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last update October 17, 1998

Unit I: Order of Operations
Unit II: Properties of Real Numbers and Words to Equations

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Unit I: Order of Operations

If the primary objective of arithmetic is to calculate, then the primary objective of pre-algebra may be described as understanding the instructions and/or questions that will utilize these calculations. The Order of Operations is the BRIDGE between these objectives. The primary purpose of this unit is to begin a tour of this BRIDGE and its component parts.

The student will be able to [TSWBAT]:

• Recognize and utilize the proper format for Order of Operations
• Understand the individual components of Order of Operations
• Gain experience in applying Order of Operation concepts to real world situations
• Understand the basic mathematical terms used to describe Order of Operations instructions and activities.

Skills focus:

1. Writing in Mathematics
   • note-taking using the CPM Algebra Tool Kit
   • utilizing the PJHS header and math HW format
   • utilizing HW assignments for study
   • problem of the week assignments
2. Recognizing Order of Operations situations
3. Grouping terms
   • parentheses and 'invisible' parentheses
4. Intro to variables and substitution
5. Intro to powers
   • exponents, powers of 10, decimals and rounding
6. Recognizing and utilizing several different forms of multiplication and division, including ratios and conversions
7. Intro to the notion of the number 1

[see homework web page listed in footer for specific HW activities]

Week I (September 1-4):

• Classroom rules and procedures [Tuesday/Wednesday]
• Using the CPM Tool Kit for note taking: basic terminology [daily]
• Introduction to Order of Operations, using selected problems from Houghton-Mifflin's Pre-Algebra textbook [hereafter referred to as the Text (W/Th)]
  • a. introduce Order of Operations process and substitution

Week II (September 8-11):

• Continue review of Order of Operations calculations, in order to increase familiarity with the process [daily Text problems, crossword puzzle game (Th)]
• Introduce the variety of methods to represent multiplication and division operations [class/blackboard discussion (M)]
• Introduce powers and their component parts [discussion/Text problems, exponent handout] [T/W]
  • factors
  • grouping factors in exponential form
  • simplifying powers
  • using a base of 10
  • explain rational behind powers of 1 and Ø
• Introduce ratios and fraction to decimal conversion using Forni 'Open House' mapping activity [3-day activity, beginning Friday]

Week III (September 14-18):

• Finish using Forni 'Open House' mapping activity [M/T]
• Practice in computer lab with Order of Operations 'train' game [W]
• Begin Introduction to the Internet in the computer lab, with a focus on developing search skills and simple Boolean Logic [using Sovel 'Internet Instruction Sheets] [Th]
• Introduce the decimal model worksheet [Text, decimal model worksheet (F)]

Week IV (September 21-25):

• Extending base 10 power system [Text, decimal model worksheet, exponent handout (M/T)] [note: substitute teacher these two days]
  • negative exponents, decimal system, rounding
  • the number line as a graphing tool
• Introducing the Basic Properties of numerical expressions
  • commutative property [Text, manipulatives (W)]
  • associative property [Text, manipulatives (Th)]
  • properties of Ø and 1 [Text, manipulatives (F)]
• Order of Operations review [daily]

Week V (September 28-October 2):

• Review for mid-chapter exam [lessons 1-4] [M]
• Mid-chapter exam [lessons 1-4] [T]
• Review Basic Properties and Order of Operations
• [worksheets (W/Th)] [note: substitute teacher these two days]
• Introduce the first Problem of the Week [handout (F)]
• note: exam make-ups, as needed

Week VI (October 5-9) Bus duty week

• Return and review mid-chapter exam [M/T]
  • review test redo policy; redo due by Friday
• Computer Lab: Hyperstudio tutorial [W/Th]
• Complete the introduction of Basic Properties
  • distributive property [Text (M)]
• Introduce Equations [Text (T)]
  • review substitution
• Introduce CPM style guess and check sheets [Text, CPM handouts (W-F)]
  • play with word problems
• Review 'Problem of the Week' assignment [ W & F]

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Unit II:

Properties of Real Numbers

Words to Equations

Week I (October 12-16)

• Introduce Properties of real Numbers [tool kits (M)]
  • commutative
  • associative
  • multiplicative identity
  • Zero properties
• Complete the introduction of Basic Properties
  • distributive property [Text (T)]
• Review 'Problem of the Week' assignment [ W & F]

Week I (October 19-23)

• Review properties and in class QUIZ [handout (M/T)
• Introduce Words to Equations [Text (W/Th)]
  • review substitution
• Introduce CPM style guess and check sheets [Text, CPM handouts (W-F)]
  • play with word problems
• Hints and suggestions for POW: focus:
  • visualization
  • strategies

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