Mifflin County School District Planned Instruction Title of Planned Instruction: Consumer Math Subject Area: Mathematics Grade Level: Grade 11-12 Prerequisites: Math Skills II with teacher recommendation Course Description: This course continues the strengthening of basic mathematical skills started in Math Skills I and II coupled with the additional focus of applications of real-life situations. It provides students with daily opportunities to develop, experience, and apply mathematical concepts and skills in order to become confident problem solvers in their world. Required Time: 180 days Major Text(s) and Resources: Consumer Mathematics, Copyright 1989 by Prentice Hall Names of District Subject Area Curriculum Writing Committee: Richard A. Keefer, Ivy Y. Stauffer, Lewistown High School Indian Valley High School Date of Board Approval: July 24, 2003
Major Topics Formulas Applications and problem solving Statistics Probability Algebraic systems and linear functions Geometry and trigonometry Calculus concepts Course Objectives and Performance Indicators Strand: 2.1 Standard: Numbers, Number Systems and Number Relationships 2.1.11A Use operations. Add, subtract, multiply, and divide real numbers with or without the use of a calculator. Strand: 2.2 Standard: Computation and Estimation 2.2.11A Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Solve problem situations that contain real numbers by applying computation concepts and skills. Using known formulas solve problem situations that pertain to those formulas. 2
2.2.11B Use estimation to solve problems for which an exact answer is not needed. Use rounding numbers or other estimating techniques to find answers to problems that do not require an exact answer. 2.2.11D Describe and explain the amount of error that may exist in a computation using estimates. Compare an estimated answer with an exact answer from the same situation by finding the difference. Explain and show how different estimating techniques will change the amount of error in a computation. 2.2.11E Recognize that the degree of precision needed in calculating a number depends on how the results will be used to generate the measure. Knowing the problem situation, correctly determine the number of decimal places in the answer or the form that the answer should take (e.g., decimal, fraction, percent). 3
2.2.11F Demonstrate skills for using scientific calculators. Correctly use scientific calculators when given the opportunity. Strand: 2.3 Standard: Measurement and Estimation 2.3.11A Select and use appropriate Determine whether linear units to the degree of units, square units, cubic accuracy required in units, or a combination of particular measurement units are appropriate in a situations. given problem situation. 2.3.11B Measure and use angles in degrees. Measure angles using a protractor. Draw angles to a given degree with respect to a budget problem. 4
2.3.11C Demonstrate the ability to Determine measurements produce measures with to the level of precision in specified levels of precision. the given situation. Strand: 2.4 Standard: Mathematical Reasoning and Connections 2.4.11B 2.4.11C Construct valid arguments from stated facts. Determine the validity of an argument. Given a problem situation s facts, find a valid solution to the problem by listing the logical sequence of steps. Solve a multi-step equation using valid properties of equality. Use the problem solving process: facts, plan, solve, and check. Determine if the solution to a problem situation is valid. 5
2.4.11E Demonstrate mathematical solutions to problems. Use algebraic and geometric techniques to solve problems involving real- life situations. Use any problem solving technique to solve problem situations. Strand: 2.5 Standard: Mathematical Problem Solving and Communication 2.5.11A Select and use appropriate Solve real life problems by mathematical concepts and using appropriate techniques from different mathematical concepts and areas of mathematics and techniques. apply them to solving nonroutine and multi-step problems. 2.5.11B Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Communicate the facts, question, plan, actual solving steps, and the solution to a problem situation using correct and appropriate mathematical representations. 6
2.5.11C Present mathematical procedures and results clearly, systematically, succinctly and correctly. Show the sequence of all the steps in the process of solving various linear and non-linear multi-step problems. Clearly label all results with correct units. 2.5.11D Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable to the initial problem and why the reasoning is valid. Explain how a problem was solved and why the chosen procedures were used. Check the solution to a problem situation for accuracy and to see if the solution makes sense. Strand: 2.6 Standard: Statistics and Data Analysis 2.6.11A Design and conduct an Design and conduct an experiment using random experiment using random sampling. Describe the data sampling while calculating as an example of a the average daily balance distribution using statistical for credit cards. measures of center and Find statistical measures of spread. Organize and center and spread. represent the results with Organize and represent the graphs. results of the random sampling with graphs. 7
2.6.11B Use appropriate technology to organize and analyze data taken from the local community. Organize local data by making graphs. Find statistical measures of center and spread. Organize data by constructing a circle budget graph. 2.6.11E Determine the validity of the sampling method described in a given study. List reasons why (or why not) a sampling method is valid. 2.6.11F Determine the degree of dependence of two quantities specified by a two-way table. Determine the relationship between two sets of data (e.g., high positive, low positive, high negative, low negative, or no relationship). 8
2.6.11G Describe questions of experimental design. Create questions that would assist in the selection of the appropriate sample group. Create questions that could be used to sample a population. 2.6.11H Use sampling techniques to draw inferences about large populations. Use sampling information to make predictions about the whole population. 2.6.11I Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed. Describe how the normal curve fits a set of data. Use the properties of a normal curve to find answers to questions about sets of data that fit the normal curve. 9
Strand: 2.7 Standard: Probability and Predictions 2.7.11A Compare more complex odds and probability. Determine the number of combinations or permutations for an event and use the information to find and compare probabilities for similar situations. Compare odds for similar situations. 2.7.11B Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population. Make generalizations for an entire population based on a single data sample of the population and the appropriate calculations. 2.7.11C Draw and justify a conclusion regarding the validity of a probability or statistical argument. Compare the calculated results of a probability or statistical problem situation with the actual results. Explain why differences between calculated and actual results might exist. 10
2.7.11D Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations. Calculate the probability of an event happening by using appropriate probability techniques. Conduct experiments which provide data that can be used to predict the probability of an event happening. 2.7.11E Solve problems involving independent simple and compound events. Determine probabilities of independent simple or compound events and use the information to solve problem situations. Strand: 2.8 Standard: Algebra and Functions 2.8.11B Give examples of patterns List examples of patterns that occur in data from other that occur in data from disciplines. real-life situations. 11
2.8.11C Use patterns, sequences and Solve problems that series to solve routine and contain patterns, non-routine problems. sequences, and series. 2.8.11D Formulate expressions, equations, and inequalities to model routine and nonroutine problem situations. Formulate expressions, equations, and inequalities to model routine and nonroutine problem situations. 2.8.11F Identify whether systems of equations are consistent or inconsistent. Find, if possible, the time where the charges for utilities from different companies are the same. 12
2.8.11G Analyze and explain systems of equations. Compare and contrast the consumer charges based on time for utilities (or other related situation e.g., renting a car) after writing linear equations for each company and solving the related system of equations. 2.8.11H Select and use an appropriate strategy to solve systems of equations. Solve a system of equations by graphing or using algebra (elimination or substitution). Determine the most appropriate strategy to use when solving a system of equations. 2.8.11N Solve linear equations symbolically and graphically. Solve linear equations by symbol manipulation. Solve linear equations graphically. 13
2.8.11O 2.8.11Q Determine the domain and range of a relation, given a graph or set of ordered pairs. Represent functional relationships in tables, charts and graphs. Using a graph or set of ordered pairs, find the domain and range of a relation. Represent linear functions in tables. Represent linear functions graphically. 2.8.11R Create and interpret functional models. Use known relationships from real-life to create a graph that shows the relationships and use the graph to answer questions. 14
Strand: 2.9 Standard: Geometry 2.9.11A Construct geometric figures using geometry tools. Construct various geometric figures using a compass, straight-edge, and a protractor. 2.9.11D Identify corresponding parts in congruent triangles to solve problems. Solve problems that involve congruent triangles by writing proportions that compare corresponding parts. 2.9.11F Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles. Solve problems involving circles and their properties. 15
2.9.11I Model situations Draw diagrams to help geometrically to formulate solve a problem situation. and solve problems. Strand: 2.10 Standard: Trigonometry 2.10.11B Identify, create and solve Solve right triangle practical problems problems by using the involving right triangles Pythagorean Theorem. using the Pythagorean Find examples of right Theorem. triangle problem situations in real-life. 16
Strand: 2.11 Standard: Concepts of Calculus 2.11.11A Determine maximum and Find a maximum or minimum values of a minimum value over a function over a specified specified interval. interval. 2.11.11B Interpret maximum and minimum values in problem situations. Determine if a solution is a maximum or minimum value for a problem situation. 2.11.11C Interpret rates of growth/decay. Using a graph that compares braking distance and speed of an automobile, find answers to questions about the situation. Using graphs that show total amount of money in a compound interest situation and time, find answers to questions about the situation. Using graphs that show growth or decay situations, find answers to questions about the situation. 17
2.11.11D Determine sums of finite sequences of numbers. Find the total amount of money in a compound interest account for a given situation. Find the sum for finite sequences of numbers. 2.11.11E Estimate areas under curves. After graphing a curve on graph paper, find an estimated area for the curve by counting squares contained in or under the curves. 18
District Recommended Instructional Approaches For the Course To Drive Teacher s Instructional Activities Whole group instruction Small group instruction Projects Class discussion Peer evaluation Teacher and peer conferencing Oral presentations Individual instruction Research Dramatization Role playing Independent reading Read aloud Directed reading-thinking activities Modeling process Games Self-reflection Self-evaluation Independent study Guest speaker Guest reading Writing activities Thematic units Student generated notebook that can be used with tests and quizzes Study Guides Computer technology 19