Pyramid Volume and Spheres

Yep, that’s what we did today.  We first did a warm-up on Surface Area of pyramids and cones, as well as Volume of prisms.  All good examples of benchmarks 51, 52, 55, and 56.  We then watched a super-cool clip from YouTube about the volume of a pyramid and cone.  The point was made that the volume of a pyramid or cone is:

We looked at some examples, and then went right into spheres.  We can find the surface area and volume of a sphere using these two formulas:

and

There is also a video on YouTube comparing the volume of a sphere with a cylinder.  You should check it out.  With just a few minutes to spare, we got our two homework assignments: HW: #75 12.5 WS and #76 12.6 WS. 
On a super-fantastic sad note, today was our last day of NEW notes.  We will still do a few review lessons, but as far as new stuff, nothing else.  Please hold back the tears.  And make sure you bring a party hat box of Kleenex Monday since we will take our LAST benchmark of the year. 
Coming Up:

• Circles Unit Test closes TODAY!!!!!  Take it on Moodle.
• BM 50-59 on Monday, with retakes on the second block days (Thurs/Fri) the next two weeks
• Grade Report #4 due Thurs/Fri May 24/25
• Last day for Benchmark Retakes on Thurs. May 31, at lunch

Posting for points question.
We now have all the surface area and volume formulas.  Which one is your favorite and which one is your least favorite?

 

TSA of Pyramids and Cones

What a day!  Tons of instruction today.  6 benchmarks total!
We started with a warm-up of surface area of prisms and checked HW #72 from yesterday.  There was a poor homework return, so make sure you get this assignment done before the benchmarks on Monday!
We then started total surface area of a pyramid and cone.  This is very similar to the TSA of a prism, except that we only have 1 base and the lateral sides are triangles, so the formula is:

B is the Base Area, P is the Base perimeter, and l is the slant height.  Here are the notes that we took.  The homework is HW #73 12.3A WS.
With the little bit of time we had left, we also looked at Volume of prisms and cylinders.  The Volume formula for a prism or cylinder is:

Where B is the Base area and h is the prism height.
There was also an assignment on volume, HW #74 12.4A WS.
Coming Up:

• Circles Unit Test closes Friday at Midnight (or 11 pm) on Moodle
• BM 50-59 on Monday (5/21)
• Last Day for Benchmark retakes Thursday May 31 at lunch

Posting for Points Question:
First, DID YOU TAKE YOUR CIRCLES UNIT TEST???
Then, I am starting to prepare my review for the semester.  Where have you been struggling or are just not clear yet?  The topics are Similarity, Trigonometry, Polygons, Circles, and 3-D solids.  Be specific (i.e. Which benchmark or standard?  Is there a specific problem?)

 

More Similar Solids

Here’s what we did today:
First off, now that I’m back and we are in our groups, I collected the CST Review assignment that we worked on 2 weeks ago.  This is a 50-point assignment, so make sure you turn it in if you were absent.
Second, we reviewed our benchmarks from Friday (44-48) and also reviewed the notes from yesterday on .
There were two homework assignments: first off was to finish #70 from yesterday (or check it to make sure you did it correctly).  The second assignment is the review for the Circles Test, HW #71 Circle Review part 2.
Coming up:

• BM 44-48, 26, and 49 on Monday, 5/14
• Circles Unit Test on Moodle completed by Fri. 5/18

Posting for points question:
Today we looked again at using ratios of similar solids to find perimeters, areas, and volumes.  Create an example using similar solids ratios and find a perimeter, area, OR volume of a similar solid. 
Example:
2 solids have a ratio of 6 to 5.  Solid A has a lateral surface area of 223 sq. in.  Find the lateral surface area of solid B.
Solution:
so
Cross-multiply and divide, and the LSA of solid B=154.86 sq. in.

 

10.4 Angles in a Circle

Here’s what we did today:
First, Grade Report #3 was collected.  You can still turn them in next week, but it will be for 1/2 credit.
Second, we check our answers to the CST Review.  I will officially collect the reviews on Monday/Tuesday of next week (after the first part of the CST). 
Third, 10.4 Notes on various Angles with Circles.  These notes cover benchmarks 44, 45, and 46 on angles formed “On, In, or Out” of a circle.
Last, HW #69 page 624 #8-34 (even), 50, 51
I will also be working on practice benchmarks on Moodle and screencasts on the blog this weekend so watch for those!
Coming up:

• CST Monday through Thursday next week.  We have block starting Monday with periods 1-6 on Friday.  Get plenty of sleep each night so we perform at our highest level!!
• Benchmarks 44-48 Friday (5/4)
• Last day for Benchmarks: Thurs May 31

Posting for Points Question:
Today looked at 3 different scenarios for when lines (tangents, chords, and/or secants) intersect in a circle.  What are the three relationships/formulas and how will you remember the difference for the benchmarks?

 

10.3 Inscribed Angles

After we checked #67 from Monday and took our Vocabulary Quiz on Circle Terms, we learned about inscribed angles.  There were 4 examples, but I did notes old school today (white board).  You can check out this link or search for Inscribed Angles to get the background.  The assignment is HW #68 page 617 #9-29 (odd) skip 21,23, 41-43 (all), and 49-61 (odd). 
Coming Up:

• Monday: Moodle Projects are due
• Book Day on Tues/Wed (24/25)
• Benchmarks 44-48 on Thurs/Fri (26/27)
• CST Testing for Geometry starts Monday, 4/30 (odd block schedule Monday)

Posting for points question:
Describe an inscribed angle.  What is special?  What are some properties (theorems)?  Give an example of finding an arc measurement or inscribed angle measurement.

 

Circles Review

Today’s class seemed to fly by very quickly.  Perhaps  because we haven’t had a normal Monday schedule for awhile.  Well, here’s the events:
First, we checked our homework from the weekend (#66).
Second, we got back and then re-took benchmarks 40 and 42.
Third, we worked on HW #67 Circles Review, Part 1. 
Finally, we went to our next class.
On a sad note- you may have heard of the shooting at Virginia Tech.  Just two weeks ago a received an e-mail from an assistant professor there who came across my podcasts in the iTunes store and expressed interest in how I created them.  Our thoughts and prayers go out to staff, students, and their families as they deal with this tragic event.
Coming up:

• Moodle Vocab should be done today!
• Circles Vocab quiz on Thurs/Fri (19/20)
• Book Day Thurs/Fri (19/20)
• Moodle Projects due Monday (23)
• Book Day Tues/Wed (24/25)
• Benchmarks 44-48 and Grade Report #3 due on Thurs/Fri (26/27)
• NOTE: If you want more benchmarks to show up for this grading period (which ends Friday), you need to make them up Tuesday after school or Wed/Thurs at lunch.

Posting for Points Question:
Tomorrow and for the next two weeks we start our review for the CST test (April 30th-May 3rd is when we take the test).  This test will cover the whole year and then some.  What do you feel is your strongest area and what do you feel is your weakest?  Be specific!  This will help me tailor our review to fit everyone’s need.

 

10.2 Arcs and Chords

Lots of announcements today.  We checked the three assignments from last class (63-65), discussed the screencasts, blog, and Moodle Scavenger Hunt.  On top of that, we signed up for our “favorite circle term” to define in the Circles Dictionary on Moodle.  But the fun didn’t stop there!  We had enough time for some brief notes on Arcs and Chords (available on Moodle), as well as getting our 66th assignment: HW #66 page 607 #12-46 (even).  Yep.  More even ones.  No looking in the back to cheat get help.  The textbook examples are good, so check those out.
I also found this video on YouTube put out by Nutshell Math.  They create some great animated tutorials.  I really like the way they found the central angle using inverse trigonometry.
Coming up:

• Benchmark 40, 42 Retake Monday 4/16
• STAR Testing starts Tues, 4/17
• Book Day Thurs/Fri, 4/19-20

Posting for Points question:
How do we find the measure of an arc?  I’m not looking for the length of the arc [(fraction)(Circumference)], just the measurement.  It would be helpful to give an example.

 

New Kind of Tangent

Welcome back from Spring Break!  I hope you had tons of fun!  It’s all downhill from here!  Time will fly by really fast, so don’t get behind.  We are only half way through our benchmarks!!!
Today we started looking at tangents of circles.  The notes were short due to our extensive vocabulary list before break.  Download them here.  There were a plethora of assignments, too.  Three in all.  2 of them are due at the end of class, and one is for homework.  The two due in class are #63 10.1B WS and #64 Basic Terms, Tangents WS.  The homework assignment (due next class!) is #65 page 599 #10-16 (e), 17-25 (all), 26-46 (e), 65-71 (all).
I also posted a new Moodle assignment.  It’s a photo scavenger hunt.  Check it out.  Due date is 4/23.
Coming up:
Book Day on Thurs/Fri (12/13)
Posting for Points Question:
What is so special about a tangent line?  How do you know a line is tangent to a circle?

 

Benchmarks and Vocab

Today we took benchmarks 40 and 42 on Arc Length and Sector Area.  After that we worked on some Vocabulary.
There were two vocabulary assignments: #62 Circles Vocabulary and “Daffy Definitions.”  The focus was the Circles Vocabulary since this is what we will have our vocab quiz on when we come back from break. 
Because I’m a nice guy, there is not homework over break since #62 was due at the end of class.  We will add definitions to our Moodle glossary when we get back, too.
Coming up:

• Polygon Unit Test #2 closes at Midnight Friday, 3/30 on Moodle

Posting for Points Question:
Our Daffy Definitions activity gave some funny definitions for some of our common geometric terms.  Your task is to make up your own “daffy definition” with any of our terms so far.  Be creative!

 

Arcs and Sectors: Day 2

Today we continued with Arcs and Sectors. We did a few more examples and discussed the difference between answers in terms of π and decimal answers. You can review the notes on last Thursday’s blog entry.  In case you were wondering, you can do either one. There was an assignment that we worked on the rest of the class: HW #61 Arcs and Sectors WS.
Coming up:

• Book Day and BM 40-42 on Thurs/Fri (/29-30)
• Polygon Unit Test #2 (on Moodle) closes on Friday at midnight

Posting for points:
Today we looked at two different ways to solve arc length and sector area (fraction x whole and proportions). Which way is easier for you and why? Remember, I’m looking for quality responses. Then go back to the Arcs and Sectors: Day 1 entry and give an example. The best examples will be the benchmarks!