Journal Writing as a Means of Genuine Reflection and Retention

Home Nugget #29
Assigned on Thursday December 18 (technically handed out Dec 17)
Due on Monday December 22

Journal Entry #2 of the 2nd Term
"THE TOP TEN LIST"

Students were provided with directions in class but the gist of the lesson is that students are compiling the top ten most important themes/topics from the five chapters of the Algebra 1 book we have covered thus far. Each of the chosen topics must be accompanied by an argument for what makes it top ten-worthy and also a representative example of what it looks like.

For example, order of operations is likely to be a topic that makes it to many students' top ten lists. The student has to make a compelling argument for why this theme is so integral to our course and give an example(s) of what order of operations looks like when in use.

The grading criteria for this lesson are included on the direction sheet.

Systems of Equations - THE LAST ASSESSMENT!

Home Nugget #28
Assigned on Tuesday December 16, 2008
Due on Thursday December 18, 2008

In Algebra 1 text,

Pages 286 - 288
Numbers 11 - 35 (problems that will take you on a journey through lessons 5-1 through 5-5)

Summative test on chapter 5 will be administered tomorrow.

FCAs

Applying Myriad Methods to Solving Systems of Equations

Home Nugget #27
Assigned on Monday December 15, 2008
Due on Tuesday December 16, 2008

In Algebra 1 text, page 283 # 6 - 18

In Cornell Notes, work on key terms/ideas section and reflection sections.


FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for all pertinent problems.

Elimination/Substitution Using Multiplication

Home Nugget #26
Assigned on Friday December 12, 2008
Due on Monday December 15, 2008

In Algebra I text

Page 276 # 7 - 15 odd (so that you can check your solutions in the back of the book)
# 17 - 23

Page 277 # 27, 28, 31, 32

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for all pertinent problems.

Systems of Equations: Having Different Methods Helps

Home Nugget #25
Assigned on Thursday December 11, 2008
Due on Friday December 12, 2008

In Algebra text,

Page 269 #13 - 27
Page 271 #3 - 18

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for all pertinent problems.

Augmenting our System of Equations Toolbelt: Combination/Elimation as an Option

Home Nugget #24
Assigned on Wednesday December 10, 2008
Due on Thursday December 11, 2008

From 5-2 Practice Sheet # 10 - 23

From 5-2 Word Problem Practice # 1 - 6

ALL WORK/SOLUTIONS SHOULD BE SHOWN ON A SEPARATE SHEET

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for all pertinent problems.

Solving Systems of Equations Using Substitution

Home Nugget #23

Assigned on Monday December 8, 2008

Due on Wednesday December 10, 2008

In Algebra text,

Page 263 # 9 - 19 odd (so that you can check your solutions in the back of the book)

Page 264 #21, 26 - 29, 31

Page 265 # 32, 35, 36

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for all pertinent problems.

Solving Systems of Equations Via Graphing Methods

Home Nugget #22

Assigned on Friday December 5, 2008

Due on Monday December 8, 2008

In Algebra I textbook, read pages 253 - 255

Do problems 10 - 24 even and #28, 29

ALSO on SAT sheet (pages 42 - 43) numbers 1 - 16

ALSO for homerooms 216 and 239, finish quiz on SAT questions. Best 8 out of 10.

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

Cleaning House on Chapter 4

Home Nugget #21

Assigned on Wednesday Dec 3, 2008

Due on Friday Dec 5, 2008

In Algebra I text,

Pages 242 - 246

# 1 - 57

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

Finishing Touches on Chapter 4

Home Nugget #20
Assigned on Tuesday December 2, 2008
Due on Wednesday December 3, 2008

In Algebra text
Page 726
Lesson 4-6 # 1 - 5
Lesson 4-7 # 1 - 6

Page 247 # 1 - 25

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

How Much Math Have Students Retained as of Dec. 1st?

Home Nugget #19

Assigned on Monday December 1, 2008

Due on Tuesday December 2, 2008

All problems from sheet titled "Cold Summative Assessment"

Show all work/evidence on a separate sheet of paper such that tomorrow we can exchange papers in class and grade 5 random questions as a quiz grade. This lesson will be graded as a 50 point quiz.

The lesson draws on content stretching back to Chapter 1 and extends through Chapter 2. The goal here is to remind students that they are responsible for all content covered this year and it is misleading to wait until the mid or end of the year before we assess content.

Scatterplots and Correlation

Home Nugget #18

Assigned Wednesday November 26, 2008

Due on Monday December 1, 2008

Read pages 227 - 230 focusing on examples and vocabulary

Then, do problems on:

Page 230 # 1 - 7

Page 231 # 8 - 11, 15 - 17

Page 232 # 18 - 22

FCAs

2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

Parallel and Perpendicular Lines

Home Nugget #17
Assigned on Tuesday November 25, 2008
Due on Wednesday November 26, 2008

In Algebra 1 text

Page 240

Numbers

13 - 22
26 - 29
31 - 33

FCAs
2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

Weaving SAT Prep into our Investigations

We are approximately in our second week of intermittent SAT prep on Number and Operations. (Only double-period time is spent on these topics) and students have been made aware that they are accountable for all of the material we cover even though the philosophy here is one of enrichment. While the SAT is a standardized test students will not see for another three years, the breadth and depth of questions and the dynamics of the test are such that it is highly advantageous for us to explore these concepts at this level.

Home Nugget #16
Assigned on Monday November 24, 2008
Due on Tuesday November 25, 2008

From SAT Prep Sheet
Open-Response Problems Pages 40 and 41
Questions 9 - 18

FCAs
2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process is provided for ALL pertinent problems

Problem Sets that Will Allow Students to Reflect on Chapter 4

Home Nugget #15
Assigned on Friday November 21, 2008
Due on Monday November 24, 2008

From Algebra 1 text,

Pages 243 - 245 # 11 - 47

FCAs
2 points: all problems completed in their entirety. Your effort at the end of the lesson is as evident as at the start.

2 points: evidence/explanations for your thought/solution process are provided for ALL pertinent problems (we have discussed ad nauseum in class what is meant by pertinent)

A Chance to Buckle Down and Find Accurate Solutions for Problems from Chapter 4

Home Nugget #14
Assigned on Thursday November 20, 2008
Due on Friday November 21, 2008

Double-sided practice sheet labelled "Chapter 4 Mid-Chapter Test" and "Chapter 4 Quiz 1"

Do ALL problems. Show ALL work on a separate sheet of paper. Show the solutions on the practice sheet itself.

FCAs
4 points: all problems are completed and evidence of your thought process and work is evident for all relevant problems

4 points: four random problems will be graded for accuracy

Point-Slope form of Linear Equations

Home Nugget #13
Assigned on Tuesday November 18, 2008
Due on Thursday November 20, 2008

In Algebra 1 text,
Page 223 #1 - 15 and 18 - 22

Page 224 #36 - 44

FCAs 

3 points: evidence/explanations for all relevant problems

1 point: all problems completed

Puzzle Pieces: Missing Slopes and Hidden Y-Intercepts

Home Nugget #12
Assigned on Monday November 17, 2008
Due on Tuesday November 18, 2008

In Algebra text,
Page 212 # 1 - 16
Page 217 # 10 - 14 and 22 - 29

ALSO BRING IN YOUR GRAPHING CALCULATORS!

FCAs
3 points: explanations/evidence for all relevant problems
1 point: all problems completed

Glorified Re-Examination of Slope-Intercept Form for Linear Relationships

Home Nugget #11
Assigned by Substitute Teacher during my absence on Friday November 14.
Due on Monday November 16, 2008

In Algebra 1 text,

Page 201 #26 - 45

Page 202 #50 - 59

ALSO

Read pages 204 - 206 on graphing equations in slope-intercept form and then solve problems on page 207 # 1 - 11

FCAs
1 point: all problems completed (ATTEMPT ALL PROBLEMS - NO EXCEPTIONS!)
3 points: evidence of your problem-solving procedures or thought process is evident for all pertinent problems.

Using Journal Entry #1 as a Mechanism for Exploring Higher-Order Concepts from Chapter 3

Home Nugget #10
TWO PARTS

Part 1: due on Thursday November 13, 2008
Read and be accountable for all material on pages 196-199 on the topic of direct variation.

Part 2: due on Friday November 14, 2008
Journal Entry #1 of the 2nd term

That Slippery Slope - What Does it Really Mean?

Home Nugget #9
Assigned on Monday November 10, 2008
Due on Wednesday November 12, 2008

A. Write a one page study guide that 'tells the story' of slope - what it is, how to find it and all the relevant information you can think to include.

B. Read and be accountable for pages 187 - 191.

C. Solve the following from the Algebra 1 text

Page 192 #1 - 17
Page 194 # 54 - 62 except for 57, 58

Gearing up for an Assessment on Chapter 3

Home Nugget #8
Assigned on Friday November 7, 2008
Due on Monday November 10, 2008

In Algebra 1 text,

Page 181 numbers 1 - 25

FCAs
3 points: evidence of your work/reasoning is evident for all pertinent problems
1 point: all problems completed

Proportional and Non-Proportional Relationships

Home Nugget #7
Assigned on Thursday November 6, 2008
Due on Friday November 7, 2008

In Algebra 1 textbook
Page 177 - 180
# 1 - 38

FCAs
3 points: explanations/evidence shown for all relevant problems
1 point: all problems attempted

Arithmetic Sequences

Home Nugget #6
Assigned on Tuesday November 4, 2008
Due on Thursday November 6, 2008

In Algebra 1 textbook,

Page 164 # 1 - 20
Page 168 # 12 - 21
Page 169 # 28 - 37

FCAs
3 points: evidence/explanations provided for all relevant problems
1 point: all problems completed

Expecting Assessments on Lessons 3-1 through 3-3

Home Nugget #5

Assigned on Monday November 3, 2008

Due on Tuesday November 4, 2008

From sheet labelled "chapter 3 mid-chapter test" all problems

AND

On blank side of the aforementioned sheet complete problems 61 - 70 from page 161 of Algebra 1 textbook

AND

Read pages 165 - 167 of Algebra 1  book on arithmetic sequences (independent study)

Further Practice with Linear Functions

Home Nugget #4

Assigned on Friday October 31, 2008

Due on Monday November 3, 2008

Double sided practice sheet labeled on one side as 3-3 Practice Linear Functions and on the other as 3-3 Word Problem Practice Linear Functions

All problems should be completed

Also, students are to read pages 165 - 167 on arithmetic sequences.

FCAs

3 points: all relevant problems are accompanied with explanations/evidence of thought process

1 point: all problems are completed

Linear Functions: Identifying them, Finding Intercepts and Laying Down the Line

Home Nugget #3 of the 2nd Term

Assigned on Wednesday October 29, 2008

Due on Friday October 31, 2008

Review, reflect on and refine Cornell Notes on lessons 3-1, 3-2 and 3-3

This is an opportunity to prepare for a possible Cornell Notes collection as well as think about concepts including relations, mappings, inverse relations, functions and function notation.

In Algebra 1 book,

Page 158 # 1 - 11

Page 159 # 12 - 23

Page 160 # 36 - 42, 51 - 55

FCAs

3 points: evidence of your work/reasoning is shown for all pertinent problems

1 point: all problems are completed

Bear in mind that elements including a complete heading, general lesson appearance and demonstration of effort are all still considered in assigning home nugget grades. Have these themes in mind as you complete lessons.

First Day of the Second Term!

Much of today's class discussion revolved around expectations for the 2nd term and the standards we need to meet as a collective body of learners. Some of these themes/items included:

a. A need to show greater urgency in our class interactions in terms of maximizing our use of time and resources. I often relate to students that I want them to have a greater sense of immediacy and assertiveness than I do as a teacher. There has to be a sense of ownership for what we do in the classroom.
b. Facing adversity head-on and wanting to engage in rigorous topics.
c. A greater sense of collegiality. Students must be willing to work with one another in and out of the classroom to make sense of content. There is nothing to be gained by having only a select group of students be academically successful; we want all students to be empowered.
d. A focus on basic items like exemplary home nuggets with complete headings and overwhelming evidence of the thought process for problems.
e. A greater commitment to nightly Cornell Notes and two sections in particular: key terms/ideas and the reflection piece.

Home Nugget #2 of the second term
Assigned on Monday October 27, 2008
Due on Wednesday October 29, 2008

In Algebra text
Page 148 # 39 - 42
Page 152 # 15 - 20
Page 153 # 23 - 26, 30 - 35, 39, 40, 43, 44

FCAs
3 points: evidence of your work/reasoning is shown for all relevant problems
1 point: all problems completed

First Home Nugget of the Second Term Gives Us A Chance to Confront Adversity

Home Nugget #1 of the 2nd Term

Assigned on Friday October 24, 2008

Due on Monday October 27, 2008

From two double-sided sheets provided in class, all problems that are checked off. (Virtually all problems with the exception of a handful.) This is an opportunity to rethink and perhaps re-evaluate your approach to the topics covered in lessons 2-7, 2-8 and 2-9. [specifically, percent change, solving for a specific variable and weighted averages]

Students are also strongly encouraged to look over the test they got back today and determine both where they are proficient and areas that need further attention. Cornell notes are invaluable in helping to sort out concepts.  

While the results of our last assessment were initially discouraging, there were many factors at play that we can address immediately:

1. Students need to bring their own graphing calculators (minimizes computational errors that are unrelated to conceptual understanding)

2. Students should rethink their approach to rounding off and to converting between percents and decimal notations.

3. Students should not expect that all problems will be carbon-copies of problems we solve in class, rather that we develop problem-solving skills in class that they can then use to deal with novel situations. 

Last Major Assessment of the First Term Covering Chapter 2

Home Nugget #27

Assigned on Wednesday October 22, 2008

Due on Friday October 24, 2008

TAKE HOME QUIZ 

All problems from double-sided sheet labeled Test Form 3. 

You are to show work/explanations for all problems on a separate sheet of paper. Five random problems will be graded for accuracy as counted as a 50 point quiz.

Gearing Up for A Last Term 1 Assessment on Chapter 2

Home Nugget #26

Assigned on Monday October 20, 2008

Due on Tuesday October 21, 2008

TWO PARTS:

1. Journal Entry #3 on sections 2-7, 2-8 and 2-9 of the Algebra 1 book. This is another letter/study guide to an absent classmate. However, using the guidelines provided in class, students are expected to craft a product superior to that of their 2nd entry.

2. In Algebra 1 book,

Page 134 #44 - 52

Page 136 #1 - 13

Some Solutions to Help Get A Grip on Mixture Problems

We discussed in class on Friday that it would be useful to check as many solutions as possible when it comes to mixture problems to get a sense of whether you are on the right track or not. Since there are no even-numbered solutions provided in the book, I have included a bunch below.

#4: 15 pounds
#6: 0.20(5 - n) + 1.00n = 0.50(5)
#14: about 3.67
#16: 432g + 7.35(15 - g) = 177.21(15)
#18: 9 oz.
#20: table (good luck)
#22: 74
#26: 120 ml. of 25% solution, 20 ml. of 60% solution
#30: 40h + 30h = 245
#32: table (good luck)
#34: 15 seconds

Uniform Motion Problems, Mixture Problems, all Disguise Weighted Averages

Home Nugget #25
Assigned on Friday October 17, 2008
Due on Monday October 20, 2008

Continue to work on your Cornell Notes as they will be collected next week.

In Algebra 1 textbook,
Page 125 #4, 7
Page 126 # 13 - 18
Page 127 #20 - 23, 26, 27 and 29 - 34

FCAs
3 points: evidence for reasoning or work shown for all pertinent problems
1 point: all problems completed

Weighted Averages - Getting to the Heart of What an Average is

Home Nugget #24

Assigned on Thursday October 16, 2008

Due on Friday October 17, 2008

In Algebra 1 text,

carefully read pages 122 and 123 and solve Check Your Progress #1 and #2

These are great avenues for exploring weighted averages!

Also, hold on to home nugget #23 until tomorrow as you will have a quiz based directly on it.

Be sure to look over your solutions until you are familiar and comfortable with them.

FCAs

3 points: evidence of reasoning/work shown for all pertinent problems

1 point: all problems completed

Solving for A Specific Variable and Using Dimensional Analysis

Home Nugget #23

Assigned on Wednesday Oct 15, 2008

Due on Thursday October 16, 2008

In Algebra 1 text

Pages 120 and 121

# 9 - 21 (check your solutions in the back)

# 24, 25

# 30 - 33

# 35, 36 and 39

FCAs

3 points: evidence of reasoning/work is shown for all pertinent problems

1 point: all problems completed

Home Nugget #22
Assigned on Tuesday October 14, 2008
Due on Wednesday October 15, 2008

Read (for understanding) pages 117 through 119 of Algebra 1 text and solve all four "Check Your Progress" questions.

FCAs
3 points: evidence of reasoning/work is shown for all pertinent problems
1 point: all problems completed

Writing to Prepare for Our Next Assessment

Home Nugget #21
Assigned on Friday October 10, 2008
Due on Tuesday October 14, 2008

Journal Entry #2 of the 1st Term
Detailed directions can be found at the following link:

http://docs.google.com/Doc?id=dcszzgg_201d74xz6c6

Percent Change and the Strong Connection to Ratios and Proportions

Home Nugget #20
Assigned on Wednesday October 8, 2008
Due on Friday October 10, 2008

In Algebra 1 book,

Page 113 # 11 - 17
Page 114 # 18 - 22, 26 - 28 and 32 - 40

FCAs
3 points: evidence of your work/reasoning is provided for ALL pertinent problems
1 point: all problems are attempted and completed

**Nightly** Review, reflect and refine your Cornell Notes in anticipation of their collection for a test grade

Ratios and Proportions

Students are reminded that whenever a class involves taking a set of Cornell Notes, (which is essentially 90% of the time) part of each day's home nugget is to re-examine, reflect on and refine these notes. This means actually fine-tuning the notes by adding in thoughts you may not have had time to include in class, identifying key terms and ideas that originate in the class notes and writing a reflection/summary that really captures the essence of what that particular day's theme was.

The main idea here is not to coerce students into taking copious random notes which simply end up as clutter in a binder. Rather, we are working on organizational abilities and the skill of using notes to reinforce learning in a long-term way.

Home Nugget #19
Assigned on Monday October 6, 2008
Due on Wednesday October 8, 2008

In Algebra 1 text
Page 109 # 12 - 14, 18 - 23, 27 - 34

From double-sided practice sheet for section 2- 6 all problems on both sides
(Word Problem Practice and Enrichment)

FCAs
3 points: evidence of work/reasoning provided for ALL pertinent problems
1 point: all problems completed

Much Needed Practice with Solving Multi-Step Equations

Home Nugget #18

Assigned on Friday October 3, 2008

Due on Monday October 6, 2008

From Algebra 1 textbook

Page 101 # 17 - 24 and 31 - 34

Page 102 # 35 - 47

Page 103 # 49 -62

FCAs

3 points: explanations/evidence of reasoning evident for all pertinent problems

1 point: all problems completed

Relentlessly Pursuing Equations With the Variable on Both Side

Home Nugget #17
Assigned on Thursday October 2, 2008
Due on Friday October 3, 2008

In Algebra 1 book,

Page 97 # 47 - 58
Page 101 # 1 -1 6 and 25 - 30

FCAs
1 point: all problems completed
3 points: evidence of work/reasoning shown for ALL pertinent problems

Solving Multi-Step Equations Using All Four Math Operations

Home Nugget #16
Assigned on Tuesday September 30, 2008
Due on Thursday October 2, 2008

In Algebra 1 book,
Page 88 # 8 - 13, 14 - 19, 26 - 30
Page 89 # 34 - 37, 47 - 51, 54
Page 95 # 1 - 16, 23 - 28
Page 96 # 30 - 35

Nightly: Reflect and work on your Cornell Notes in anticipation of their collection for a test grade

FCAs
1 pt: all problems completed
3 pts: evidence of work or reasoning is shown for ALL pertinent problems

Solving Equations Using Addition/Subtraction

Home Nugget #15
Assigned on Monday September 29, 2008
Due on Tuesday September 30, 2008

In Algebra 1 text,
Page 81 # 4 - 12
Page 82 # 23 - 36
Page 83 # 48, 50, 51
Page 84 # 53 - 62

Nightly: Reflect and work on your Cornell Notes in anticipation of their collection for a test grade

FCAs
1 pt: all problems completed
3 pts: evidence of work or reasoning is shown for ALL pertinent problems

Note: It is useful to check your odd numbered answers in the back of the book to see if your solutions are accurate

Writing A Short Story with Math Terms Acquisition as Our Main Goal

Home Nugget #14
Assigned the week of September 22
Due on Monday September 29

First Journal Entry of the 1st Term
Directions and samples were provided in class and will be posted here shortly as well for reference purposes. Students will hand in their math journal with the assignment in it on Monday.

There are no FCAs for this lesson as it is graded on an all or nothing basis per the guidelines on the direction sheet.

Directions for the journal entry can be found at the following link:
http://docs.google.com/Doc?id=dcszzgg_200cbds8zgv

Launching Ourselves Towards Linear Equations

This marks the fifth time students are asked to conduct an independent study of sorts. They are asked to read through pages introducing linear equations and demonstrating representative examples. Based on their reading, they will then try out problem sets to assess their absorption and understanding of material.

Home Nugget #13
Assigned on Thursday September 25, 2008
Due on Friday September 26, 2008

From Algebra 1 text,
Pages 66 and 67 # 1, 2, 3, 5, 6, 10

Then read pages 70 - 73 paying particular attention to highlighted terms and examples.

On page 73 # 1 - 12 and page 74 # 19 - 24

FCAs
1 pt: all problems completed
1 pt: presentation does not detract from content
2 pts: evidence/explanations provided for pertinent problems

Eagerly Anticipating a Summative Assessment on Chapter One 1-1 to 1-9

We spent today's class delegating time towards topics that seem to linger in the background as potentially distracting, namely:

• place value and the logic behind rounding off numbers
• whether the Distributive Property can be applied to finding the square root of fractions (is finding the square root of a fraction the same as finding the roots of its numerator and denominator separately - the answer is YES.
• evaluating our true understanding of prerequisite skills/topic like the Pythagorean Theorem

I also shared with students the idea that we should acknowledge our strengths in regards to the first chapter and view our few areas of weakness, not in terms of remediation, but rather reflection. It was agreed that the following topics are ones requiring attention:

Sequential Topics for Further Thought

1. Translating accurately between verbal and algebraic expressions

2. Notation of ‘greater than OR equal to’ and its impact on solutions

3. Wording of math properties: identity vs. equality, the distinction between reflexive and symmetric

4. Using the distributive property to simplify operations and to simplify expressions by ‘sharing equally’

5. Telling the difference between appropriate use of commutative vs. associative property

6. How counterexamples entail keeping the hypothesis true and making the conclusion false in order to sabotage the original conditional statement

7. Using the inside-out method to classify numbers according to a particular number system

8. Deciding whether a set of numbers is closed for a particular operation

9. Identifying functions and the terms within the topic (domain, range, discrete and continuous)



Home Nugget #12
Assigned on Wednesday September 24, 2008
Due on Thursday September 25, 2008

In Algebra 1 text
Pages 717 - 719 have practice exercises for sections 1-1 to 1-9 of the book. Students should complete as many of these problems as needed to feel confident and competent about the content contained.

There are no FCAs for this lesson as it is completed entirely at the discretion of individual students.

Functions and Graphs

The last section in our first unit, chapter 1-9, allows us to revisit both familiar and novel concepts. Students are reminded that graphing on a coordinate grid is an involved process which incorporates number sense and strategic planning and they are introduced to terms like continuous and discrete functions that invite them to think more carefully about interpreting graphs.

Tonight's home nugget focuses exclusively on reviewing for our upcoming Test #1 and is summative in nature. 

Home Nugget #11

Assigned on Tuesday September 23, 2008

Due on Wednesday September 24, 2008

From Algebra 1 text,

Pages 63 and 64 # 43 - 53 and #54 - 63

Page 66 and 67 # 1 - 10

FCAs

2 points: evidence/explanations provided for all pertinent problems

1 point: all problems completed

1 point: your presentation/format DO NOT detract from the content presented

Categorizing Numbers, Mulling Over Closure and Other Varied Topics

Students are being reminded constantly that they are accountable for taking Cornell Notes on a daily basis, in alignment with the criteria prescribed to them in class. On an unannounced day, class notes will be collected and graded as a test grade.

Today was yet another opportunity for students to demonstrate their willingness and ability to successfully complete an independent study and show their mastery of material in class. Topics covered included:

• Assigning numbers to specific number systems
  
• Deciding whether a number system is closed under a particular operation
  
• Finding square roots of values, whether they have perfect roots or not
  
• Graphing on a number line
  

Tonight's lesson will be spot-checked tomorrow and is an opportunity to practice the skill sets covered in class today.

Home Nugget #10

Assigned on Monday September 22, 2008

Due on Tuesday September 23, 2008

Double-sided sheet for section 1-8. All problems are included.

Number Systems

Home Nugget #9

Assigned on Friday September 19, 2008

Due on Monday September 22, 2008

Read pages 46 - 49 paying special attention to highlighted terms and the examples that are provided. Please remember that this is the third such assignment where you are being asked to commit yourself to studying material independently. While I cannot expect for you to figure out everything about the chapter on your own, I can and will expect that you are familiar with topics and most importantly, that you ATTEMPT everything.

Also,

Page 50 # 2 - 21

Page 51 # 25 - 27 and  # 32 - 37

Page 52 # 69 - 77

FCAs

1 point: all problems attempted

1 point: presentation does not interfere with the content being presented

2 points: evidence for pertinent problems is provided

Logical Reasoning and Counterexamples

Home Nugget #8

Assigned on Thursday September 18, 2008

Due on Friday September 19, 2008

Double-sided sheet with both Practice and Word problems

All problems should be completed. Work can be completed directly on sheet.

This lesson will be spot-checked on scale of 0, 1, 2 or possibly if it is exemplary, a 3. 

Commutative and Associative Properties

Home Nugget #7

Assigned on Tuesday September 16, 2008

Due on Thursday September 18, 2008

In Algebra 1 textbook,

Page 35  

# 1 - 10

Page 36

# 16 - 22 even

# 23 - 27

# 33 - 40

Page 37  

# 46, 48, 49

# 50 - 56

FCAs

1 point: all problems attempted and completed

1 point: the presentation does not distract or detract from the content

2 points: evidence of work or reasoning shown on all pertinent problems

Accessing Prior Knowledge - Is the Distributive Property Part of Your Repertoire?

Having spent a number of days exploring, discussing and making use of math properties, we are continuing this line of reasoning to ask, "what other properties do we already use in evaluating expressions?"

A trip down recent memory lane reveals:

Identity Properties
As a class, we have practiced the additive and multiplicative identities (0 and 1 respectively), we have reasoned the usefulness of both the additive and multiplicative inverses (which yield 0 and 1 respectively) and discussed the logic behind the multiplicative property of 0 (where 0 transforms all willing factors to a product of 0).

Equality Properties
Students took the lead in deciphering and perhaps more importantly, distinguishing among these properties, which at times, can appear to be interchangeable. We will continue to see the Reflexive, Symmetric, Transitive and Substitution Properties in action throughout the school year.

Tonight's home nugget poses two unique challenges.

• The first is that it asks students to now take the role for accurately deciding which problems require evidence or explanations. The idea being that any time a question involves some level of computation or reasoning, it is imperative to demonstrate this in writing.
• The second is that students are asked to explore two properties on their own and come to class with a modicum of preparation based on their independent reading. At this level of our math studies, students are expected to conduct these kinds of inquiries and to take more direct ownership for their level of competency.

Home Nugget #6
Assigned on Monday September 15, 2008
Due on Tuesday September 16, 2008

From the Algebra 1 textbook.
Page 32 # 1 - 12, # 15 - 17 and # 18 - 22
Then read pages 33 - 35 and be prepared to answer questions about the Commutative and Associative Properties in class tomorrow.

FCAs
1 point: all problems attempted
1 point: a random problem will be checked for accuracy and justification
2 points: evidence of work or reasoning is shown for all pertinent problems

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.

An Introductory Math Topic Meant to Ease Our Transition into Cornell Notes and Accountable Talk

As the blog heading states, students dealt with the relatively benign topic of translating algebraic expressions into verbal expressions (chapter 1-1 of the Algebra 1 textbook) and vice versa for the purpose of trying out two classroom routines, the use of the Cornell method for note-taking and the use of "accountable talk" for whole-class discussions.

Cornell notes are essentially a standard way of taking notes by dividing one's paper into three major sections: an area for key terms and ideas, an area where the actual notes are taken in shorthand and an area for the summary. Students are asked to record all notes from the board along with all the work they complete independently. They will then flush out all key terms and ideas in the left margin. Finally, they should look over the notes and write a summary that captures the essence of that particular set of notes. Please bear in mind that as these are math notes, there are likely to be copious mistakes which is encouraged. Here are two links to websites with further info on Cornell notes:

http://coe.jmu.edu/learningtoolbox/cornellnotes.html

http://lifehacker.com/software/note-taking/geek-to-live--take-studyworthy-lecture-notes-202418.php

Please bear in mind that both Home Nugget #1 and #2 are due on Monday and that this is a valuable opportunity to set a strong tone for the school year.

First Day of School - A Wave of Critical Information to Absorb

Welcome 8th graders to your 2008-2009 math class and school year!

This web log will serve as one means of communication so that we may focus on our challenge of engaging with and mastering the Algebra 1 curriculum. Given your background in our middle school, you will likely find many of the concepts we encounter to be familiar and will discover that our unique challenge this year is to prepare for studies in higher-level mathematics that demand a comprehensive Algebra background.

In addition to posting homework lessons on this blog (known as home nuggets in our class), I will also periodically post messages regarding class issues and topics and relevant web links that may prove useful in better understanding content.

The first two days of school (Thurs Sept 8 and Fri Sept 9) will be dedicated to presenting and coming to terms with class procedures and expectations. It is unrealistic to begin our math explorations without first laying some groundwork for how the class works and what your specific role is in making it successful. To this end, students will be provided with a significant amount of paperwork, detailing class particulars. The following links are online versions of the documents provided in class.

Document detailing materials needed for class, class rules, grading policy and web resources
http://docs.google.com/Doc?id=dcszzgg_118cs8d6td4

Document detailing math binder setup
http://docs.google.com/Doc?id=dcszzgg_120dd3bxkck

Document detailing home Nugget setup and concept
http://docs.google.com/Doc?id=dcszzgg_119fpnxzxmg

Document asking for parent/student information
http://docs.google.com/Doc?id=dcszzgg_121crqg7mds

It is recommended that students and their families review these documents as a family such that all expectations are clear at the outset of the course.

Next week students will be provided with printed direction sheets on how to log in to an online grading program, Snapgrades.net that will be used to keep families updated on student academic progress throughout the year.

The first two home nuggets of the year are due on Monday September 8 and are posted below along with their grading criteria known as Focus Correction Areas (FCAs). The vast majority of home nuggets are worth 4 points and the FCAs specify how the student can earn the points available.

Home Nugget #1
Assigned Thursday September 4, 2008
Due Monday September 8, 2008

Student must have obtained and set up math binder according to directions provided in class
(2 points)
Student must return completed general info sheet (2 points)

Home Nugget #2
Assigned Thursday September 4, 2008
Due Monday September 8, 2008
Algebra 1 Course Sampler Sheets (20 multiple-choice and open-response problems)

FCAs
1 point: all problems attempted
1 point: all work is completed on separate sheets with proper format
2 points: evidence/explanations provided for all problems

I welcome thoughts, suggestions and concerns at nkhodjat@gmail.com and encourage families to be as engaged as possible to guarantee a productive school year.

Cheers,
Mr. Hodjat