Advanced Mathematics I s1

ADVANCED MATHEMATICS I (SECONDARY)

SELECTIVE UNIT 3 (S03)

(Modeling) (July 2013)

Unit Statement: All measuring methods have limits. All measurements are subject to uncertainty. There is a degree of variability and randomness in everything around us. All this leads to data sets that do not exactly fit a given mathematical function. In this unit students explore different techniques of determining how to represent given data with the different functions explored in the Advanced Math I course.

Essential Outcomes: (must be assessed for mastery)

1. The Student Will perform a measurement and present it with appropriate uncertainty.

2. TSW manually create a scatter plot of a given data (2.5)

3. TSW use a calculator or computer software to draw a line of best fit to a given data set and to find the equation of the line. (2.5)

4. TSW analyze a linear fit by interpreting the value of the correlation coefficient. (2.5)

5. TSW model a set of data with a quadratic function (4.3)

6. TSW model a set of data with a logarithmic or exponential function (7.5)

7. TSW compare and contrast extrapolation and interpolation.

8. TSW apply unit facts and concepts to a Real-Life application

Introduced and Practiced Outcomes:

1. The Student Will identify number of significant digits in different numbers.

2. TSW describe difference between random and systematic errors.

3. TSW model a set of data with a polynomial function.

Key terms and concepts:

Significant digit uncertainty scatter plot uncertainty bars correlation a mathematical model correlation coefficient

Suggested Assessment Tools and Strategies:

Attached Rubric or teacher-generated rubric that assesses ALL Essential Outcomes (TSWs). * Examples of possible hands-on activities for this unit: Any activity that leads to students searching for a mathematical relationship between independent and dependent variables is appropriate. Students should perform measurements and then use the data to look for mathematical models to describe the relationship. Example: what is the relationship between number of spaghetti and the breaking force? Encourage students to think of their own sets of variables they want to investigate – art, music, sports…. This is a chance for a student to see that mathematics can be used to model almost any situation. Computer simulations, such a PhET simulations, may be used to collect appropriate data to investigate relationships.

Suggested Resources:

Textbook: Prentice Hall, Algebra 2, Pearson, ISBN -13: 978-0-13-350043-1, the online version of the textbook can be accessed at https://www.pearsonsuccessnet.com Solve it! – short exercises in the textbook/also listed in teacher resources online Practice form G, Practice form K – in teacher resources online Additional Problems - in teacher resources online Enrichment activities – in teacher resources online

Technology Links:

PhET simulation: http://phet.colorado.edu/en/simulations/category/new Equation Grapher: http://phet.colorado.edu/en/simulation/equation-grapher

Teacher and student resources available through the publisher at https://www.pearsonsuccessnet.com/snpapp/login.do?method=login

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………………..

 To receive a ‘B’ in the unit a student must demonstrate mastery of all TSWs  To receive an ‘A’ in the unit a student must demonstrate ‘A’ level mastery on at least 3 of the 4 identified TSWs.

Student name:______Date:______

TSW ‘A’ LEVEL ‘B’ LEVEL Notes 1. perform a Student measures one quantity Student measures length or time measurement and and uses this to calculates a or other quantity and justifies the present it with different quantity. Student finds reported uncertainty. appropriate uncertainty the uncertainty in the calculated value. 2 manually create a Student conducts a survey in Student manually creates a scatter Students could look for scatter plot of a given order to generate a set of data plot given a set of data. correlations between data that would be represented by a variables of their choice. scatter plot. 3 use a calculator or Given a dataset with Student uses the linear regression computer software to uncertainties, student finds the capability of a graphing calculator draw a line of best fit line of the minimum and to draw a best fit line to a given to a given data set and maximum fit and represents the data set and to find the equation to find the equation of slope of the line of the best fit of the line. the line. and the y-intercept with an appropriate uncertainty. 4 analyze a linear fit by Student interprets the value of the interpreting the value correlation coefficient . of the correlation coefficient. 5 model a set of data Student uses a calculator or with a quadratic computer software to find a function quadratic function that best represents a given dataset. Student records the equation and interprets the correlation coefficient. 6 model a set of data Student uses a calculator or with a logarithmic or computer software to find a exponential function logarithmic or exponential function that best represents a given dataset. Student records the equation and interprets the correlation coefficient. 7 compare and contrast Student discusses the two terms extrapolation and and uses a graph or equation of a interpolation best fit line to extrapolate and interpolate data. 8 apply unit facts and Reflects on the project and Activity clearly demonstrates This is a very important concepts to a Real-Life consistently justifies the mastery of key concepts of the TSW in this unit. Do not application mathematical concepts used and unit as defined in this rubric. skip it!! how they apply to the activity. Student articulates and explains mathematical concepts used. The criteria for demonstration of mastery and beyond mastery of this TSW is developed by the teacher based on the activity (see Suggested Assessment Tools for examples of possible activities)