# Algebra, Functions, and Data Analysis (AFDA) Curriculum

## Quarterly Overview of Algebra, Functions, and Data Analysis (AFDA)

The objectives and outcomes for each unit are common across FCPS and based on the Virginia Standards of Learning. The pacing by quarter and by week provides an example of how the curriculum can be organized throughout the year. Teacher teams may adjust the pacing or order of units to best meet the needs of students.

Week 1Week 2Week 3 Week 4Week 5Week 6 Week 7Week 8Week 9

## Units and Details

### Unit 1: Sampling and Data Collection

Students will:

• Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling then determine which sampling technique is best, given a particular context.
• Given a plan for a survey, identify possible sources of bias, and describe ways to reduce bias.
• Compare and contrast controlled experiments and observational studies and the conclusions one may draw from each.
• Plan and conduct an experiment or survey. The experimental design should address control, randomization, and minimization of experimental error.
• Write a report describing the experiment/survey and the resulting data and analysis.

### Unit 2: Functions

Students will:

• Represent relations and functions using verbal descriptions, tables, equations, and graphs. Given one representation, represent the relation in another form.
• Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically. Domains may be limited by problem context or in graphical representations.
• Identify intervals on which the function is increasing or decreasing.
• Identify the location and value of the absolute maximum and absolute minimum of a function over the domain of the function graphically or by using a graphing utility.
• For any x value in the domain of f, determine f(x).
• Describe the end behavior of a function.

### Unit 3: Linear Functions

Students will:

• The student will use knowledge of transformations to write an equation, given the graph of a linear function.
• For a linear function find the domain and range, intervals on which a function is increasing or decreasing, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Describe relationships between data represented in a table, in a scatterplot, and as elements of a function.
• Determine an equation for the line of best fit, given a set of no more than 20 data points in a table, on a graph, or practical situation.
• Make predictions, using data, scatterplots, or the equation of the line of best fit, including for practical problems.
• Determine the appropriate representation of data derived from real-world situations and evaluate the reasonableness of a mathematical model of a practical situation.

### Unit 4: Linear Programming

Students will:

• Model practical problems with systems of linear inequalities.
• Solve systems of no more than four linear inequalities with pencil and paper and using a graphing utility.
• Solve systems of no more than four equations algebraically and graphically.
• Identify the feasible region of a system of linear inequalities.
• Identify the coordinates of the vertices of a feasible region.

Students will:

• The student will use knowledge of transformations to write an equation, given the graph of a quadratic function.
• For a quadratic function, find the domain and range,  intervals on which a function is increasing or decreasing, zeros, intercepts, absolute maxima and minima, values of a function for elements in its domain, and end behavior.
• Determine an equation for the quadratic curve of best fit, given a set of no more than 20 data points in a table, on a graph, or practical situation.
• Make predictions, using data, scatterplots, or the equation of the quadratic curve of best fit, including for practical problems.
• Determine the appropriate representation of data derived from real-world situations and evaluate the reasonableness of a mathematical model of a practical situation.

### Unit 6: Transformations

Students will:

• Write an equation of a line when given the graph of a line.
• Recognize graphs of parent functions for linear, quadratic, exponential and logarithmic functions.
• Write the equation of a linear, quadratic, exponential, or logarithmic function in vertex form, given the graph of the parent function and transformation information.
• Describe the transformation from the parent function given the equation written in vertex form or the graph of the function.
• Given the equation of a function, recognize the parent function and transformation to graph the given function.
• Recognize the vertex of a parabola given a quadratic equation in vertex form or graphed.
• Describe the parent function represented by a scatterplot.

### Unit 7: Probability

Students will:

• Analyze, interpret and make predictions based on theoretical probability within practical context.
• Determine conditional probabilities for dependent, independent, and mutually exclusive events.
• Represent and calculate probabilities using Venn diagrams and probability trees.
• Given two or more events in a problem setting, determine whether the events are complementary, dependent, independent, and/or mutually exclusive and be able to define and give examples of the above.
• Compare and contrast permutations and combinations, including those occurring in practical situations, then be able to calculate permutations and combinations.

### Unit 8: Normal Distributions

Students will:

• Identify the properties of a normal distribution.
• Describe how the standard deviation and the mean affect the graph of the normal distribution.
• Given standard deviation and mean, calculate and interpret the z-score for a data point.
• Compare two sets of normally distributed data using a standard normal distribution and z-scores, given mean and standard deviation.
• Use a graphing utility or a table of Standard Normal Probabilities to determine probabilities associated with areas under the standard normal curve.

### Unit 9: Final Project

In this unit, teachers will provide differentiated opportunities for students to review and reinforce earlier concepts and to explore content at a deeper level.

## Assessments

Student assessments are part of the teaching and learning process.

• Teachers give assessments to students on an ongoing basis to
• Check for understanding
• Gather information about students' knowledge or skills.
• Assessments provide information about a child's development of knowledge and skills that can help families and teachers better plan for the next steps in instruction.

For testing questions or additional information about how schools and teachers use test results to support student success, families can contact their children's schools.

In Fairfax County Public Schools (FCPS), tests focus on measuring content knowledge and skill development.

EPF

English 9
English 10
English 11
English 12

Health 9
Health 10