Course title

Advanced Math

Pre-requisite

Algebra 1-2, Geometry, and Algebra 3-4 or equivalent

Course description

AAEC: Arizona Agribusiness & Equine Center

High School Mathematics Curriculum

2020-2021

Advanced Math 1-2

AAEC: Arizona Agribusiness & Equine Center

High School Curriculum

Course summary/Overview

Name of Course: Advanced Math

Department: Mathematics

Core or Elective: Core

Length of Course: 2 semesters (16 weeks, 80 instructional periods x 2 semesters)

Class Meetings Each Week: (55 minutes)

High School Credits: 1 high school credit (0.5 per semester)

Number of Instructional Units in Curriculum Plan: 13

Primary Enrollment: Juniors/Seniors

Prerequisites: Algebra 1-2, Geometry, and Algebra 3-4 or equivalent

Instructional goals: This course was designed with three specific purposes:

Prepare the students for the mathematics they will encounter in other college courses, particularly core courses in social and natural sciences.
Develop the students ability to reason with quantitative information in a way that will help them achieve success in their career
Provide the student with the critical thinking and quantitative reasoning skills needed to understand major issues in life.

Format of Course: The class meets 5 times per week for 55 minutes. The course is divided into 13 units. The class will consist of guided practice in class, homework assignments, math projects, and unit tests.

Texts: Using and Understanding Mathematics; Bennett, J., & Briggs, W.; Addison-Wesley; Third Edition; 2005

ARIZONA AGRIBUSINESS & EQUINE CENTER

High School Curriculum (Unit Plan)

Course Summary/Overview

Course: Advanced Math

Instructional Unit: 1

Book Reference: Chapter 1

Instructional Goal: Critical Thinking

Timeline: 25 class periods

2010 Common Core State Standards:

HS.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

HS.A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

HS.S-ID.9 Distinguish between correlation and causation.

HS.S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using

characteristics (or categories) of the outcomes, or as unions, intersections, or

complements of other events (“or,” “and,” “not”).

HS.MP.1 Make sense of problems and persevere in solving them.

HS.MP.2 Reason abstractly and quantitatively.

HS.MP.3 Construct viable arguments and critique the reasoning of others.

HS.MP.4 Model with mathematics.

HS.MP.5 Use appropriate tools strategically.

HS.MP.6 Attend to precision.

HS.MP.7 Look for and make use of structure.

HS.MP.8 Look for and express regularity in repeated reasoning.

Content/Concepts:

Recognizing fallacies
Propositions and truth values
Sets and Venn diagrams
Analyzing arguments
Critical thinking in everyday life

Performance Objectives:

Examination of deceptive arguments and fallacies
Define and study basic components of logic
Explore how many propositions express relationships
Study basic differences between inductive and deductive arguments
Become proficient in analyzing information

Activities:

1) Lecture lesson 1-1

Present topic
Present example problems
Assign practice problems
Assign written exercises

2) Lecture lesson 1-2

Present topic
Present example problems
Assign practice problems
Assign written exercises

3) Lecture lesson 1-3

Present topic
Present example problems
Assign practice problems
Assign written exercises

4) Lecture lesson 1-4

Present topic
Present example problems
Assign practice problems
Assign written exercises

5) Lecture lesson 1-5

Present topic
Present example problems
Assign practice problems
Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

Dice Breaker

http://media.pearsoncmg.com/aw/aw_bennett_usundermat_5/activities/ch01/Dice_Breaker_source.pdf

Evaluation:

Complete Unit 1 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 2

Book Reference: Chapter 2

Instructional Goal: Approaches to Problem Solving

Timeline: 20 class periods

2010 Common Core State Standards:

HS.N-RN.1

Explain how the definition of the meaning of rational exponents follows from

extending the properties of integer exponents to those values, allowing for a

notation for radicals in terms of rational exponents. For example, we define 5^1/3to

be the cube root of 5 because we want (5^1/3)³ = 5(^1/3)³ to hold, so (5^1/3)³ must

equal 5.

HS.N-RN.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

HS.N-Q.1

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

HS.A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

HS.G-MG.2

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

Power of Units
Standardized units
Guidelines and hints

Performance Objectives:

Learn how to work with units
Review U. S. and Metric standardized units
Develop a general set of guidelines and hints for problem-solving

Activities:

1) Lecture lesson 2-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 2-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 2-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

Working with Units Algebraically

https://www.khanacademy.org/math/algebra/introduction-to-algebra/units- algebra/v/dimensional-analysis-units-algebraically

Evaluation:

Unit 2 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 3

Book Reference: Chapter 3

Instructional Goal: Study the use of numbers in the real world

Timeline: 25 class periods

2010 Common Core State Standards:

HS.N-Q.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

HS.A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

HS.S-IC.6

Evaluate reports based on data.

HS.S-ID.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

HS.F-IF.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

Uses and abuses of percentages
Putting numbers in perspective
Dealing with uncertainty
Index numbers; the CPI and beyond
How numbers deceive

Performance Objectives:

Study the uses and abuses of percentages
Examine several techniques giving meaning to numbers
Consider types of errors that affect measured numbers
Examine the important role of indices
Study cases involving deceptive numbers

Activities:

1) Lecture lesson 3-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 3-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 3-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

4) Lecture lesson 3-4

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

5) Lecture lesson 3-5

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

How Many Grains of Sand On All the Beaches in the World?

http://media.pearsoncmg.com/aw/aw_bennett_usundermat_5/activities/ch03/Ch3B_GrainsOfSand_source.pdf

Evaluation:

Complete Unit 3 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 4

Book Reference: Chapter 4

Instructional Goal: An understanding of key issues in personal financial management

Timeline: 25 class periods

2010 Common Core State Standards:

HS.F-LE.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

HS.F-LE.5

Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

HS.A-SSE.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

HS.N-Q.2

Define appropriate quantities for the purpose of descriptive modeling.

HS.A-CED.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HS.A-CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HS.A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

HS.A-REI.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HS.A-REI.10

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

The power of compounding
Savings plans and investments
Loan payments, credit cards and mortgages
Income taxes
Understanding the Federal budget

Performance Objectives:

Study how money grows with compound interest
Calculate future value
Study investments
Calculate monthly payments
Explore loan issues
Calculate income taxes
Discuss Federal budget and politics

Activities:

1) Lecture lesson 4-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 4-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 4-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

4) Lecture lesson 4-4

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

5) Lecture lesson 4-5

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

Budget Blast

http://aaecmathresources.weebly.com/Advanced-math-resources.html

Evaluation:

Complete Unit 4 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 5

Book Reference: Chapter 5

Instructional Goal: Statistical Reasoning

Timeline: 15 class periods

2012 Common Core State Standards:

HS.S-IC.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

HS.S-IC.6

Evaluate reports based on data.

HS.S-ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

HS.S-ID.5

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

HS.S-ID.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

HS.S-ID.9

Distinguish between correlation and causation.

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

Fundamentals of Statistics
Statistical studies
Statistical tables and graphs
Graphics in the media
Correlation and causality

Performance Objectives:

Discuss statistical studies and sampling
List guidelines for evaluating statistical claims
Understand statistical tables and graphs
Interpret media graphics
Interpret correlations and causality

Activities:

1) Lecture lesson 5-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 5-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 5-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

4) Lecture lesson 5-4

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

5) Lecture lesson 5-5

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

Take a Sample

http://aaecmathresources.weebly.com/Advanced-math-resources.html

Describing Distributions

http://aaecmathresources.weebly.com/Advanced-math-resources.html

Evaluation:

Complete Unit 5 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 6

Book Reference: Chapter 6

Instructional Goal: Putting Statistics to Work.

Timeline: 10 class periods

2010 Common Core State Standards:

HS.N-Q.1

HS.A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

HS.S-ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

HS.S-ID.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

HS.S-ID.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

HS.S-ID.4

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

HS.S-IC.1

Understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population.

HS.S-IC.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

HS.S-CP.4

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

Characterizing data
Measures of variation
Normal distribution
Statistical inference

Performance Objectives:

Understand descriptive statistics
Measure and apply standard deviation
Describe and recognize normal distribution
Comprehend statistical significance
Calculate margin of error and confidence interval
Set up and evaluate Hypothesis

Activities:

1) Lecture lesson 6-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 6-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 6-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

4) Lecture lesson 6-4

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

Empirical Rule

http://aaecmathresources.weebly.com/Advanced-math-resources.html

Evaluation:

Complete Unit 6 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 7

Book Reference: Chapter 7

Instructional Goal: Fundamentals of Probability

Timeline: 15 class periods

2010 Common Core State Standards:

HS.S-CP.2

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

HS.S-CP.3

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

HS.S-CP.4

HS.S-CP.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

HS.S-CP.6

Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

HS.S-CP.7

Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

HS.S-CP.8

Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

HS.S-CP.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

HS.S-MD.2

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

HS.S-MD.3

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

HS.S-MD.4

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?

HS.S-MD.5

Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

a. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

b. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

HS.S-MD.6

Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

HS.S-MD.7

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

HS.S-IC.2

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

HS.MP.1

Make sense of problems and persevere in solving them.

HS.MP.2

Reason abstractly and quantitatively.

HS.MP.3

Construct viable arguments and critique the reasoning of others.

HS.MP.4

Model with mathematics.

HS.MP.5

Use appropriate tools strategically.

HS.MP.6

Attend to precision.

HS.MP.7

Look for and make use of structure.

HS.MP.8

Look for and express regularity in repeated reasoning.

Content/Concepts:

Fundamentals of Probability
Combining probabilities
The law of large numbers
Assessing risk
Counting and probability

Performance Objectives:

Examine basic concepts of probability
Calculating more complex probabilities
Study the law of large numbers and its application
Explore and describe risk and its applications
Study permutations and combinations and their application to probability

Activities:

1) Lecture lesson 7-1

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

2) Lecture lesson 7-2

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

3) Lecture lesson 7-3

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

4) Lecture lesson 7-4

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

5) Lecture lesson 7-5

a) Present topic

b) Present example problems

c) Assign practice problems

d) Assign written exercises

Instructional Resources:

Using and Understanding Mathematics; Bennett, J., Briggs, W.; Addison-Wesley; 2005; 0-321-22773-5

Supplemental Resources:

The Jury

http://aaecmathresources.weebly.com/Advanced-math-resources.html

Evaluation:

Complete Unit 7 Study Guide to 75% accuracy.

Comprehensive Unit Exam completed to 75% accuracy.

Course: Advanced Math

Instructional Unit: 8

Book Reference: Chapter 8

Instructional Goal: Exponential Astonishment

Timeline: 10 class periods

2010 Common Core State Standards:

HS.A-CED.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HS.A-CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HS.A-CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling contex

School state

Arizona

School / district Address

315 E. Mulberry Dr.

School zip code

85012

Requested competency code

Math

Date submitted

03/29/2021

Approved

Yes

Approved competency code

MTHA
4 years of Math

Approved date

04/7/2021