We took a quiz today over Circle Properties - 24 pts.
Over 20 students missed the quiz. It must be taken by Tuesday A&E, no excuses. Sign up now for A&E unless you have made other arrangements for a specific time with me. 
Today we started a new important topic, the last new material of the Circle Unit. Next time we meet we will: finish learning about unit circle, practice writing equations of circles (learned previously), do some area problems based on circle properties.
We did a warm-up with practice over quadrilateral inscribed in a circle (attached).
We went over the worksheet (answers attached) and HW #8 from p 478 and 483. I demonstrated how to find radius algebraically if you know arc length. Any questions were answered.
Then we started learning about special degrees and coordinates on the unit circle. (Blank and partially answered is attached.)
HW #9: finish finding coordinates of special points on the unit circle. Also from textbook (circumference and arc length): p 479:13,14,16 and p 483-4: 5-7, 9-10, 17-18. Show work or sketch.
Unit Circle is an important new idea: a circle with a radius of 1 centered at the origin. We used our 30-60-90 and 45-45-90 to find points on the circle for angles of rotation that are multiples of 30 degrees or 45 degrees. You can google "unit circle" video and find help.
Only 9 more blocks of new material... every day is important!
Tests: 0B will test circles next Thurs, April 25 (at least the first part of the test). A day will test Fri, April 26. 6th will test Monday, April 29. We will start 3-D geometry on the same day as the unit test in all but zero hour.

The next block (April 18-19) will include a short quiz (24 pts) over circle properties at the end of class. We will be continuing on with other new content in the unit: circumference, arc length, and unit circle.
The quiz will have 4 sketches with 12 pieces of missing information. 2 pts per blank. If you can do all problems from p 455:1-6, p 461:1-12, and p 468:1-16 plus the worksheet attached below, then you will be ready.
Our warm-up included writing definitions of "inscribed angle" (p 458), "cyclic quadrilateral" (top of p 467) and "secant" (bottom of p 467). We also added the following problems to HW #7: p 474:8, p 494:50-51. And then we investigated and wrote up C-85 from p 467: Parallel chords or secants in a circle have congruent intercepted arcs.
We went over HW #7 p 468 in detail (answers attached below).
Then we took notes and did practice over circumference and arc length. Those notes are attached below. HW #8: is p 483:1-4, and p 478:1-12 AND complete the review worksheet that we started in class. The review worksheet will help with the quiz. Circumference and arc length are NOT ON THE QUIZ.
​Extra Practice is available on the button below (scroll down for answers).
You are still welcome to come during advisory if you need to look at your area quiz or do a retake.
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The purpose of today's block was to discover almost all of the necessary properties of chords, angles, and arc that are part of the circle unit.
There will be a quiz on Thurs-Fri this week over missing information related to circle properties - 24 pts
We warmed up with a quick fill-in-the-blank based on recently written Geometric Truth. Then students did an investigation (attached below) over C-76-80 on pp 459-60.
If you have congruent chords in a circle, then the corresponding central angles are congruent (C-76) and the intercepted arcs are congruent (C-77). The perpendicular from the center to a chord is a bisector of the chord (C-78). Congruent Chords are equidistant from the center of the circle (C-79). AND If you construct the perpendicular bisector of any chord, it will pass through the center of the circle (C-80, the converse of C-78).
A grade was taken over HW #6 and the new entries to Geometric Truth (6 pts). In 6th, a grade was taken over HW #5 (Aspire practice) - 4 pts.
Students practiced C-76-80 application by starting p 461:1-12. Most did not finish in class. 
We also did Geogebra investigations of Conjectures 81-84. Those are attached below, with answers.
HW #7: finish p 461:1-12. Give conjecture number that helped you decide. Then do p 468:1-16, also giving conjecture number(s) that helped you decide.
Finish Geometric Truth entries for C-76 - 84, using class activities and notes to create good sketches for the conjectures.
Upcoming: Quiz Thurs-Fri, 9.1-3 - 24 pts. Circle Unit Test will be Thurs (0B), April 25 - Mon, April 29 (6th).
You need Geogebra as an APP on your device in order to open the .ggb files. I recommend opening on a computer.
Recommend for HW #7: print off p 468 and enlarge it a bit. Highlight intercepted arcs as you are working. Remember that each angle of the inscribed quadrilateral is also an inscribed angle with its own (very large sometimes) intercepted arc.

April 10 was a short day for 1st and 2nd due to testing.
Our goal today was to dig into the circle unit, constructing vocabulary terms for chord, secant, diameter, and tangent, as well as discovering/proving our first two circle properties, which are:
C-74 on p 353: A line tangent to a circle is perpendicular to a radius of the circle at the point of tangency.
C-75 on p 354: Two lines tangent to the same circle intersect to form congruent tangent segments (see sketch on p 353).
The attachment below includes HW as well as the new content to add to Geometric Truth (vocabulary and C-74-5). Follow instructions precisely. The problems for HW #6 are listed and needs explained on the same attachment.
We discovered C-74 by modeling a discus throw; we argued deductively for C-75 to be true because of congruent right triangles.
A couple problems that create difficulty with "seeing" were demonstrated, particularly using C-75 to find the perimeter of a circumscribed quadrilateral.
In some classes, we previewed the conjectures from section 9.2 about chords in circles (76-80).
Quizzes were viewed in all classes. Make-ups need to be done yesterday!!! You are always welcome to come by during advisory and go over your quiz with me to see what went wrong if it did not go well.
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No homework tonight! However, I have added a link below for the Test Nav questions that used in class today. Feel free to try a few "live" questions like the ones we tried. It does not record your responses. The username is: mathEHS
The password is: actaspire
We started class (except 6th) with some work from the textbook and your notes over circles. That is attached below, with answers to the textbook questions.
I took a grade over HW #5 in all classes except 6th period for 4 pts. We shared the textbook work over circles and share quite a bit of student work on the open response. Hints for improving your open response score: Type 3 sentences. Answer the question asked. Use good math terminology. Think in terms of a sound argument where you have "covered all the bases". Examples of good answers are also attached below. Remember that you have graph paper on the back of your test ticket for scratch work. Try to use words as much as possible to make the typing more efficient.
We also practiced some multiple choice and drag and drop from the web link below.

FIrst and foremost: 43 pt quiz on Thurs-Fri over Area and Surface Area. If you can do all the problems on HW #1-4, then you are ready for the "quest."
In class, we warmed up with area of parts of a circle, reasoning our way to the formula for a sector (a slice of pizza):
Area of a sector is angle/360 times area (Pi * radius squared).
Resource in the textbook: p 425.
We went over homework and warm-up, took a 6 pt grade on HW #3 plus bounded area worksheet (scroll to next blog to get that worksheet and answers).
Then we used models and information from pp 432-436 to briefly discuss surface area of solids (the sum of all the faces of the solid, using area formulas we already know). There is good information on these pages to help you with your work.
In class, we did p 436:1-8, and p 423: 1-3,6, and 15. These answers are attached below. Finish if you did not finish in class.
HW #4 is a review assignment: pp 445-448: 1 a-c, 2-11, 18-25, 27, 30-32, 48. Check your answers from attachment below.
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First off, there was a mistake on problem 7 on the bounded area worksheet. The 4 sides are supposed to make a parallelogram. Please change the word "x-axis" to "y-axis". The corrected form is attached below.
Our big picture today was circles: Pi, Circumference, Area, where they come from, and how to manipulate algebraically to get from one known to an unknown. We also discussed the idea of "leaving in terms of Pi" to get an accurate answer, versus an approximate answer that comes from putting Pi in the calculator and rounding. Watch out for both on the homework.
We added 3 problems to HW #2 and checked it for a 4 pt grade (except in 4th period). The problems were 11, 19, and 20 on pp 422-3. The answers were 11) P = 254 cm, 19) A = 996 cm squared, and 20) A is approximately 497 cm squared.
We went over homework carefully, showing algebra, answering questions.
The last part of class was used to work on 7 bounded area problems (attached, with answer document).
Then HW #3 is p 422-3: 1-8, 13-14, 17-18, and p 424: 23-24, p 417: 9,12. In 4th and oB, I gave 13-15 on p 422 and did not assign the problems from p 417 or 424.
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Answers to problems on p 416-7 are included in the attached notes below (hotel room painting, deck finishing, garden area).
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Today was our second block on area. ​We are trying to approach area from a "big picture" concept: what do you think area is? Is there always a formula? Can I estimate an irregular area?  Can I find an accurate area for a space for which I don't know a formula? How can I find area by surrounding a figure with a rectangle? What does it mean to "slide a vertex" on a triangle? Can I find an area bordered by linear functions in the coordinate plane? Since we live in a 3-D world, isn't all area actually surface area (because everything has a thickness)? As we work, we are also thinking in terms of potential ASPIRE questions and how we would handle them correctly.
Today we did some warm-up questions that could be ASPIRE questions, went over homework #1 in detail, viewed tests in most classes, and then spent some time with graph paper, making sketches and deriving area formulas for triangle, trapezoid, kite, and regular polygons.
Notes are attached.
HW #2: pp 413-4:7-14, 20-21, p 422: 9-10, 12, 16, p 416:1,4,5. Use formulas, show work!!! IF solving for a dimension: write formula, plug in what you know, solve for what you don’t know algebraically. Answer in correct units.
Quiz next Thurs-Fri, April 4-5, 40 pts.
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Today we begin a mini-unit on area, including some alternative methods of finding area, deriving formulas, and using some algebra and graphing of lines to start reviewing for Aspire.
We wrote descriptions of perimeter, area, and volume by looking at a photo of a fenced-in doggie area at a park.
We used a Geoboard app on Chromebooks to look at different polygons to find their area without a formula.
Some of the methods students used and described: area by composition (break into parts), area by counting squares, area by subtraction (surround with a bigger easy figure and subtract right triangles), and area by "sliding vertex" (maintaining base and height but getting an easier figure to look at).
Activities we did in class, along with answers, are attached.
We built notes on square dot paper about finding area of rectangles and parallelograms.
HW #1 was from old textbook, so it was a handout, attached below. Do all of the problems. Best to do in homework section of notebook. Show what you put in your calculator.
All tests should be made up by now.  Tests will be seen during the next class.
40 pt quiz on Thurs-Fri, April 4-5.
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