MATH 2110 Introductory Geometry for Middle School Teachers (Barsamian)

Class Presentation Topics

Each of you will be called upon to do ten *Class Presentations* during the semester. After the first week of class, you will always receive your assignment at least a week before you have to make your presentation. The presentations will involve you presenting a basic example during lecture. The basic examples are always about *new material that we will be covering in class that day*. To prepare for these Class Presentations, you will need to read the textbook and study its examples. If you are confused about your Class Presentation Assignment, you are welcome to come to my office hours to discuss it. However, before coming to me for help, you need to be sure and read the book and study its examples, and do some work on the assignment. I will not discuss your assignment with you if you have not studied the book. Each assignment is worth 10 points, with the points given according to the usual 90,80,70,60 scale. Please note that the Class Presentation assignments *cannot* be made-up in the case of absence, even excused absence, because they involve participation in a class discussion.

The daily assignments are listed below.

**Baesman (CP01):**Present solutions to book exercises 1.2 # 2**Bell (CP01):**Present solutions to book exercises 1.2 # 4**Cummings (CP01):**Present solutions to book exercises 1.2 # 6**Diiullo (CP01):**Present solutions to book exercises 1.2 # 18**Dixon (CP01):**Present solutions to book exercises 1.2 # 19**Ferguson (CP01):**Present solutions to book exercises 1.2 # 25**Finnearty (CP01):**Present solutions to book exercises 1.2 # 26**Flowers (CP01):**Present solutions to book exercises 1.2 # 27

**Gilkey (CP01):**Present solutions to book exercises 2.1 # 17**Hohenbrink (CP01):**Present solutions to book exercises 2.1 # 18**Kennedy (CP01):**Present solutions to book exercises 2.1 # 19**Malone (CP01):**Present solutions to book exercises 2.1 # 20**Meisman (CP01):**Present a solution to book exercise 2.1 # 22

**Nickerson (CP01):**Present solutions to book exercises 2.2 # 5 but using 10 toothpicks**Platfoot (CP01):**Present solutions to book exercises 2.2 # 6 but using 11 toothpicks**Schira (CP01):**Present solutions to book exercises 2.2 # 28a, and draw the lines of reflection symmetry**Somogyi (CP01):**Present solutions to book exercises 2.2 # 28b**Sundheimer (CP01):**Present solutions to book exercises 2.2 # 30a, and draw the lines of reflection symmetry**Whitty (CP01):**Present solutions to book exercises 2.2 # 30b**Wilder (CP01):**Present solutions to book exercises 2.2 # 31a(i)**Wright (CP01):**Present solutions to book exercises 2.2 # 31a(ii)

**(Draw your solutions on paper, using big, clear illustrations. In class, we'll project them using the document camera.)**

**Lowe (CP01):**Leftover from Section 2.2: Present solutions to book exercises 2.2 # 35**Baesman (CP02):**Present a solution to book exercise 2.3 # 2**Bell (CP02):**Present a solution to book exercise 2.3 # 4a**Cummings (CP02):**Present a solution to book exercise 2.3 # 4b**Diiullo (CP02):**Present a solution to book exercise 2.3 # 6a**Dixon (CP02):**Present a solution to book exercise 2.3 # 6b**Ferguson (CP02):**Present a solution to book exercise 2.3 # 4c**Finnearty (CP02):**Present a solution to book exercise 2.3 # 33, but not using the pattern from the back of the book.

**Flowers, Gilkey, Hohenbrink, Kennedy (CP02):**I would like for you four students to present a solution to book exercise 2.4 # 6. Get together in advance of class and figure out which hexominoes can be folded up to form a cube. Present a drawing of all those hexominoes (all on one page). Each of you chose one of those hexominoes. (Just one for each of you.) Before class, each of you make a big drawing of your one hexomino, and have it pre-cut and show in class how it can be folded up into a cube.**Lowe (CP02):**Present a solution to book exercise 2.4 # 16abc Which of the drawings in a,b,c is a net for a square pyramid? For the drawings that are, make a big drawing of the net. Have your net pre-cut and show how it can be folded up into a pyramid.**Malone (CP02):**Draw a net for a square pyramid that is*not*one of the drawings in 2.4 # 16abc. Have your net pre-cut and show how it can be folded up into a pyramid.**Meisman (CP02):**Present a solution to book exercise 2.4 # 28

**(I'll have you present your conversions on the chalkboard.)**

**Nickerson (CP02):**Present a solution to book exercise 2.5 # 22. Present the conversion as a single line equation.**Platfoot (CP02):**Present a solution to book exercise 2.5 # 18. Present the conversion as a single line equation.**Schira (CP02):**Present a solution to book exercise 2.5 # 23. Present the conversion as a single line equation.**Somogyi (CP02):**Present a solution to book Section 2.5 Review Exercise #2 (page 99). Present the conversion as a single line equation.**Sundheimer (CP02):**Present a solution to book Section 2.5 Review Exercise #4 (page 99). Present the conversion as a single line equation.**Whitty (CP02):**Present a solution to book Section 2.5 Review Exercise #5 (page 99). Present the conversion as a single line equation.**Wilder (CP02):**Present a solution to book Chapter 2 Test Problem #21 (page 100). Present the conversion as a single line equation.**Wright (CP02):**Present a solution to book Chapter 2 Test Problem #23 (page 101). Present the conversion as a single line equation.

**Baesman (CP03):**(More general version of 3.1 # 11) (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown area
*A*. - Then substitute the particular value
*A*= 25*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
**Bell (CP03):**(More general version of 3.1 # 12) (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown area
*A*. - Then substitute the particular value
*A*= 18.45*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
**Cummings (CP03):**(More general version of 3.1 # 17) (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown perimeter
*P* - Then substitute the particular value
*P*= 72*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown perimeter
**Diiullo (CP03):**(More general version of 3.1 # 18) (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown area
*A* - Then substitute the particular value
*A*= 1440*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
**Dixon (CP03):**Make a large copy of the figure in exercise 3.1#13(a) that you can project using the document camera.- Find the area by using the area of smaller shapes. Explain how you get your answer.
- Find the area again, but this time use
*Pick's Theorem*(See Exercise 3.1#38). Present your calculation.

**Ferguson (CP03):**Make a large copy of the figure in exercise 3.1#13(b) that you can project using the document camera.- Find the area by using the area of smaller shapes. Explain how you get your answer.
- Find the area again, but this time use
*Pick's Theorem*(See Exercise 3.1#38). Present your calculation.

**Finnearty (CP03):**Make a large copy of the figure in exercise 3.1#13(c) that you can project using the document camera.- Find the area by using the area of smaller shapes. Explain how you get your answer.
- Find the area again, but this time use
*Pick's Theorem*(See Exercise 3.1#38). Present your calculation.

**Flowers (CP03):**Present a solution to 3.1 # 53 (a). Use graph paper to make a large, clear version of the figure, and then cut out the pieces answer question (a). Then jump to question (d) and then explain what is happening.

**(I'll have you present your conversions on the chalkboard.)**

**Gilkey (CP03):**Present a solution to a general version of 3.2#14 (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown length
*OP*and known length*PQ*= 1 - Then substitute the particular value
*OP*= 5.3*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown length
**Hohenbrink (CP03):**Present a solution to a general version of 3.2#16 (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 10.5*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
**Kennedy (CP03):**Present a solution to a general version of 3.2#18a (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 5*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
**Lowe (CP03):**Present a solution to a general version of 3.2#18b (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 1*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
**Malone (CP03):**Present a solution to a general version of 3.2#19 (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown side length
*x*. - Then substitute the particular value
*x*= 8*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown side length
**Meisman (CP03):**Present a solution to 3.2#20. (Make a large copy of the figure that you can project using the document camera.)

*Hint:*- Use more colors: Instead of all of the shaded regions being shaded blue, shade them red, green, blue, and gray, with the lower left region red, the lower right region green, the upper right region blue, and the innermost region gray.
- Introduce variables: Use the letters
*x,y,z*to denote the three unshaded regions, starting with*x*for the lower left unshaded region, and then proceeding counterclockwise. - Then compute the red area. your result should involve
*x*. - Then compute the green area. your result should involve
*y*. - Then compute the blue area. your result should involve
*z*. - Then compute the sum of the red, green and blue areas. your result should involve
*x,y,z*. - Then compute the gray area. your result should involve
*x,y,z*.

**Nickerson (CP03):**Present a solution to 3.2#22. (Present your work on the chalkboard.)

(Present your work on the chalkboard.)

**Platfoot (CP03):**A regular hexagon has sides of length*x*. What is the area*A*of the hexagon? (Make a diagram and show the steps clearly.)**Schira (CP03):**A regular hexagon has area*A*. What is the length*x*of the sides of the hexagon? (Make a diagram and show the steps clearly.)**Somogyi (CP03):**Present a solution to a general version of 3.3#22 (Present your work on the chalkboard.)- First, present an analytical solution, using an unknown radius
*R*. (Make a diagram and show the steps clearly.) - Then substitute the particular value
*R*= 15*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius

(Present your work on the chalkboard.)

**Sundheimer (CP03):**Present a solution to 3.3#23 (Make a diagram and show the steps clearly.)**Whitty (CP03):**Present a solution to 3.3#24 (Make a diagram and show the steps clearly.)

(Present your work on the chalkboard.)

**Wilder (CP03):**Present a solution to 3.3#25 (Make a diagram and show the steps clearly.)**Wright (CP03):**Present a solution to 3.3#26 (Make a diagram and show the steps clearly.)

**Baesman CP04:**(Similar to 3.4#3a)- A right prism has height
*h*and has a base that is an equilateral triangle with sides of length*x*. Draw the prism and find its surface area. - Now suppose that the height is 7 and the base has side length 5. Find the surface area.

- A right prism has height
**Bell CP04:**(Related to 3.4#3a)- A right pyramid has sides with slant height
*L*and has a base that is an equilateral triangle with sides of length*x*. Draw the pyramid and find its surface area. - Now suppose that the slant height is 7 and the base has side length 5. Find the surface area.

- A right pyramid has sides with slant height

**Cummings CP04:**(Similar to 3.4#8a)- A right pyramid has a base that is a square with sides of length
*x*and has slant height*L*. Draw the pyramid and find its surface area. - Now suppose that the base has side length 5 and the slant height is 7. Find the surface area.

- A right pyramid has a base that is a square with sides of length
**Diiullo CP04:**(Similar to 3.4#12)- A right pyramid has a base that is a rectangle that has sides of length 2
*a*and 2*b*and has height*h*. Draw the pyramid and find its surface area. - Now suppose that the base has sides of length length 10 and 18 and the height is 12. Find the surface area. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)

- A right pyramid has a base that is a rectangle that has sides of length 2

**Dixon CP04:**(Similar to 3.4#17a)- A right circular cone has base radius
*4*and has slant height*L*. Draw the cone and find its surface area. - Now suppose that the base has radius 5 and the slant height is 13. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.

- A right circular cone has base radius
**Ferguson CP04:**(Similar to 3.4#12)- A right circular cone has base radius
*r*and has height*h*. Draw the cone and find its surface area. - Now suppose that the base has radius 9 and the height is 12. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.

- A right circular cone has base radius

**Finnearty CP04:**Present a solution to to 3.4 # 29, but instead of dimensions 1.25 and 1.86 shown in the picture, use numbers 4 and 7. Give an exact answer in symbols. Then give a decimal approximation

**Flowers (CP04):**(Similar to 3.5#10) A right pyramid has a base that is a regular pentagon that has the following attributes:- The sides of the base have length
*L*= 2*a* - The perpendicular distance from the center of the base to one of its sides is
*b*. - The height is
*h*.

- Draw the pyramid and find its volume.
- Now suppose that
*a*= 5 and*b*= 18 and*h*= 12. Find the volume. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)

- The sides of the base have length
**Gilkey (CP04):**Present a solution to 3.5 #13 about the volume of right circular cones. For both (a) and (b) of the problem, do the following:- Present an answer in exact, simplified form without using a calculator
- Then type your exact answer into a calculator to get a decimal approximation, rounded to two decimal places.

**Hohenbrink (CP04):**(based on 3.5 # 41 about volume of rubber in a tennis ball)- Use circumference
*C*cm and thickness*T*cm. - Use circumference
*C*= 22 cm and thickness*T*= 0.6 cm. Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.) Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.

- Use circumference
**Kennedy (CP04):**Present a solution to 3.5#44 about a steel pipe. Give exact answers in symbols, ready to type into a calculator. Then use a calculator to get decimal approximations rounded to two decimal places

**Lowe (CP04):**(similar to 3.5#17c) Convert 0.47 ft^{3}to cm^{3}- Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.)
- Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.
- Present the conversion as a single line equation (like we did in class).

**Malone (CP04):**(Related to 3.5#43 about pumping liquid out of a spherical tank)- The book's presentation of the problem says to
*recall that 1 ft*. What is the exact conversion? (Show how it is obtained.) (Use the fact that the US gallon is legally defined as 231 cubic inches.)^{3}≈ 7.48 gal - Present a solution 3.5 # 43 but use diameter
*D*ft and liquid volume*G*gallons, and use the exact conversion of ft^{3}to gallons that you found in part (a). - Now find the answer when
*D*= 6 ft liquid volume*G*= 200 gallons. Give an exact answer in symbols, ready to type into a calculator. Then use a calculator to get a decimal approximation rounded to two decimal places

- The book's presentation of the problem says to

**Meisman (CP04):**(similar to 3.5#22) How much do the surface area and volume of a sphere change if its radius is doubled? If its radius is multiplied by some constant*k*? Explain.**Nickerson (CP04):**(similar to 3.5#23) How do the surface area and volume of a rectangular box change if its*length*,*width*, and*height*are all doubled? If they are multiplied by some constant*k*? Explain.

**Platfoot (CP04):**Give an example of a conditional statement*S*such that*S*is true but the converse of*S*is false.**Schira (CP04):**Give an example of a conditional statement*S*such that*S*is true and the converse of*S*is also true.**Somogyi (CP04):**Give an example of a conditional statement*S*such that*S*is false but the converse of*S*is true.**Sundheimer (CP04):**Give an example of a conditional statement*S*such that*S*is false and the converse of*S*is also false.**Whitty (CP04):**Present a solution to Exercise 4.1#22**Wilder (CP04):**Present a solution to Exercise 4.1#26**Wright (CP04):**Present a solution to Exercise 4.1#28

**Baesman (CP05):**Solve 4.2 # 19**Bell (CP05):**Solve 4.2 # 33**Cummings (CP05):**Solve 4.2 # 35**Diiullo (CP05):**Solve 4.2 # 37**Dixon (CP05):**Solve 4.2 # 40**Ferguson (CP05):**Solve 4.2 # 41**Finnearty (CP05):**Solve 4.2 # 42

**Flowers (CP05):**Solve 4.3 # 4 But use ∠*ADE*=*x*and ∠*BAC*=*y***Gilkey (CP05):**Solve 4.3 # 7**Hohenbrink (CP05):**Solve 4.3 # 8**Kennedy (CP05):**Solve 4.3 # 9**Lowe (CP05):**Solve 4.3 # 10**Malone (CP05):**Solve 4.3 # 11**Meisman (CP05):**Solve 4.3 # 12

**Nickerson (CP05):**Solve 4.3 # 13**Platfoot (CP05):**Solve 4.3 # 14**Schira (CP05):**Solve 4.3 # 15**Somogyi (CP05):**Solve 4.3 # 16**Sundheimer (CP05):**Solve 4.3 # 17**Whitty (CP05):**Solve 4.3 # 18**Wilder (CP05):**Solve 4.3 # 19**Wright (CP05):**Solve 4.3 # 22

Do your work on paper, large and clear, ready to project using the document camera.

**Wright (CP06):**Solve 5.1#18 (Present using Document Camera)**Wilder (CP06):**Solve 5.1#30 (Present using Document Camera)**Whitty (CP06):**Solve 5.1#31 but use angle sizes 50 and 85 instead of 55 and 80. (Present using Document Camera)**Sundheimer (CP06):**Solve 5.1#32 (Present using Document Camera)**Somogyi (CP06):**Solve 5.1#36 (Present using Document Camera)**Schira (CP06):**Solve 5.2#21 but use angle sizes 68 and 153 instead of 65 and 150 (Present using Document Camera)**Platfoot (CP06):**Solve 5.2#22 (Present using Document Camera)**Nickerson (CP06):**Solve 5.2#26 (Present using Document Camera)

**Meisman (CP06):**What is the definition of a*parallelogram*? (Find it in the reading.) (Present using Document Camera)**Malone (CP06):**The book says in Corollary 5.15 that in a parallelogram, the opposite sides are congruent and the opposite angles are congruent. Where does that come from? (Present using Document Camera)**Lowe (CP06):**Solve 5.3 # 14 (Present using Document Camera)**Kennedy (CP06):**Solve 5.3#16 (Present using Document Camera)**Hohenbrink (CP06):**Solve 5.3#18 (Present using Document Camera)**Gilkey (CP06):**Solve 5.3#28 (Present using Document Camera)**Flowers (CP06):**Do the proof for 5.3#38 (Present using Document Camera)

First six students: I would like you to do a translation exercise. (You don't have to actually prove anything!) Each of the exercises 5.4 # 39, 40, 41, 42, 43, 44 says to prove some statement. But the statements are worded in a way that is not so helpful for setting up a proof. It would be more helpful if the statements were worded as conditional statements. For each of the five exercises, I want one of yoou to translate the statement to be proven into a new statement that is a conditional statement, "If P then Q." For starters, you can look at the book's presentationm of Theorem 5.27, on page 271. That will actually give you one of the translations that you need. But beware: some of the five exercises that I have assigned to you are worded in a way that is misleading, that makes the translation tricky. (That's why I assigned this as a Class Presentation.) (Each of you: Write both the original statement and your translation clearly on a page ready to project using the document camera.)

**Finnearty (CP06):**Translate 5.4#39.**Ferguson (CP06):**Translate 5.4#40.**Dixon (CP06):**Translate 5.4#41.**Diiullo (CP06):**Translate 5.4#42.**Cummings (CP06):**Translate 5.4#43.**Bell (CP06):**Translate 5.4#44.

Problem Involving Variables and Solving Equations

**Baesman (CP06):**Solve 5.4#12 Write your solution clearly on a page ready to project using the document camera.

(page maintained by Mark Barsamian, last updated Aug 21, 2019 )