Lesson 1: Intro to Function and Modeling with Tables

Unit Title: Linear Functions
Lesson: 1 Intro to Functions and Modeling with Tables / Approx. time:
2 days / CCSS-M Standards: 8.EE. 5, 8.F.1, 8.F.4
A. Focus and Coherence
Students will know…
·  Relationships between two quantities can be represented in a table
·  Linear functions are distinct from non-linear functions (e.g. linear functions increase or decrease by the same rate)
·  Linear functions are used to model relationships between 2 quantities, and can be modeled in graphs, tables, and equation
Students will be able to…
·  Represent linear functions in the form of a table, given a situation that expresses a linear relationship between two quantities.
·  Identify linear from non-linear functions, given a table of values
·  Create a scenario that describes the relationship between two quantities, from data given in a table
Student prior knowledge:
·  Multiplication Facts
·  Calculating Unit Rates
·  Organizing Data in a Table
·  Graphing points on a coordinate plane (specifically Quadrant 1)
·  Interpreting Graphs
Which math concepts will this lesson lead to?
·  Generating Linear Equations from Tabular Data
·  Understanding the meaning of Slope / B. Evidence of Math Practices
What will students produce when they are making sense, persevering, attending to precision and/or modeling, in relation to the focus of the lesson?
SMP #1: Students will intuit the purpose of a function. (Example: Students will say “The amount of money that Juan will spend on Go Karts depends on how many laps he races.”)
SMP #1: Students will persevere by continuing the inquiry of the dependent factors. (Example: Students will try on the math with different factors.)
SMP #4: Students will represent and organize their math thinking for a real world problem. (Example: Students will accurately construct a table to represent their math thinking.)
SMP #6: Students will accurately create a table and linear graph to represent the data. (Example: Students will multiply accurately and create and label a graph on a coordinate plane.)
Essential Question(s)
1.  Why is it useful to understand rate of change?
2.  When is it appropriate to use rate of change?
3.  In what kinds of situations is it appropriate to use a linear function as the model?
4.  How does understanding the structure of a linear equation help us understand the relationship between an independent and dependent variable?
Formative Assessments
Use handouts:
·  Illustrative Mathematics “US Garbage, Version 1”
·  “Linear Equations: Fully Charged”
Anticipated Student Preconceptions/Misconceptions
1.  Students may think there has to be only one answer to a question.
2.  Students do not know they can control the dependent factor?
3.  Students may not know which values are graphed on which axes.
Materials/Resources
Rulers, Graph Paper, Poster Post-its, Scotch Tape, Formative Assessment Handouts
C. Rigor: fluency, deep understanding, application and dual intensity
What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of the Math Practices? (Detailed Lesson Plan)
Warm Up : (Quick Write: Then have students pair/share)
1.  When you go shopping how do you decide how much money to ask your parents for?
(Listen for students discussing topics related to total cost, unit rates, etc.)
Lesson
Part 1
Teacher poses question to the class: Juan went to Speed Racer to ride Go Carts. A lap around the track costs $3. Juan wants to spend the day racing Go Carts, how much will it cost?
Allow time for Think, Pair, Share
Students should realize there is not enough information to answer the question.
Students might ask for more information by saying , “it depends” or they may ask “How many laps is Juan doing?”
Teacher DOESN’T give them a specific number of laps , instead teacher asks a follow-up question: “What do you mean by “it depends?” or “How many laps would YOU want to do?”
“What does it depend on?”
Teacher brings class together to discuss the different outcomes students found. Then teacher asks students, “Talk to someone around you about what you discovered about how much it will cost Juan.”
Students should explain the cost will depend on the number of laps.
Teacher asks class to share examples of different outcomes. (Teacher writes student responses on the board)
Teacher says, “Talk to your small group (for 2 minutes) about a way we can organize our results.”
Students should create and organize a table or graph.
Teacher selects best example of a table (if graph is created keep for later) from the groups to share with whole group.
Teacher asks students to identify: Title, “each student choose a number from the left hand side of the table, now turn your neighbor and explain what that number represents” Discuss placement of values on the table.
Teacher states, “Let’s represent this table graphically. Turn to your partner and discuss which quadrant you will use to represent the information.”
Students should say, quadrant 1
Teacher will say, now discuss what pieces are required to complete the graph.
Teacher turns back to whole group and asks, if we have an x and y axis where will cost and laps go?
Students will respond, cost is the label for the y axis and laps is the label for the x axis.
Teacher states, we’re going to graph points on the graph to represent Juan’s cost per lap. I’m going to start at the origin (0,0) and move right along the x axis tell me when to stop for 1 lap.
Students: “STOP!”
Teacher states, now I will move up the y axis tell me to stop when I reach the cost for 1 lap ($3)
Students: “STOP!”
Teacher asks, does this line have the potential to end? (Will this line ever end?)
Students respond, the number of laps (points) can never end, therefore you need an arrow at to represent a line going on forever.
Teacher explain, the definition of Domain: the numbers in this example go on for infinity.
Teacher congratulates the class, “We just modeled this information graphically and in a table!”
Teacher says, “Brainstorm with your partner/group another situation that can be modeled using a table and a graph. You will have 10 minutes to create a problem with your partner/group and represent it in a table and graphically. Your work will be displayed for a gallery walk.” (Students can use post-it posters and graph paper).
After 10 minutes: (Gallery Walk) Teacher says, “You have 2 minutes to identify the quantities being compared in each problem.”
Teacher asks, “Did anybody notice anything in common in the problems?” (Checking to see if any problem did not involve money.”
Part 2
Starting with a graph, students will create a corresponding table (work backwards from
Part 1)
Students will need to use points in a graph and represent them in a table by identifying what each coordinate represents.
After this task, teacher can give the two formative assessment handouts and have students work in groups.
Closure
Pick a point on the graph that your group/partner made and explain using complete sentences what the point represents.
Suggested Homework/Independent Practice
Create a linear function that does NOT involve money and model the information graphically and in a table.

Formative Assessment Questions – Lesson 1

Illustrative Mathematics 8.F.US Garbage, Version 1

Linear Equations: Fully Charged

Sam wants to take his MP3 player and his video game player on a car trip. An hour before they plan to leave, he realized that he forgot to charge the batteries last night. At that point, he plugged in both devices so they can charge as long as possible before they leave.

Sam knows that his MP3 player has 40% of its battery life left and that the battery charges by an additional 12 percentage points every 15 minutes.

His video game player is new, so Sam doesn’t know how fast it is charging but he recorded the battery charge for the first 30 minutes after he plugged it in.

time charging (minutes) / 0 / 10 / 20 / 30
video game player battery charge (%) / 20 / 32 / 44 / 56

a.  Create two graphs, one for each situation.

b.  If Sam’s family leaves as planned, what percent of the battery will be charged for each of the two devices when they leave? Justify your answer.

c.  Clearly explain in words how you know how much time Sam would need to charge the battery 100% on both devices.

8th Grade Linear Functions