Missing Values

Exploring 2-Variable Relationships Using Patterning

I.  Objectives: The learner will describe patterns produced by relationships between two variables. The learner will use the table and patterns to write an equation involving two variables. The learner will make a graph to display data using correct labels and scales. The learner will recognize that a constant rate of change is evident in the pattern established by the data. The learner will use a given equation to produce a table of ordered pairs and graph the ordered pairs.

II.  Materials: Copies of Missing Values Worksheet (1 per student), ACE Cab Company WS (1 per student).

III.  Lesson:

  1. State the lesson objectives.
  2. Go over Shapes homework assignment. Discuss the results as a class.
  3. Hand out the Missing Values worksheet to each student.
  4. Ask students to answer questions 1-5 on the Missing Values worksheet.
  5. Ask a student to explain #1. What reasons do the students give for finding the missing values in the data table? Is the pattern explained using a recursive pattern or an explicit pattern? Do students note the constant rate of change? Ask for other explanations that may be different.
  6. Ask another student to explain #2. What scales did the students decide to use for the x and y axis? What labeling do the students use, if any? Ask for other explanations.
  7. Ask a third student to explain #3. When they determined their general rule, did they “add 4” multiple times (a recursive strategy) or did they see a relationship between the x value and the y value (an explicit strategy)? What is their reasoning behind the rule they wrote? Ask for other explanations until you hear both strategies.
  8. Ask a fourth student to explain #4. Is the student able to extend their understanding to include points that are not on the table-in this case, a point below the x-axis?
  9. Ask students to identify the variables in the table. What does each variable represent?

IV.  Summary: The students created a data table and wrote ordered pairs from the table. The students graphed the ordered pairs and determined if other given ordered pairs were solutions to the equation. Students examined the relationship between an equation, a table of values, and a graph.

V.  Assessment: Hand out the ACE Cab Company worksheet. Ask students to complete #1-3.