Solving 2-Step Equations
Solving 2-Step Equations
Grade Levels
6th Grade, 7th Grade, 8th Grade
Course, Subject
Mathematics
Related Academic Standards
Rationale
Vocabulary
- coefficient: the coefficient of a term in an expression is the number that is multiplied by one or more variables or powers of variables in a term
- expression: numbers, symbols and operators (such as + and ×) grouped together that show the value of something; we simplify these
- simplify: to reduce (an equation, fraction, etc) to a simpler form by cancellation of common factors, regrouping of terms in the same variable, etc.
- equation: is a statement indicating that two algebraic expressions are equal; we solve these
- solve: to work out the answer or solution to (a mathematical problem)
- linear equation (in 1 variable): an equation containing one variable raised to the power of 1; usually has only 1 solution (but may have no solution or infinitely many solutions)
- solution: the answer to an equation; a value that, when substituted in to an equation, yields a true statement
- evaluate: substitute a value in for a variable & simplify the expression
- "check [the solution to an equation]": to evaluate an equation for a specific value (the potential solution); check to see that the resulting statement is true
- order of operations: (sometimes called operator precedence) is a rule used to clarify which procedures should be performed first in a given mathematical expression (grouping symbols, exponents, multiplication / division from left to right, addition / subtraction from left to right)
- inverse operation: opposite operations that undo each other (EX: + & -, x and division, etc.
Objectives
Students will (1) review the order of operations and how to solve 1-step equations and (2) extend this knowledge to solve 2-step linear equations. They will:
- reinforce their understanding of the inverse operations of +/- and x/division
- use inverse operations to isolate a variable
- compare / constrast the "appearance" and solution techniques for 1- vs. 2-step equations
- solve 1- and 2-step equations
- check their answers to 1- and 2-step equations
- work independently (persevere) to solve problems
- express their understanding through mathematical communication with their "elbow buddy"
- engage in meaningful self-evaluation (1 to 3 scale)
- analyze and critique others' work for correctness and report their findings
- select the correct answer from a multiple choice list
Lesson Essential Question(s)
How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
Duration
1 class period (40-50 minutes)
Materials
- Assignment from previous evening (on solving 1-step equations)
- "Bellringer" notebook
- Guided notes handout
- Calculator
- Assignment handout (on solving 2-step equations)
Suggested Instructional Strategies
| W: | Students will do the "bellringer" and discuss the previous evening's assignment as an anticipatory set. They will define Tier 3 vocabulary that will be utilized in the lesson, will see from the title what topic they are working on (and will connect this to the previous day's material), and will be evaluated in ways that are similar to other class days. |
| H: | Students will compare and contrast 1- vs. 2-step linear equations and will actively participate in the lesson. Students can follow their "progress" through the lesson by viewing the "progress bar" at the right side of the flipchart that increases as they go. |
| E: | Students will actively participate in the lesson via: (1) answering questions directed at them individually by the teacher, (2) putting problem work and solutions on the board, (3) interacting with peers in a small group format, and (4) self-evaluating. Teacher will use a variety of instructional techniques and questioning strategies, provide positive and constructive feedback during questioning and while students are working independently or in small groups. |
| R: | Students will check ALL of their answers and will, through "Think-Pair-Share, " metacognitive strategies, and self-reflection, be able to reflect and then revisit, revise, and rethink answers that are incorrect. |
| E: | Students will express their understanding through random reporting, putting problems on the board, "Think-Pair-Share, " metacognitive strategies, and self-reflection (scale of 1 to 3). Step-by-step solving gives students a tool with which they can make their own representations of adding or taking away equal values from both sides of the equation. Each step is transparent, easy, quick, and supports continuous evaluation. |
| T: | Differentiation will be accomplished through the use of guided notes, teacher questioning strategies (directing specific questions at specific students), clever student grouping for TPS, and generally providing a safe and positive learning environment where all learners to be successful. The understanding and use of inverse operations is an important element in this lesson and should be emphasized as a key to solving equations. Also emphasize the importance of applying the same operation to both sides of the equation to keep it "balanced" and to preserve the "truth" of the equation. |
| O: | The goal of the lesson is for students to learn to solve simple, 2-step linear equations in 1 variable using inverse operations. The activities are designed to move students from a clear understanding of inverse operations to the application of this understanding in solving equations. The technique of substituting a solution value into the original equation is emphasized to help students check their answers (get immediate and constructive feedback for themselves) as well as gain a deeper understanding of the process. Teacher will scaffold learning following the "I do - We do - You do" model of explicit instruction and will build on prerequisite knowledge through the use of vocabulary and questioning techniques. Teacher will encourage active engagement and metacognition through the aforementioned activities and will set the stage for future learning by ensuring that basic skills are taught and understood (through the use of informal formative assessment during the lesson and formative assessment at the end of the lesson (ticket out the door)). |
Instructional Procedures
- Check student assignment for completion / spot-check for correctness while students work on "bellringer" (bellringer problems chosen from results of previous day's "ticket out the door," homework questions, or concerns / aspects of understanding that the teacher feels need to be addressed)
- Students put up the work for the bellringer problems on the board, class critiques the correctness of the work
- Teacher directly instructs students (leads them through guided notes handout), using questioning techniques and strategies, giving students time to work independently, circulating throughout the room to see if students are on-task and are being successful
- Students put problem work on the board (when appropriate) and/or answer teacher questions
- Teacher checks for understanding throughout the lesson via various types of formative assessment, but specifically: (1) students "think-pair-share" with their "elbow" buddy, (2) students work individually and rate themselves on a scale from 1 to 3 on their understanding, and (3) students analyze and critique the work of a fictitious student over the course of 3 "challenge problems"
- Students complete a "ticket out the door" to inform the next day's lesson
- Students complete a homework assignment (~10 questions on a handout or 80% on IXL.com) on 2-step equations - they must show all solving work and check their solutions (on the handout)
Formative Assessment
INFORMAL:
- Completion / correctness / discussion of HW problems [see HW handout on 1-step equations]
- Completion / correctness / discussion of bellringer problems [see ActivInspire flipchart]
- Teacher questioning techniques / strategies during instruction and while observing students working example and challenge problems both at their seats and on the board [see ActivInspire flipchart]
- Student conversations when "talking math" about their solving / metacognition, critiquing others' work
- TPS
- Scale of 1 to 3
- Ticket out the door [see ActivInspire flipchart for questions]
- (Next day) Completion / correctness / discussion of HW problems [see HW handout on 2-step equations or IXL.com]
Related Materials & Resources
- https://www.kutasoftware.com/free.html (Two-Step Equations)
- https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/e/linear_equations_2
- http://www.algebralab.org/lessons/lesson.aspx?file=algebra_onevariabletwostep.xml
- http://www.ixl.com/math/grade-7/solve-two-step-linear-equations
- https://www.mathsisfun.com/
- http://www.mathwords.com/
- https://www.purplemath.com/
solving equations, 2-step equations, equations in 1 variable
Author
E. Barley
Date Published
May 13, 2015
