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, 14 April 2017
- 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
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 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.
Today's Assignment: 10.6 on p. 543: 1-16. Topics: Deriving the formula for the volume of a sphere using Cavalieri's principle and then applying the formula for the volume of a sphere to solve volume problems.
Tuesday, 11 April 2017
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
And then that is the area of the triangular base, so . So we are essentially solving
And we know all the values of variables except for so we can re-arrange by the commutative property of multiplication
With the known information we have
Monday, 10 April 2017
Saturday, 8 April 2017
Wednesday, 5 April 2017
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, 4 April 2017
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, 3 April 2017
Link to blog of all past email updates
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
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.
- 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.