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?)

 

BM 26 and Surface Area Cont.

We started the week off with benchmark 26 (similar solids) and a retake of 44-48. We now have officially 10 benchmarks left!
Even though we had a shorter day due to staff development, we still had time for an example and homework. Here are more examples of surface area (for benchmarks 50 and 54), as well as the homework #72 12.2B worksheet on Surface Area.
In class today I also clarified the meaning of B (Base Area), P (Base Perimeter) and h(prism height) in the formula for Total Surface Area: 2B+Ph. Finding the Base Area, B, is EXTREMELY important since Surface area AND volume depend on the area of the base. I also talked about the 4 steps to find surface area:
1. Identify the base shape
2. Find the Base Area (B)
3. Find the Base Perimeter (P)
4. Find the prism height (h)
Then plug it all into the formula!
Coming up:

• Circles Test closes on Friday at midnight (take it on Moodle)
• BM 50-59 on Monday, 5/21
• Practice Final coming soon!

Posting for points question:
Finding the area and perimeter of a solid’s base is very important. From the list below, select a Base shape and choose values for the variables. Then find the area and perimeter of your shape. Be sure to show your work, and this comment is worth more points than normal posts!

• Equilateral Triangle (side length)
• Right Triangle (Leg lengths)
• Rectangle (base and height)
• Trapezoid (base 1, base 2, height, and 2 legs)
• Regular Pentagon, Hexagon, Octagon, or Decagon (side length)

 

Similar Solids

While I was out doing really geeky stuff (technology meeting), we covered Similar Solids.  This is what benchmark 26 is all about.  There was an assignment, HW #70: Similar Solids WS.  Use proportions to solve for the missing value.  We will discuss this topic in greater detail tomorrow and get some practice benchmarks (both in class and on Moodle), and then take the actual benchmark Monday.
Coming Up:

• BM 26 and 49 on Monday (14)
• Last day for benchmark retakes is Thursday, May 31 at lunch

Posting for points question:
Today we got this formula:

What does it mean?  What is r, r², r³?

 

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.

 

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?

 

Arcs and Sectors: Day 1

Today we started our unit on Circles.  Our first (of many) topics was calculating the arc length and the area of a sector, or what I like to call “the crust and the pizza.”  This is what benchmarks 40 and 42 will cover.  We also got a few vocabulary words, but the big vocabulary list will come next week.  Here are the notes if you missed them.  The only homework assignment is to study for Monday’s Polygon Test.
Coming up:

• Monday: Polygon Unit Test
• Thurs/Fri: Book Day and Benchmarks 40, 42

Posting for Points question:
Make up a problem finding the sector area or arc length (or both) of a circle.  List the given parts (central angle and radius).  Then find the respective information (Circumference or Area and Fraction).  Simplify and give your final answer.  Make sure your question is unique (no copying and pasting).  Try using notation for you work (help here and more help here).

 

Quad Intro

Today we took the polygon area benchmark #38 (along with the retakes for 34-37).  If you didn’t pass BM 38, take the practice benchmarks on Moodle before we retake it next Monday.
After that, we took a page of notes on the Quadrilaterals and their properties.  This is what the next benchmark (#39 on Monday) will cover.  You will need to know all the properties of all the quadrilaterals (and pictures, too).
The only homework was to check your grade report and make sure you are all caught up on assignments 52-57. 
Coming up:

• Grade Report #2 Due Thurs/Fri (15/16)
• BM #38 and 39 on Monday (3/19)
• Pi Day Party on Monday (3/19)
• Polygon Test on Monday (3/26)

Posting for Point Question:
What mistake did you make on the area of a polygon benchmark?  If you got it right, how did you remember which solving method to use?