Algebra: Expressions and Multi-Step Equations

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Objective

SWBAT review writing and simplifying expressions by preparing for a trashketball game. SWBAT review writing and solving multi-step equations by playing trashketball

Big Idea

Students work on algebraic topics, expressions and equations, across two days, collecting opportunities to “shoot for points” on the second day in a game of trashketball

Do Now

15 minutes

Students enter silently according to the Daily Entrance Routine. For the next two days students will be reviewing key algebraic topics to prepare for the state exam. The Do Now assignments will therefore include introductory skills needed for this topic.

In the first day of algebraic review we will cover expressions and on the second day we will cover equations. The first Do Now includes some translation practice, a skill students struggled with at the beginning of the school year, when we first covered this topic. It is thus important to continue reviewing these key topics in an introductory manner. They should be further reviewed, with more details and examples, during class notes:

  • Identify the question and the unknown; what does the problem want you to find?
  • Study and be able to identify the operation words (sum, product, separate groups, etc.)
  • Use verbal models to translate multi-step expressions

 

  • The meaning of “in terms of [x]”
  • Watch out for reverse order (i. e. “five take from a number” is written n – 5 not 5 – n)

 

In the second day of algebraic review we will cover solving multistep equations. The Do Now on this second day includes three equations, each with more steps that the previous. The first example includes a 2 step equation with negatives. The following equation is multi-step, including distribution and combining like terms. The final equation includes the same skills but uses decimals, thus more complex. Again, the key topics that ought to be reviewed and further detailed during classwork are:

  • To solve equations, always follow the same basic steps:
    • Ask yourself, what is the goal? To isolate the variable
      • What does this mean? Leave the x alone
  • Use opposite operations to accomplish this goal
    • Remember, an equation is like a balance. Always keep the equation balanced by applying the same operation to both sides
  • There are no rules about which operation should be done first, only rules about the way these operations must be carried out (this one will most likely need more time to be reviewed, ideally during the class notes section)
    • If you choose to add/subtract first, you can only do so to like terms
    • If you choose to multiply or divide first, you must do so to the entire equation, including all terms

 

 

For this second day, solving multi step equations, it is key to target students struggling at each level. Those who struggle with 2-step equations should NOT be moving on to multistep equations. They should spend as much time as possible mastering two step equations, even if they never get to multi step equations. MP8 is at work as students are pushed to solve using different steps and methods. Questions such as “did anyone solve a different way and get the same answer?” are important as well as allowing these students to explain their process to the entire class. As much as possible, always refer to a concrete equation where all variables are known to check the validity of a process

 

 

 

After reviewing key topics and solutions to Do Now problems, we review the answers to the homework only. Students are responsible for asking each other, or me, about solutions they do not understand during the class work section.

Class Notes

20 minutes

This is the time during class that the bulleted list of key topcs can be reviewed in more detail. 

On the first day, we begin by working with numeric expressions alone. After checking classwork and exit tickets the previous days (number operations), data showed students needed to continue working with their operations. I try to merge this need with expressions so that we may continue moving through our test prep unit. Students are given 10 minutes to complete as many problems as possible from pages 1 – 3. They are told that each page that is completed in full and correctly will be used tomorrow in a Trashketball game at the end of class. Working in pairs or independently is acceptable. Students will have any number of opportunities to bring me their answers to check so that they may achieve this goal within this first ten minutes. Trashketball is a big motivator! For more details on how to play this game please review my first trashketball lesson in our first unit.

After 10 minutes have passed, students are asked to move on to the word problems at the end of the class work. These are also pages to be included in trashketball should all problems be compelted correctly. I will be guiding students through the first two problems, focusing on using MP2 to drive our review. This means the following questions are in use as much as possible:

  • What is the unknown? How are we representing it? What letter are we using?
  • What does this term represent?
  • What does the value ___ represent? The number of hours? Weeks? Something else?
  • Can we write the expression a different way without changing the meaning?
  • How can we organize the information to better understand the relationships? i.e. using a table

 

For the second day, I will be guiding students through the first couple of examples in the classwork, using MP8 to drive that discussion. Students ought to be asked:

  • Did anyone solve using different steps? Can you show us?
    • Is the equation balanced?
    • Are we using opposite operations?
    • Is the variable alone?
    • How can we prove that this step works? That we are allowed to use it? Using concrete equations
    • How did you discover this new way to solve?

 

This section is longer than other class notes because it is important to allow students to discuss and ask as many questions as needed. Group work along with pauses to display student work  on the board and explanations from students are key components in this section.

Class Work

10 minutes

Students will also be given some time to work independently to complete the class work. Again, they will be reminded that complete sheets from the first day and second day of algebraic review will count towards “shot” at the trash basket at the end of class. 

As students work independently, this is a great opportunity to pull a small group aside to work closely and address any misunderstanding in a smaller setting. As much as possible, cycling through the same questions detailed in the class notes will be important. The use of white boards can release some of the anxiety students feel when they struggle to solve. Also, being in a smaller setting with other students may help them feel more comfortable asking and sharing misunderstandings.

Closing

10 minutes

On the first day of Algebra review students will use this time to finish any work left undone or ask questions. This is a good time to cycle back to struggling students, giving them additional tips or problems on white boards to continue working toward mastery.

On the second day, after lots of hard work, students need this time to decompress and have some fun. Any sheet of class work paper that was checked and signed by me will need a name on it. Three trash baskets will be set up throughout the room and students will line up in front of them to shoot. At the end, I will be collecting any papers that made their way in and tally the points per student. A winner will be announced. He/she will be allowed to pick the movie to be shown after the state test, Day 1 (our school builds “decompression” time into the schedule on these days), and the snack to be provided.