Algebraic Properties of Identity and Equality: Fundamental Ideas with Broad Implications

Our study of math properties, namely identity and equality properties, raises ideas that are integral to our class goals.

The first is that we are actively striving to augment what is known as our "working math vocabulary." Put plainly, we seek to avoid the meaningless and temporary acquisition of math terms in favor of defining concepts for ourselves and using them with frequency in the context of our math arguments and conversations. For instance, students were challenged today to evaluate algebraic expressions and identify the math property used at each stage. The activity requires the student to fully grasp the meaning of each property and then recognize its use in context.

The second idea brought up as a result of our investigation of properties is the idea of spiraling themes. This is to say that the concepts we encounter early in the year will continue to appear throughout our explorations, allowing us to engage with them from a number of perspectives throughout the year.

Home Nugget #5
Assigned on Thursday September 11, 2008
Due on Monday September 15, 2008
From Algebra 1 textbook

Page 25 #36 - 38 and #40, 41

Page 61 #8 - 17 and #18 - 26

Page 62 #27 - 42

FCAs
1 pt: all problems attempted
1 pt: proper format and a presentation that reveals quality effort was invested in the lesson
2 pts: all problems in red above are accompanied by either evidence of work or explanations

Set Notation, Open Sentences and a Grab-bag of Math Terms

The last two classes have seen students admitting prior use of set notation which essentially means looking through a list of items and seeing whether they fit a given condition. We were able to acquire a good deal of terminology along the way including words like replacement and solution sets, elements of a set and open sentences.

Students also investigated the concept of needing to be comfortable with a significant number of prerequisite skills if they are to be successful with our math inquiries. Some of these prerequisites include fraction and integer operations. The textbook students have access to contains a fair amount of prerequisite study material at the tail end of the book and students are strongly encouraged to pursue these topics if need be.

Tonight's home nugget will be spot-checked in class tomorrow and is graded according to a different scale than those lessons that are collected. They are as follows:

Home Nugget #4
Assigned on Wednesday September 10, 2008
Due on Thursday September 11, 2008

From Algebra 1 textbook
Page 717
Lesson 1-1 # 1 - 18
Lesson 1-2 # 7 - 12 and 19 - 21
Lesson 1-3 # 5, 10 - 12, 18

FCAs
2 pts: all problems are attempted accompanied by evidence of work
1 pt: at least 70% of problems are attempted accompanied by evidence of work
0 pts: less than 70% of problems are attempted accompanied by evidence of work

Who Says Order Doesn' t Matter?

Lesson 1-2 from the Algebra 1 textbook allows us to weave together the topic of order of operations with that of writing algebraic expressions. Students will receive their books today, having signed for specific book numbers and are asked to cover their texts before week's end.

Home Nugget #3
Assigned on Monday September 8, 2008
Due on Wednesday September 10, 2008

From Algebra 1 textbook
Page 8 # 10 - 12, 13 - 18, 30 - 40
Page 9 # 46 - 48
Page 12 #4 - 13
Page 13 #23 - 31, 41 - 43

FCAs (Grading Criteria)
1 point: correct format
1 point: all problems attempted in their entirety
2 points: explanations and/or evidence for all problems requiring some degree of written work must be provided. (All problems in red above included)

Also complete your summary in your class notes every evening as a means of reviewing what you explored in class.