Objective map design and implementation

Mathematics

Grade 9

H.S School Curriculum

Lynchburg, VA

Spiritual Principle

To everything there is a season, and a time to every purpose under heaven (KJV Ecclesiastics 3:1-8)

Standard 1: Students will be able to explain the principles of, graph, and solve step and piecewise functions.

They will be able to convert absolute into piecewise functions.

Standard 2: Students will be able to graph and solve exponential functions and use them to model and predict real life scenarios.

Standard 3: Students will be able to solve quadratic equations and inequalities in one variable. Students will be able to determine and graph the inverses of linear, quadratic and power functions, including restricted domains

Suggested Activities and Experiences

Standard

Students will list the types of real world experiences that must be measured in terms of functions or rates of change over time, like changes in distance, temperature, and amounts of interest.

Students will find real world examples of piecewise functions in the newspaper and online, such as the rates of change of distance and speed, cell phone plans, and the value of buying in bulk and then graph these scenarios while in class (McClain & Rieves 2010, p.12).

3. The class will be divided into two halves and given transparencies and markers: one half will graph a linear function, the other half a quadratic function. After graphing both on transparences, students will lay the graphs together and see if the final, combined graph demonstrates or is a new type of function (McClain & Rieves 2010, p.11).

Standard 2:

1. Students will use the principles of compound interest to solve real-world investment goals. For example, a student might ask how he or she can save a specific amount of money within a defined time period to meet a life goal. If he or she has the opportunity to invest in a financial instrument yielding a particular amount of compound monthly interest, how much should he or she invest? Students could discover current interest rates by calling local banks and consulting the financial section of the newspaper (Exponential functions, 2010, Purple math). Students will present their findings to the class.

2. In groups, students will graph population growth and predict future trends using exponential functions (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/quantskillsworldpop.pdf. Students will discuss the political and environmental implications of their findings.

3. Students will perform an exercise using exponential functions graphing increases in atmospheric CO2 concentrations (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/co2moe2edit.pdf

Students will discuss the political and environmental implications of their findings.

Standard 3:

4. Students will be divided into groups, given problems of quadratic inequalities and 'race' to see what group can come up with the correct solutions the fastest.

5. Students will be asked to periodically write and graph homework problems on the board to 'teach' graphing to the rest of the class.

6. Students will be given examples of graphs or tables of values of functions and asked to identify what type of function they are, based upon the appearance (Mathematics benchmarks, 2010, UT Dana Center).