# OASD Mathematics Unit Frameworks COURSEEssentials of Math

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```					OASD Mathematics Unit Frameworks
COURSE: Essentials of Math
OVERARCHING QUESTIONS:
Mathematical Processes: How can I use math knowledge, skills, and strategies to solve real-world
and non-routine problems?

Number Operations and Relationships: How can I use numbers effectively to quantify, describe,
and label things in my world?

Geometry: How can I use geometric concepts, relationships, and procedures to interpret,
represent, and solve problems?

Measurement: What appropriate tools and techniques can I use to measure things accurately?

Statistics and Probability: How can I use data collection and analysis, statistics and probability to
solve problems?

Algebraic Relationships: How can I use algebraic relationships in personal, scientific, economic,
social, medical, artistic and civic fields of inquiry?
STANDARDS:
MATHEMATICAL PROCESSES:
A1: Understand a broad body of mathematical knowledge and apply a variety of
mathematical skills and strategies, including reasoning, oral and written communication,
and the use of appropriate technology, when solving mathematical, real-world and non-
routine problems.

NUMBER OPERATIONS AND RELATIONSHIPS:
B1: Know how to use numbers effectively for various purposes, such as counting,
measuring, estimating, and problem solving.
GEOMETRY:
C1: Know how to use geometric concepts, relationships and procedures to interpret,
represent, and solve problems.
MEASUREMENT and REFERENCE FRAMES:
D1: Select and use appropriate tools (including technology) and techniques to measure
things to a specified degree of accuracy. Use measurements in problem-solving
situations.
DATA AND CHANCE:
E1: Know how to use data collection and analysis, statistics and probability in problem-
solving situations, employing technology where appropriate.

PATTERNS, FUNCTIONS and ALGEBRA:
F1: Discover, describe, and generalize simple and complex patterns and relationships. In
the context of real-world problem situations, use algebraic techniques to define and
describe the problem to determine and justify appropriate solutions.

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Essentials of Math
COURSE: Essentials of Math
UNIT: Paper and Pencil Calculations
PACING: 7-8 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.4 In problem-solving situations involving the application of different number systems select and use
appropriate:
• Computational procedures
• Properties;
o Commutatively
o Associatively
o Inverses
• Modes of representation.
o Rationales as repeating decimals
o Indicated roots as fractional components

E1.12.1 Work with data in the context of real-world situations.
• Formulate hypotheses that lead to collection and analysis of one- and two-variable data
• Design a data collection plan that considers random sampling, control groups, the role of
assumptions, etc.
• Conduct an investigation based on that plan

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Essentials of Math
•   Use technology to generate displays, summary statistics, and presentations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use addition, subtraction, multiplication, and division?
*Can I identify whole numbers, decimals, fractions, and percents?
How can I solve problems in this unit?
*How can I use tables and charts to solve problems?
*Do I understand how to round decimals to the correct place value?
How can I use this in the real world?
*How can I use median, median, and mode to evaluate real world data?
*How can I interpret graphs of real world data to solve problems?

KEY CONTENT LANGUAGE:
Mean, median, mode, percent, evaluate, whole numbers, decimals

RESOURCES:

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Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Using the Calculator and Estimation
PACING: 9-10 days

BENCHMARKS:
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use addition, subtraction, multiplication, and division?
*Can I identify whole numbers, decimals, fractions, and percents?
How can I solve problems in this unit?
*How can I use tables and charts to solve problems?
*Do I understand how to round decimals to the correct place value?
How can I use this in the real world?
*How can I use median, median, and mode to evaluate real world data?
*How can I interpret graphs of real world data to solve problems?

KEY CONTENT LANGUAGE:
Mean, median, mode, percent, evaluate, whole numbers, decimals

RESOURCES:
Calculator

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Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Part Time and Summer Jobs
PACING: 8-9 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*Can I read and write/fill out job applications?
* How can I use addition, subtraction, multiplication, and division?
How can I solve problems in this unit?
*How do I compute total earnings/tips/social security?
*How can I use the guess and check method to solve problems?
How can I use this in the real world?

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*How can I evaluate and apply for jobs?

KEY CONTENT LANGUAGE:
Minimum wage, tips, social security, FICA,

RESOURCES:

Classified ads, internet (WISCareers), job application forms, resume examples

5/23/2006                                                                       6
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Full-Time Work
PACING: 11-12 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•      Perceive patterns
• Identify relationships
•      Formulate questions
• Pose problems
• Make and test conjectures
•      Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-
world situations.
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

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ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, and division?
How can I solve problems in this unit?
*Can I calculate total time and wages for a particular job?
How can I use this in the real world?
*How can I evaluate jobs in terms of pay and benefits?

KEY CONTENT LANGUAGE:
Weekly/biweekly/annual pay, piecework, commission, net pay, deductibles, face value,
beneficiary, term, straight life

RESOURCES:

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Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Recreation and Sports
PACING: 9-10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-
world situations.
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, and division?
* Can I evaluate the meaning of fractions and their remainders?
How can I solve problems in this unit?
*How can I evaluate the cost of memberships, tickets, and necessary materials for
particular recreational activities?
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Essentials of Math
How can I use this in the real world?
*How can I evaluate and choose a recreational activity based on associated costs?

KEY CONTENT LANGUAGE:
Membership fee, cost per visit, all day pass, remainder

RESOURCES:

YMCA flyers with prices, Menus, Store flyers with prices, sales tax tables

5/23/2006                                                                           10
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Basic Purchases
PACING: 9-10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, division, and percents?
How can I solve problems in this unit?
*How can I calculate the amount of discount and the discount rate?
*How can I calculate the sales tax of a purchase?
How can I use this in the real world?
*How can I evaluate the cost of buying audio/video equipment, clothing, or food?
*How do I order from a catalog/online/telephone?

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Essentials of Math
*How can I evaluate the best buy at a store using unit pricing?

KEY CONTENT LANGUAGE:
Markdown, discount, discount rate, sales tax, unit prices

RESOURCES:

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Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Savings and Checking Accounts
PACING: 7-10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, and division?
How can I use this in the real world?
*How can I use a checking/savings account responsibly?
*How can I compute the simple/compound interest earned on investments or paid on
loans?
*How can I compare/evaluate different checking accounts to determine the best option?

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Essentials of Math
KEY CONTENT LANGUAGE:
Checking accounts, savings accounts, deposit slips, withdrawal slips, check register, bank
statement, I = prt, compound interest

RESOURCES:

“How to do your banking” handour

5/23/2006                                                                              14
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Credit
PACING: 8-10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Display of data.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

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Essentials of Math
ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, and division?
How can I solve problems in this unit?
*How can I use patterns to predict future payment amounts?
How can I use this in the real world?
*How can I responsibly use credit cards?
*How can I calculate finance charges so that I may calculate/estimate future balances?
*How do I take out a loan and calculate the amount of interest due?
*How can I purchase something on an installment plan, and how do I calculate the
finance charge?

KEY CONTENT LANGUAGE:
Credit card, charge receipt, credit card statement, finance charge, unpaid balance, new
balance, overdraft, annual percentage rate (APR), installment price, installment plan,

RESOURCES:

Credit card applications, credit card statements, consolidate loan flyers

5/23/2006                                                                                 16
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Automobile Expenses
PACING: 8-10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
* How can I use addition, subtraction, multiplication, and division?
How can I solve problems in this unit?

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Essentials of Math
*How can I calculate the monthly payment for a car loan?
*How can I calculate the total operating expenses for a car?
How can I use this in the real world?
*How can I evaluate the total cost and options to determine which car to purchase?
*How can I negotiate a price, and determine a finance charge?
*How can I determine the cost of renting an automobile?

KEY CONTENT LANGUAGE:
Sticker price, options, negotiated price, trade-in allowance, vehicle registration fee, title,
EPA, mpg, cpg, insurance, liability, collision, comprehensive, premiums, deductibles

RESOURCES:

Insurance info, online insurance quotes, classified ads

5/23/2006                                                                                    18
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Transportation
PACING: 10-12 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

5/23/2006                                                                                             19
Essentials of Math
ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use addition, subtraction, multiplication, and division?
*How can I use charts, graphs, maps, and schedules to gain the necessary information
needed to solve problems?
How can I solve problems in this unit?
*How can I convert times to different time zones?
How can I use this in the real world?
*How can I estimate distance and travel time for a trip?
*How can I determine the cost, travel time, and distance traveled for a bus, train,
airplane, subway, and taxi?
*What factors need to be considered when choosing the most economical way to travel?

KEY CONTENT LANGUAGE:
Time Zones

RESOURCES:

Hand clocks and time zone charts, maps with scales, “mapquest”, travel agent

5/23/2006                                                                          20
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Taxes
PACING: 11-13 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
A1.12.3 Analyze non-routine problems and arrive at solutions by various means including models and
simulations, often starting with provisional conjectures and progressing, directly or indirectly, to a solution,
justification, or counter-example.
A1.12.4 Develop effective oral and written presentations employing:
• Mathematical terminology
• Notation,
• Symbols
• Conventions for mathematical arguments
• Display of data.
A1.12.5 Organize work and present mathematical procedures and results clearly, systematically, succinctly,
and correctly.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root

5/23/2006                                                                                                    21
Essentials of Math
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use tax forms, booklets, and tax tables to help me complete my taxes?
How can I solve problems in this unit?
*How can I fill out the tax forms so that I correctly calculate the refund/amount owed?
How can I use this in the real world?
*How do I determine which tax form to use and then gather the necessary information for
calculating the refund/amount owed?

KEY CONTENT LANGUAGE:
W-2 form, 1099 form, IRS, deductions, exemptions, adjusted gross income, taxable
income, 1040 EZ, 1040 schedule A

RESOURCES:

Tax forms (W1-2, 1040EZ, 1040, WI) and booklets, Tax tables, W-2 forms, W-4 forms,
1099 forms

5/23/2006                                                                           22
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Housing
PACING: 10 days

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
A1.12.5 Organize work and present mathematical procedures and results clearly, systematically, succinctly,
and correctly.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.
C1.12.2 Use geometric models to solve mathematical and real-world problems.
D1.12.3 Determine measurements using
• Estimation

5/23/2006                                                                                              23
Essentials of Math
•   Proportional reasoning, including those involving squaring and cubing
•   Techniques of algebra
•   Geometry
•   Right triangle trigonometry
•   Formulas in applications
•   Geometric formulas to derive lengths, areas, or volumes of shapes and objects
•   Geometric relationships
•   Properties of circles and polygons
•   Conversion constants to relate measures in one system to another.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use want ads, perimeter, area, and proportions to help solve problems?
How can I use this in the real world?
*How can I rent an apartment or buy a condo/house?
*How can I calculate what my monthly mortgage would be for a particular home?
*How can I estimate my real estate taxes and homeowners insurance?
*How can I calculate the cost of utilities, decorating, and remodeling?
*How can I compare mortgages to analyze, which is the best?

KEY CONTENT LANGUAGE:
Mortgage, real estate taxes, homeowners insurance, condominium, perimeter, area,
proportions

RESOURCES:

Rulers, tape measures, apartment ads, mortgage charts, sample utility bills

5/23/2006                                                                              24
Essentials of Math
Mathematics
COURSE: Essentials of Math
PACING: 2 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.4 In problem-solving situations involving the application of different number systems select and use
appropriate:
• Computational procedures
• Properties;
o Commutatively
o Associatively
o Inverses
• Modes of representation.
o Rationales as repeating decimals
o Indicated roots as fractional components
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.
C1.12.2 Use geometric models to solve mathematical and real-world problems.
D1.12.3 Determine measurements using
• Estimation
• Proportional reasoning, including those involving squaring and cubing

5/23/2006                                                                                               25
Essentials of Math
•   Techniques of algebra
•   Geometry
•   Right triangle trigonometry
•   Formulas in applications
•   Geometric formulas to derive lengths, areas, or volumes of shapes and objects
•   Geometric relationships
•   Properties of circles and polygons
•   Conversion constants to relate measures in one system to another.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use area, perimeter, addition, subtraction, multiplication, division, and
operations with fractions to solve problems?
How can I solve problems in this unit?
*How can I draw diagrams to help solve problems?
How can I use this in the real world?
*How can I calculate costs associated with carpentry, plumbing, electrical work, painting,
and masonry, as well as utilize comparative consumerism?

KEY CONTENT LANGUAGE:
Board foot, inside/outside diameter, area, and perimeter

RESOURCES:

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Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Other Professions
PACING: 2 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
A1.12.4 Develop effective oral and written presentations employing:
• Mathematical terminology
• Notation,
• Symbols
• Conventions for mathematical arguments
• Display of data.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.4 In problem-solving situations involving the application of different number systems select and use
appropriate:
• Computational procedures
• Properties;
o Commutatively
o Associatively
o Inverses
• Modes of representation.

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Essentials of Math
o Rationales as repeating decimals
o Indicated roots as fractional components
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I read and create charts and tables of information and utilize proportions to
solve problems?
How can I solve problems in this unit?
*How can I read schedules and calculate to time according to hours, minutes, and
seconds?
How can I use this in the real world?
*How can I solve problems involving advertising costs, presenting data in an organized
fashion, currency exchange, quality control sampling, determining health care drug
dosages, radio and television programming, and evaluation of raises/promotions?

KEY CONTENT LANGUAGE:
Area, column inch, line graphs, bar graphs, currency exchange rate, quality control

RESOURCES:

5/23/2006                                                                             28
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Personal Finance
PACING: 2 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I utilize basic mathematical operations to solve problems?
How can I solve problems in this unit?
*How can I design a personal budget so that I may solve personal financial problems?
How can I use this in the real world?

5/23/2006                                                                              29
Essentials of Math
*How can I calculate inflation rate and/or use the inflation rate to determine purchasing
power?
*How can I determine the costs of raising a family?
*How can I determine a person’s net worth based on their total assets and liabilities?

KEY CONTENT LANGUAGE:
Purchasing Power, inflation rate, fixed and variable expenses, assets, liabilities, net worth

RESOURCES:

Newspaper Articles

5/23/2006                                                                                 30
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Investments
PACING: 2 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I utilize basic mathematical operations to solve problems?
How can I use this in the real world?
*How do I calculate the redemption value of a US savings bond?
*How do I calculate interest earned on a CD?
*How do I invest in stocks and calculate net profit/loss?

5/23/2006                                                                      31
Essentials of Math
*How do I invest in mutual funds?
*How do I calculate annual pension benefit?

KEY CONTENT LANGUAGE:
US Savings Bonds, certificates of deposit, stocks, shares, dividends, mutual funds,
pension plans

RESOURCES:

5/23/2006                                                                             32
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Probability
PACING: 2 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•     Perceive patterns
• Identify relationships
•     Formulate questions
• Pose problems
• Make and test conjectures
•     Pursue ideas that lead to further understanding and deeper insight.
A1.12.2 Communicate logical arguments and clearly show:
• Why a result does or does not make sense
• Why the reasoning is or is not valid
• Understanding of the difference between examples that support a conjecture and a proof of the
conjecture.
B1.12.2 Compare real numbers using:
• Order relations
• Transitivity
• Ordinal scales including logarithmic
• Arithmetic differences
• Ratios
• Proportions
• Percents
• Rates of change.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I perform basic operations with fractions?
How can I solve problems in this unit?
*How can I calculate the probability of independent and dependent events?
*How can I draw a tree diagram in order to list the sample space?
How can I use this in the real world?
*How can I use probabilities to make predictions about real world events?

5/23/2006                                                                                             33
Essentials of Math
KEY CONTENT LANGUAGE:
Simple probability, sample space, independent events, dependent events, tree diagram,
counting principle

RESOURCES:

Dice, cards, card games

5/23/2006                                                                               34
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Measurement
PACING: 2-3 weeks

BENCHMARKS:
A1.12.1 Use reason and logic to:
• Evaluate information
•    Perceive patterns
• Identify relationships
•    Formulate questions
• Pose problems
• Make and test conjectures
•    Pursue ideas that lead to further understanding and deeper insight.
• Mathematical texts and other instructional materials
• Mathematical ideas as they are used in other contexts.
B1.12.3 Perform and explain operations on real numbers.
• Subtract
• Multiply
• Divide
• Raise to a power
• Extract a root
• Take opposites or reciprocals
• Determine absolute value
B1.12.6 Routinely assess the acceptable limits of error.
• Evaluate strategies
• Test the reasonableness of results
• Use technology to carry out computations.
D1.12.2 Select and use tools with appropriate degree of precision to determine measurements directly
within specified degrees of accuracy and error.
D1.12.3 Determine measurements using
• Estimation
• Proportional reasoning, including those involving squaring and cubing
• Techniques of algebra
• Geometry
• Right triangle trigonometry
• Formulas in applications
• Geometric formulas to derive lengths, areas, or volumes of shapes and objects
• Geometric relationships
• Properties of circles and polygons
• Conversion constants to relate measures in one system to another.

ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I perform basic operations on integers as well as fractions?

5/23/2006                                                                                              35
Essentials of Math
How can I solve problems in this unit?
*How can I measure an object with a ruler and estimate its length to the nearest 16th of an
inch/nearest mm?
How can I use this in the real world?
*How can I estimate lengths in English and metric units?
*How can I use rulers/measuring tapes to calculate area and perimeter?

KEY CONTENT LANGUAGE:
English units, metric units, area, perimeter

RESOURCES:

Rulers, micrometers, measuring tape

5/23/2006                                                                               36
Essentials of Math

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