Mathematics – Mathematical Models
Unit 7: Financial Models
CURRICULUM OVERVIEW
Third Grading Period – Weeks 1- 5 (19 days)
Enduring Understandings (Big Ideas)
Unit Rationale
The foundation of understanding finances is understanding mathematics.
The students must understand financial models in order to solve problems related to
financial markets, such as: (APR) annual percentage rate, life insurance, money market,
mortgage rates, credit cards and internet finance charges.
Essential Questions
Guiding Questions
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What mathematical functions are financial models?
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Do financial problem situations limit the domain and range of these
mathematical functions?
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Can more than one mathematical function “adequately” model a given
financial problem situation?
by amortization model?
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√How do you determine the amount financed, the installment price, and the finance
charge of an installment loan?
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TEKS (Standards)
√How do you determine the monthly mortgage payment?
√How do you distinguish between term life insurance and whole life insurance?
√How do you distinguish between a stock and a bond?
TEKS Specificity - Intended Outcome
M.3 The student develops and implements a plan for collecting and analyzing data
in order to make decisions. The student is expected to:
M.3B communicate methods used, analyses conducted, and conclusions drawn
for a data-analysis project by written report, visual display, oral report, or multimedia presentation.
M.5 The student uses functional relationships to solve problems related to
personal income. The student is expected to:
M.5B solve problems involving personal taxes.
M.6 The student uses algebraic formulas, graphs, and amortization models to
solve problems involving credit. The student is expected to:
M.6A analyze methods of payment available in retail purchasing and compare
relative advantages and disadvantages of each option;
M.6B use amortization models to investigate home financing and compare buying
and renting a home; and
M.6C use amortization models to investigate automobile financing and compare
buying and leasing a vehicle.
M.7 The student uses algebraic formulas, numerical techniques, and graphs to
solve problems related to financial planning. The student is expected to:
SAISD © 2010-11 – Third Grading Period
√How do you determine the interest on a credit card account using the average daily
balance method?

Concepts
√How do you distinguish between simple and compound interest?
√How do you solve problems involving repaying a loan or liquidating a sum of money
” I CAN” statements highlighted in yellow should be displayed for students.
I can :
 report clearly the methods used and conclusions made from a data analysis project
(M.3B)
 solve problems involving personal finances. (M.5B)
 determine the interest on a credit cared account using the average daily balance
method (M.6A)
 solve problems involving repaying a loan or liquidating a sum of money by the
amortization model (M.6B)
 use a table to determine the total interest on a mortgage, the amount of down payment
and points in a mortgage (M.6B)
 prepare a partial amortization schedule of a mortgage (M.6B)
 determine if borrowers qualify for a mortgage (M.6B)
 use the (APR) annual percentage rate and a table to determine the APR of a car loan
(M.6C)
 analyze the advantages and disadvantages of savings options for both types of
interest – compound or simple rate (M.7A)
 analyze insurance options for coverage and cost (M.7B)
 analyze investment options between stocks, bonds, annuities, and retirement plans
(M.7C)
Mathematics: Mathematical Models with Application
Page 1 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
M.7A analyze types of savings options involving simple and compound interest
and compare relative advantages and disadvantages;
M.7B analyze and compare coverage options and rates in insurance; and
M.7C investigate and compare investment options including stocks, bonds,
annuities, and retirement plans.

ELPS Specificity – Intended Outcome
ELPS Student Expectations
ELPS 1c– use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and gradelevel vocabulary
ELPS 1e– internalize new basic and academic language by using and reusing it
in meaningful ways in speaking and writing activities that build concept and
language attainment
ELPS 2c – learn new language structures, expressions, and basic and academic
vocabulary heard during classroom instruction and interactions
ELPS 2d – monitor understanding of spoken language during classroom
instruction and interactions and seek clarification as needed
ELPS 2e – use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language
ELPS 3d – speak using grade-level content area vocabulary in context to
internalize new English words and build academic language proficiency
After completing this unit, students will be able to:
 communicate methods used, analysis conducted, and conclusions drawn for a data
analysis project by written report, visual display, oral report, or multi-media
presentation ELPS 1e, ELPS 2c, ELPS 2e
 analyze data to make decisions about banking ELPS 2d
 analyze methods of payment available in retail purchasing and compare relative
advances and disadvantages of each option ELPS 2d
 use amortization models to investigate home financing and compare buying and
renting a home ELPS 1c, ELPS 3d
 use amortization models to investigate automobile financing and compare buying and
leasing a vehicle ELPS 1c, ELPS 3d
College and Career Readiness – Intended Outcome
College and Career Readiness Expectations
Mathematics Standards
II-B1: Manipulating Expressions – recognize and use algebraic properties,
concepts, procedures, and algorithms to combine, transform, and evaluate
expressions (e,,g., polynomials, radicals, rational expressions)
VII- A2: Representation of Functions – recognize and distinguish between
different types of functions.
VII-B1: Analysis of Functions – understand and analyze features of a function.
VII-C1: Modeling – apply known functional models.
VIII-C2: Real World Problem Solving – use a function to model a real world
situation.
Cross-Disciplinary Standards
I-C2: Problem Solving – develop and apply multiple strategies to solve a
problem
II-E4: Technology – use technology appropriately
After completing this unit, students will be able to:
 communicate methods used, analysis conducted, and conclusions drawn for a data
analysis project by written report, visual display, oral report, or multi-media
presentation VII-C1, VIII-C2
 analyze data to make decisions about banking VII-B1, I-C2
 analyze methods of payment available in retail purchasing and compare relative
advances and disadvantages of each option VII- A2, I-C2
 use amortization models to investigate home financing and compare buying and
renting a home II-B1, II-E4
 use amortization models to investigate automobile financing and compare buying and
leasing a vehicle II-B1, II-E4
Evidence of Learning
 Given a short term course data analysis project, students will communicate their methods used, analyses conducted, and conclusions drawn by written report, visual display,
or multi-media presentation at least 80% of the time
 On a periodic quiz, students will solve problems involving personal taxes at least 80% of the time
 On a unit assessment, students will analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option at least
80% of the time
 On a multi-day take home assessment, students will use amortization models to investigate home financing and compare buying and renting a home at least 80% of the time
 On a unit assessment, students will use amortization models to investigate automobile financing and compare buying and leasing a vehicle at least 80% of the time
 On a graded homework assignment students will analyze types of savings options involving simple and compound interest and compare their relative advantages and
disadvantages at least 80% of the time
 On a weekly quiz, students will analyze and compare coverage options and rates on insurance products at least 80% of the time
 On a long term class project, students will investigate and compare investment options including stocks, bonds, annuities, and retirement plans at least 80% of the time
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 2 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Mathematics – Mathematical Models
Unit 7: Financial Models
CURRICULUM GUIDE
Third Grading Period – Weeks 1- 5 (19 days)
Essential Pre-requisite Skills
Algebra 1
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interpret and make decisions, predictions, and critical judgments from functional relationships (A.1E)
interpret situations in terms of given graphs or create situations that fit given graphs (A.2C)
relate direct variation to linear functions and solve problems involving proportional change (A.6G)
analyze data and represent situations involving inverse variation using concrete models, tables, graphs or algebraic methods (A.11B)
analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs or algebraic methods (A.11C)
Geometry
 identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are
Pythagorean triples (G.5D)
 use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures (G.7A)
 find areas of regular polygons, circles, and composite figures (G.8A)
 find areas of sectors and arc lengths of circles using proportional reasoning (G.8B)
 use ratios to solve problems involving similar figures (G.11B)
 describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems (G.11D)
The Teaching & Learning Plan
Instructional Model & Teacher Directions
The teacher will…
Days 1 and 2
MMA Activity 4.1
Income and Expenses
So the students can demonstrate competency,
the students wii…
Days 1 and 2
MMA Activity 4.1
Income and Expenses
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Ask employed students for examples of their personal pay checks, noting the Gross
Base Salary and Net Base Salary
Explore
 Group students in pairs to discuss and solve problems on (pp411-415) #1-5
involving personal finances.
Explain
 Direct students to problem #6 (pg 416) to determine how many hours of overtime
are needed to purchase a TV
Elaborate
 Lead a discussion with whole class on meeting expenses and not spending more
than their income.
Evaluate

Assess students on discussion as well as practice exercises for accuracy.
SAISD © 2010-11 – Third Grading Period
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Write their Gross Base Salaries and Net Base Salaries on the board, so that they
can compare salaries with other classmates that are employed. (M.7A)
Explore
 Use Activity 4.1 (pp411-415) #1-5 to solve problems involving finances. (M.5B,
M.7A)
Explain
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Take notes in their math journal, verbalizing and computing the solution to
problem #6 pg 416 (M.7A)
Elaborate
 Discuss, as a whole class, spending practices with their means.
Evaluate
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Solve problems on (pp416-417) #6,7 (M.7A)
Mathematics: Mathematical Models with Application
Page 3 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Day 3 and 4
MMA Activity 4.2
Time is Money, Simple Interest and Compound Interest
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Hand out index cards with a designated amount of money that each student
inherited. Then ask students to answer pp 418 #1a,b
Explore
 Group students in pairs to discuss and solve problems on pg 425 #1-6 and
demonstrate on the overhead.
Explain
 Define and use the Simple and Compound Interest formulas in Example #1, p419
Elaborate

Provide students with graphing calculators and assign problems in Example
#2, 3 on pp 421-422
Evaluate

Day 3 and 4
MMA Activity 4.2
Time is Money, Simple Interest and Compound Interest
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Pick a card and solve using problems 1, a, b on pg 418 (M.7A)
Explore
 Solve problems 1-6 on pg 425 and demonstrate on the overhead. (M.7A, M.7C)
Explain
 Solve problem #1, pg 419 with the use of the formulas provided. (M.7A)
Elaborate
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Use their TI-84 graphing calculator to help solve problems in Example #2,3
pp 421-422 (M.7A)
Evaluate
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Assess students on discussion as well as practice exercises for accuracy.
Days 5 and 6
MMA Activity 4.3
Saving for Retirement, Annuities
Days 5 and 6
MMA Activity 4.3
Saving for Retirement, Annuities
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Facilitate a discussion regarding a retirement plan similar to problem #1 pg 427
Explore
 Group students in pairs
 Assign #7,8 pg 430 to assist them in understanding retirement plans
Explain
 Define and give examples of terms such as annuity, annuity due, future value,
present value
Elaborate
 Provide students with graphing calculators and assign exercises #7,8 pg 433
Evaluate

Work problems on pp 426 #7,8,9 (M.7A)
Assess students for accuracy on discussions, group activities and practice
exercises #1-6 pp 427-433
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results

Write in their math journals a simulated retirement plan and determine how
much they should save per year, after examining and discussing #1 pg 427 (M.7A,
M.7C)
Explore
 Discuss, solve and write in their math journal the solutions to #7,8 pg 430 (M.7C)
Explain
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Take notes in their math journals, verbalizing in writing the meaning of all
terms related to annuities (M.7C)
Elaborate
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Using the graphing calculator, solve problems exercises #7,8 pg 433 (M.7A,
M.7C)
Evaluate

SAISD © 2010-11 – Third Grading Period
Answer practice exercises #1-6 pp 427-433 (M.7A, M.7C)
Mathematics: Mathematical Models with Application
Page 4 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Days 7 and 8
MMA Activity 4.4
Buy or Lease? Amortization
Days 7 and 8
MMA Activity 4.4
Buy or Lease? Amortization
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Group students in pairs and provide them with newspaper, poster board, scissors
and glue, in order to create a poster on leasing a car.
Explore
 Group students in pairs and discuss problem on pg 436 #5, 6, 7, 8
Explain
 Define amortization and calculate amortization payments by formulas
Elaborate
 Pair students to solve problems on pg 438 #1, 3 and discuss in class.
Evaluate
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Assess each group on practice problems pp 434-438 #4, 5, 6
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Use materials to create a poster with Examples of car leasing prices. (M.3B, M.6C)
Explore
 Discover and explain in their journals and in a class discussion, the best options to
buy or lease after working pg 436 #5, 6, 7, 8 (M.6A, M.6C)
Explain

Take notes in their journals, verbalizing the definition of amortization. ( M.6C)
Elaborate
 Solve problems pg 438 #1, 3 and have a class discussion. (M.6A, M.6C)
Evaluate

Day 9
Chapter 4.1-4.4 Quiz
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Assess students on Ch. 4, 4.1-4.4 (pp411-439) TRG p 193, #1-5 for accuracy.
Days 10 and 11
MMA Activity 4.5
Buy Now, Pay Later Installment Payment
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Discussion cost of High-Definition Televisions pg 440 #1, 2
Explore
 Pair students to solve problems involving finance pp 450-451 #1-4
Explain
 Define Annual Percentage Rate (APR), finance charge, closed-end installment and
installment plan and supply students with construction paper to write definitions for
the Word Wall
Evaluate

Assess students on take home project for accuracy TRG pg 189, #1, 2
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Solve problems independently p193, #1-5 TRG
Days 10 and 11
MMA Activity 4.5
Buy Now, Pay Later Installment Payment
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Compare prices on High-Definition Televisions and solve problems 1, 2 pg 440
(M.6A)
Explore
 Compute finance charge, interest, installment payments pp 450-451 #1-4 (M.6A,
M.6C)
Explain
 Create Posters, using construction paper to write the definition of APR, Installment
plan and finance charge and place on the Word Wall. (M.3B, M.6A)
Evaluate

SAISD © 2010-11 – Third Grading Period
Solve problems pg 438 #4, 5, 6 (M.6A, M.6C)
Day 9
Chapter 4.1-4.4 Quiz
Solve problems on take home project TRG pg 189, #1, 2 (M.6B)
Mathematics: Mathematical Models with Application
Page 5 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Days 12 and 13
MMA Activity 4.6
Home Sweet Home Mortgage
Days 12 and 13
MMA Activity 4.6
Home Sweet Home Mortgage
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
 Benchmark results
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Discuss and demonstrate how to determine mortgage payments using Table
4.2 (pg 454) and TI-84 Graphing Calculator.
Explore
 Have students analyze information that is necessary in making a rent versus a buy
comparison in Appendix D pg A-31.
Explain
 Define mortgage, amortization, amortization schedule, monthly housing expenses.
Evaluate

Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results

Assess students’ work for accuracy pp 452-460 #1, 2, 3
Explore
 Analyze the information and calculations necessary to make a comparison between
renting and buying a home PA-31 Appendix D (M.6A, M.6B)
Explain

Take notes in their math journal, verbalizing the definitions for mortgage,
amortization, amortization schedule and monthly housing expenses. (M.6B)
Evaluate

Day 14
MMA Activity 4.7
Insuring the Future, Term and Life Insurance
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 (Option: teacher may provide the policies) Assign students to research, on the
internet, five different life insurance and term insurance policies. After comparing
policies, students will select the best option.
Explore
 Pair students to discuss and solve problems involving qualifying for a mortgage
pg 456, #6
Explain
 Define Life Insurance, face value, insurance premium, term insurance, permanent
life insurance, non-forfeiture options.
Evaluate
 Assess students on journal writing and practice exercises for accuracy.
Use a graphing calculator and Table 4.2 (pg 454) to determine the monthly
payment for a 30-year mortgage. #3 pg 453 (M.6B)
Solve Exercise problems #1, 2, 3 on pp 452-460 (M.6B)
Day 14
MMA Activity 4.7
Insuring the Future, Term and Life Insurance
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Research, on the internet, five different life insurance and term insurance policies in
order to select the best policy. (M.7B)
Explore
 Solve problem pg 456, #6 and have a class discussion on how to qualify for a
mortgage. (M.7B)
Explain
 Define Life Insurance, face value, insurance premium, term insurance, permanent
life insurance, non-forfeiture options. (M.7B)
Evaluate
 Solve problems and verbalize steps to solving in their math journal. (pp461)
Exercises #1,5 (M.7B)
Days 15 and 16
MMA Activity 4.8
The Stock Market
Days 15 and 16
MMA Activity 4.8
The Stock Market
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
SAISD © 2010-11 – Third Grading Period
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
Mathematics: Mathematical Models with Application
Page 6 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
 Group students in pairs, to discuss and solve Example 1 on pg 468
Explain
 Define stock, share, common stock, preferred stock, proceeds, bond and accrued
interest.
Evaluate

Assess students’ work for accuracy.
 Determine number of shares needed, closing price of stock, dividends, stock
transactions, using Table, Example 1 on pg 468. (M.7C)
Explain

Take notes in their math journal, verbalizing the definitions for stock, share,
common stock, preferred stock, proceeds, bond and accrued interest. (M.7C)
Evaluate

Day 17
MMA Activity 4.9
Which is the Best Option?
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Group students and assign each group a financial situation in which they must
select the best option. Have each group prepare an oral presentation of their
findings.
Explain
 Discuss and guide students in selecting the best option on problem #3 pg 477
Evaluate
 Assess students work for accuracy.
Exercises #3, 4 pp 475-476 (M.7C)
Day 17
MMA Activity 4.9
Which is the Best Option?
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Present their best options from the given financial situation with visual displays
showing tables, equations or graphs used in the problem solving process. (M.3B,
M.6A, M.7A, M.7C)
Explain

Take notes in their math journal, verbalizing the best selection from pg 477 #3
(M.6A)
Day 18
Unit Review
Day 18
Unit Review
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
Explain
 Assign the students to work in pairs (one does evens and one does odds) problems
1-9 on pp 478-479 and 5 a-g on pp 480-481.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
 Discuss their work with each other when finished.
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
Explain
 Work in pairs (one does evens and one does odds) problems 1-9 on pp 478-479
and 5 a-g on pp 480-481.
 Discuss your work with partner when finished.
Day 19
Unit Assessment
Day 19
Unit Assessment
Evaluate
 Answer any student questions
 Administer assessment over Chapter 4 using TRG pp 193-194 or 195-196 in
Section 7 assessment
 Ensure that assessment questions are aligned with the guiding TEKS verbs and
nouns
SAISD © 2010-11 – Third Grading Period
 Ask any questions
 Complete assessment over Chapter 4
Mathematics: Mathematical Models with Application
Page 7 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
 Ensure the following are available to students
graphing calculators
TAKS Math Cart
Paper and pencil
Vocabulary: Math content specific
 Tax table
 Social Security
 Deductions
 Expenses
 Simple interest
 Compound interest
 Annual yield
 Annuities
 Annuity payment
 Future value
 Present value
 Down payment
 Leasing
 Amortization payment
 Installment loan
 Installment price
 Annual Percentage Rate (APR)
 Actuarial Method
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Average daily balance
Finance charge
Mortgage
Face Value
Life insurance
Term insurance
Face value
Dividends
Proceeds
Bonds
Accrued interest
Stock
Share
Treasury bond
Corporate bond
Municipal bond
Vocabulary: TEKS
verbs
 Develop
 Implement
 Collect
 Analyze
 Communicate
 Solve
 Calculate
 Compare
 Investigate
 Apply
 Select
 Model
 Represent
 Present
 Display
Resources:
Text: Mathematical Models with Applications
Chapter 4
Activities 4.1 – 4.8
Teacher Resource Guide and Printed Test Bank
Evidence of Learning
Formative Mini-Assessment
TAKS
College-Readiness i.e.,
Anticipated Skills for SAT/ACT/AP/Career/Life
2004 TAKS Exit Level (G.11D)
2004 TAKS Exit Level (G.8D)
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 8 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 9 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Mathematics – Mathematical Models
Unit 8: Geometric Models
CURRICULUM OVERVIEW
Third Grading Period – Week 5-9 (19 days)
Enduring Understandings (Big Ideas)
Unit Rationale
Geometry is used in a variety of academic and real-world settings.
Students should internalize geometric formulas, concepts and skills well enough to solve
a variety of real world applications.
Essential Questions
Guiding Questions
What problem situations lend themselves to the use of geometric models for
solutions?
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combinations of formulas?
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TEKS (Standards)
√How do you use unit analysis to solve problems involving perimeters?
√How do you calculate areas of polygons using appropriate formulas?
√How do you solve problems in context using geometric models?
√How do you perform a transformation on a given figure?
√How do you recognize the geometric properties of similar triangles?
√How do you use similar triangles in indirect measurement?
√How do you understand the one-point and two-point perspective?
TEKS Specificity - Intended Outcome
M.1 The student uses a variety of strategies and approaches to solve both routine
and non-routine problems. The student is expected to:
 M.1B use multiple approaches (algebraic, graphical, and geometric methods) to
solve problems from a variety of disciplines.
Concepts
√How do you calculate perimeters of many sided plane figures using formulas and
M.8 The student uses algebraic and geometric models to describe situations and
solve problems. The student is expected to:
M.8B use trigonometric ratios and functions available through technology to
calculate distances and model periodic motion.
” I CAN” statements highlighted in yellow should be displayed for students.
I can :
 use multiple approaches to problem-solving. (M.1B)
 calculate distances and represent repeating or cyclic motion using trigonometric
ratios and functions (M.8B)
 describe mathematical patterns and structure in art and architecture with geometric
transformations, symmetry, and perspective drawings (M.9A)
 describe mathematical patterns and structure in music with geometric
transformations and proportions (M.9B)
M.9 The student uses algebraic and geometric models to represent patterns and
structures. The student is expected to:
M9A use geometric transformations, symmetry, and perspective drawings to
describe mathematical patterns and structure in art and architecture; and
M.9B use geometric transformations, proportions, and periodic motion to describe
mathematical patterns and structure in music.
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 10 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
ELPS Specificity – Intended Outcome
ELPS Student Expectations
ELPS 1c– use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level
vocabulary
ELPS 1e– internalize new basic and academic language by using and reusing it in
meaningful ways in speaking and writing activities that build concept and language
attainment
ELPS 2c – learn new language structures, expressions, and basic and academic
vocabulary heard during classroom instruction and interactions
ELPS 2d – monitor understanding of spoken language during classroom instruction
and interactions and seek clarification as needed
ELPS 2e – use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language
ELPS 3d – speak using grade-level content area vocabulary in context to internalize
new English words and build academic language proficiency
After completing this topic, students will be able to:
 use multiple approaches (algebraic, geometric, and graphical) to solve problems from a
variety of disciplines ELPS 1c
 use geometric transformations, symmetry, and perspective drawings to describe
mathematical patterns and structure in art and architecture ELPS 1e, ELPS 3d
 distinguish between problems requiring area formulas and perimeter formulas ELPS
1c, ELPS 2d
 recognize geometric properties of three-dimensional figures ELPS 2c, ELPS 2e
College and Career Readiness – Intended Outcome
College and Career Readiness Expectations
Mathematics Standards
II-B1: Manipulating Expressions – recognize and use algebraic properties,
concepts, procedures, and algorithms to combine, transform, and evaluate
expressions (e,,g., polynomials, radicals, rational expressions)
VII-A2: Representation of Functions – recognize and distinguish between
different types of functions.
VII-B1: Analysis of Functions – understand and analyze features of a function.
VII-C1: Modeling – apply known functional models.
VIII-C2: Real World Problem Solving – use a function to model a real world
situation.
Cross-Disciplinary Standards
I-C2: Problem Solving – develop and apply multiple strategies to solve a problem
II-E4: Technology – use technology appropriately
After completing this topic, students will be able to:

use multiple approaches (algebraic, geometric, and graphical) to solve problems
from a variety of disciplines VII-A2, VII-C1, VIII-C2, I-C2

use geometric transformations, symmetry, and perspective drawings to describe
mathematical patterns and structure in art and architecture II-B1, VII-B1

distinguish between problems requiring area formulas and perimeter formulas VIIA2, VII-C1, I-C2

recognize geometric properties of three-dimensional figures II-B1, II-E4
Evidence of Learning
 On a semester assessment, students will use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines at least 80% of
the time
 On a periodic quiz, students will use trigonometric ratios and functions available through technology to calculate distances and model periodic motion at least 80% of the time
 On a unit assessment, students will use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and
architecture at least 80% of the time
 On a graded homework assignment, students will use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music at
least 80% of the time
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 11 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Mathematics – Mathematical Models
Unit 8: Geometric Models
CURRICULUM GUIDE
Third Grading Period – Week 5-9 (19 days)
Essential Pre-requisite Skills
Algebra 1
 interpret and make decisions, predictions, and critical judgments from functional relationships (A.1E)
Geometry
 use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations (G.5C)
 identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are
Pythagorean triples (G.5D)
 find areas of regular polygons, circles and composite figures (G.8A)
 find areas of sectors and arc lengths of circles using proportional reasoning (G.8B)
 use and extend similarity properties and transformations to explore and justify conjectures about geometric figures (G.11A)
 use ratios to solve problems involving similar figures (G.11B)
 Describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems (G.11D)
The Teaching & Learning Plan
Instructional Model & Teacher Directions
The teacher will…
Days 1 and 2
MMA Activity 6.1 Geometry Models
Walking around Bases, Gardens, Trusses and Other Figures
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Ask students to recognize and document a variety of two-dimensional shapes
appearing in natural settings ranging from sports to building materials
 Supply students with chart paper and markers to document their findings
Explore
 Direct students to investigate and research pi using the internet and report their
findings
Explain
 Define two dimensional figures: square, rectangle, triangle, parallelogram, trapezoid,
polygon and review perimeter formulas for these two dimensional figures pg 674
Elaborate
 Group students to discuss problem #5 on pg 669
Evaluate
So the students can demonstrate competency,
the students wii…
Days 1 and 2
MMA Activity 6.1 Geometry Models
Walking around Bases, Gardens, Trusses and Other Figures
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Brain storm a variety of two-dimensional shapes appearing in natural settings
ranging from sports to building materials and after discussing them in class will
document them in their math journals and on Chart paper
Explore
 Investigate and research pi using the internet and report their findings.
Explain

Take notes in their math journal, verbalizing in writing the definitions of two
dimensional figures: square, rectangle, triangle, parallelogram, trapezoid, polygon
and review perimeter formulas for these two dimensional figures pg 674
Elaborate
 Work problem #5 on pg 669 and discuss their reasoning as a group activity.
Evaluate

Assess student work for accuracy as class/homework on Exercises #1-12 pp
675-680.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
SAISD © 2010-11 – Third Grading Period

Work on exercises #1-12 pp 675-680 (M.9A)
Mathematics: Mathematical Models with Application
Page 12 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Days 3 and 4
MMA Activity 6.2 (Perimeters)
Lance Armstrong and You
Days 3 and 4
MMA Activity 6.2 (Perimeters)
Lance Armstrong and You
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Group students in pairs to discuss and solve problems 1-6 on pg 681
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Explore
 Group students in pairs to discuss and solve problems #1,2 on p.682
Elaborate
 Assign journal problem on pg 76 TRG to all students (Section 5 Writing to learn)
Evaluate

Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Discuss and solve problems 1-6 on pg 681. (M.8B)
Explore
 Solve problems #1, 2 on pg 682 and discuss in class
Elaborate
 Answer in complete sentences the solutions to the journal problem on p76 TRG
Section 5 Writing to learn (M.8B)
Evaluate

Assess students’ work for accuracy.
Exercises #3, 4 pp 683-684
Days 5 and 6
MMA Activity 6.3 (Area)
Walking around Revisited
Days 5 and 6
MMA Activity 6.3 (Area)
Walking around Revisited
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Ask students to recognize and document a variety of two-dimensional shapes
appearing in natural settings ranging from sports to building materials observing the
area of each
 Supply students with chart paper and markers to document their findings
Explore
 Group students in pairs to discuss and solve problems #17-20 on pg 692
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Explain
 Define two dimensional figures: square, rectangle, triangle, parallelogram, trapezoid,
polygon and
 Review area formulas for these two dimensional figures on pp 692-693
Evaluate

Assess student work for accuracy on Exercises #1-11, pp 694-697
 Quiz p.224 TRG
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Brain storm a variety of two-dimensional shapes appearing in natural settings
ranging from sports to building materials, observing the area of each, and after
discussion will document them in their math journals and on Chart paper
Explore
 Discuss and solve problems #17-20 on pg 692
Explain

Take notes in their math journal, verbalizing in writing the definitions of two
dimensional figures: square, rectangle, triangle, parallelogram, trapezoid, polygon
and review area formulas for these two dimensional figures pp 692-693
Evaluate

Complete exercises #1-11, pp. 694-697 (M.1B)
 Quiz p.224 TRG, Section 7 Assessment, Ch 6 Geometry Models
Day 7
Chapter 6.1-6.3 Quiz
Day 7
Chapter 6.1-6.3 Quiz
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Assess students on Ch. 6, 6.1-6.3 (pp 667-697) TRG pp 222-229, for accuracy.
SAISD © 2010-11 – Third Grading Period
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Complete assessment on Ch. 6, 6.1-6.3 (pp 667-697).
Mathematics: Mathematical Models with Application
Page 13 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Days 8 and 9
MMA Activity 6.4 (Perimeter and Area)
A New Pool and Other Home Improvements
Days 8 and 9
MMA Activity 6.4 (Perimeter and Area)
A New Pool and Other Home Improvements
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Facilitate a discussion on the differences of perimeter and area formulas and the
need for the use of each when solving Problem #6 pg 699
Explore
 Group students in pairs to discuss, analyze and solve problems #6-9 on pg 702
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Explain
 Define the Area, Perimeter Circumference formulas
Elaborate
 Group students to discuss problem #8 pg 700
Evaluate

Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Discuss the differences of perimeter and area formulas and the need for the use
of each when solving Problem #6 pg 699 (M.1B)
Explore
 Discuss, analyze and solve problems #6-9 on pg 702 (M.1B)
Explain

Take notes in their journals, verbalizing in writing and drawing examples of
all terms related to Area, Perimeter Circumference formulas
Elaborate
 Work problem #8 on pg 700 and discuss their reasoning as a group activity
Evaluate
Assess student work for accuracy on discussions and exercises

Exercises #1-5 pp 701-702
Day 12
MMA Activity 6.7
Math in Art
Day 12
MMA Activity 6.7
Math in Art
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Assist students in visualizing the golden rectangle by using reference to problems on
pg 722,#1, 2
 And ask for examples of Golden rectangle found in real life context
Explore
 Supply the students with ruler and paper and assign them problem #9 pg 727
Explain
 Define the Golden rectangle, one and two point perspective and Fibonacci
sequences of numbers
Evaluate

Assess student work for accuracy Exercises #1-6 pp.729-730
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 After examining and discussing the problems on pg 722,#1, 2
 Identify examples of Golden rectangle found in real life context
Explore
 Create the illusion of depth by utilizing two vanishing points as described in
problem #9 pg 727 (M.9A)
 Discuss and write the findings in math journal
Explain

Take notes in their math journal, verbalizing in writing the Golden rectangle,
one and two point perspective and Fibonacci sequences of numbers (M.9A)
Evaluate

Day 13
MMA Activities 6.1-6.7
How Can I Practice?
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Group students in pairs to discuss and work problems on pp.731-739
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Explain
SAISD © 2010-11 – Third Grading Period
Solve problems in Exercises #1-6 pp.729-730 (M.9A)
Day 13
MMA Activities 6.1-6.7
How Can I Practice?
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Discuss and solve problems on pp.733-737
Explain
Mathematics: Mathematical Models with Application
Page 14 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
 Define all concepts covered on pp 733-737 for understanding and clarification
Evaluate

Discuss and assess student work for accuracy on exercises #2-10 even pp 733-

Take notes in their math journals verbalizing in writing the definitions and
concepts discussed in this chapter and give visual examples for each
Evaluate
737

Day 14
MMA Activity 6.8
Painting Your Way through the Summer
Day 14
MMA Activity 6.8
Painting Your Way through the Summer
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Ask the students to guess which of the three buildings on page 738 will require the
most paint.
Explain
 Assign the students to work through problems 1-8 in pairs answering how much
paint, how long and how much is earned by completing the task.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Evaluate

Discuss and solve exercises #2-10 even pp 733-737
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Guess which of the three buildings on page 738 will require the most paint.
Explain
 Work through problems 1-8 in pairs answering how much paint, how long and
how much is earned by completing the task.
 Use the TAKS Math Chart
Evaluate

Complete for class/homework Exercises #1-6 on pp.741-742.
Assess student understanding by assigning for class/homework
Exercises #1-6 on pp.741-742.
Day 15
MMA Activity 6.9
Truth in Labeling
Day 15
MMA Activity 6.9
Truth in Labeling
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
 Ask the students to guess which of the products – Coke or ice-cream – advertises its
true amount enclosed.
Explain
 Assign the students to work through problems 1-8 in pairs evaluating the truth in
advertising.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Evaluate

Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
 Guess which of the products – Coke or ice-cream – advertises its true amount
enclosed.
Explain
 Complete problems 1-8 in pairs evaluating the truth in advertising.
 Use the TAKS Math Chart
Evaluate

Complete for class/homework Exercises #1-7 evens only on pp 746-747.
Assess student understanding by assigning for class/homework
Exercises #1-7 evens only on pp.746-747.
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 15 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Day 16
MMA Activity 6.10
Analyzing an Ice Cream Cone
Day 16
MMA Activity 6.10
Analyzing an Ice Cream Cone
Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
 Ask the students which flavor of ice cream cone they prefer and whether they order 1
or 2 scoops.
Explain
 Assign the students to work through problems 1-9 in pairs determining all the various
measurements associated with ice cream cones.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
Evaluate

Engage
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
 Which flavor of ice cream cone do you prefer and do you order 1 or 2 scoops?
Explain
 Complete problems 1-9 in pairs determining all the various measurements
associated with ice cream cones.
 Use the TAKS Math Chart
Evaluate

Complete for class/homework Exercises #1-10 odds only on pp.751-753.
Assess student understanding by assigning for class/homework
Exercises #1-10 odds only on pp.751-753.
Days 17 and 18
Review
Days 17 and 18
Review
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
Explain
 Assign the students to work in pairs (one does evens and one does odds) problems
1-9 on pp 757-759 and 3 a-g on pp 761-762.
 Assign the students to work in pairs (one does evens and one does odds) problems
1-10 on pp 771-775.
 Ensure the availability of the TAKS Math Chart and student ability to use it well
 Discuss their work with each other when finished.
Evaluate
 7-10 minute TAKS review using Reteach guide from Math Dept based on latest
Benchmark results
 Review homework
Explain
 Work in pairs (one does evens and one does odds) problems 1-9 on pp 757-759
and 3 a-g on pp 761-762.
 Use the TAKS Math Chart
 Discuss your work with partner when finished.
Day 19
Assessment
Day 19
Assessment
Evaluate
 Answer any student questions
 Administer an assessment of Chapter 6 (TRG pp230-233 or pp234-237
 Ensure that assessment questions are aligned with the guiding TEKS verbs and
nouns
 Ensure the following are available to students
graphing calculators
TAKS Math Cart
Paper and pencil
SAISD © 2010-11 – Third Grading Period
 Ask any questions.
 Complete assessment of Chapter 6
Mathematics: Mathematical Models with Application
Page 16 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Vocabulary: Math content
specific
 Square
 Trapezoids
 Parallelograms
 Rectangles
 Perimeter
 Circumference
 Polygons
 Triangle
 Area
 Tessellation
 Vertex
 Regular polygon
 Rigid motion
 Axis reflection














Vocabulary: TEKS verbs
 Describe
 Solve
 Model
 Calculate
 Develop
 Implement
 Analyze
 Compare
 Investigate
 Identify
 Apply
 Select
 Justify
Translation
Symmetry
Line of symmetry
Symmetrical
Reflective symmetry
Transformation
Similar triangles
Right triangle
Acute triangle
Scalene triangle
Obtuse triangle
Perspective
Two point perspective
Pythagorean Theorem
Resources:
Text: Mathematical Models with
Applications
Chapter 6
Activities 6.1 – 6.10
Teacher Resource Guide and Printed
Test Bank
Evidence of Learning
Formative Mini-Assessment
Jorge is designing a roof to a large office building. He
has a choice of two shapes – an isosceles triangle (20 m,
20 m and 10 m) or an isosceles trapezoid (bases are 10
m and 20 m, sides are 7.5 m). To minimize the
perimeter of the roof, which shape should he use and by
how much is its perimeter smaller?
A.
B.
C.
D.
College-Readiness i.e.,
TAKS
2004 TAKS Exit Level (8.16B)
Anticipated Skills for SAT/ACT/AP/Career/Life
SAT Prep
A triangle has sides that measure 3 feet, 5 feet, and 7
feet. Determine the remaining dimensions of a similar
triangle that measures 2 feet on its shortest side.
triangle by 5 m
triangle by 10 m
trapezoid by 5 m
trapezoid by 10 m
A
7
1
1
feet by 10 feet
2
2
B 10 feet by 14 feet
C
3
1
3
feet by
4
2
3
D 15 feet by 21 feet.
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 17 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
2004 TAKS Exit Level (8.14C)
SAISD © 2010-11 – Third Grading Period
Mathematics: Mathematical Models with Application
Page 18 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.