Course title

Pre-requisite

Course description

PRINCIPLES OF MATH TECHNOLOGY 1
5338000
INCLUSION 5338008
One-semester course; grade level 11; 12
Prerequisite: Passing grade in Algebra 3-4 or Algebra 3-4 H
Meets PUHSD and Arizona Mathematics Standards graduation requirements

This course is aligned with the Arizona College and Work Readiness Mathematics Standards and fulfills the fourth mathematics credit needed for graduation. Principles of Math Technology will provide students the basics on how computers and hand-held technology can make mathematical analysis more powerful and efficient. Mathematical concepts include: equations; functions and relations with technology; data preparation; statistics; regressions; and set theory. Mathematical skills involving setting up equations; basic set theory; and using logical processes are needed.

Concept Units
Concept unit 1): Equations; Functions and Relations with Technology-
Standards include:
Use technology to exhibit the effects of parameter changes on the graphs of linear; polynomial; exponential; and logarithmic.-S1C2-03
S1C2-04
S1C2-06
S4C2-01
S4C2-02-A.IF.10
-I can determine the effects on a graph and generate a family of graphs by varying the parameters.-Use a calculator or spreadsheet to automatically generate families of curves.
-Identify the effect on the graph of replacing ; ; and for specific values of k (both positive and negative). Experiment with cases and illustrate an explanation of the effects on the graph using technology.-S4C2-01S4C2-02- A.BF.7
-I can experiment with transformations and identify the effect on the graph of replacing ; ; and .
I can find the values of k given the graph. -Use a calculator or spreadsheet to automatically generate graphs transformations of the form ; ; ; and .
-Find the value of k for ; ; etc. given a graph and the base function -S4C2-01
S4C2-02- A.BF.7
-I can find the value of k for ; ; given the graph of ; etc.-Use a calculator or spreadsheet to automatically generate graph transformations.
-Understand that a quantity increasing exponentially eventually exceeds a quantity increasing linearly; quadratically; or (more generally) as a polynomial function.-S3C2-01
-I can compare the values and graphs of quantities that increase exponentially to those that increase linearly or quadratically and make conclusions about the long-term behavior.-Use technology to compare the graphs of several functions that increase exponentially; linearly; and as a polynomial function.
-Approximate solutions using technology Solve approximately graphically and numerically. Include cases where and/or are linear; polynomial; exponential; and logarithmic functions-S3C2-01
S3C2-04
S3C3-03
-A.REI.13
-I can find approximate solutions to a variety of equations by using technology.
-Use technology to graph the functions and find solutions graphically or numerically (e.g.; ?solver? function or examination of a generated table of values).

Concept unit 2) Data Preparation
-Use and interpret quantities and units correctly in graphs and data displays.--N.Q.6-I can correctly display the units and multiplying factors in the headings of a table; graph; or chart using technology.-Use internet to gather data.
Use TI-84 and excel spreadsheet to represent and manipulate data using conditional formatting.
-Organize; analyze; and display data using multiple representations through technology.-S2C2-02--I can organize and display data using a graphing calculator and excel.-Use TI-84 and excel to enter data into lists and display data in a box-whisker; stem-leaf & scatter plots.
-Understand that simulation-based techniques are powerful tools making inferences and justifying conclusions from data.--S.IC.3-I can make inferences and justify conclusions from simulations.-Use the internet to find and use simulations.
-Evaluate reports based on data.
C2S1-05
C2S2-03
C2S2-04
C2S2-05-S.IC.8-I will identify misleading uses of data and explain why they are misleading.-Use internet to gather data and reports
-Communicate methods used; analyses conducted; and conclusion drawn for a data-analysis project by written report; visual display; oral report; or multi-media presentation.-C2S1-06
C5S2-01
C5S2-06
-S.SI.6-I can communicate conclusions from data via writing a report; visual display; and/or multi-media presentation.-Use Word; power point and excel to present results and conclusions.

Concept unit 3) Statistics ?
Solve problems by estimating and computing with one-variable statistics with understanding the best measure of central tendency. - S2C1-01-S.S1.1 S.S1.2 S.S1.3 S.S1.6 S.S1.8 S.S1.9
-I can solve problems with variable data..
I can determine and justify which measure of center best represents the data. -Use graphing calculator and/or Excel to:
?Solve problems
?Create and compare lists of data
-Compare data sets using graphs and summary statistics; including variance and standard deviation.-S2C1-02-S.S1.2-I can compare data sets using graphs and summary statistics; including variance and standard deviation.-Compare summary statistics of the data sets.

-Compute and explain summary statistics for distributions of data including measures of center and spread; variance and standard deviation.-S2C1-03-S.S1.2-I can compute and explain summary statistics including variance and standard deviation.-Calculate 1-variable statistics.

-Develop and implement a plan for collecting and analyzing data. Formulate a meaningful question; determine the data needed to answer the question; gather the appropriate data; analyze the data; and draw reasonable conclusions.-S2C1-01
S2C1-02
S2C1-03
S2C1-04
S2C1-05-S.S1.1
S.S1.2
S.S1.3
S.S1.6
S.S1.8
S.S1.9-I can develop and implement a plan for collecting and analyzing data.-Collect data through technology.

-Use mean and standard deviation of a data set to fit a normal distribution and to estimate population percentages. -S2C1-01
S2C1-02-S.S1.1
S.S1.2-I can use mean and standard deviation of a data set to fit a normal distribution and estimate population percentages.-Estimate area under normal curve.

Concept unit 4) Regression -Use regression methods available through technology to describe various models for data such as linear; quadratic; exponential; etc.; select the most appropriate model; and use the model to interpret information-C2S2-08-S.SI.7
S.SI.8
S.SI.9-I will use the appropriate regression method and technology to describe a data model; and to interpret information.-Use technology** to: input and graph data; then perform the appropriate regression.
-Develop and implement a plan for collecting and analyzing data in order to make decisions. Formulate a meaningful question; determine the data needed to answer the question; gather the appropriate data; analyze the data; and draw reasonable conclusions-C2S1-01
C2S1-02
C2S1-03
C2S1-04
C2S1-05-S.SI.3-I will develop and implement a plan for collecting data that will be used to formulate meaningful questions; and to draw reasonable conclusions.-Select a technological tool; either TI-84 or Excel; to collect and analyze data.
-Communicate methods used; analyses conducted; and conclusions drawn for a data-analysis project by written report; visual display; oral report; or multi-media presentation-C2S1-06-S.SI.6-I will communicate methods used; analyses conducted; and conclusions drawn for a data-analysis project through a variety of medium.-Use technology to assist in creating a thorough explanation for a data analysis project. Use technology to present results.
-Determine the appropriateness of a model for making predictions from a given set of data-C2S1-08--I will determine the appropriateness of a model for making predictions from a given set of data.

-Use technology to generate a correlation coefficient to help determine the appropriateness of a model. Use the model to make predictions for the given data set.
Concept unit 5) Set Theory
- C2S4-01 C2S4-02--I will define the set of data-
----I will know the difference between a complement of sets and the empty set-
-Symbolic logic---I will be able to write the set of data in sample space and set builder notation-
----I will use set notation to distinguish the difference between union and intersection;( i.e. and/or statement)-Use internet search to discover the difference between .
-Evaluate the conclusions of others data and recognize flaws or gaps in the reasoning. -C5S2-06--I will use statements and put the information into a math set -
----I will recognize when more information is need or if an assumption is being made and state that assumption. -
-Use Venn diagrams to solve applied problems involving the union; intersection; and complement of sets.-Above standards --I will use a Venn diagram to organize the data and answer questions from the Venn diagram-
-Know the components of a relational database---I will be able to define a table; a file; a record; a relation; data types and a key-
-Design a relational database with 3 or more tables ---I will determine the groups of data and how they fit in table-I will build a database schema in a presentation tool (word or PowerPoint)
----I will determine the key for each table-
----I will determine the relationship between each table. -I will build the database in MS Access

*Based on AZ Mathematics College and Work Readiness Standards (2008)
** Aligned to the Common Core Standards (June 2010)

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Approved

Approved competency code

• MTHA
• 4 years of Math

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Online / Virtual