AFM Curriculum Map
AFM (Advanced Functions and Modeling)
- The AFM Common Exam will be based on the 2003 NC Standard Course of Study found at: (document pg. 56–57; print pg. 60–61)
- The common exam will consist of multiple choice questions and short constructed response items for a total of 35 to 40 items.
- The test will be in two parts, each part given forty-five minutes to complete.
- Constructed response items will require students to give a correct numeric answer and show their work.
- Constructed response items will receive 0, 1, 2, or 3 points.
- Calculators will be allowed on all items.
- According to the NC Assessment Specifications Summary, the following weights will be applied to each standard on the Common Exam:
Standard / Multiple Choice / Constructed Response
Data Analysis and Probability
1.01, 1.02 / 9% to 15% / 10% to 14%
1.03 / 18% to 26% / 0%
Algebra
2.01, 2.04, 2.05 / 32% to 47% / 0%
2.02, 2.03 / 4% to 8% / 4% to 8%
Total Percent of Items / 78% to 86% / 14% to 22%
Total Percent of Score Points / 56% to 66% / 34% to 44%
- This information was taken from:
The following document is a curriculum map developed to assist in the pacing of AFM to ensure that all standards are addressed with regards to the common exam. There are 7 units total. Each unit identifies the standard being addressed and various essential questions based on each substandard. A suggestion of pacing is included. This suggestion includes any unit tests. The total pacing of the course is over 80 days which allows a 10 day buffer. It is recommended that at least part of this 10 day buffer be used at the end of the course for a final review before taking the common exam. Each unit includes key academic vocabulary. These words are key words but it is likely that more vocabulary will be needed throughout each unit. The key academic vocabulary is not organized in any specific order. Internet resources are also included within each unit. These resources include tutorials, teacher notes, and student worksheets. All resources listed are internet based but Algebra 2 textbooks, Trigonometry textbooks, and Higher Algebra textbooks may be utilized as well.
Unit Name: Univariate Data AnalysisUnit Number: 1
Enduring Understanding
Collect, display, analyze, compare, and interpret univariate data.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
1.02 (a–f)
Summarize and analyze univariate data to solve problems. / 1.02a,e) Can I compare methods of data collection? Can I choose a correct method and accurately collect and display data? Can I choose the best method to display data?
1.02b) Can I apply various statistical principles and methods in sample surveys and draw conclusions about the sample data?
1.02c) Can I determine measures of central tendency and spread given a set of data? Can I interpret what various values of tendency and spread suggest about a set of data?
1.02d) Can I recognize, define, and use the normal distribution curve? Can I determine if a set of data models the normal distribution curve?
1.02f) Can I compare distributions of univariate data? / 8 Days / Quantitative
Qualitative
Population
Sample
Random
Simple
Stratified
Systematic
Biased
Convenience
Voluntary
Normal Distribution Curve
Mean
Median
Mode
Range
Quartiles
Interquartile Range
Line Plot
Box and Whisker Plot
Histogram
Center
Shape
Spread
Unit Name: Univariate Data Analysis
Unit Number: 1
Sample Resources / Location of Resources
**Multiple Resources
Online Notes
Descriptions/Examples
Videos /
Data Collection /
Display Data /
Statistical Principles /
- Interesting Article/Real life application:
- Interesting Article/Real life application:
Central Tendency and Spread /
Normal Distribution Curve /
Unit Name: Probability
Unit Number: 2
Enduring Understanding
Use counting principles and theorems to solve problems.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
1.03a-f
Use theoretical and experimental probability to model and solve problems. / 1.03a) Can I use addition and multiplication principles to solve problems?
1.03b) Can I calculate and apply permutations and combinations to solve problems? Can I determine when to use a permutation and when to use a combination?
1.03c) Can I create and use simulations for probability models? Can I answer questions about various outcomes given a model?
1.03d) Can I find expected values and determine fairness?
1.03e) Can I identify and use discrete random variables to solve problems?
1.03 f) Can I use the binomial theorem to expand a binomial raised to a large power? Can I use the binomial theorem to identify the nth term of an expanded binomial raised to a power? Can I use the binomial theorem to assist in solving a probability problem? / 10 Days / Probability
Counting
Event
Experiment
Outcome
Mutually Exclusive
Independent Events
Addition Principle
Multiplication Principle
Combination
Permutation
Factorial
Theoretical
Empirical
Fairness
Discrete Random Variable
Binomial Theorem
Pascal’s Triangle
Expected Values
Random
Biased
Sample
Sample Space
Binomial Coefficient
Unit Name: Probability
Unit Number: 2
Sample Resources / Location of Resources
Probability in KhanAcademy /
Addition and Multiplication Principles /
Permutations and Combinations /
Probability Models /
Expected Values and Fairness /
Discrete Random Variables /
Binomial Theorem /
Unit Name: Recursive Functions
Unit Number: 3
Enduring Understanding
Use recursively-defined functions to solve problems.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
2.05 (a-d)
Distinguish between arithmetic and geometric sequences and series and use formulas to solve problems. / 2.05a) Can I find the sum of a finite sequence? Can I use and interpret summation notation? Can I determine the specific term of a sequence? Can I distinguish between arithmetic and geometric sequences?
2.05b) Can I find the sum of an infinite sequence? Can I distinguish between finite and infinite sequences? Can I determine the specific term of a sequence?
2.05c) Can I determine whether or not a series converges or diverges?
2.05d) Can I translate between recursive and explicit representations? / 12 Days / Term
Finite Sequence
Infinite Sequence
Series
Recursion
Explicit
Arithmetic Sequence
Arithmetic Series
Geometric Sequence
Arithmetic Mean
Geometric Mean
Partial Sum
Convergent
Divergent
Geometric Series
Common Difference
Common Ratio
General Term
Unit Name: Recursive Functions
Unit Number: 3
Sample Resources / Location of Resources
Overall/Culmination /
Finite Sequences /
Infinite Sequence /
Convergence vs. Divergence /
Recursive vs. Explicit /
Unit Name: Linear and Polynomial Bivariate Data
Unit Number: 4
Enduring Understanding
Create and use calculator-generated models of linear and polynomial functions to solve problems (should be review from previous math courses).
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
1.01 (a-b)
Determine a line of best fit based on data points and make predictions based on the line of best fit. / 1.01a) Can I interpret the constants, coefficients, and bases in the context of the data of linear and polynomial functions?
1.01b) Can I check models for goodness-of-fit and use the most appropriate model to draw conclusions and make predictions? / 5 Days / Constant
Coefficient
Best Fit Line
Linear Regression
Correlation
Unit Name: Linear and Polynomial Bivariate Data
Unit Number: 4
Sample Resources / Location of Resources
Calculator Info /
Linear /
Polynomial /
Unit Name: Logarithmic Functions
Unit Number: 5
Enduring Understanding
Solve logarithmic functions using various methods and create calculator-generated models to solve problems.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
2.01 (a-b)
1.01 (a-b)
Solve logarithmic functions and create models of best fit to make predictions. / 2.01a) Can I solve logarithmic functions using tables, graphs, and algebraic properties? Can I expand and condense logarithms?
2.01b, 1.01a) Can I interpret the constants, coefficients, and bases in the context of the problem?
1.01b) Can I check models for goodness-of-fit and draw conclusions and make predictions based on the data? / 13 Days / Logarithm
Logarithmic Form
Exponential Form
Base
Natural Log
Product Rule
Quotient Rule
Power Rule
Expanding
Condensing
Exponentiation
Logistic Growth
Unit Name: Logarithmic Functions
Unit Number: 5
Sample Resources / Location of Resources
Overall /
Logarithmic Functions /
Models/Regression /
Unit Name: Piece-Wise and Power Functions
Unit Number: 6
Enduring Understanding
Solve Piece-Wise and Power Functions using various methods. Determine the goodness-of-fit of Power Functions and interpret the results.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
2.02 (a-b)
2.03 (a-b)
1.01 (a-b)
Solve piece-wise functions and draw conclusions based on equations. Solve power functions, draw conclusions based on equations, and find the line of best fit. / 2.02a) Can I solve piece-wise functions using tables, graphs, and algebraic properties? Can I evaluate piece-wise functions?
2.02b, 1.01a) Can I interpret the constants, coefficients, and bases in the context of the problem?
2.03a) Can I solve power functions using tables, graphs, and algebraic properties? Can I evaluate power functions?
2.03b, 1.01a) Can I interpret the constants, coefficients, and bases in the context of the problem?
1.01b) Can I check models for goodness-of-fit for power functions and make predictions and draw conclusions based on generated models? / 14 Days / Floor Function
Domain
Range
Interval
Continuous
Discontinuous
Parameters
Scaling Factor
Standard Notation
Exponentiation
Unit Name: Piece-Wise and Power Functions
Unit Number: 6
Sample Resources / Location of Resources
Piece-Wise Functions /
Power Functions /
Power Regression /
Unit Name: Trigonometric Functions
Unit Number: 7
Enduring Understanding
Use trigonometric functions to model and solve problems.
Standard / Essential Questions / Pacing Suggestion / Key Academic Vocabulary
2.04 (a-d)
Solve and graph trigonometric functions. Solve oblique triangles using the law of sines and law of cosines. / 2.04a) Can I solve sine and cosine functions using tables, graphs, and algebraic properties? Can I use trigonometric definitions to find angles and sides given a right triangle? Can I solve a right triangle?
2.04b) Can I graph and identify transformations of the sine and cosine function?
2.04c) Can I develop and use the law of sines and law of cosines to solve oblique triangles? Can I distinguish between the scenarios of when to use the different laws to solve? / 18 Days / Unit Circle
Sine
Cosine
Tangent
Period
Periodic
Amplitude
Shifts
Even
Odd
Cofunction
Identities
Oblique Triangle
Right Triangle
Pythagorean Theorem
Law of Sines
Law of Cosines
Ambiguous Case
Unit Name: Trigonometric Functions
Unit Number: 7
Sample Resources / Location of Resources
Combination /
Sine /
Cosine /
Law of Sines
Law of Cosines /
Last Updated 11/10/12