# Monday, April 17

Assignment

1. 10.6 on p. 547: 1-8, 12-19

2. Select topic for volume project. Write question to explore. You may work with a partner or by yourself.

3. Complete the 10.5/10.6 worksheet

# Friday, April 14

In class students had time to complete yesterday's assignment and a challenge worksheet also I reviewed with students how to derive the formula for the volume of a sphere. In the proof that $\dpi{300}\inline V_\text{sphere} = \dfrac{4}{3}\pi r^3$ we assume

• Cavalieri's principle: If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal
• $\dpi{300}\inline V_\text{Cylinder} = \pi r^2 \cdot h$
• $\dpi{300}\inline V_\text{Cone} = \dfrac{1}{3} \pi r^2 \cdot h$

In order to be proficient, students should be able to solve volume problems involving spheres and other shapes we have studied. Today's worksheet and the ability to prove the volume of a circle is $\dpi{300}\inline \dfrac{4}{3}\pi r^3$ are both areas in which students can reach the highly proficient level.

Assignment: Complete 10.6: 1-16 and the 10.5/10.6 worksheet handed out today.

# Thursday, April 13

Wednesday's Assignment: 10.5 on p. 536: 1-8, 10-16. Topics: displacement method for calculating volume of a 3-d object and density. Also, students completed a short volume/surface area quiz.

Today's Assignment: 10.6 on p. 543: 1-16. Topics: Deriving the formula for the volume of a sphere $\dpi{300}\inline V = \dfrac{4}{3} \pi r^3$ using Cavalieri's principle and then applying the formula for the volume of a sphere to solve volume problems.

# Tuesday, April 11

Assignment: 10.4 on p. 532: 1-11. Topic: Density and problem solving with volume.

Topic: Density and problem solving with volume. Students should be able to use equations to find the missing lengths using the volume. For example in a triangular pyramid with volume 180, height of the base triangle = 12, and altitude of the pyramid = 6, we could first notice that the volume of a pyramid is

$\dpi{300}\inline V = \dfrac{1}{3}B \cdot h$

And then that $\dpi{300}\inline B$ is the area of the triangular base, so $\dpi{300}\inline B = \dfrac{1}{2}bh_2$. So we are essentially solving

$\dpi{300}\inline V = \dfrac{1}{3} \cdot \dfrac{1}{2} \cdot b \cdot h_2 \cdot h$

And we know all the values of variables except for $\dpi{300}\inline b$ so we can re-arrange by the commutative property of multiplication

$\dpi{300}\inline V = \dfrac{1}{3} \cdot \dfrac{1}{2} \cdot h_2 \cdot h \cdot {\color{red}b}$

With the known information we have

$\dpi{300}\inline 180 = \dfrac{1}{3} \cdot \dfrac{1}{2} \cdot 12 \cdot 6 \cdot {\color{red}b}$

So

$\dpi{300}\inline 180 = \dfrac{1}{6} \cdot 12 \cdot 6 \cdot {\color{red} b}$

Then

$\dpi{300}\inline 180 = 12{\color{red} b}$

And finally

$\dpi{300}\inline 15 = {\color{red} b}$

# Monday, April 10

Today's Assignment: Pyramids worksheet.

# Thursday/Friday Update

Yesterday complete 10.2/10.3 worksheet. (period 5 assigned only 10.3). Today in class we did practice problems finding volume and surface area of pyramids given only minimal information about their side lengths and students needed to find many unkown lengths using right triangles. No HW today.

# Wednesday, April 5

Today's assignment: Complete 10.3 on p. 524: 1-12, 17-23.

Topic: Volume of pyramids and cones. Also, we discussed the difference between feet, square feet, and cubic feet.

How many people do you think would fit into one cubic mile?

# Tuesday, Apr 4

Today's Assignment

1. Complete the conjectures in chapter 10.2 (A-C and Prism/Cylinder) from pages 514-6

2. Complete 10.2 on p. 517-20: 1-14, 19-26

Handed back: Chapter 9 test from Friday before Spring Break. Scores will go in Synergy at the end of the day perhaps 🙂

# Monday April 3

Today's assignment: 10.1 on p. 508: 1-35, 38-41

# Change to these emails + a few class updates

Hi students and parents in Geometry —

It is nice to see everyone again, and I hope that you were lucky to spend Spring Break doing something interesting! I had out of town nephews come visit which was great. We took Alma and Evan (now 2 months) to see the please-don't-touch-the-legos at OMSI. Wow! That was amazing, but also, a bit stressful keeping two year old hands from touching lego sculptures at eye level. We spent lots of hours climbing and sliding and I even read a few pages of a book… for fun!

Ok, so on to the business at hand. I need to change expectations for these emails a bit and wanted to let you know what's going on in class.

"Almost Daily Email" becomes mostly daily but loses content

I've been thinking about my emails/lack thereof as of late and wanted to send out a more general email and update you on what's going on from my end. Since my son was born my duties before/after school have shifted and I now do the morning routine dropoff and pickup for my daughter most days before and after school. This has made it very difficult for me to send regular email updates to you after school since I have no planning time on A-days and during my plan time on B-days I have a number of responsibilities to balance including email writing. Email updates don't make much sense if I send them after my daughter goes to bed at 8pm because you probably don't want to check for them, and, again, I have other school work to take care of as well. The best solution for me is to switch from sending an explanation to simply sending an email containing the assignment for the day. I will try to send this out during class or right after 3rd period during lunch so that it is there, but I will not necessarily include narrative or explanation to go along with the assignment, it will just say something like

Today's assignment: complete 10.1 on p. 508: 1-35, 38-41

I'm sorry I haven't been able to send the same level of updates as I would like, I know that communication is important but at the moment I need to prioritize a bit. As always, if you have questions for me please feel free to send me an email.

Current unit: Volume in the real world

We are focusing on volume in the real world for our next chapter. Students will learn about a variety of topics related to volume, including how to derive volume formulas for a variety of shapes including prisms, pyramids, cones, cylinders and spheres.

Our end of unit assessment will involve students creating their own question that CANNOT be googled. This question will likely follow a format like "What would it look like if … ?" Last year a few examples of questions are

• If you gathered up all the cell phones on earth that have ever been made, and put them into one giant conical pile, how would that pile compare to Mt. Hood?
• This questions involved a number of interesting estimations (the student considered the changing volume of cell phones through the years) the dimensions of the pile.
• What would it look like if I stored all the water that falls on my roof in a barrel next to my house?
• If all the CO2 in the atmosphere were to suddenly separate out of the atmosphere and form a sort of ring around the surface of the earth at sea-level, how thick would a typical person be able to breath fresh air when sitting, standing or sleeping?
• If all the air I breath today were to be compressed into a set of weights at the gym, could I bench press my breath? Could the average american? Could I bench press my breath for a week or a month?

Smarter Balanced testing will take place in math during May.

If you made it all the way down to here, bravo! Thanks for reading and let's have a great spring!