of any quadrilateral is 360º. Use this information to solve problems.
Performance Objective(s):
The sixth graders will correctly identify the measures of nine out of ten missing angles of
different triangles when given a corresponding worksheet.
Assessment:
Students will be given a worksheet with ten math problems. They will be assessed by the
completion and correction of each problem on the worksheet. They will be evaluated by
the amount of problems that are answered correctly. If the student correctly answers the
problems on the worksheet, full credit will be given. Students will be expected to answer
sixteen out of the twenty problems that they are given.
Advance Preparation by Teacher:
Materials:
Triangle Cutouts
Worksheets
Dry Erase Board
Dry Erase Markers
Preparation:
To prepare for the lesson, make sure that there are enough copies of the worksheet for
each student (worksheet is attached). Also make sure that there are enough triangle
cutouts for each student. Before the students arrive, write some sample problems on the
board (attached) that you will discuss with the students before the worksheet is given to
them.
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about complementary and
supplementary angles. Refresh the students’ memories on how to create both types of
angles. Then explain to the students that each triangle has three interior angles that add
up to a total of 180º. Do the example problems that are written on the board with the
class. Answer any questions they may have regarding those problems or the information
that you covered.
Step-by-Step Plan:
14. Draw the example problems on the dry erase board.
15. Do the example problems with the entire class. Make sure they understand that for
every triangle, the three interior angles sum up to 180º (Bloom Level I
Knowledge).
16. Pass out the triangle cutouts to each student.
17. Then tell the students to open up their books to the section on Angles In Triangles.
There is an activity in the section that explains the sum of all the angles inside of
a triangle. Read aloud with the students the directions for the activity. It will help
them understand and absorb the information more easily. Explain each step
thoroughly with the triangle cutouts (Bloom Level II Comprehension) (Gardner
Linguistic):
a. Label the three corners of the triangle cutout with the numbers 1, 2, and 3.
(Bloom Level I Knowledge)
b. Rearrange the torn pieces so that the corners all meet at one point. Notice
that together they form a straight line, which equals 180º (Gardner
Logical/Mathematical).
18. Ask the class if they have any questions on why or how the angles add up to 180º.
19. Pass out the worksheets to the students. (Attached).
20. Have the students independently complete (Gardner Intrapersonal) the
worksheet problems based on what they have learned and assist those who need
help (Bloom Level III Application) (Gardner Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding the angles within a triangle. If they do need help, spend the last amount of
class time working with them. If they do not need help, review what the students learned
throughout the class by asking them questions (Bloom Level II Comprehension).
.
5. How many angles are there in a triangle?
6. What do the angles of each triangle add up to?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand that three angles of each triangle sum up to 180º?
Adaptations/Enrichment:
Student with ADHD:
 The hands-on activity will help the student with ADHD stay focused and
interested in the lesson.
 The directions are also brief and to the point. That way the student will be able to
keep their focus on the directions and completely understand what they have to
do.
 The lesson includes both verbal and written directions, which means the student
has more than one way of receiving information. If he/she doesn’t hear all of the
information that is verbally given, there is also written directions that may be
followed.
 Positive reinforcement will also help the student with ADHD because it will give
encouragement, if needed.
Name __________________________
Angles In Triangles
Directions: Two angles of a triangle are given. Find the remaining missing angle.
1. 65º, 25º
_______________
2. 72º, 80º
_______________
3. 104º, 16º
_______________
4. 90º, 50º
_______________
5. 16º, 74º
_______________
6. 60º, 40º
_______________
7. 43º, 47º
_______________
8. 150º, 15º
_______________
9. 5º, 100º
_______________
10. 25º, 85º
_______________
SAMPLE PROBLEMS (write on dry erase board before class)
85º
35º
?
60º
90º
?
?
45º
45º
Lesson Plan #4
Danielle Cancelli
Lesson: Identifying Triangles
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.4.3 Draw quadrilaterals and triangles from given information about them.
Performance Objective(s):
The sixth graders will correctly draw four out of five different types of triangles when
given a corresponding worksheet.
Assessment:
Students will be given a worksheet with five math problems. They will be assessed by
the completion and correction of each problem on the worksheet. They will be evaluated
by the amount of problems that are answered correctly. If the student correctly answers
the problems on the worksheet, full credit will be given. Students will be expected to
answer four out of the five problems that they are given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry Erase board
Individual dry erase boards
Dry erase markers
Preparation:
To prepare for the lesson, make sure that there are enough copies of the worksheet for
each student (worksheet is attached). Before the students arrive, write some sample
triangles on the board (numerous examples of each type of triangle) that you will discuss
with the students before the worksheet is given to them.
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about the angles inside of a triangle.
Refresh the students’ memories by reminding them that each triangle has three interior
angles that add up to a total of 180º. Then explain the definitions of the different types of
triangles. Tell the students the difference between acute, obtuse, and right triangles. Then
tell them the difference between isosceles, equilateral, and scalene triangles. Definitions
are given below. Do the example problems that are written on the board with the class.
Answer any questions they may have regarding those problems or the information that
you covered.
Step-by-Step Plan:
21. Draw some example problems on the dry erase board.
22. Do the example problems with the entire class. Make sure they understand the
definitions of each different type of triangle (Bloom Level I Knowledge).
Definitions:
 Acute: all angles within the triangle are less than 90º.
 Obtuse: there is one angle within the triangle that is greater than 90º.
 Right: there is one angle within the triangle that is 90º.
 Isosceles: there are at least two sides of the triangle that are congruent.
 Equilateral: all sides of the triangle are congruent.
 Scalene: no sides of the triangle are congruent.
23. Pass out a dry erase board and dry erase marker to each student.
24. Give the students information about a triangle (ex-right, scalene) and have them
draw a triangle fitting the description on the dry erase board (Bloom Level III
Application) (Gardner Spatial). Let them hold up their drawings when they are
finished and check to make sure they are all correct. Do this step several times
until you feel that the students are comfortable with the concept. Once finished,
have the students put the dry erase boards and markers away.
25. Ask the class if they have any questions on the different types of triangles.
26. Pass out the worksheets to the students. (Attached).
27. Have the students independently complete (Gardner Intrapersonal) the
worksheet problems based on what they have learned and assist those who need
help (Bloom Level III Application) (Gardner Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding the different types of triangles. If they do need help, spend the last amount
of class time working with them. If they do not need help, review what the students
learned throughout the class by asking them questions (Bloom Level II
Comprehension).
7. What is the difference between acute, obtuse, and right triangles?
8. What is the difference between isosceles, equilateral, and scalene triangles?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the different types of triangles?
Adaptations/Enrichment:
Student with Learning Disabilities:
 The classroom will be neatly organized and rid of all types of distractions in order
to help the student with LD focus on his/her learning.
 He/she will be seated either near the teacher or a peer assistant so that the lesson
is more understandable and help is nearby, if needed.
 The student may also be placed closer to the board in order to make sure he/she
can see the information that is being given.
 A daily schedule will be written on the board so the student can be prepared and
can know what is expected each day.
Name __________________________
Identifying Triangles
Directions: Draw the correct triangle with the given information.
1. Right, Scalene
2. Acute, Isosceles
3. Obtuse, Isosceles
4. Acute, Equilateral
5. Obtuse, Scalene
Lesson Plan #5
Danielle Cancelli
Lesson: Similar Shapes
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.4.5 Identify and draw two-dimensional shapes that are similar.
Performance Objective(s):
The sixth graders will correctly identify eight out of ten similar or non-similar shapes
when given a corresponding worksheet.
The sixth graders will correctly draw eight out of ten different types of shapes when
given a corresponding worksheet.
Assessment:
Students will be given two worksheets, each with ten math problems. They will be
assessed by the completion and correction of each problem on the worksheet. They will
be evaluated by the amount of problems that are answered correctly. If the student
correctly answers the problems on the worksheet, full credit will be given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry erase board
Individual dry erase boards
Dry erase markers
Envelope (containing cutouts)
Preparation:
Before the students arrive, draw some samples of shapes that are similar to each other and
some that are not on the board. You will use the shapes to explain the concept of similar
shapes with the students before the worksheet is given to them. Make sure that there are
enough copies of the worksheet (worksheet is attached) and enough individual dry erase
boards/markers for each student. Also make sure that there are cutouts of shapes in each
envelope (there should be several pairs of similar shapes and several shapes that are not
similar).
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about identifying triangles. Refresh
the students’ memories by reminding them of all the different triangles:
 Acute: all angles within the triangle are less than 90º.
 Obtuse: there is one angle within the triangle that is greater than 90º.
 Right: there is one angle within the triangle that is 90º.
 Isosceles: there are at least two sides of the triangle that are congruent.
 Equilateral: all sides of the triangle are congruent.
 Scalene: no sides of the triangle are congruent.
Explain to the students that figures are similar if they are the same shape, not necessarily
the same size. Show the students the different pairs of similar shapes that are drawn on
the dry erase board. Answer any questions they may have regarding those problems or
the information that you covered.
Step-by-Step Plan:
28. Draw some examples of similar shapes on the dry erase board.
29. Show the students the different similar shapes that are on the board. Explain to
them why the shapes may or may not be similar to one another (must be the same
shape, and do not have to be the same size). Make sure they understand the
concept of similar figures (Bloom Level I Knowledge).
30. Ask the class if they have any questions about similar shapes.
31. Pass out a dry erase board and dry erase marker to each student.
32. Draw a shape on the board and have the students draw a similar shape on their
individual boards (Bloom Level III Application) (Gardner Spatial). Let them
hold up their drawings when they are finished and check to make sure they are all
correct. Do this step several times until you feel that the students are comfortable
with the concept of similar shapes. Once finished, have the students put the dry
erase boards and markers away.
33. Place the students into groups of two or three (Gardner Interpersonal). Pass out
an envelope of shape cutouts to each group. Have the groups sort out the cutouts
into similar shapes (Bloom Level III Application). Walk around and makes sure
they are sorting correctly. This is important because sometimes shapes seem as if
they might be similar, but without truly looking at characteristics of both it is hard
to see. Once finished, have the students put the cutouts back into the envelope
and collect the envelopes.
34. Pass out the worksheets to the students and go over the directions with them so
they know what is expected.
35. Have the students complete the worksheet problems based on what they have
learned and assist those who need help (Bloom Level III Application) (Gardner
Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding similar shapes. If they do need help, spend the last amount of class time
working with them. If they do not need help, review what the students learned
throughout the class by asking them questions (Bloom Level II Comprehension).
9. What makes shapes similar to one another?
10. Do shapes have to be the same size to be similar?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of similar shapes?
Adaptations/Enrichment:
Gifted and Talented:
This unit may be modified for students who are gifted and talented. There are
many ways that the instructional materials and procedures can be modified and adapted
to those students. There are also many advanced learning opportunities that may be
provided that not only will help them, but may also help their fellow students.
Each lesson in the unit may be adapted for high ability students. Enrichment
activities will be offered to those students so that they can study more in-depth in the
subject that is being taught. Homework and worksheets will be modified so that they are
more of a challenge and still advance the students’ learning. There will also be
opportunities for those students to move ahead in the curriculum in order to continue the
learning process.
Those identified as gifted and talented will also be able to use their advanced
knowledge to help their peers (Gardner Interpersonal). They will be able to help those
in need of educational assistance. In turn, it will keep the high ability students active and
push them to use their knowledge at a different level.
Name __________________________
Similar Shapes
Directions: Identify which pairs of shapes are similar. Circle either “SIMILAR” or
“NOT SIMILAR”.
1. SIMILAR
NOT SIMILAR
2. SIMILAR
NOT SIMILAR
3. SIMILAR
NOT SIMILAR
4. SIMILAR
NOT SIMILAR
5. SIMILAR
NOT SIMILAR
6. SIMILAR
NOT SIMILAR
7. SIMILAR
NOT SIMILAR
8. SIMILAR
NOT SIMILAR
9. SIMILAR
NOT SIMILAR
10. SIMILAR
NOT SIMILAR
Directions: Draw a shape that is similar to the given shape.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Lesson Plan #6
Danielle Cancelli
Lesson: Slide and Flip
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Geometry Standard 4
6.4.6 Draw the translation (slide) and reflection (flip) of shapes.
Performance Objective(s):
The sixth graders will correctly translate and reflect eight out of ten problems involving
different types of shapes when given a corresponding worksheet.
Assessment:
Students will be given a worksheet with ten math problems. They will be assessed by the
completion and correction of each problem on the worksheet. They will be evaluated by
the amount of problems that are answered correctly. If the student correctly answers the
problems on the worksheet, full credit will be given. Students will be expected to answer
eight out of the ten problems that they are given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry erase board
Dry erase markers
Graph paper (large and small)
Markers
Shape cutouts
Preparation:
Before the students arrive, draw a large graph on the board. You will use the graph to
explain the concepts of translating and reflecting shapes with the students before the
worksheet is given to them. Make sure that there are enough copies of the worksheet
(worksheet is attached) and pieces of graph paper for each student.
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about similar shapes. Refresh the
students’ memories by reminding them that figures are similar if they are the same shape,
but not necessarily the same size. Have the students partner up and discuss what they
think the difference between translating and reflecting a figure is. Then explain to the
students the difference between translating a figure and reflecting a figure (explained
below). Draw a triangle on the graph and show an example of translating and reflecting
it. Answer any questions they may have regarding the information that you covered.
Step-by-Step Plan:
36. Draw a large graph on the dry erase board.
37. Allow the students to partner up and discuss what they think the difference
between translating and reflecting a figure is (Bloom Level IV Analysis)
(Gardner Interpersonal).
38. Explain to the students how to translate and reflect different shapes on a graph.
Make sure they understand the concept of similar figures (Bloom Level I
Knowledge).
a. Translating a figure means sliding it without turning or flipping it.
b. Reflecting a figure means flipping it across a line of reflection. It is
positioned the same distance from the line as the original shape.
c. Translating and reflecting figures does not change the shape.
39. Draw any shape on the board and show the students how to translate and reflect it
to different areas of the graph.
40. Place the students into groups of two or three (Gardner Interpersonal). Pass out
a large piece of graph paper, markers, and three different shape cutouts to each
group. Tell the groups to start with one of the shapes. Have them trace the shape
onto the graph paper. Tell them to translate that shape a certain amount of units
up and over and to trace that shape at the new location. Then tell them to reflect
the original shape over a certain reflection line and to trace the shape at the new
location. Have them repeat the steps with all three shapes (Bloom Level III
Application) (Gardner Spatial). Walk around and makes sure they are correctly
translating and reflecting the shapes.
41. Pass out the worksheets and regular graph paper to the students and go over the
directions with them so they know what is expected.
42. Have the students complete the worksheet problems based on what they have
learned and assist those who need help (Bloom Level III Application) (Gardner
Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding similar shapes. If they do need help, spend the last amount of class time
working with them. If they do not need help, review what the students learned
throughout the class by asking them questions (Bloom Level II Comprehension).
11. How do you translate a shape?
12. How do you reflect a shape?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of translating and reflecting shapes?
Adaptations/Enrichment:
Student with Behavior Disorder:
 The students will be carefully placed into groups for the group activity. That way
those with a behavior disorder will not be encouraged to display that bad
behavior.
 The rules and consequences will be set in the beginning so that the students know
what is expected of them. They will know what behavior is not accepted in the
classroom.
 Positive behavior will be reinforced. The students will have more of an incentive
to display positive behavior.
 As a teacher, I will be tolerant and patient in order to help these students perform
to the best of their abilities without behavioral problems.
Name __________________________
Slide and Flip
Directions: Slide and flip the figures as instructed.
1. Reflect figure over the x-axis
2. Translate figure 6 units to the left and 8 units down
3. Reflect figure over the line x = -2
4. Translate figure 3 units to the right and 5 units down
5. Reflect figure over the line y = 3
6. Translate figure 9 units to the right and 5 units up
7. Reflect figure over the line y-axis
8. Translate figure 12 units to the right and 9 units down
9. Reflect figure over the x-axis
10. Translate figure 15 units to the left and 14 units up
UNIT TEST
The unit test is given at this point because the standards up to this point all include
information on Geometry. The lessons following the test all include information on
measurements. It will be easier for the students to take a test that is all based on the same
type of information. There is also a modified version of the test. There are fewer
questions, and those questions are at an easier level. That way, the students who need the
modified version may successfully complete each and every problem on time and more
accurately. They won’t have to worry about the complexity of the problems or being
rushed for time. The problems will challenge the students, but they won’t be too difficult.
With the unit test and the modified unit test, I will be able to assess what my students
have learned from the unit.
Name __________________________
Geometry
Unit Exam
Use a protractor to measure the following angles:
1.
2.
3.
Define the following terms:
4. Supplementary angles:
5. Complementary angles:
Identify each pair of angles as supplementary, complementary, or neither:
6. 35º, 55º
____________________
7. 124º, 56º
____________________
8. 28º, 62º
____________________
Given is the measure of one angle. Give the correct measure of the second angle in order
to make the two angles supplementary and complementary.
45º
9. Supplementary:
10. Complementary:
72º
11. Supplementary:
12. Complementary:
Two angles of a triangle are given. Find the remaining missing angle.
13. 44º, 122º, __________
14. 83º, 67º, __________
Identify whether the pairs of shapes are similar or not. Circle one:
15. SIMILAR
NOT SIMILAR
16. SIMILAR
NOT SIMILAR
17. SIMILAR
NOT SIMILAR
Draw a shape that is similar to the given shape:
18.
19.
Given is a figure on a graph. Translate and reflect the figure as instructed:
22. Reflect figure over the x-axis
23. Translate figure 5 units to the right and 4 units down
24. Reflect figure over the line y = 3
25. Translate figure 7 units to the left and 3 units up
Name __________________________
Geometry
Unit Exam
(MODIFIED)
Use a protractor to measure the following angles:
1.
2.
Circle the correct term that matches with the definition:
3. A pair of angles that add up to 90º
Supplementary angles
Complementary angles
4. A pair of angles that add up to 180º
Supplementary angles
Complementary angles
Add the given pair of angles and identify them as supplementary or complementary:
5. 35º, 55º
____________________
6. 124º, 56º
____________________
Given is the measure of one angle. Give the correct measure of the second angle in order
to make the two angles supplementary and complementary.
45º
7. Supplementary:
8. Complementary:
The angles of a triangle always add up to 180º. Two angles of a triangle are given. Find
the remaining missing angle.
9. 45º, 125º, __________
10. 100º, 60º, __________
Identify whether the pairs of shapes are similar or not. Circle one:
11. SIMILAR
NOT SIMILAR
12. SIMILAR
NOT SIMILAR
Draw a shape that is similar to the given shape:
13.
14.
Given is a figure on a graph. Translate and reflect the figure as instructed:
15. Reflect figure over the x-axis
16. Translate figure 5 units to the right and 4 units down
Lesson Plan #7
Danielle Cancelli
Lesson: Surface Area
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Measurement Standard 5
6.5.7 Construct a cube and rectangular box from two-dimensional patterns and use these
patterns to compute the surface area of the objects.
Performance Objective(s):
The sixth graders will correctly compute the surface area of eight out of ten different
cube and rectangular boxes when given a corresponding worksheet.
Assessment:
Students will be given a worksheet with ten math problems. They will be assessed by the
completion and correction of each problem on the worksheet. They will be evaluated by
the amount of problems that are answered correctly. If the student correctly answers the
problems on the worksheet, full credit will be given. Students will be expected to answer
eight out of the ten problems that they are given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry erase board
Dry erase markers
2-dimensional cutouts
Scissors
Tape
Preparation:
Before the students arrive, write the definition and formula for the surface area of
different rectangular prisms on the board (given below in the Step-by-Step). You will use
these to explain how to compute the surface area. Make sure that there are enough copies
of the worksheet (worksheet is attached), cutouts, scissors, and tape for each student.
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about translating and reflecting
different shapes on a graph. Refresh the students’ memories by reminding them how to
do each one.
 Translating a figure means sliding it without turning or flipping it.

Reflecting a figure means flipping it across a line of reflection. It is
positioned the same distance from the line as the original shape.
 Translating and reflecting figures does not change the shape.
Explain to the students that surface area is the sum of the areas of each face. Give them
the definition and formula for the surface area of rectangular prisms (given below in the
Step-by-Step). Answer any questions they may have regarding surface area or the
information that you covered.
Step-by-Step Plan:
43. Write down the definition and formula for the surface area of different rectangular
prisms on the board (Bloom Level I Knowledge).
Definition: The surface area S of a rectangular prism with length l, width w,
and height h is the sum of the areas of the faces.
Formula: S = 2lw + 2lh + 2wh
44. Using the definition and the formula on the board, explain to the students that in
order to find the surface area of a rectangular prism, they must find the area of
each face and add up all of those areas together.
45. Do a couple of examples of finding the surface area with the students so that they
understand the concept. Allow them to work with a partner, if needed (Gardner
Interpersonal) (Gardner Logical/Mathematical).
EX 1: Find the surface area of the cube with dimensions:
l = 5cm h = 5cm w = 5cm
2(5)(5) + 2(5)(5) + 2(5)(5) =
50 + 50 + 50 =
150cm2
EX 2: Find the surface area of the rectangular prism with dimensions:
l = 3in h = 4in w = 5in
2(3)(5) + 2(3)(4) + 2(5)(4) =
30 + 24 + 40 =
94in2
EX 3: Find the surface area of the rectangular prism with dimensions:
l = 4in h = 7in w = 6in
2(4)(6) + 2(4)(7) + 2(6)(7) =
48 + 56 + 84 =
188in2
46. Pass out the 2 different cutouts to each student.
47. Show the students that the 2-dimensional cutout is a way to see each face of the 3dimensional figure separately. Tell them that the areas of the individual faces
must be added together in order to find the surface area.
48. Have the students compute the surface area for each of the three 2-dimensional
cutouts. Help those who have questions on computing any of the surface areas
(Bloom Level III Application).
49. Once the students are all finished, go over the answers to the surface area of each
cutout.
50. Ask the students if they have any questions on how to find the surface area of
rectangular prisms.
51. Allow the students to cut out the 2-dimensional figures and fold/tape them
together so that they can see how it transforms into a 3-dimensional figure
(Bloom Level V Synthesis) (Gardner Spatial).
52. Pass out the worksheets to the students and go over the directions with them so
they know what is expected.
53. Have the students complete the worksheet problems based on what they have
learned and assist those who need help (Bloom Level III Application) (Gardner
Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding surface area. If they do need help, spend the last amount of class time
working with them. If they do not need help, review what the students learned
throughout the class by asking them questions help (Bloom Level II Comprehension).
13. What is the definition of surface area of a rectangular box?
14. What is the formula for the surface area of a rectangular box?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of finding the surface area of rectangular box?
Adaptations/Enrichment:
Autism:
 This lesson may be adapted for students with autism. Optimal communication
patterns and strategies will be designed in order to keep those students prepared
and ready for the lesson.
 If needed, behavior analysis will be applied and reinforcement will be used to
display the appropriate behaviors that are expected.
 The direct instruction that is structured according to the students’ needs will help
make the lesson more understandable.
 The lesson will be prepared in a way that will fit the normal routine that the
students are used to avoid any added stress.
Name __________________________
Surface Area
Directions: Compute the surface area of the rectangular box from the given dimensions.
1. l = 6cm
h = 2cm
w = 4cm
2. l = 7in
h = 3in
w = 3in
3. l = 9ft
h = 12ft
w = 2ft
4. l = 8in
h = 8in
w = 8in
5. l = 10ft
h = 5ft
w = 12ft
6. l = 20cm
h = 1cm
w = 7cm
7. l = 22ft
h = 4ft
w = 3ft
8. l = 9in
h = 5in
w = 9in
9. l = 11cm
h = 18cm
w = 6cm
10. l = 3ft
h = 14ft
w = 16ft
Lesson Plan #8
Danielle Cancelli
Lesson: Surface Area and Volume of Right Prisms and Cylinders
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Measurement Standard 5
6.5.8 Use strategies to find the surface area and volume of right prisms and cylinders
using appropriate units (Core Standard).
Performance Objective(s):
The sixth graders will correctly compute the surface area of four out of five different
objects around the room when given a corresponding worksheet.
The sixth graders will correctly compute the volume of four out of five different objects
around the room when given a corresponding worksheet.
Assessment:
Students will be given a worksheet with ten math problems. They will be assessed by the
completion and correction of each problem on the worksheet. They will be evaluated by
the amount of problems that are answered correctly. If the student correctly answers the
problems on the worksheet, full credit will be given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry erase board
Dry erase markers
3-dimensional objects (already labeled with dimensions)
Preparation:
Before the students arrive, write down the definitions of surface area, volume, and right
prism on the dry erase board. Also write down formulas for surface area and volume of
right prisms and cylinders (given in the Step-by-Step). Place the five different 3dimensional objects around the room (make sure they are labeled with dimensions).
Make sure that there are enough copies of the worksheet (worksheet is attached).
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about finding the surface area of a
rectangular box or cube. Refresh the students’ memories with the following information:

Definition: The surface area S of a rectangular prism with length l,
width w, and height h is the sum of the areas of the faces.
 Formula: S = 2lw + 2lh + 2wh
Explain to the students the difference between surface area and volume (given in the
Step-by-Step). Answer any questions they may have regarding those problems or the
information that you covered.
Step-by-Step Plan:
54. Write down the definitions of surface area, volume, and right prism on the dry
erase board. Also write down formulas for surface area and volume of right
prisms and cylinders (Bloom Level I Knowledge).
Surface Area: The total area of the surface of a 3-dimensional object.
Volume: The amount of units needed to occupy a space inside of an object.
Right Prism: prism with bases aligned one directly above the other and with
lateral faces that are rectangles.
Surface Area:
a. Right Prism: sum of areas of all faces
b. Cylinder: sum of areas of the two circular faces and the area of the
middle (2πr2 + πrh)
Volume:
 Right Prism: area of base x height
 Cylinder: area of one of the circular faces x height (πr2 h)
55. Pass out a dry erase board and dry erase marker to each student. Allow the
students to work out the examples in the next few steps with you on their dryerase boards (Bloom Level III Application) (Gardner Spatial).
56. One the board, do a few examples of surface area (Gardner
Logical/Mathematical).
EX 1: Find the surface area of the rectangular prism with dimensions:
l = 2in h = 4in w = 3in
2(2)(3) + 2(2)(4) + 2(3)(4) =
12 + 16 + 24 =
52in2
EX 2: Find the surface area of the triangular prism with dimensions:
Base (triangle) dimensions: b = 4in, 2in, 6in h = 6
Height: 4in
2(1/2)(4)(6) + 2(4) + 4(4) + 6(4) =
24 + 8 + 16 + 24 =
72in2
EX 3: Find the surface area of the cylinder with dimensions:
r = 5cm h = 4
2π(5)2 + π(5)(4) =
50 π + 20 π =
70 π cm2
57. One the board, do a couple of examples of volume (Gardner
Logical/Mathematical).
EX 1: Find the volume of the rectangular prism with dimensions:
l = 2in h = 4in w = 3in
2(4)(3) =
24in3
EX 2: Find the volume of the triangular prism with dimensions:
Base (triangle) dimensions: b = 4in, 2in, 6in h = 6
Height: 4in
1/2(4)(6)(4) =
48in3
EX 3: Find the volume of the cylinder with dimensions:
r = 5cm h = 4
π(5)2(4) =
100πcm2
58. Have the students get out a piece of paper and a pencil. They will be doing a
writing to learn strategy to help them better understand the content on their own
(Bloom Level II Comprehension)(Gardner Intrapersonal). Have them answer
the following questions:
1. What is the definition of surface area?
2. What is the formula to find the surface area of a cylinder?
3. What is the definition of volume?
4. What is the formula to find the volume of a cylinder?
5. How do you find the surface area of a right prism and a cylinder?
6. How do you find the volume of a right prism and a cylinder?
59. Allow the students to discuss their answers when everyone is finished.
60. Make sure they understand the concept of finding surface area or volume of right
prisms or cylinders (Bloom Level I Knowledge).
61. Ask the class if they have any questions. Answer any questions they may have.
62. Pass out the worksheets to the students and go over the directions with them so
they know what is expected.
63. Put the students into groups of two or three and allow them to walk around the
room and find the surface area and volume of all of the labeled objects (Gardner
Interpersonal).
64. Have the students complete the worksheet problems based on what they have
learned and assist those who need help (Bloom Level III Application) (Gardner
Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding how to find surface area or volume of right prisms or cylinders. If they do
need help, spend the last amount of class time working with them. If they do not need
help, review what the students learned throughout the class by asking them questions
(Bloom Level II Comprehension).
15. How do you find the surface area of right prisms and cylinders?
16. How do you find the volume of right prisms and cylinders?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of finding surface area and volume of right
prisms and cylinders?
Adaptations/Enrichment:
Mental Retardation:
 Preparations will be made in order to make sure that the classroom is an open and
accepting environment. That way that way the students will comfortable and
more willing to learn each day.
 Instruction may be modified by reducing reading, writing, and language
requirements or by simplifying the worksheets.
 Some students may need a more functional curriculum. In that case the teacher
may use a specialized curriculum using domestic skills, leisure skills, and
communication.
 If needed, the teacher may pre-teach the daily routing so that the students know
what to expect and what is expected of them.
 Also, in order to make sure that the students are not being taken advantage of,
peer relationships will be monitored.
Name __________________________
Surface Area and Volume
Directions: Compute the surface area and volume of each labeled, 3-dimensional figure
in the room.
1. Surface Area:
Volume:
2. Surface Area:
Volume:
3. Surface Area:
Volume:
4. Surface Area:
Volume:
5. Surface Area:
Volume:
Lesson Plan #9
Danielle Cancelli
Lesson: Decimals and Money
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Academic Standard(s):
Measurement Standard 5
6.5.10 Add, subtract, multiply, and divide with money in decimal notation (Core
Standard).
Performance Objective(s):
The sixth graders will correctly answer eight out of ten different decimal (money)
problems when given a corresponding worksheet.
Assessment:
Students will be given a worksheet with ten math problems. They will be assessed by the
completion and correction of each problem on the worksheet. They will be evaluated by
the amount of problems that are answered correctly. If the student correctly answers the
problems on the worksheet, full credit will be given.
Advance Preparation by Teacher:
Materials:
Worksheets
Dry erase board
Individual dry erase boards
Dry erase markers
Fake money (both bills and coins)
Preparation:
Before the students arrive, write down four different examples of the lesson (given in the
Step-by-Step) on the dry erase board. Make sure that there is enough fake money for each
group. Also make sure that there are enough copies of the worksheet (worksheet is
attached).
Procedure:
Introduction/Motivation:
Begin the lesson by reviewing the previous lesson about surface area and volume.
Refresh the students’ memories with the following information:
 Surface Area: The total area of the surface of a 3-dimensional object.
 Volume: The amount of units needed to occupy a space inside of an
object.

Right Prism: prism with bases aligned one directly above the other
and with lateral faces that are rectangles.
Surface Area:
a. Right Prism: sum of areas of all faces
b. Cylinder: sum of areas of the two circular faces and the area of the
middle (2πr2 + πrh)
Volume:
 Right Prism: area of base x height
 Cylinder: area of one of the circular faces x height (πr2 h)
To grab the student’s attention, ask them who in the classroom likes money. Then ask
them why they think being able to add, subtract, multiply, and divide money is important.
Tell them that in order to do those things, they must know how to work with decimals
because money is handled in decimal form. Answer any questions they may have
regarding those problems or the information that you covered.
Step-by-Step Plan:
65. Write down some examples of adding, subtracting, multiplying, and dividing
decimals on the dry erase board so that the students can see the format for each
(Bloom Level I Knowledge).
66. Pass out the graphic organizer for the students to complete while practicing the
example problems in the next steps (attached).
67. Show the students the correct way to add and subtract decimals (money). Make
sure they know to line up the decimals each time.
EX: 34.05
+ 4.92
------------38.97
EX: 87.62
- 2.50
------------85.12
68. Show the students the correct way to multiply decimals (money). Make sure that
they know they do not have to line up the decimal the same way.
EX: 10.40
x2
------------20.80
69. Show the students the correct way to divide decimals (money). Make sure that
they know they have to move the decimal over so that it is at the end of the
dividend, and that they move the decimal the same amount for the divisor.
EX: 35/.5 =
70. Do several examples so that they understand the concept.
71. Put the students into groups of four or five (Gardner Interpersonal). Pass out a
dry erase board and dry erase marker to each group. Tell the students that they
will be competing for fake money. The teacher will give them all a problem to
work out at the same time. When the groups are done they need to hold up their
answers on the dry erase board. The group that comes in first gets a fake $100.
The second group gets a fake $50. The third group gets a fake $25. The fourth
group gets a fake $10. If the answer is wrong, the group must subtract $0.25
(Bloom Level III Application) (Gardner Spatial) (Gardner
Logical/Mathematical).
72. Once the game is finished, have the groups add up their total amount of money.
The group with the most amount of fake money wins.
73. Make sure they understand the concept of adding, subtracting, multiplying, and
dividing decimals and money (Bloom Level I Knowledge).
74. Ask the class if they have any questions. Answer any questions they may have.
75. Pass out the worksheets to the students and go over the directions with them so
they know what is expected.
76. Have the students individually (Gardner Intrapersonal) complete the worksheet
problems based on what they have learned and assist those who need help (Bloom
Level III Application) (Gardner Logical/Mathematical).
Closure:
At the end of class, ask the students if they have any questions or need help with
understanding the concept of adding, subtracting, multiplying, and dividing decimals and
money. If they do need help, spend the last amount of class time working with them. If
they do not need help, review what the students learned throughout the class by asking
them questions (Bloom Level II Comprehension).
17. How do you line up the decimals when adding and subtracting decimals or
money?
18. How do you line up the decimals when multiplying decimals or money?
19. How do you line up the decimals when dividing decimals or money?
Self-Reflection:
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of finding surface area and volume of right
prisms and cylinders?
Adaptations/Enrichment:
Visual Impairments:
 Students with visual impairments will be familiarized with the physical
arrangement of the room, and they will be notified of any changes.



Printed materials may be enlarged and enhanced to help increase visibility. If
needed, print may be converted to Braille.
Since it takes more time to read enlarged print or Braille, sufficient time will be
provided in order to ensure students time to complete what they need to complete.
Presentations will be precise and vague phrases will be avoided.
Hearing Impairments:
 Students with hearing impairments will be seated towards the front of the
classroom. That way they are more easily able to hear or read speech.
 If available, technology will be used. That technology may include things like
hearing aids, television captions, computer-assisted instruction, and the Internet.
 Language cards containing important vocabulary and concepts may be used for
those with hearing impairments.
 Important information or questions will be written down on the overhead or the
board.
Name __________________________
Decimals and Money
Directions: Add, Subtract, Divide, or multiply the dollar amounts as instructed.
1. $73.91 + $15.48
2. $345.23 + $98.55
3. $73.30 - $54.91
4. $823.08 – $247.39
5. $62.62 x 4
6. $12.50 x 12
7. $150.75 / 25
8. $84.05 / .015
9. $73.72 + $8.02 - $ 15.60
10. $12.20 x 2 + $5.99
Example
Example
Subtracting
Decimals
Adding
Decimals
Decimals
Multiplying
Decimals
Example
Dividing
Decimals
Example
Unit Reflection
I believe that experiences and observations are a huge influence on how a teacher
is shaped, but I also believe that information and knowledge gained from textbooks is a
vital part in forming a successful teacher. Throughout the semester I have learned a lot
about the different types of exceptionalities and how to adapt to them as a teacher. It was
extremely helpful to me to read and learn more about each type of
disability/exceptionality because I wasn’t quite aware of how each one affects the
students. I feel as if I now have a much better understanding of how the different types
of students live and act. The readings have helped to show different ways to be
successful in teaching general education and those exceptional students at the same time.
As a teacher, not only do I have to be prepared for students with exceptionalities,
but I also have to be prepared for the general education students as well. Each individual
student, whether he/she is exceptional or not, has certain needs and expectations. I have
to learn how to adapt to each and every one of those needs in order to give my students
the most effective learning environment. I also have to learn how to be successful as an
inclusive teacher. From the reading, I learned that effective communication is the key to
making that happen. This includes using active listening skills, depersonalizing
situations by avoiding negative comments, finding common goals, brainstorming possible
solutions, summarizing goals and solutions, and following up to monitor progress. With
those steps, students will be more comfortable in the classroom, which makes them more
willing to learn to the best of their abilities.
One of the things that I think will be most beneficial in helping teach my class is
the PASS variables, which is helpful with including those with special needs in the
classroom. By prioritizing my instruction by the importance level of the curriculum,
students will be able to learn what is most important, rather than focusing on more
insignificant information. Adapting instruction, materials, and the environment is an
important key in making sure that the needs of students of all types are met. There are
several ways that I can adapt to the needs of students through different types of learning
techniques (discrimination learning, factual learning, rule learning, procedural learning,
etc). By systematically teaching the SCREAM variables (structure, clarity, redundancy,
enthusiasm, appropriate rate, and maximized engagement), I can more effectively teach
my students the content that they need to know. By methodically evaluating the
outcomes of my instruction, I can keep track of my students’ progress and the success of
my lessons. Putting the PASS variables to use is an effective way to ensure effective
inclusion in the classroom. That is why I feel that it is one of the most helpful pieces of
information that I received from the textbook. I will be more prepared and effective with
creating a successful classroom environment.
Reading the textbook has provided me with a lot of helpful information that I will
carry on with me to my classroom in the future. With the combination of reading and the
experiences in the classroom, I hope to be successful in providing an effective inclusive
classroom for my students.