Equations, Tables, and Graphs Day 2

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Objective

SWBAT: • Define and identify independent and dependent variables. • Use and create a table to display data. • Use and create a line graph to display data. • Write an algebraic equation that fits a given situation. • Solve one-step and two-step equations.

Big Idea

For the equation y = 3x + 4, if y is 25 what must x equal? Students work with input-output tables and then work together to create equations, tables, and graphs to represent various situations.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to practice matching a situation with a graph.  Some students may have difficulty with graph 1 and graph 3, since they are not changing at a steady rate and this is okay. Some students may struggle with the fact that there are no exact values identified on the graphs.  I want students to focus on the “story” so that they can match each situation with a graph. 

I ask students to share their thinking.  I also ask students to share specific words in the situations that helped them find a matching graph.  I want students to understand that “steady” means that the price is changing the same amount for every change in time.  These steady changes create graphs that are straight lines.  Students are engaging in MP2: Reason abstractly and quantitatively, MP3: Construct viable arguments and critique the reasoning of others, and MP4: Model with mathematics.

Problems

10 minutes

I want students to continue to work with input-output tables.  For today I introduce two-step equations.  I present these input-output tables to students as a puzzle.  I have a rule for how x and y are related in my head and their job is to use the clues to determine my rule.  I begin by giving students a series of three x and y-values that follow my rule.  I make sure that my x-values are not consecutive so students must focus on the relationship between the x and y value.  Then I call out a fourth x value and ask for volunteers for guesses for the corresponding y-value.  I emphasize to students that it is okay if they haven’t figured out the rule yet, they need to keep trying.  I call out a fifth y-value and ask for volunteers for guesses of the corresponding x-value.  To finish the table I call on volunteers to share corresponding x and y-values that they think match my rule.  If they work, we add them to our table.  Then students participate in a Think Pair Share to brainstorm how to find y if they are given the x-value.  Students share out their thinking and then we talk about how to represent that rule with an equation.  Students are engaging in MP2: Reason abstractly and quantitatively and MP8: Look for and express regularity in repeated reasoning.

Students work independently on the last two tables.  I want students to be able to use an equation to generate missing x and y values.  I do not teach students a procedure, but rather I want students to reason out the values.  Some students may guess and check while others may work backwards.  I tell students that it is important to check their answers using the actual equation to prove that they are correct.

Group Work Expectations

5 minutes

Notes:

  • Before this lesson, I use the data from the ticket to go in the previous lesson to Create Homogeneous Groups.
  • For each group I fill out a copy of the “Group Members and To Do List” document.  I want each group to complete at least 2 situations (1 that involves a one-step equation and 1 that involves a two-step equation).  I write these assignments on their paper.

Together we review independent and dependent variables.  I go over the expectations and inform students of their groups.  Students take their materials and move into their groups.

Group Work

23 minutes

Notes:

  • I print out the situations separately.  I place them in a labeled folder and set them out in the room.
  • Each group receives a Group Work RubricI use this to give students feedback on their behavior and cooperation.

While groups are working, I walk around and monitor student progress and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP8: Look for and express regularity in repeated reasoning.

If groups are struggling, I may ask one of the following questions:

  • What is going on in the problem?
  • What are the two variables in this problem?
  • Which variable is the independent variable? Which variable is the dependent variable?  How do you know?
  • What is the relationship between x and y?  How can you represent that in an equation?  How can you prove that your equation works?

 I Post A Key so that students can check their work once they are finished.  If a group completes a situation, they raise their hand and check in with me.  If they are on the right track I allow them to send a representative to check the key.  If they are not on track, I ask them questions or point out a problem.    

If students successfully complete the practice problem, they can work on the challenge problems.  

Closure and Homework

5 minutes

I ask students to share out specific things their group did well today.  Then I ask students to share out struggles that their group encountered.  Some groups may share out parts of the task that were challenging while other groups may share about a conflict between group members that challenge them.  I ask students, “How did they cope with it or did it not get resolved?”  Part of being able to persevere through problems is acknowledging conflict and struggle and generating strategies of coping and working through it. I share positive things I saw groups doing and things that the class can improve on.

Instead of giving a ticket to go, I collect student work so I can analyze it.  I pass out the Homework.