Solving Multi Step Equations with Candy (Day 1 of 4)

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Objective

SWBAT solve multi-step equations using inverse operations.

Big Idea

Students will conceptualize the process of solving a linear equation by representing variables and constants with candy.

Do-Now

10 minutes

The purpose of this activity is to encourage students to check their work when solving an equation. Students will complete the Multi Step Do Now in 4 minutes. We will then review the answers as a whole group. I will say aloud the equation and solution, and students will silently respond with a thumbs up if they agree and a thumbs down if they disagree. I will call on volunteers to justify a new solution for each response that was labeled incorrect, "(e) ten divided by two plus added to five is equal to fifteen, so the solution for letter e has to be x = 2)"

Next, a student will read the objective to the class: SWBAT solve multi step equations using inverse operations. I will ask students to reflect on the entire journey our class has taken up to this (translating, combining like terms, one step equations, two step equations, distributive property) and to make a prediction about how all the pieces will connect in order for us to complete today's objective.

Group Activity

30 minutes

Students will work in groups of two (homogeneous ability levels). Each pair will need about 30 gummy bears (2 groups of 15 in a single color) and about 30 m&m candies (2 groups of 15 in a single color). I also gave students four dixie cups to sort and store candy that wasn't in use, but this is not necessary. This activity will run more smoothly, if the candy is sorted into cups prior to the beginning of class.

Each student will need the balance beam sheet, and the equation handout to complete this activity. I will explain to the class that we will use the candy to represent the variables and constants that are in a multi step equation, in order to give our equations a physical model. I have the students create a key on the top of the equation handout by placing a piece of candy next to the corresponding item.

I tell students that we are going to balance our equations, and that our goal is to ensure that each gummy bear receives an equal distribution of m&m's as the other gummy bears in the equation. The only rule that students must abide by is to make their actions balanced; whatever is removed from one side of the balance beam has to be identically removed from the other side. In this video (candy lab) a student gives a thorough explanation on how to solve a multistep equation using candy.

 

Notes + Guided Practice

30 minutes

The group activity is a great segue to the guided notes and practice section of the lesson.

During each example I do not deviate from the order "Distributive property -> Combine like terms on the same side -> Undo addition and subtraction --> Undo multiplication and division". This is done to get students into a solid routine. Even if a particular example does not require distributive property or combining like terms, I still will include it in my explanation so that students get used to following this sequence every time. 

For the last few lessons I have had students label each side of the equation with the heading variables and constants. I will still refer to these heading as we solve equations and use the heading to guide students to mastery:

  • If we only want constants on this side of the equation, which term doesn't belong?
  • How can I undo a positive four?
  • If I move a constant to the other side of the equation, what is the only term on the other side of the equation that I can combine it with? Why?
  • Why do you think I am stressing the word "same" during the second part of the equation process? Aren't inverse operations and combining like terms the same thing? Why or why not?
  • How does solving equations on paper relate to the equations that we solved  with candy?

Closing

10 minutes

To close out this lesson I will ask students to make a connection between the variable/constant headings that we have been using to solve equations, and how those headings translate to the gummy bears and m&m's. I will also ask students to justify why 2x + 5 doesn't equal 7 using the candy as a manipulative. 

Students will then complete an Exit Card. There are two versions of the Exit Card; I will decide which Exit Card to give students based on the the level of mastery that I observe in class.

Exit Card A (focuses on algebraic problem solving)

Exit Card B (focuses on visual representation)

The exit cards should be graded directly after class, and the students should then be grouped by the percentage of correct for a remediation group during the next lesson.