Unlocking Linear Functions: Finding Missing Values in Tables

Algebra 1 Grades High School 2:13 Video
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Lesson Description

Learn how to identify and complete linear function tables by understanding the constant rate of change. This lesson focuses on finding missing values in a table representing a linear equation.

Video Resource

Linear and nonlinear functions (example 3) | 8th grade | Khan Academy

Khan Academy

Duration: 2:13
Watch on YouTube

Key Concepts

  • Linear Functions
  • Constant Rate of Change
  • Tables of Values

Learning Objectives

  • Students will be able to determine if a table of values represents a linear function.
  • Students will be able to calculate the missing value in a table representing a linear function, given sufficient information to determine the constant rate of change.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a linear function and its key characteristic: a constant rate of change. Briefly discuss how this constant rate of change is reflected in a table of values.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Linear and nonlinear functions (example 3) | 8th grade | Khan Academy.' Encourage students to take notes on the example problem and the steps taken to solve it.
  • Guided Practice (10 mins)
    Work through a similar example problem on the board, emphasizing the process of identifying the change in x and the corresponding change in y. Guide students to calculate the constant rate of change and use it to find the missing value.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing several tables of values, each with a missing value. Instruct them to determine if the table represents a linear function and, if so, to calculate the missing value. Emphasize showing their work.
  • Wrap-up and Assessment (8 mins)
    Review the solutions to the independent practice problems as a class. Address any remaining questions or confusion. Administer the multiple choice or fill-in-the-blank quiz to assess student understanding.

Interactive Exercises

  • Table Completion Game
    Create a simple online game where students are presented with incomplete tables of linear functions and must fill in the missing values to earn points. This can be done using a spreadsheet program or a simple website.

Discussion Questions

  • How can you tell if a table of values represents a linear function?
  • Why is it important to find the constant rate of change when working with linear functions?

Skills Developed

  • Problem-solving
  • Analytical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

Which of the following best describes a linear function?

Correct Answer: A function with a constant rate of change.

Question 2:

In a linear function table, if x increases by 2, and y increases by 6, what is the rate of change?

Correct Answer: 3

Question 3:

Given a linear function table with points (1, 4) and (2, 7), what is the increase in y when x increases by 1?

Correct Answer: 3

Question 4:

If a table does NOT have a constant rate of change, is it a linear function?

Correct Answer: No, never.

Question 5:

In a linear function, if x increases, what MUST happen to y?

Correct Answer: y must change by a constant amount.

Question 6:

Which of the following represents a linear function?

Correct Answer: y = 2x + 1

Question 7:

What is the first step in finding a missing value in a linear function table?

Correct Answer: Calculate the rate of change

Question 8:

In a linear function table, if (0, 2) and (1, 5) are points, what is the y-intercept?

Correct Answer: 2

Question 9:

A linear function passes through (1, 3) and (2, 5). What will y be when x = 3?

Correct Answer: 7

Question 10:

Why is it important to know the constant rate of change?

Correct Answer: To solve for the missing values in the table

Fill in the Blank Questions

Question 1:

A linear function has a ________ rate of change.

Correct Answer: constant

Question 2:

In a table, to find the missing y-value, first find the change in ____.

Correct Answer: x

Question 3:

If x increases by 3 and y increases by 9, the rate of change is ____.

Correct Answer: 3

Question 4:

If the rate of change is 2, for every increase of 1 in x, y increases by ____.

Correct Answer: 2

Question 5:

The graph of a linear function is a ________ line.

Correct Answer: straight

Question 6:

A function that does not have a constant rate of change is called _________.

Correct Answer: nonlinear

Question 7:

The rate of change can also be called the ____.

Correct Answer: slope

Question 8:

If a point is (0,b), b is the ____.

Correct Answer: y-intercept

Question 9:

To be a linear function, as x increases, y must increase or decrease by a _________ amount.

Correct Answer: constant

Question 10:

Linear functions are important because they help us ________ real-world relationships.

Correct Answer: model

Educational Standards

A1.F.2.1:Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric). A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.4.1:Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line.

Teaching Materials

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