Algebra for All Online

Lesson Plan Template

Mathematics Professional Development
Marianne Reid

Title: Choose Wisely – grade 9

Key Ideas: Linear / Non-linear Models

Strands:

A: Algebra and Functions

L: Quantitative Literacy and Logic

Standards:

A2: Functions

L1: Reasoning about Numbers, Systems, AND Quantitative Situations

Topics:

A2.1 – Definitions, Representations, and Attributes of Functions

A2.3 – Representations of Function

L1.2 – Representations and Relationships

Content Expectations:

A2.1.3 – Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.

A2.3.1 –Identify a function as a member of a family of functions based on its symbolic or graphical representation; recognize that different families of functions have different asymptotic behavior.

A2.3.2 – Describe the tabular pattern associated with functions having a constant rate of change (linear); or variable rates of change.

L1.2.4 –Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media

Lesson Outcome: What will the students be able to do at the end of the lesson?

  • Students will be able to recognize linear and non-linear functions represented in tables and graphs.
  • Students will be able to plot different sets of data on the same graph and draw conclusions from the data.
  • Students will be able to make decisions based on data presented in a graphical or tabular format.
  • Students will be able to describe the differences in the graphs of linear and non-linear functions.

Materials and Resources: List all supplies and resources to be used in the lesson, including texts, computers, calculators, software, web-based resources, manipulatives, and art supplies.

  • “Choose Wisely” activity sheet (one for each student)
  • Calculators
  • Computer with Excel (optional)
  • Excel spreadsheet template

Procedures:Describe the anticipatory set or “hook” to start the lesson, sample questions to students, and activities and tasks to be used in the lesson. The flow of the lesson, step by step, should be described, particularly in relation to what students will be doing.

Students will be presented with a hypothetical scenario and asked to choose between three different payment options. The payment options involve linear, polynomial of degree two and exponential functions. Students need to analyze the situations both numerically (making a table) and graphically. At the end of the activity, students will identifywhich type of equations (linear, polynomialor exponential) is the best model for each option.

This lesson is adapted from “The Thousand Dollar Proposition” lesson plan on the Algebra for All social network. The link for this lesson is:

I modified the lesson slightly by changing the scenario and the options. We have been working with linear functions, and I want to use this lesson as a bridge activity to introduce the students to non-linear functions. I also added an optional Excel graphing activity to integrate with the lesson.

Teacher Prompts:

  • Before: The teacher will read through the scenario with the students. Ask each student to write down his or her choice prior to doing the activity.
  • During: Monitor students while they are working, the teacher will ask leading questions as necessary.
  • After: The teacher will be able to informally assess students’ knowledge of linear models and their ability to distinguish between linear and non-linear models.

What Comes Next?

  • This is an introductory lesson to non-linear functions. Follow with additional activities and lessons to teach exponential growth and decay and other types of non-linear functions.

Choose Wisely Activity Sheet

You are walking down the street and you see an older gentleman who needs assistance. You stop to lend him a hand, and he is very grateful. This is your lucky day. Unbeknownst to you, this man is a wealthy business man who is doing philanthropic work in your city. Being unfamiliar with the area, he offers you a job as his personal assistant for the next two weeks. He offers to pay you one of the following salaries:

Option 1:You earn $500 each day you work.

Option 2: You earn $100 on the first day, $200 on the second day, $300 on the third day, and so on with your pay increasing by $100 each day you work.

Option 3: You earn $1 on the first day, $2 on the second day, $4 on the third day, and so on with your pay doubling each day you work for 14 days.

Comparing the Options

  1. Compute the daily earnings and the cumulative earnings for fourteen days and record them in the table below.

Number of Days / Option 1:
Earnings per day / Option 1:
Cumulative earnings / Option 2:
Earnings per day / Option 2:
Cumulative earnings / Option 3:
Earnings per day / Option 3:
Cumulative earnings
1
2
3
4
5
6
7
8
9
10
11
12
13
14
  1. Graph the data on the grid below. Use a different color for each option.
  • Put the number of days on the x-axis (horizontal axis). This is the independent variable.
  • Put the total earnings on the y-axis (vertical axis). This is the dependent variable.
  1. Analyze the graphs.
  1. Explain what these graphs show you about your options.
  1. Explain the shape of each graph. What about the situation leads to the shape?
  1. After looking at the data and analyzing the graphs, do you still think you chose the best option? Explain.
  1. Determine the best fit equation for each option from the following choices:

Linear: where and b = y-intercept

Polynomial of degree 2:

Exponential growth: – 1

Option 1

  1. Decide whether option 1 is linear, and if so, find the slope and y-intercept and write the linear equation for option 1.
  1. If option 1 is not linear, then pick the best fit equation from the above choices. Try a few points in the non-linear equations given to determine which equation works best for the option 1 data.
  1. Use your equation to find the amount you will earn if you choose option 1 and you work for two weeks (14 days). Compare this with your graph.
  2. Use the equation to find the amount you would earn if you worked for 3 weeks (21 days).

Option 2

  1. Decide whether option 2 is linear, and if so, find the slope and y-intercept and write the linear equation for option 2.
  1. If option 2 is not linear, then pick the best fit equation from the above choices. Try a few points in the non-linear equations given to determine which equation works best for the option 2 data.
  1. Use your equation to find the amount you will earn if you choose option 2 and you work for two weeks (14 days). Compare this with your graph.
  2. Use the equation to find the amount you would earn if you worked for 3 weeks (21 days).

Option 3

  1. Decide whether option 3 is linear, and if so, find the slope and y-intercept and write the linear equation for option 3.
  1. If option 3 is not linear, then pick the best fit equation from the above choices. Try a few points in the non-linear equations given to determine which equation works best for the option 3 data.
  1. Use your equation to find the amount you will earn if you choose option 3 and you work for two weeks (14 days). Compare this with your graph.
  2. Use the equation to find the amount you would earn if you worked for 3 weeks (21 days).

Assessment: How will you determine if the students have achieved the learning outcome(s).

Assessment will be informal, by observing the students as they interpret the data, asking questions, and listening to the students’ questions and reasoning.

Additional Notes: Fill in additional comments and considerations, such as special instructions, extension opportunities, differentiation strategies, re-teaching resources, etc.

Excel spreadsheet extension

Take students to the computer lab and work with them to create an Excel spreadsheet. Go through the steps with the students and have them follow along on their own computers, or provide written instructions and help students individually.

Students will:

  • Create an Excel spreadsheet, with seven columns.
  • Label the columns as:
  1. Day
  2. Option 1: Earnings per Day
  3. Option 1: Cumulative Earnings
  4. Option 2: Earnings per Day
  5. Option 2: Cumulative Earnings
  6. Option 3: Earnings per Day
  7. Option 3: Cumulative Earnings
  • Enter data for Day 1 Earnings per Day for each option.
  • Use formulas to compute the remaining data. The teacher will guide the students in creating the formulas.
  • Create a scatter chart in Excel showing all three options. The teacher will guide the students in creating the chart.
  • Select each data set in the graph, right click somewhere on the line, and choose “Add trendline”
  • Experiment with the “Trend/Regression Type” options to find the best fit for each data set.

Attachments: Provide copies of any worksheets, handouts, and other associated elements related to the lesson. Make a list of the attachments for reference in this space.

The activity sheet is included in this document.

The Excel spreadsheet is: Choose Wisely Extension.xls