Verbal Models and Equations

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Objective

SWBAT write and solve equations to solve word problems by using verbal models.

Big Idea

Students work independently, in pairs, and in groups to identify unknowns, create verbal models, and translate equations to solve word problems.

Do Now

10 minutes

Students enter the class silently according to the Daily Entrance Routine. They find a Do Now assignment already at their table. I created this warm up to prepare students for translating algebraic phrases. We begin the day by translating simple one step expressions. I focus on one step translations to identify students who struggle with these simpler phrases. As I walk around the room during the first 5 minutes while students work independently on this assignment, I watch for students struggling to write phrases or students struggling to read the phrases. If I cannot determine whether the student is struggling to write the phrase or read it, I may ask them to read the phrase out loud. I also keep an eye out for the common error when writing quotient or difference expressions, where the commutative property can affect the order in which the constant and the variable term are placed.

After 5 minutes, we review the answers and I make sure to ask students to talk to their neighbor about questions 4 and 5. I ask them to discuss the property that affects the order in which these terms are written and have an answer ready to share out after 1 minute. We discuss the important of the commutative property and the two operations where it is applied (division and subtraction). We also make sure to write down some words that may alert us to look out for this property (i.e. taken/subtracted from, less than, fewer than, etc)

Guided Practice

15 minutes

I ask students to clip their Do Now into the correct part of their binder. Then I distribute our guided practice. I ask students to fill out the heading on their paper and copy the aim at the top. I explain to students that we will be using verbal models to translate equations.


Each of the first three problems includes the first step, identifying the unknown. For these three problems, students must focus on building the verbal model. If a student does not ask about the variable choice, I make sure to tell them that the letter does not always have to be x. It is more helpful to choose an appropriate letter according to the situation in the problem (i.e. b for balloons, h for hours). Before they move on to the last two problems, students must write a verbal model to match the problem situations in the first three problems. Students who struggled during the Do Now on translating expressions will be working with me in a smaller group at the front of the room. All other students will be allowed to pair up or work independently to solve the rest of the problems. The expectations for showing work are displayed on the SMARTBoard as follows:

For each problem you MUST:

  • Identify the unknown with a statement that says, “Let x = …”
  • Write a verbal model
  • Translate this model to an equation
  • Solve at the end for achievement points

 

After 8 minutes of work time, all students will be asked to return to their desks and we will review answers. I will display the work we completed in my small group and ask all other students for answers to any problems we did not complete. The answer document attached shows the work and answers for each question.

Independent Practice + Closing

25 minutes

Students are asked to keep their guided practice papers out to help during independent practice.  There are 6 problems on the next worksheet. Half of the room is assigned the odd numbered problems and the other half is assigned the even numbered problems. All students must work silently for ten minutes, making sure they are first identifying the unknown with the statement “Let x = …”, then write a verbal model, then translate to an equation. Students who finish their three problems early will need to raise their hand to have me check their work. If the work is acceptable, these students are given the option to solve the problem to find an answer OR go to the board to copy their work. Students who copy their work on the board will be asked to explain and justify their work to the class. Students who choose to solve, will be asked to explain to the class why their answer makes sense in the context of the situation. If a student is not sure how to explain their reasoning, I will model these explanations using one of the guided practice problems.

After 10 minutes, most students should be done writing verbal models and translating equations for their three problems. In this lesson I am leaving myself lots of time-cushioning because I anticipate that the explanations and justifications of work and answers will be difficult for my students. I want to be able to give ample time for students to persevere in making sense of these problems and the equations that they are translating (MP1). My own goal today is not to dominate conversations about these problems, but to instead place the responsibility on students to help each other makes sense of the situations. There will be multiple instances of “turn and talks” and of cold calling students to explain situations and work in their own words.

5 minutes before the end of class I will distribute homework making sure I ask students to tell me what kind of work I should see on everyone’s papers:

  • A sentence identifying the unknown in the form “Let x = …”
  • A verbal model
  • An equation
  • A solution with a proper label