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)

 

Surface Area Explained

Today was devoted to solids. But first, here’s the warm-up on areas. This is a great resource for Base Areas of our solids.
We looked at polyhedrons and their faces, vertices, and edges. We talked about how to find the Base of a solid (VERY IMPORTANT!!). And we used nets to discover the formula for Surface Area of prisms. We will continue with Surface Area as well as Volume of our 5 solids next week.
Your only homework is to study and practice benchmark 26 (on Moodle) and take the Circles Unit Test (also on Moodle).
Coming up:

• BM 26 on Monday (14th)
• Circles Test closes Friday, May 18 at midnight (Take it on Moodle)
• BM 50-59 on Monday (21st)

Posting for Points question:
What is the surface area formula for prism 2B+Ph? What does B, P, and h represent?

 

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.

 

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?

 

Benchmarks

Friday we took our benchmarks 44-48. We had some time to review before we took them. I’ve graded them and we did pretty well on 44 and 45, but still need some practice on 46. We get confused with which arc measurements to subtract!
I’ve also updated the grades with benchmark scores and extra points for our benchmark goals, but I still need to do some blog point recording.

 

More Blog Issues

I noticed some things while working on the blog from my school PC.  Equations seemed to be blocked.  They show up just fine on my Mac, so I was confused.  Here’s where I need your help.  Below are some mathematical expressions and a 2 pictures.  Let me know if you see any of them and if you could answer these 4 questions (or at least the first 2 since that’s where I think the problem is):

1. Location (home or school),
2. PC or Mac,
3. operating system (OS X, Vista, XP, 95, Linux, etc),
4. web browser (Explorer, Firefox, Safari, etc).

Equations: and
Pictures:
and 

 

One Quarter of 10,000

What’s of 10,000?  What about or 100 times 25?  That would be the number of comments now on the blog.  Yep, 2500 comments.  The big winner? 

Ivey of Period 4

We did make it to 2500, so show me 3000!  Sorry to Ryan, Josh, Kris, and everyone else who said, “I will be #2500!”  There is still #3000.  I’m broke, so Homework Passes are in store for Ivey, but more importantly she has the title of “Comment number 2500.”

 

BM 44-48 Review

Due to the lack of time left over after testing, I went ahead and uploaded the review so you have it to study. Download it here or on Moodle. I also decided to NOT count benchmarks 47 and 48. They are still on the review/benchmark/test, but because we have less than a month left and LOTS to do- something had to be cut. Don’t worry, we still have plenty more benchmarks to take! So, Benchmarks 44-46 will be on Friday, 5/4.