There was no homework.
Be prepared to have HW #13 (the unit review) graded for a 6 pt grade.
ACTM Practice Friday morning at 8 am.
Geometry 

Block 14 was our Unit Test on Right Triangles, worth 75 points. IF you missed to you need to contact me as soon as possible about makeups.
There was no homework. Be prepared to have HW #13 (the unit review) graded for a 6 pt grade. ACTM Practice Friday morning at 8 am.
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Today is Right Triangle Review Day. By the end of class, students should be aware of how much they need to prepare for the test over right triangles and trigonometry for the next block. We did two different inclass review worksheets today and checked and questioned them, as well as going over homework #12 from pp 6289. (4 pt grade taken) The review assignment is posted on the next blog post down from this one, HW #13. It is due WedThurs for 6 pt grade. On all trig, write the equation if you are solving for a side or an angle. On problem 14 on p 495 you must show use of the distance formula for all three sides and how you figured out if it is a right triangle. We took a 12 pt quiz at the end of class today that will be returned at the beginning of the next block so that you can ask questions before the test. We will also go over the review homework. The homework quiz and 22 pt quiz were returned today. Test topics were passed out as well. Attached below are both review sheets and answers as well as the topic list.
Our big picture goal to.day was to gain fluency with application of trigonometric ratios while understanding why we do what we do to find unknowns. The new content: using inverse ratios to find acute angles of right triangles; interpreting angle of elevation or depression to solve realworld applications of trigonometric ratios.
The textbook is excellent. Read pp 620624 and 628 for assistance. We did a warmup with completing the square to find the standard form equation of a circle, as well as p 625: 22. After we learned about inverse ratios (switch input and output to find angles) we applied them by doing 1013, 17, and 19 on p 625. We had a 4 pt homework quiz over HW #11 at the end of class. Homework #12 (due next block)  pp 6289: 13, 56, 816. On the first 5, be sure to make a good sketch. Unit Review (HW #13) not due until WedThurs next week: pp 4967: 18, 1315, 18, 23, 25; p 65960: 19, 1316. THERE WILL BE A SHORT QUIZ ON MONDAY TUESDAY. About 10 pts or 12. One distance formula problem, one equation of a circle problem, 2 trig problems (one like 79, one like 1419 on p 625). If you were absent, the textbook is essential to your understanding of Trigonometric Ratios. Please read carefully and work all examples from pp 620624. The gold box at the top of p 622 is essential notetaking. The acronym for memorizing the trig ratios is "SOH CAH TOA".
We spent quite a bit of class working on practicing equations of circles. Will attach that worksheet tomorrow. We went over homework for understanding and took a grade (HW #10 from p 489:13,510) Then we learned what trig ratios are based on similar right triangles and relationships between sides given one of the acute angles. Please follow instructions above. Quizzes need to be made up. Will be shown to all students during Block 12. HW #11: pp 6245:19,1416, 18. In block 10, we demonstrated mastery over the Pythagorean Theorem and its proof with a 24 pt quiz. If you were absent, you must make up the quiz right away. Come during advisory on Monday. We finished up an inclass worksheet where we applied the 306090 and 454590 shortcuts to find missing sides, including dividing by a radical and then simplifying it (notes and worksheet attached to Block 9 below). We worked at coming to understanding on HW #9, including 3D Pythagorean Theorem and area of equilateral triangles, as well as a point on the unit circle. Notes and practice on Distance Formula and equation of a circle are attached. These are also addressed in the textbook on pp 486489. HW #10 is p 489:13,510. On 13, 56, use the distance formula (from notes attached). We then took the quiz. Next ACTM Practice is Wednesday during advisory on circles. $2.00 for contest is due by Feb 14.
Block 10 will include a quiz over the Pythagorean Theorem, appr 25 pts.
We learned about using the Pythagorean Theorem in three dimensions to find the longest diagonal in a rectangular prism. We also practiced simplifying a simple radical in a denominator in order to find legs if hypotenuse is a whole number, etc. Attached notes. We did 12 more problems in class using the shortcuts. On a few of them, we had to simplify radicals. (worksheet attached) HW #9  p 4825: 23, 7, 1314; p 478: 7, 911, 16 When you are applying the shortcuts, continue to use your notes from Block 8 as a template to guide your work.
Today was the second block of our new Right Triangle Unit. The big idea for today is the "Pythagorean Shortcuts". In an isosceles right triangle (454590), if the legs have length a, then the hypotenuse is a times the square root of 2. In a 306090 right triangle, if the short leg has length x, then the hypotenuse has length 2x and the long leg is x times the square root of 3. See attached notes and proof. We figured this out from our warmup. We practiced simplifying radicals, went over our homework with questions, looked at the proof again and thought about how we could reproduce it ourselves. HW #8  p 471:1417 (Pythagorean Theorem, show work), p 477:16 (shortcuts, use notes, no work shown), and p 482:1,4. Make sketches and use PT to solve. All makeup tests have been taken. I will distribute the originals and answer documents next block and let students figure out their mistakes and ask questions.
Today was a big day as we began our Right Triangle Unit by covering a lot of bases! 1) If you have not taken the test, tomorrow is the day! Email me and let me know when you are taking it if you did not tell me today. Thanks! 2)1st and 2nd saw their test results. 3rd will get next time. 0B and 6 should see Friday. In some classes I announced the ACTM Contest. Will give out entry forms next time. And catch up all classes on this. Our learning time consisted of a warmup to discover the Converse of the Pythagorean Theorem: If three sides of a triangle work in the P.T., then it is a right triangle. Also, we can use these results to determine if the nonright triangle is acute or obtuse. See notes attached. We also learned about the concept of Pythagorean Triples as we were learning about converse. See p 468 in textbook and attached notes. We developed, understood, and copied a proof of the Pythagorean Theorem into our notes. It is based on similarity. There are actually hundreds of proofs. This will be on problem on our first quiz of the unit on FridayMon, Feb 2,5. We then practiced simplifying radicals. If we round to get answers in P.T. work, our answer is now an estimate. Hence, math people tend to leave in radical form because it is accurate. We worked on basics of simplifying radicals (a bit like reducing fractions). There is homework over this and some explanation on p 473 in textbook. No notes attached. Just lots of practice. HW #7: p 474:114. Simplify radicals and show work. p 4701:17,911,13. On 16 state if the triangle is acute, obtuse, or right. Show work. If you see a triple, you can write "this is a 3,4,5 triple (or whichever it is)" and you can write the answer without showing algebra.
I know that the last post said "Block 6", but it was actually an addon to block 5.
Block 6 was our test day. If you were not here, please come take during advisory tomorrow unless your absence is long term. The test should be a 60 pt grade. I should have it graded by the next block. We spent some time going over the review. Grades were taken over any homeworks that had not yet been graded. Those are all posted in Gradeviewer. You did have textbook homework over the Pythagorean Theorem. HW #6 is due on Jan 2526. P 465:113. Use the Pythagorean Theorem and algebra to solve each problem. Round as indicated. Remember that your right triangle might be isosceles and you would call the equal sides both "a". So a squared plus a squared equals c squared. No attachments today. ACTM Contest is coming up. Signups will be $2.00. The contest will be at the University of Arkansas on Saturday morning, March 3, from 9:45  11:00 am. Block 6 was a review day. We shared answers to the congruence practice questions, looked at and shared answers to HW #4 (half worksheet review), and worked on the review in class. B day got quizzes returned. A day will get on Tuesday. THE UNIT TEST is 60 pts and will be given in Block 7 on TuesWed, Jan 2324. The review answers are attached below. Topic list and blank review are on the previous post.

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February 2018
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