MATH
APPLICATIONS - 2007
Semester 1:
Basic Math Skills and Geometry
Basic Math Skills (entire unit 2-4
weeks)
1. Understand and use numbers
a. Use place value to read and write rational numbers.
b. Round numbers to the given place value.
c. Compare magnitudes and relative magnitudes of rational numbers.
d. Convert fractions to decimal.
e. Convert decimal to percent.
f. Compute percentages.
g. Express a ratio as a fraction in lowest terms.
h. Find equivalent ratios.
i. Use scientific notation.
2. Perform computations accurately
a. Add, subtract, multiply, and divide decimals.
b. Add, subtract, multiply, and divide fractions.
c. Add, subtract, multiply, and divide integers.
d. Word problems add, subtract, multiply, and divide integers.
e. Compute elapsed time.
3. Collect organize and display data
a. Read tables, charts, and graphs.
b. Construct graphs such as line graphs and vertical bar graphs.
4. Understand and use
a. Use dimensional analysis to convert from one unit to another.
b. Convert from one currency to another.
c. Measure to the nearest half, fourth, eighth, and sixteenth of an inch.
d. Measure to the nearest meter, centimeter, and millimeter.
e. Know and understand precision, accuracy, and significant digits.
5. Estimate and judge reasonableness of results
a. Estimate using rounding.
b. Use front-end estimation.
c. Estimate using compatible numbers.
d. Estimate by clustering.
6. Use reasoning skills
a. Use the four-step method of problem solving.
b. Use problem-solving skills such as identifying information, looking for
a pattern, constructing a table, working backward, and writing an equation.
Geometry Applications
1. Know, understand, and use basic geometric terminology
(1 week)
a. Point, ray, line, segment, plane, angle, parallel, perpendicular,
intersecting, metric/customary units, congruent, midpoint, deductive/inductive
reasoning, radius, chord, diameter, circumference.
2. Measure and calculate angles and segments (1 week)
a. Measure and calculate radius, chord, diameter, circumference
b. Calculate central angles, vertical angles, right angles, obtuse
angles, straight angles, complementary & supplementary angles.
c. Measure angles and determine whether right, straight, acute, or
obtuse.
d. Apply in real-life situations (for example: verify that
right angles are formed in construction or measuring distances between objects)
3. Identify concepts of polygons and polyhedra (2 weeks)
a. Identify concave and convex polygons
b. Name by number of sides/faces
c. Draw and determine the number of diagonals
d. Distinguish among isosceles, scalene and equilateral triangles
e. Identify acute, obtuse, and right triangles
f. Name quadrilaterals, prisms and polyhedra
g. Identify lateral faces and bases
h. Classify prisms
i. Draw prisms using perspective drawing.
4. Identify congruent figures and transformations (1 week)
a. Use congruency statements
b. Identify corresponding sides
c. Identify lines of reflection and symmetry
d. Identify and use reflection (flip), translation (slide), and
rotations
e. Tessellations
5. Basic triangle measurement and calculations (1 week)
a. Altitude
b. Median to find balancing point
c. Identify situations where triangles cannot be formed
d. Identify which angles are larger in two comparable triangles
6. Triangle congruency (1 week)
a. Use SSS, SAS, ASA, AAS, HL, CPCTC
7. Concepts of parallel lines and polygons(1 week)
a. Identify congruent & supplementary angles with parallel lines
and transversals
i. Alternate interior
ii. Alternate exterior
iii. Same-side interior
iv. Corresponding
b. Calculate angles in triangles using the triangle-sum theorem
c. Calculate exterior and interior angles in polygons
8. Identify quadrilateral types and segments within
quadrilaterals (1 week)
a. Parallelogram and diagonals
b. Rectangle and square and diagonals
c. Rhombus and diagonals
d. Trapezoid and diagonals and median
9. Calculations in circles and polygons (1 week)
a. Identify arcs, tangents, points of tangency
b. Perimeter and area of square, rectangle, parallelogram,
triangles, and other polygons
c. Circumference and area of circles
d. Understand and use p (pi)
e. Apply in real-life situations (for example: calculate
fertilizer for a yard of given dimensions)
10. Understand and use similarity calculations (1 week)
a. Ratios, fractions in simplest form, proportions, unit rate
b. Use cross multiplication
c. Determine whether figures/polygons are similar
d. Calculate and use scale factors and map scales
e. Apply in real-life situations (for example: laying out
evenly-spaced objects such as plants or studs, mathematics of constructing a
staircase)
11. Triangle similarity (1 week)
a. Using parallel lines and triangles, find proportional segments
b. Calculate measurements indirectly
c. Use and apply the golden ratio
d. Apply in real-life situations (for example: find the height
of a tree using shadow lengths)
12. Pythagorean Theorem (1 week)
a. Estimate and calculate square roots of numbers, including perfect
squares
b. Use Pythagorean theorem
c. Use special right triangles
d. Apply in real-life situations (for example: find how far a
ladder would extend on a building)
13. Area and volume of prisms (1 week)
a. Calculate total surface area, lateral surface area, and volume
b. Understand equivalent capacities
c. Apply in real-life situations (for example: find the cost
of painting a room, concrete needed for a driveway/sidewalk or find the
required number of pieces of aluminum siding for a project)
14. Area and volume of other space figures (1 week)
a. Cylinder: lateral area, surface area and volume
b. Cone: volume
c. Sphere: surface area and volume
Semester 2:
Consumer Math and Data Analysis
with Probability
1. Understand Data Analysis (2 weeks for 1-4)
a. Read and interpret data in tables, charts, and graphs including:
frequency tables, scatter plots, line plots, line graphs, broken line graphs,
bar graphs, histograms, circle graphs, stem-and-leaf plots, and box-and-whisker
plots.
b. Recognize misleading statistics.
2. Collect, Organize, and Display Data in Various Forms
a. Collect, organize, and display data in tables, charts, and graphs
including: frequency tables, scatter plots, line plots, line graphs, broken
line graphs, bar graphs, histograms, circle graphs, stem-and-leaf plots, and
box-and-whisker plots.
3. Apply Simple Statistical Measurements
a. Calculate the mean, median, and mode of a set of data.
b. Explore and discuss distribution of data, including range,
frequency, gaps, and clusters.
4. Understand basic concepts of probability.
a. Calculate the probability of a simple event
b. Recognize equally likely outcomes
c. Use tree diagrams and the fundamental counting principle
determine the number of outcomes in an event.
d. Find the number of permutations of a set of objects.
e. Use permutation notation.
f. Find combinations by using a list.
g. Use combination notation.
h. Calculate experimental probability
i. Make predictions based on simple experimental and theoretical
probabilities
j. Find the complements and odds of events
k. Find the probability of independent and dependent events
l. Simulate a problem and make an organized list to find all the
outcomes possible for a given situation
5. Income (Ch 1and 2, 2-3 weeks)
Show how to recognize and identify some of the real and hidden costs and
benefits of working, distinguish between gross pay and net pay, and provide
practice reading and interpreting pay stubs.
a. Calculate hours on a weekly time card.
b. Calculate overtime pay.
c. Compute commission.
d. Interpret a pay stub.
e. Calculate gross income.
f. Read tables to find the amount withheld for federal income tax.
g. Determine state taxes.
h. Determine amount of income withheld for Social Security and
Medicare taxes.
i. Calculate deduction for health insurance.
j. Compute net pay.
k. Identify some of the hidden costs of a job.
l. Identify some of the benefits companies often offer employees.
6. Budgeting (ch 3, 1 week)
Identifying and prioritizing personal and financial goals. create a plan to
achieve those goals, and provide practice setting up and maintaining a personal
budget.
a. Identify and prioritize some of your personal and financial goals.
b. Identify the steps you can take and the resources you will need
to achieve your goals.
c. Identify and examine your current spending behaviors and
patterns.
d. Understand what it means to budget, and identify the reasons to
maintain a budget.
e. Create and maintain a personal budget that supports your personal
and financial goals.
7. Banking Services (ch 4, 1-2 weeks)
Provide practice in comparing and evaluating various banking services including
checking and savings accounts, ATM/check cashing cards, and online banking.
Perform the tasks associated with maintaining checking and savings accounts.
a. Understand the services offered by banks, savings and loans, and
credit unions.
b. List some of the factors to consider when shopping for bank
services.
c. Understand the responsibilities of having a checking account.
d. Write checks and keep a running balance in a checkbook.
e. Describe how to deposit a check.
f. Read and interpret a checking account statement.
g. Reconcile a checking account using a checking account statement
and a check register.
h. Describe what an ATM card is and explain how it is used.
i. Describe what a debit card is and explain how it is used.
8. Savings and Investing (ch 5, 2 weeks)
Introduce the advantages and disadvantages of common savings and investment
vehicles, and show the short- and long-term effects of various savings and
investment choices. Compute simple and compound interest.
a. List and prioritize some of your short- and long-term budget goals.
b. List and explain some of the advantages of saving money.
c. Understand the concept of "pay yourself first" and list
some ways to encourage this habit.
d. List and explain the differences among the most common saving
methods.
e. Complete a savings deposit and withdrawal slip.
f. Calculate the new balance on a savings account statement.
g. Compute simple and compound interest.
h. Understand the advantages and disadvantages of popular investment
vehicles such as certificates of deposit, stocks, and bonds.
i. Determine the effective annual yield of an investment.
j. Solve for the total cost of a stock investment.
k. Compare and contrast the short- and long-term consequences of
investment decisions.
9. Cash Purchases (ch 6, 1 week)
Determine the exact price of an item including sales tax and discounts such as
rebates and coupons.
a. Compute sales tax.
b. Calculate the total purchase price.
c. Compute and use unit price to determine the better buy.
d. Compute the final price after a discount.
e. Solve for the dollar amount of the markdown.
f. Compute the sales price when the markdown rate is known.
10. Charge Accounts and Credit Cards (ch 7, 1 week)
Provide an awareness and understanding of what credit is and of the rights
and responsibilities of using credit. Develop skills to compare and evaluate
the terms and conditions of various credit cards, and understand the legal and
financial responsibilities involved.
a. Understand some of the reasons for getting credit.
b. Understand some of the advantages and disadvantages of using
credit.
c. Understand why banks issue credit.
d. List and understand some of your rights and responsibilities as a
consumer.
e. List and understand the three principal types of consumer credit.
f. Determine a safe debt load.
g. Calculate the new balance on a charge account.
h. Find the finance charge by using the Unpaid-Balance method.
i. Find the finance charge by using the Average-Daily Balance
method.
j. Read and interpret a credit card statement.
k. Determine safe personal debt loads.
11. Cars and Loans (ch 8 and 9, 2 weeks)
Investigate the legal and financial responsibilities of buying, maintaining,
insuring, and operating a car, and translate those responsibilities into a
monthly budget.
a. List some of the costs of owning and operating a car.
b. Given a budget, decide how much you can afford to pay for a car.
c. List some of the things you should research and some decisions
you should make before you begin to shop for a car.
d. Understand the differences between various kinds of warranties
and service contracts.
e. List some of the factors to consider when shopping for a car
loan.
f. Define amortization.
g. Calculate the total cost of various car loans.
h. Understand what a co-signer is, and describe when one is
necessary.
i. List some of the factors to consider when shopping for car
insurance.
j. List some of the factors used to set car insurance rates.
k. Given a budget, decide how much money can safely be spent each
month to own, operate, and maintain a car.
l. Know the advantages and disadvantages of leasing a motor vehicle.
12. Housing Costs (ch 10, 2 weeks)
Examine the process and costs involved with renting and buying a home.
a. Compare benefits and drawbacks of renting and buying a home
b. Develop a knowledge of the home-buying and renting process
c. Understand steps involved in applying for a mortgage
d. Understand and compare various types of mortgages
e. Compute the mortgage loan amount
f. Determine the monthly payment, total amount paid, and total
interest charged
g. Calculate total closing costs
h. Calculate assessed value and real estate taxes
i. Calculate the cost of annual homeowners insurance
j. Set up a budget that includes rent, moving expenses, and the
expenses associated with setting up a household
13. Insurance and Investments (ch 11 and 12, 2 weeks)
Compare various health insurance plans to find the one to best fit a given
situation. Compare and contrast term life and whole life insurance.
a. Compute health insurance premiums
b. Calculate the amount the patient pays for health care
c. Compute the annual premium for term life insurance
d. Compute the annual premiums for different types of insurance