Friday, 14 April 2017

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 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
  • V_text{Cylinder} = pi r^2 cdot h
  • 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 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.

Friday, April 14

In class we reviewed yesterday's homework, I handed back the Module 6 tests, and we worked on construction problems and angle relationships.

Assignment: Complete "Construction Problems 7.11" handout

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 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.

Thursday, April 13

Wednesday's Assignment: 7.1 Task + RSG
Thursday's Assignment: Angles worksheets 2.5/2.6. Topic: angle names and relationships.

Extra help? As we study constructions, students will need to be able to complete a variety of constructions cleanly with compass and straight edge. If your student needs some extra help practicing constructions one nice resource is at math open ref. They have nice short animations of how to perform each construction and make it easier to practice.

Constructions game. Euclid the Game is another great way for students to practice/learn constructions.

Tuesday, 11 April 2017

Compasses in Student Store, $5

We just bought ALL the compasses at office Depot. They are now for sale at CPMS for $5
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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

V = dfrac{1}{3}B cdot h

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

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 b so we can re-arrange by the commutative property of multiplication

V = dfrac{1}{3} cdot dfrac{1}{2} cdot h_2 cdot h cdot {color{red}b}

With the known information we have

180 = dfrac{1}{3} cdot dfrac{1}{2} cdot 12 cdot 6 cdot {color{red}b}

So

180 = dfrac{1}{6} cdot 12 cdot 6 cdot {color{red} b}

Then

180 = 12{color{red} b}

And finally

15 = {color{red} b}

Tuesday, April 11

In class we started Module 7, learned about compasses and geometric construction.

Materials. All students will need their own compass. They will need these everyday for the remainder of the unit. Not having a compass will make them unable to participate or complete assignments.

If your student needs a compass, as of 2:29pm today, Office Depot on Cedar Hills Blvd has 22 in stock. This is the model I recommend.

Inline image 1

Students need to take care to not break the metal tip off and not lose the plastic screw. If a metal tip breaks I can glue it back in fairly successfully. If they lose it, it can be replaced with the head of a nail.

Assignment: No HW, students should have completed the rhombus and square constructions in the 7.1 Task.

Monday, 10 April 2017