Today we began with a warm-up problem about a quadrilateral inscribed in a circle, finding missing arcs and angles based on "an inscribed angle is half of its intercepted arc" and "opposite angles of a quadrilateral inscribed in a circle are supplementary".

We shared answers and suggestions and questions from the review worksheet and from HW #8 over circumference and arc length.

We also looked at prior knowledge of points on a circle centered at the origin with a radius of 1 (right triangle unit). We used that to get to "what is a unit circle?" "What is standard position?" Which way do we rotate from there? We filled in angle measures of all the special radii on the unit circle. Then we worked on coordinates (based on prior knowledge of 30-60-90 and 45-45-90 shortcuts).

HW #9 is to finish finding coordinates of all the special points on the unit circle. Also do p 323: 22, p 338: 1,2,6,9, and p 343-4: 7-10.

We then took the quiz over circle properties... 4 sketches, 12 unknowns, 2 pts each.

Attached are answers to the worksheet and some information about unit circle.

circle_review_worksheet_answers.pdf |

We added p 575:11-12 to HW #7 and took a grade. We went over HW #7 in detail so that we could understand what we did not "see" in the sketches.

We spent some time reviewing circumference (its definition based on Pi being the ratio of circumference to diameter of every circle). We practiced applying these formulas. Then we went on to arc length, a measure that is not degrees but actual distance around part of a circle (part of a circumference).

Each arc length problem can be solved by applying this definition-based ratio: arc length/ circumference = arc measure/ 360.

HW #8: p 334: 7-14, 16, p 343:1-6.

We then spent the balance of our class time working on a fairly difficult review worksheet with a complex sketch of a circle and its parts that required applying circle properties (C-54-65) to find unknowns.

Quiz next block: 24 pts - study HW #6 & 7 and be able to do the review worksheet (harder than the quiz).

The worksheet is attached below.

circle_properties_worksheet.pdf |

A grade was taken over HW #6 for 4 pts.

We are adding a good amount of content to our geometric truth:

Use the document from Block 30 to follow for writing up definitions concerning circles from pp 67-69 and p 307 and C-54-58 on pp 307-310.

For tonight, you need to write up C-59-65 from pp 313 - 321. You can find sketches from your notes or attached below.

Also define: cyclic quadrilateral and secant from p 321.

For tonight's homework #7, you will do p 322:1-17. Read conjectures and look for "what you are supposed to see" in the sketches. It may be anything from C-54 to 65. Show what you put in your calculator if it is more than one calculation so that you can "debug" your work. It may be helpful to work with a friend and discuss the problems using correct terminology.

pre-ap_geometry_2018_c_59-60_notes.docx |

pre-ap_geometry_2018_c-61-65_notes_and_sketches.docx |

Grades were taken for HW #4 & 5 if not already done (4 pts each).

After sharing the warm-up, we paid attention to being very careful and precise with the marks used in naming parts of circles. For example: arc PQR is not the same as angle PQR nor is either the same as triangle PQR. The symbols are important!

We took notes on C-54-60 over chord and tangent properties. We used a deductive approach to determine why each is true. We recorded enough information in our notes to be able to figure out the homework and write up our conjectures.

The handout below has the homework listed as well as instructions on what to write and sketch in Geometric Truth. Follow instructions carefully.

On your homework, you only need to show enough work to figure out what you put in your calculator. The best approach to the homework is to use the conjectures to figure how what you should be seeing in the sketches. So when you are asked to say which conjecture or definition tells you how to solve the problem, just put down the conjecture number that helped you figure out the problem.

circle_unit_hw#6 and_geometric truth.docx |

We practiced ASPIRE released items in class from many different topics with different strategies and shared answers.

There is no homework.

Click below to go to website to practice with TestNav like we did in class.

Choose Math, Student Sandbox and then log in with username: mathEHS and password: actaspire

On the original screen, you can scroll down to a downloadable PDF file where you can find answers.

Answers to HW #5 are available below.

aspire_practice_answers_hw_5.docx |

The first hour was used for a quick go-over of the review with questions, followed by a notes activity that was a preview of the circle unit.

During the notes activity, we read the attached circle sketches and notes document and highlighted terms with which we lacked familiarity. Class questioning from sketches led to some reasonable definitions of new terms. More notes were created on the back of the document to represent relationships related to tangent lines and inscribed angles. Again, this was a quick preview of the whole unit, with a focus on "what might be on the ASPIRE."

A homework assignment #5 (attached) is to answer the 5 open response questions with 3-4 sentences each as though you were answering on the ASPIRE test. It is recommended to type, but not necessary.

HW #5 aspire_open_response_practice.docx |

circle_preview_notes.pdf |

We practiced finding area of sectors and reasoning through that idea.

We went through all of the content together about surface area on pp 445-449 and we practiced in class and checked our answers: p 450:1-8, pp 439-41: 1-3, 6, 17.

Homework #4 to prepare for the quiz Thurs-Fri was assigned: pp 455-8: 1-10, 17-24, 26, 29-31, and 44.

In the previous blog (one down from here) the answers to this assignment are posted. However, I left out problems 29-31:

#29 - 300 sq cm

#30 - 940 sq cm

#31 - 1356 sq cm.

Remember: quiz next class!]]>

answers_to_chapter_8_review.pdf |

Today in class we had three different pieces of learning:

1) Apply the regular polygon formula until you understand it (warm-up from pp 427-8: 3-6,12).

2) Learn (derive, apply) formulas for Pi, circumference, and area of circles.

3) Find areas in the coordinate plane formed by 3 or 4 graphed lines enclosing a region.

We also went over homework and warm-up thoroughly.

For #2 above, the key issue is to understand that Pi is just the ratio of circumference to diameter for every circle (measure around a round lid, measure across, divide). Circumference is Pi times the Diameter of any circle (just rearrange the definition of Pi. This also leads to C= 2 X Pi X r.

We derived the area of a circle by dissection: take a circle and cut into 16 "pizza slices" (sectors). More would be better, but 16 is enough. Rearrange into a rectangle with side lengths of r and Pi X r, so area = Pi X radius squared.

The bounded area activity and answers are attached. Do this activity on graph paper if you were absent. You can find graph paper online by googling "graph paper PDF" and printing something that you find in an image.

HW #3: pp 427-8: 7-8, 13, 15-16, p 435: 1-14.

Show work. When solving for a dimension, use algebra. On p 435, play attention to = vs. appr =. Approximate means to use the Pi key in the calculator.

pre-ap_geometry_2018_bounded_area_worksheet_and_answers.pdf |

Block 25 was part of our area unit. Our big focus was to derive and apply the area formulas for triangle, trapezoid, kite, and regular polygon.

We began class with a warm-up to find partial area (shaded area) and to find area of a composite figure given vertices. A grade was taken over HW #1. We shared answers and strategies for HW #1 and the warm-up. Problem 9 from the homework was used as foreshadowing for how to find area of any triangle (every triangle is half of a parallelogram).

We then spent time creating notes on graph paper to give ourselves a visual demonstration of the formulas for triangle, trapezoid, kite, and regular polygon.

Everyone should have seen their test by now or taken it for make-up.

HW #2: pp 418-20: 1-11,13,16,17,19,20,23-25, p 427:1-2.

Please show your work! If solving for a dimension, write out the formula, substitute what you know, solve for what you don't know with algebra.

The quiz is Thurs-Fri, April 5-6, 40 pts.

Attached: the notes on the four formulas. Also look at the investigation on p 426.

pre-ap_geometry_2018_area_notes_8.2-3.pdf |