Wednesday, 14 December 2016

Tuesday, Dec. 13

In class students took notes on logarithms, got back Chapter 4 tests and had a bit of time to start looking at the assignments dealing with Logarithms or reviewing their tests. The Chapter 4 scores were not good overall. I told the class that some students are earning low scores because they are not putting enough effort into learning the material and that if this is the case then they have to step up and take responsibility for their work. At the same time when I see low scores I feel responsible and want to help them improve. So, I am meeting with students tomorrow during my plan time and would like to see many students do a retake when they are ready. I imagine this would be after winter vacation.

Assignment:
For Thursday: 5.6 investigation on p. 273 steps 1-8, and on p. 276: 1-7, 9
To be assigned on Thursday due when we return
5.7 on p. 282: 1-5, 8, 10
5.8 on p. 289: 1-5, 7

Tuesday, Dec. 13th

In class work day. Students had the class period to complete their write-ups. In order to earn a Highly Proficient score on this task students must explain their ideas in exceptional clarity and present rich reasoning to support their responses. I have seen a lot of great work happen over the last two days and while I'm not looking forward to the hours of grading, I am really proud of the work I see happening in class.

Assignment: Complete your Chapter 4 Reasoning Assessment and be ready to hand it in at the beginning of class.

Tuesday, Dec. 13

In class we played "Graphing Stories" and I gave students a project which we will work on tomorrow in class and present on Thursday and Friday. Students are working in teams to create a "Graphing Stories" contest for the class. They will create a 15 second video, accompany it with a graph and explain their graph to the class.

Assignment: No HW tonight – tomorrow we will work on creating the videos, graphs and presentations for Thursday/Friday.

Tuesday, 13 December 2016

Monday, Dec. 12th

Hi All —
 

I was informed that I was incorrect when I predicted 100% chance of school for last Thursday. The question is why would I have been wrong even if we had in fact had school last Thursday. If I said 100% chance of school and then school happens surely my estimate was correct. Anyway, I hope you stayed warm or found a way to enjoy the cold!
 

In class today students worked on their chapter 4 assessment. This will be a write-up and not a test. Students can work independently or in pairs. They are allowed to use notes and to discuss problems with each other but must use their own words to explain their ideas. If they get help from someone else they should credit that person and explain in what way they were helped. I will give more work time tomorrow in class and the write-up is due on Wednesday at the start of class. Need the ch. 4 assessment? Click here.
 
Assignment: Chapter 4 Reasoning Assessment due Thursday

Friday, 2 December 2016

Friday, Dec. 2 – Flow Proofs

In class we learned to create flow proofs. I have attached an example and students worked on practice. In order to be proficient, a student should be able to create a proof on their own for problems in which the diagram can be understand fairly quickly (#7 on this assignment). Highly proficient students should be able to create proofs similar to the one I attached and in cases when a clear proof would require them to see segments or shapes that are not given as well as identifying important relationships between triangles which may be overlapping etc. (some examples of this from 4.6 problem set).

Assignment: 4.7: (4-6 talk through, don't need to write anything), complete 7-13, 15

Question:

* What is the significance of the arrows in a flow proof?

* What are some different ways you could organize this flow proof into a 2-column proof?

Answers

* Arrows are used to indicate when one statement follows from another. The arrow shows the order of the logic.

* Statements could, arguably be put into many different orderings so long as no statement comes before a statement which pointed to it in the flow proof. So there are many ways to arrange these statements into a valid proof, it would be preferable to set up the statements so that one line of reasoning is presented without interruption.

Thursday, 1 December 2016

Thursday, Dec 1st

In class we worked on a set of proofs in groups and put the proofs up on the board. I have attached pictures of the proofs from period 3 if you would like to see some in progress work.

Components of a good proof
 

  • Clear question or statement to be proved
  • Multiple well labeled, helpful diagrams. Especially useful when isolating an important triangle out of a figure in which many triangles overlap.
  • Every statement is supported by a reason (and also proof indicates if a reason follows from some other statement)
  • The proof has a logical structure in which there are no gaps in reasoning, each statement follows from the previous statements or stands on its own.
  • The proof ends with the statement we desired to prove at the outset.

Assignment: 4.6 on p. 231: complete 1-12 (you may skip the two problems your group worked on together)
 

Pictures of student's proofs.

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Ch. 4 Test

In class students worked on the chapter 4 test all period. I also gave out a practice quiz for the beginning of chapter 5 which would be helpful to have back tomorrow.
 

Assignment: previously assigned sections 5.1 – 5.4 + practice quiz w/s

Thursday, Dec. 1st

In class today we reviewed the questions worksheet from yesterday. I gave students three options to prepare for the test tomorrow (1) work on more practice problems (2) work with me to answer questions and do examples together or (3), do mathcounts practice because you are totally ready for the test tomorrow.
 

Assignment: Study for the Mod 2 test tomorrow.

Wednesday, Nov. 30th

In class today we started in to work on writing proofs involving triangle congruence. Students are learning to prove congruence relationships between segments and angles. I worked through a few examples in class – and students have a couple problems to do tonight.

Assignment: 4.6 on p. 231: 1-4

Questions all apply to this figure

Inline image 1
‚Äč
1. Are angles 1 and 2 congruent in the figure?
2. Are angles 3 and 4 congruent in the figure?
3. What else would you need to know in order to prove triangle ABD and triangle CDB are congruent?

Answers
1. Yes, angles 1 and 2 are congruent because they are alternate interior angles formed by parallel lines CB and AD and the transversal BD.

2. Cannot be determined. Since we do not know if CD and AB are parallel, we cannot say whether or not angles 3 and 4 are congruent. To avoid doing assuming we can eyeball parallel lines you could imagine the shape with AD still parallel to segment BC but if BC and AD are different lengths angle 3 and 4 can have different measurements.

Inline image 2
3. Many possible answers. Here are a few

  • If we knew that BC = AD we could prove the triangles congruent by SAS.
  • If we knew that angle 3 and 4 were congruent, we could use ASA
  • If we knew that angle C and angle A were congruent, we could use AAS.