Mathematics Grade 8
Strand: EXPRESSIONS AND EQUATIONS (8.EE) Standard 8.EE.7
Solve equations by isolating the variable
Enduring Understanding (Big Ideas):
Solving equations
Essential Questions:
Skill Focus:
Use inverse operations to find
the solution for an equation
Vocabulary Focus:
equation, inverse operation, isolate the variable, working
solve, solution
Ways to Gain/Maintain Attention (Primacy): Manipulatives, story, game, sketching, graphic organizer
Starter:
X − 1 = -2 | X = ___ | Check: | ___ − 1 = -2 |
3 | 3 |
X − 1 | a. X | b. X |
3 | 3 |
Lesson Segment 1: How can inverse operations be used to transform an equation to isolate the variable? What value of the variable will create two equivalent expressions? How can this solution be checked?
A. Model using the inverse operations to isolate the variable and to solve the equation by having students set up the equation and isolate the variable using Cups and Counters (attached) or by using Hands-On Equations (if you have a set). Go through the steps on the Cups and Counters page through the two-step equations, having student pairs set-up, solve, represent and record on the worksheet (attached).
B. Sometimes a story or scenario can remind us how to do a procedure. Following is a scenario or story that can help students remember the procedural steps for solving two step equations. Tell and demonstrate the story. Have the students write all models as journal notes for solving equations.
Xavier's Party (Procedural Story)
Xavier is having a party. He invites a very close friend and some more casual
friends to the party. Because he can only invite a few, several friends did not receive
an invitation. See if you can identify the host of the party-Xavier, the close friends,
the casual friends and the friends who didn't get invited at all in this equation:
2x + 4 = 14 (X is Xavier, 2 is the closest friend, 4 is the casual friends, and 14 is
the friends who weren't invited.) Can you identify which expression is where the
party is happening and which is where there is no party? (The party is the variable
expression) The equal sign represents the door to the party. When anyone leaves the
party, they go the opposite way they came. So, the inverse operation must be
performed to get them out the door.
When the party is over, and people leave, does the host leave? No, the host stays, and the friends leave. Who usually leaves a party first, the casual friends or the closest friends? Usually, the close friends stay to help clean up or to sleep over. So, who would leave the party first (4)? And, when 4 goes out the door, what operation must be used to go out? (subtract). So, four goes out and is subtracted from 14 leaving 10 outside and who is left at the party (2 and the host, X)? Who leaves last (2)? When 2 goes out the door, what operation in used (divide)? So, 2 goes out and divides into 10 leaving only the X at the party and 5 outside the door.
Repeat the scenario as you model the procedure for solving these problems and have the students work on their paper as you model.
C. Movement: Use Stand-Up Cards (#s 1-20, operation signs, equal sign, negative sign) cards to have student teams set up and solve this equation. -2x + 5 = 11. students actually stand holding symbols and move as the variable is isolated.
Lesson Segment 2: Practice
A. Play Solving Equations Jeopardy (game board attached)
Print the game on a transparency and cover the statements with post-its. Divide the
class into two teams. Ask a person to choose a category and a value. Reveal that
statement. Give students a minute to discuss with team members, then the selected
person must ask the appropriate question. If she/he does not, call on a person from
the other team to answer. When a person answers correctly, they get to choose
another category and value. The team with the most points at the end of a
predetermined time period wins.
B. Have student pairs play the Equation War game. Each person writes on a game paper. The players each pick two or three cards (depending on how many boxes need to be filled) from a deck of cards. Using a regular card deck, the Ace can be 1 and the face cards should be pulled. Or, a graphing calculator can be used to generate numbers from 1-10. Each player decides where to place the numbers that they rolled in the boxes for the first equation on the paper. Then, each player solves their equation and players compare solutions to see which player had the greatest solution. They should check each other's work, because the player whose solution is the greatest value, gets a point. They re-roll the dice to get numbers to fill the next equation and continue playing.
Lesson Segment 3: Summarize Use the "Solving Two-Step Equations" foldable (attached) for students to write examples of the steps to solving equations. The fill in the blanks. The foldable is a fan fold.
performance tasks, observation, quiz
This lesson plan was created by Linda Bolin.