Algebra 1 Unit 3: Functions

Unit Driving Question 

How can we use data to determine patterns and relationships in real-world situations?

Essential Questions 

1. How do we measure change?

2. How do we quantify the relationships between quantities?

3. How can different representations show relationships?

4. What patterns exist among quantities?

Launch Task 

Big Ideas for Development Lessons--click on each for its activities

Closure & Assessment

1 Lesson 

4 Weeks (approximately 1 week per big idea)

1 Week 

Click on each Big Idea to see Lesson Overviews, including teacher notes and lesson activities:

1. A function is a rule that describes the relationship in a set of data for which each input has one and only one output.

2. Functions are written and manipulated using function notation.

3. Functions can be evaluated and interpreted both algebraically and graphically.

4. Function families share similar graphs, behaviors, and properties. 

1. Unit 3 Formative Assessment 1
2. Re-engagement Activity (not provided, to be based on formative assessment results)
3. Tesla Performance Assessment (covers A1.F.1.2, A1.F.1.4, A1.A.4.1)- For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.  

Big Idea 1: A function is a rule that describes the relationship in a set of data for which each input has one and only one output.

Lessons and Additional Activities

Big Idea 1 Lesson Overview

• Lesson 1: Identify domain and range given in graph, table, mapping and ordered pair form.
• Lesson 2: Know that relations are simply a mapping from the domain to the range and understand that functions are a well-mapped subdomain of a relation.
• Lesson 3: Identifying and Describing Relationships Between Variables
• Lesson 4: Connecting the Graph to the Situation and Justifying the Connection
• Lesson 5: Find restrictions to the domain and range when necessary. 

Bootstrap Computer Science Integration Activity

• Bootstrap Algebra/Computer Science Integration Activity: This activity features types, circles of evaluation, racket code, and contracts. This activity is for Bootstrap trained teachers.
• Applying Functions  (Note, this lesson is for Bootstrap trained teachers)  

Evidence of Understanding 

Know that relations are simply a mapping from the domain to the range.

Understand that functions are a well-mapped subdomain of a relation

• Realize that each element of the domain mapped to only one element in the range

Identify domain and range of given function, equation or graph

• Domain is the set of x-coordinates within a  set of points on a graph or within a  written set of ordered pairs.  

• These values are the input to a function or relation.

• Range is the set of y-coordinates within a set of points on a graph or within a written set of ordered pairs.

• These values are the output to a function or relation.

Identify independent and dependent variables of a given function, equation or graph.

• Independent variables are the variable whose value determines the value of other variables.

• Dependent variables are the  variable whose value is determined by the value of an independent variable.

• Understand that there are restrictions on domain and range in algebraic situations as well as real-world situations.

• Recognize when the domain or range may have values that do not exist in a real world situation

Interpret functions both verbally and graphically

Big Idea 2: Functions are written and manipulated using function notation 

Lessons and Additional Activities

Big Idea 2 Lessons 1-4 Overview (with links to teacher notes and activities)

Additional Collaborative Activity:

• Station Activity: Real-World Situation Graphs- Students will work in collaborative groups to complete station activities providing opportunities to develop concepts and skills related to creating and interpreting graphs representing real-world situations.

Bootstrap Computer Science Integration Activity:

• Bootstrap Function Composition (Note: This is for Bootstrap Trained Teachers)

Evidence of Understanding

Understand what function notation represents in terms of the two variables and the relationship between them

• Know that f(x) is the dependent variable and x is the independent variable

• Recognize how changing x, changes f(x)

• Understand f(x) = mx + b is a linear function

Understand rate of change in real-world situations is the slope of a function and initial value is the y-intercept

Perform arithmetic operations on functions

• Add and subtract functions in function notation

• Multiply functions in function notation

Big Idea 3:  Functions can be evaluated and interpreted both algebraically and graphically

Lessons and Additional Activities

Big Idea 3 Lessons 1-2 Overview (with links to teacher notes and activities)

Additional Activities

Bootstrap Computer Science Integration Activity

• Defining Functions (Note: This is for Bootstrap trained teachers)

Evidence of Understanding

Recognize piecewise functions as a combination of equations

• Linear piecewise functions are formed by linear segments that correspond to a specific part of the domain.

Evaluate a function and interpret meaning in real-world situations both algebraically and graphically.

Big Idea 4: Function families share similar graphs, behaviors, and properties. 

Lessons and Additional Activities

Lesson Plans and Activities:

Big Idea 4 Lessons 1-4B Overview (with links to teacher notes and activities)

Additional Collaborative Activities:

• Station Activity: Relations vs. Functions and Linear vs. Nonlinear- Students will work in collaborative groups and complete station activities providing opportunities for students to develop concepts and skills related to recognizing the differences between linear and nonlinear functions and the differences between functions and relations.

• Pandemic: How do viruses spread through a population? (Mathalicious) In this lesson, students use exponential growth and logarithms to model how a virus spreads through a population and evaluate how various factors influence the speed and scope of an outbreak.

Evidence of Understanding

Recognize linear and nonlinear functions from tables, graphs and equations

• Realize linear functions change by equal intervals while exponential functions increase by equal factors over equal intervals

Identify similarities and differences among linear, quadratic, absolute value, and exponential function families based on features of their graphs or tables.

• Interpret rate of change, domain and range patterns, and intercepts for each type of function family.

• Relate the rate of change and other key features of each function family to its parent function: f(x) = x (linear), f(x)= x^2 ( quadratic), f(x) = |x| (absolute value) and f(x) = 2^x (exponential)

Compare functions within a family and describe transformations from the parent function

• Describe the vertical or horizontal shift given a graphical representation of a parent function and other function in the same family

• Compare tables of values for different functions within the same function family (the parent function and one other)

Identify geometric sequences as exponential functions:  f(x) =a(r)^x

• Define a and r within the context of the problem

• Create various models of the given data including equations, graphs, tables and verbal descriptions.

• Find the next term in the sequence when given the formula

Understand that an arithmetic sequence is a linear function and changes by adding (or subtracting) the same value each time.

• Be able to recognize an arithmetic sequence and write a rule to describe it using the formula

• Use the rule to find the nth term in the sequence.