Solving Multi-Step Equations

For the past few days we've explored whether there are generic guiding principles that help us in solving 1st degree linear equations. It appears as though the following concepts have worked thus far and may be of use in the future.

1. Balance - this notion that we can use the rules of equality to change the appearance of an equation by performing the same operation on both sides, while preserving the original value of the variable and maintaining the equality that we started with.

2. Isolating the Variable - students seem convinced that getting the variable by itself or finding the value of just one unknown is a dependable pathway for finding its value.

3. Opposite Operations or Applying Math Properties - while some students view opposite operations as 'undoing' an operation, still other view these steps as fundamental math properties. For instance, given the equation x + 3 = 9, adding a -3 to both sides is making use of the additive inverse to achieve a value of 0 on the left side of the equality.

Furthermore, it is becoming clear to students that they have to be in complete control of fraction algorithms if they are to be successful in solving equations. Rather than simply 'go over' these processes for what may be the umpteenth time, we seek to ask, "why do these algorithms work." For instance, the common algorithm for dividing fractions is to invert and multiply. But very few students examine what may have led to such a process.

Themes of notation have been a feature of our discussions as well. Some of these include:

* Where is it appropriate to place a negative sign relative to a fraction? (numerator, denominator or next to the division bar)

* Reporting solutions with the variable on the left side and the numerical value on the right side of the equality and how the symmetric property allows us this liberty.

* The convenience of cross-simplification as a means of simplifying a product ahead of time.

Tonight, students apply all of these concepts as they solve multi-step equations and prepare for equations that will feature variables on both sides of the equation.

Home Nugget #15
Assigned on Thursday Sept 30
Due on Friday Oct 1

In Algebra book,

Page 95 # 17 - 22, 25 - 27

Page 96 # 31 - 32, 34, 35, 39 - 42

Page 97 # 47 - 49

Solving Equations Using Multiplication and Division

Home Nugget #14
Assigned on Wednesday Sept 29, 2010
Due on Thursday Sept 30, 2010

In Algebra I book,

Page 88 # 20 - 27

Page 89 # 36 - 42 and 49 - 51

Solving Equations Using Addition/Subtraction

Home Nugget #13
Assigned on Tuesday Sept. 28
Due on Wednesday Sept. 29

In Algebra I book,

Page 82 # 19 - 38

Page 83 # 41 - 48 and 51

Defining Variables and Writing Equations

Home Nugget #12
Assigned on Monday Sept. 27
Due on Tuesday Sept. 28

In Algebra I book,

Page 74 # 16 - 26

Page 75 # 35 - 43

Preparing for Summative Assessments on Chapter 1 and Related Content

Home Nugget #11
Assigned on Friday Sept 24, 2010
Due on Monday Sept 27, 2010

Using the directions sheet provided in class (and posted at obryant.us under the file name re-inventing problems), you are to both re-invent AND solve the 14 questions/problems I referenced for you.


Please be aware that this lesson will be collected so be particularly mindful of presentation and legibility.

Functions and the Stories they Tell

Home Nugget #10
Assigned on Wednesday September 22
Due on Thursday September 23

In Algebra book,

Page 61 # 8 - 26

Page 62 # 27 - 42

Page 63 # 48, 49, 51 - 53

Page 64 # 54 - 59 and 61 - 63

* Please note that these problems are taken from the chapter summary for chapter 1. This indicates that we have reached the end of a particular unit and that by Monday, you will likely have a summative or cumulative test.

Number Systems

Home Nugget #9
Assigned on Tuesday September 21
Due on Wednesday September 22

In Algebra book,

Page 51 # 22 - 33, 38 - 41, 48 - 59

Page 52 # 64, 65

Logical Reasoning and Counterexamples

Home Nugget #8
Assigned on Monday September 20
Due on Tuesday September 21

In Algebra book,

Page 42 # 15 - 24

Page 43 # 25 - 38

Page 44 # 43, 47 - 49

A Respite from the Algebra Textbook

Home Nugget #7
Assigned on Friday September 17, 2010
Due on Monday September 20, 2010

From SAT sheets that are provided in class,

Pages 37 and 38

Numbers 17 - 20 and 1 - 7

Be sure to provide evidence/explanations for all problems.

Recognizing and Applying the Commutative and Associative Properties

Home Nugget #6
Assigned on Thursday September 16, 2010
Due on Friday September 17, 2010

In Algebra textbook,

Page 36
# 12 - 22 even
# 31 - 34
# 37 - 40

Page 37
# 44 - 46

ALSO

Please bear in mind that you will have your first major assessment tomorrow! As a general rule, all questions will be derived from problems we hav either solved in class or on a home nugget assignment. Be sure to review your notes thoroughly.

Properties that Appear Everywhere in Mathematics: Identity, Equality and Distributive Properties

Home Nugget #5
Assigned on Wednesday September 15, 2010
Due on Thursday September 16, 2010

In Algebra textbook,

Page 23 # 18 - 23

Page 24 # 29, 30, 35

Page 30 # 26 - 33, 36 - 42, 44 - 45

Applying Order of Operations and Solving Open Sentences

Home Nugget #4
Assigned on Tuesday September 14, 2010
Due on Wednesday September 15, 2010

In Algebra textbook,

Page 13 # 20 - 25, 29 - 31, 35 - 38, 41 - 43

Page 18 # 25

Page 19 # 39, 49

Evaluating Algebraic Expressions

Home Nugget #3
Assigned on Monday September 13, 2010
Due on Tuesday September 14, 2010

In Algebra textbook,

Pages 8 and 9

Numbers 13 - 26, 35, 40, 46 - 48*

* Despite being multiple-choice questions, # 46 - 48 require evidence or explanations for your solutions.

End of Week One and A Chance to Learn from Your First Home Nugget

Home Nugget #2
Assigned on Friday September 10, 2010
Due on Monday September 13, 2010

a. Bring book cover to class in order to receive a textbook
b. Bring an index card with your Fib poem written out on it
c. From SAT handout pages 35 & 36 # 1 - 16

Day One - Here's Where It All Begins

Today's class should have given you a clear idea about why Algebra I is so important as a stepping stone in your academic career, what your responsibilities are as a student in the class and what you need to get to work on immediately.

Your priorities right now are:

1. Closely examining the class syllabus and getting it filled out and signed by your parents/guardians.

2. Working on answering the questions stemming from the Leap Year activity you were given.

3. Getting the following materials by Friday September 10:

* two one-subject college ruled notebooks with at least 80 pages each
* one folder with two pockets
* a book cover for your textbook

Home Nugget #1
Assigned on Wednesday Sept 8, 2010
Due on Friday Sept 10, 2010

a. Signed syllabus
b. Leap-year questions answered in homework notebook according to the specific instructions provided regarding homework assignments
c. Required Materials
* Two one subject notebooks with perforated pages for easy removal
* One folder with two pockets
* A book cover (a large paper shopping bag is ideal)
* Several pencils