BUTLER R-5 SCHOOL DISTRICT

CONSUMER MATH CURRICULUM

MATH

Approved by the Board of Education, November 1999

DESCRIPTION:

Consumer Math is a mathematics course designed not only to develop the basic fundamental skills needed to function in everyday consumer situations but also to develop an understanding of these concepts as well. Topics to be covered will include, but not restricted to, the following: bank accounts, loans, wages, salary, budgeting, taxes, insurance, and home ownership.

RATIONALE:

As adults in today's world individuals will need to apply basic mathematic skills in solving real-life situations that arise in their personal lives and careers. This course provides that information.

 

BUTLER R-5 SCHOOL DISTRICT

CURRICULUM

CONSUMER MATH 1

LEVEL 9-12

A. Demonstrate an understanding of numbers.

            1. Rename a fraction as a decimal and a decimal as a fraction.

            Strands addressed: Communication, Connections, Number Sense, Patterns and Relationships

                (Show-Me Standards 1.6, 1.8)

                2. Write a percent as a decimal and a decimal as a percent.

                Strands addressed: Communication, Connections, Number Sense, Patterns and Relationship

                (Show-Me Standards 1.6, 1.8)

B. Apply the basic operations in computational situations.

            1. Compute the sum, difference, product, and quotient of rational numbers.

            Strands addressed: Number Sense

                (Show-Me Standard 1.10)

            2. Demonstrate the use of a calculator.

            Strands addressed: Communication

                (Show-Me Standard 1.4)

                3. Find the percent of a given number.

                Strands addressed: Number Sense

                (Show-Me Standard 1.10)

                4. Determine the amount of elapsed time when given two times, and estimate to    check answer.

                Strands addressed: Number Sense

                (Show-Me Standard 1.10)

C. Estimate results and judge reasonableness of solutions.

            1. Round a number to a given place.

            Strands addressed: Reasoning

                (Show-Me Standards 1.6, 1.10, 3.4)

            2. Judge reasonableness of solutions in consumer and physical situations.

            Strands addressed: Reasoning

                (Show-Me Standards 3.4, 3.7)

D. Apply the concept of measurement to the physical world.

            1. Use unit multipliers to convert units of measure.

            Strands addressed: Geometric and Spatial Sense

                (Show-Me Standard 1.10)

            2. Compute the area/perimeter of regular and irregular shaped figures with main     focus on regular.

            Strands addressed: Geometric and Spatial Sense

                (Show-Me Standard 1.10)

E. Recognize geometric relationships.

            1. Be able to recognize simple geometric figures so as to apply appropriate formulas for area and surface area problems.

            Strands addressed: Patterns and Relationships, Geometric and Spatial Sense

                (Show-Me Standards 1.6, 1.10)

F. Use statistical techniques and interpret statistical information.

                1. Read and interpret tables, graphs, and charts.

                Strands addressed: Data Analysis, Probability and Statistics, Communication

                (Show-Me Standard 1.5)

                2. Find the mean, median, mode, and range of a given set of data.

                Strands addressed: Data Analysis, Probability and Statistics

                (Show-Me Standards 1.8, 1.10)

                3. Recognize misuse of statistical data by advertisements, etc.

                Strands addressed: Data Analysis, Probability and Statistics

                (Show-Me Standards 1.5, 1.7)

                4. Formulate and solve problems that involve collecting and analyzing statistical    data.

                Strands addressed: Data Analysis, Probability and Statistics

                (Show-Me Standards 1.2, 1.8, 3.1, 3.2)

               

                CONCEPT ANALYSIS: Finding a range of data, constructing graphs, computing the average, and reading data points as answers to specific questions are important skills, but they comprise a very narrow view of data analysis. Being able to compute an average and knowing when to compute that average and what it means are two different skills. Students need to be actively involved in each of the necessary steps to solve problems in statistics, not just compute a specific number from given data. These steps include: identifying the question, collecting and organizing the data, constructing and interpreting tables and graphs, drawing inferences to describe trends, developing convincing arguments, and evaluating the arguments of others. The ability to evaluate conclusions is vitally important to all students since statistical data is so often used in diverse areas such as advertising and forecasting, as well as in the development of public policy.

                SAMPLE TEST ITEM:

                Component Skills

                A. Describe trends by drawing inferences.

                B. Evaluate conclusions from a set of data.

                C. Solve problems involving mean, median, mode, and range.

                Specification

                Students are given statistical information in graphic or tabular form. They are asked to describe trends by drawing inferences. They are also asked to evaluate given conclusions based on statistical data. Additionally, they are asked to solve computational and non-computational problems involving mean, median, mode, or range.

                Sample Item:

                1. The median price of a house in a small midwestern city is $48,000. Which conclusion is correct?

                A. Most houses cost $48,000.

                B. The price of the most expensive house is $48,000.

                C. The best price for a house is $48,000.

                *D. There are as many houses costing less than $48,000 as there are costing more.

G. Apply problem-solving strategies.

                1. Use the calculator to solve consumer problems.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.4, 1.10, 3.2)

                2. Solve problems involving surface area and area in consumer situations (paint,     carpet, etc.)

            Strands addressed: Problem Solving, Connections, Geometric and Spatial Sense

                (Show-Me Standards 1.10, 3.1, 3.8)

                CONCEPT ANALYSIS: Consumer area and perimeter problems are sometimes very difficult for students. Lack of viable experience hampers understanding, and the multiple steps sometimes involved in obtaining an answer may cause difficulties. Adults usually do not have as much trouble with these contexts, because they grow accustomed to working with the real problems--the room to be painted or the floor to be carpeted. Students need practice in defining situations, in recognizing the various components of a problem, and in working through to a satisfactory conclusion. Using models or actual rooms, floors, etc., can help. Practice in diagramming given specifications will help those who have trouble visualizing. Problems which require the students to measure various dimensions will improve measurement skills, and this experience may make the problems easier by giving them a real context.

                TEST SAMPLE ITEM

                Component Skills:

                A. Solve problems involving area in consumer situations.

                B. Solve problems involving perimeter in consumer situations.

                Specification:

                Students are given a diagram or dimensions that involve a consumer situation and are asked to compute the area or perimeter. For example, they may be asked to find how much paint, wallpaper, sod, or shingles are required for a given situation.

                Sample Item:

                1. A wall is 40 feet long and 5 feet high. One can of paint will cover 60 square feet. How many cans of paint will be needed to paint the entire wall with two coats of paint?

                A. 3

                B. 4

                C. 5

                *D. 7

                3. Solve problems involving use of ratio and proportion in consumer situations       (better buy, scale drawing, recipe conversion, etc.)

                Strands addressed: Problem Solving, Connections, Number Sense

                (Show-Me Standards 1.10, 3.1, 3.8)

                CONCEPT ANALYSIS: Proportional thinking is a very powerful and useful tool. Comparing numbers and identifying consistent relationships often offer immediate solutions to seemingly complex problems. When faced with consumer decisions involving how much items cost, which item is cheaper, or how far one place is from another, a proportion is usually the most direct solution. The mathematics of ratio and proportion is arithmetically simple; it is the variety of applications that produces confusion. Most students do not readily see the concept of proportion as it applies simultaneously to unit pricing in a better-buy situation, or the amount of flour needed if a cookie recipe is tripled, or computation of the distance between Kansas City and Chicago based on map information. The applications must be taught both individually for context and together as examples of the same problem-solving technique: ratio and proportion.

                SAMPLE TEST ITEM

                Component Skills:

                A. Solve problems involving pricing.

                B. Solve problems involving food, recipes, and nutrition.

                C. Solve problems involving medication dosage.

                D. Solve problems involving relative distance between locations.

                Specification:

                Students are given a consumer situation and are asked to solve a problem using proportions. The problem will involve pricing, food recipes and nutrition, medication dosage, or relative distances between locations.

                Sample Item:

                1. Peanut butter is on sale at the grocery store. The price is $2.55 for a 28-ounce jar. What is the unit price in cents per ounce?

                *A. 9.1

                B. 10.1

                C. 11.1

                D. 12.1

                4. Collect data from real-life situations to apply to a given formula.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.3, 1.10)

H. Solve problems in consumer situations.

            1. Compute the total hours on a weekly time card.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standard 1.10)

                2. Compute Gross Pay from straight-time, overtime tips, commission, piece work.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.8, 1.10, 3.1, 3.2)

            CONCEPT ANALYSIS: Receiving a paycheck is an important event for most Americans. Being able to compute gross pay is therefore essential, as more and more students join the work force, at least as part-time workers, before graduation from high school. The mathematics of getting paid includes the vocabulary of the various methods by which one may be paid as well as the arithmetic. Local variations may exist in vocabulary, but basically employee wages are calculated according to hourly, monthly, commission, and piecework rates. Overtime, holiday, or Sunday pay varies from job to job. Figuring pay often motivates students to practice application of concepts considered otherwise boring, such as ratio, proportion, and percent.

                SAMPLE TEST ITEM

                Component Skills:

                A. Compute gross pay using hourly rates.

                B. Compute gross pay using monthly rates.

                C. Compute gross pay using commission rates.

                D. Compute gross pay using piecework rates.

                E. Compute gross pay using overtime rates.

                Specification:

                Students are given an employment situation and are asked to compute the employee's gross pay.

                Sample Item:

                1. Jennifer earns $4.50 per hour at her part-time job. She is paid time-and-a-half for working holidays. During the week of Thanksgiving, she worked 20 hours plus 8 hours on Thanksgiving Day. What is her gross pay for the week?

                A. $108.00

                B. $126.00

                *C. $144.00

                D. $162.00

                3. Compute the salary for a pay period.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.1, 3.2)

                4. Compute net pay using appropriate information for Social Security deductions, state and federal taxes, etc.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.1, 3.2)

                CONCEPT ANALYSIS: Our society is politically and economically very complex. For students to function well, they must have some understanding of the controlling principles and the interconnections between political and economic realities. When high school students join the work force, they must learn to calculate wages and deductions. The vocabulary, as well as the mathematics, must be taught. For example, students need to know the history and intent of Social Security laws and how tax deductions are computed. They also need to know the basic premises behind federal and state income taxes and how to read tax tables. The curriculum for college-bound students may need to be adjusted to assure them an opportunity to learn about these political and economic issues.

                SAMPLE TEST ITEM

                Component Skills:

                A. Compute net pay.

                B. Compute Social Security deduction.

                C. Compute state and federal taxes.

               

                Specification:

                Students are given data about a person's pay check and other variables; these may appear in a table. They are asked to compute net pay considering one or more of the following: Social Security deductions, state and federal taxes, and other similar deductions.

                5. Compute the total purchase price considering discounts, sale price, and taxes.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standard 1.10)

                6. Compute the unit price and determine the better buy.

            Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 4.1)

                7. Solve banking problems related to maintaining a checking account.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.1, 3.2)

                8. Compute simple and compound interest.

                Strands addressed: Problem Solving, Connections, Discrete Mathematics

                (Show-Me Standards 1.10, 3.2, 4.8)

               

                9. Compute the new balance in a charge account based on the finance charge,        previous balance, and unpaid balances.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.2, 4.8)

                10. Compute finance charges on various types of loans.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.2, 4.8)

                11. Compute sticker price, dealer's cost, and retail price of new/used cars.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.2, 4.8)

                12. Use tables to determine driver rating factor and compute automobile insurance             premiums.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.2, 4.8)

                13. Compute cost of operating and maintaining an automobile.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standard 1.10)

                14. Compute the cost of buying, maintaining a home (assessed value, taxes,            homeowners insurance, escrow)

                Strands addressed: Problem Solving, Connections

                (Show-Me Standard 1.10)

            15. Read a meter and compute cost of electricity, gas, and water.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 4.8)

                16. Use records of past expenditures to prepare a monthly budget.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.1, 1.2, 1.8, 1.10, 3.1, 3.2, 3.6, 3.8, 4.1)

                17. Compute and compare total housing cost with suggested guidelines.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.1, 1.2, 1.10, 3.1)

                18. Prepare a state and federal income tax form.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.8, 1.10, 2.2, 4.1, 4.8)

                19. Use tables to compute premiums for term and whole life insurance.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 3.1, 3.2, 4.8)

                20. Compute health insurance premiums and deductions.

                Strands addressed: Problem Solving, Connections

                (Show-Me Standards 1.10, 4.8)

 

 

 

 

RESOURCES:

                Consumer Mathematics textbook (Glencoe Macmillan/McGraw-Hill 1992, orig. 1982)

                Using Checking Account

                Your Pay Check

                Getting a Job (Media Materials, Inc.)

                Software, Cross Country USA