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Clarifications
Clarification 1: Instruction focuses the application of the properties of equality. Refer to Properties of Operations, Equality and Inequality (Appendix D).Clarification 2: Instruction includes equations in the forms px±q=r and p(x±q)=r, where p, q and r are specific rational numbers.
Clarification 3: Problems include linear equations where the variable may be on either side of the equal sign.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equation
- Rational Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
Students are building on their ability to write and solve one-step equations in grade 6 with an emphasis on operations with linear expressions being critical as students then write and solve two-step equations in grade 7 and multi-step linear equations in grade 8 (MTR.5.1).- Instruction includes real-world contexts as well as linear equations where the variable may be on either side of the equal sign (MTR.7.1).
- Instruction includes students verbalizing or writing the Properties of Operations and Properties of Equality (see Appendix D) used at each step to their solution.
- Use models or manipulatives, such as algebra tiles, bar diagrams or balances, to conceptualize equations (MTR.2.1).
- Algebra Tiles
- Bar Diagrams
- Balances
- Algebra Tiles
- Avoid a particular order when solving and allow students to proceed in multiple ways that are mathematically accurate.
- For example, in the equation 4( + 7) = 12, students may choose to divide both sides of the equation by 4 or use the Distributive Property with the 4. Compare the various strategies and ask students to determine which will be most efficient given different problem stems (MTR.3.1).
Common Misconceptions or Errors
- Some students may incorrectly use the addition and subtraction properties of equality on the same side of the equal sign while solving an equation. To address this misconception, use manipulatives such as balances, algebra tiles or bar diagrams to show the balance between the two sides of an equation (MTR.2.1).
- Students may incorrectly identify the constants and the coefficients within a real-world context of the problem.
Strategies to Support Tiered Instruction
- Teacher provides opportunities for students to practice solving equations using the addition and subtraction properties of equality using an interactive computer equation balance, manipulatives and other visual representations.
- Teacher provides support for students in identifying the coefficients and constants within a real-world context of the problem. Present students with examples of real-world problems that can be solved with equations.
- For example, Cameron’s fish tank can hold 12 gallons of water and he adds 2.5 gallons of water a minute. If there are already 3.4 gallons of water in the tank, for how many minutes can Cameron fill his tank without overflowing?
- Teacher provides opportunities for students to comprehend the context or situation by engaging in questions (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
- What do you know from the problem?
- What is the problem asking you to find?
- Can you create a visual model to help you understand or see patterns in your problem?
- Teacher provides opportunities for students to use algebra tiles to co-solve provided equations with the teacher without the need of writing the equation first.
- Teacher provides opportunities for students to co-write an algebraic equation with the teacher without requiring students to solve the equation.
- Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
- First, read the problem with the purpose of answering the question: What is the problem, context, or story about?
- Second, read the problem with the purpose of answering the question: What are we trying to find out?
- Third, read the problem with the purpose of answering the question: What information is important in the problem?
- Teacher models the use manipulatives such as balances, algebra tiles or bar diagrams to show the balance between the two sides of an equation.
Instructional Tasks
Instructional Task 1 (MTR.1.1, MTR.7.1)A plumber has been called in to replace a broken kitchen sink. The material needed costs $341.25 and the total expected cost of the job is $424.09. How many hours will the plumber need to work in order to get the job completed?
- Part A. What questions would need to be answered to approach this problem? Is there enough information given to solve the problem? Why or why not?
- Part B. The average rate for a plumber in Florida is $20.71 per hour. Write and solve an equation to determine how many hours the plumber will be working.
Instructional Task 2 (MTR.5.1)
The length of the rectangle is twice its width. The perimeter of the rectangle totals 45 feet. What is the width of the rectangle?
Instructional Items
Instructional Item 1What is the exact value of in the equation = − 7?
Instructional Item 2
What is the value of in the equation 5.6(3 − 2) = 11?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Expert
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
Tutorial
Video/Audio/Animations
MFAS Formative Assessments
Students are asked to compare an arithmetic solution to an algebraic solution of a word problem.
Students are asked to write and solve an equation of the form p(x + q) = r in the context of a problem about the perimeter of a square.
Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario.
Original Student Tutorials Science - Grades K-8
Use models to solve balance problems on a space station in this interactive, math and science tutorial.
Original Student Tutorials Mathematics - Grades 6-8
Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.
This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.
Practice solving and checking two-step equations with rational numbers in this interactive tutorial.
This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.
Student Resources
Original Student Tutorials
Practice solving and checking two-step equations with rational numbers in this interactive tutorial.
This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.
Type: Original Student Tutorial
Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.
This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.
Type: Original Student Tutorial
Use models to solve balance problems on a space station in this interactive, math and science tutorial.
Type: Original Student Tutorial
Problem-Solving Task
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Type: Problem-Solving Task
Tutorial
This video shows how to construct and solve a basic linear equation to solve a word problem.
Type: Tutorial
Video/Audio/Animations
Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.
Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.
Type: Video/Audio/Animation
The video explains the process of creating linear equations to solve real-world problems.
Type: Video/Audio/Animation
Parent Resources
Problem-Solving Tasks
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Type: Problem-Solving Task
This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.
Type: Problem-Solving Task
