Tables, Equations, and Graphs, Oh My!

10 min

Narrative

The purpose of this activity is to familiarize students with the eight relationships they will continue to work with for the rest of this lesson. In this partner activity, students take turns matching equations and tables that represent the same relationship without knowing what real-world situations the relationships represent. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Students can make use of structure (MP7) as they narrow down which tables could possibly match each equation. For example, they may recognize whether the values for the dependent variable should be greater or less than the corresponding values for the independent variable, based on the operation and numbers in the equation.

Launch

Tell students that the cards contain either an equation or a table and that they will take turns matching the cards. Explain how to set up and do the activity. If time allows, demonstrate the steps with a student as a partner. Consider demonstrating productive ways to agree or disagree, for example, by explaining mathematical thinking or asking clarifying questions.

Arrange students in groups of 2. Give each group a set of 18 cards cut from the blackline master.

Consider allowing students to use calculators to ensure inclusive participation in the activity.

Student Task

Your teacher will give you a set of cards. Take turns with your partner to match an equation with a table.

  1. For each match that you find, explain to your partner how you know it’s a match.

  2. For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

Sample Response

Table I: G=J+13G = J +13

Table J: m=8.96Vm = 8.96V

Table K: y=112xy = \frac{1}{12}x

Table L: P=I47.50P = I - 47.50

Table M: C+273.15=KC + 273.15 = K

Table N: S2=TS - 2 = T

Table O: g=28.35zg = 28.35z

Table P: E=6sE = 6s

Activity Synthesis (Teacher Notes)
The purpose of this discussion is to elicit the different characteristics of the equations and tables that students used to make their matches. Select 2–3 groups to share one of their sets of cards and explain how they matched an equation with a table. Discuss as many different sets of cards as the time allows, highlighting the ways students connect the variables and operations in each representation and use the terms “dependent variable” and “independent variable.”
Anticipated Misconceptions

Some students may struggle to relate the variables in the equation to the columns of the table. Remind students that when we have one variable expressed in terms of the other variable, we call the former the "dependent variable" and the latter the "independent variable". For example, in the equation a=b+6a = b + 6 we say that bb is the independent variable and aa is the dependent variable, because aa is expressed in terms of bb.

Standards
Addressing
  • 6.EE.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <em>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.</em>
  • 6.EE.C.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <span>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation <span class="math">\(d = 65t\)</span> to represent the relationship between distance and time.</span>

15 min

15 min