# More Solving Problems with Equations

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## Objective

SWBAT represent and solve a word problem using a linear equation.

#### Big Idea

Students should determine how the unknowns in a problem are related to each other in order to help them set up the equation.

## Warm Up

10 minutes

This Warm Up is a good opportunity to let students revisit some previously learned content.  The writing prompts push students to demonstrate MP3, by constructing a viable argument. I plan to remind my students that when they are constructing explanations, they should cite specific examples from the problem.

I developed both questions to be ones that students will have to think about. I expect all of my students to write a detailed explanation.  I expect my students will require about 7 minutes to do a good job on his Warm Up. As the complete their work, I will partner them up to complete a Think-Pair-Share. For this activity I will encourage students to find one or two ideas in the partners work that they think are clear and understandable (MP3).

## Independent Practice

20 minutes

The tasks on the Equations_Practice Sheet give students practice writing expressions and equations. As was the case yesterday, I will ask students to use the Graphic Organizer. Today, I take away the scaffold of identifying the unknown values for students.  When students are writing their expressions, I want them to be thinking about which unknown is best written in terms of the other.

Example: Arielle has a collection of grasshoppers and crickets. She has 559 insects in all. The number of grasshoppers is five less than three times the number of crickets. Find the number of each type of insect that Arielle has in her collection.

In this example, the number of grasshoppers is stated in terms of the number of crickets.  So, if we let the number of crickets equal our single variable x, then we can describe the number of grasshoppers as  3x - 5. Students always seem to have some difficulty with this concept.  It is through practice they will become better at writing these let statements.

I want to make sure that as students are working I continue to emphasize the check.  Students should not have to ask if they are getting the correct answers to these questions, they should know themselves through doing their check.  The check also serves to build meaning around the entire question.  For example, in the question above the statement "five less than three times the number of crickets" is abstract.

Once students have found a value for the number of crickets (141) and grasshoppers (418) they can verify their solution in two ways.  First they can add the numbers together to ensure they add up to 559.  Second, they can multiply 141 by 3 and subtract 5 to get 418.  It is important for students to build this habit of checking their solutions so that they do so without being asked (MP6).

## Closure

10 minutes

I like today's closing activity because of the metacognitive nature of the problem statement:

Word Problem_Equation_Close

Students first need to rank the questions in terms of difficulty.  This approach forces students to concentrate on reading, understanding, and making a plan for solving each problem in order to determine the difficulty level.

Students will then solve the problems.  If students would like to continue to use the Graphic Organizer I have extra copies on hand and available.  I also encourage students to construct the three columns right on their paper and make sure that they are thinking about how the sections help them to organize their thoughts

I plan to collect this Ticket out the Door and use it as a formative assessment of using equations to solve problems.  The next lesson in this progression deals with using inequalities to model and solve problems. If I identify students who are having difficulty, I will put them with an appropriate group of students for tomorrow's lesson.