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Clarifications
Clarification 1: Instruction includes using manipulatives, drawings, number lines and inverse operations.Clarification 2: Instruction includes equations in the forms x/p = q, where p ≠ 0, and px = q.
Clarification 3: Problems include 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
- Associative Property
- Commutative Property of Multiplication
- Division Property of Equality
- Equation
- Identity Property of Multiplication
- Integer
- Multiplicative Inverse (reciprocal)
- Multiplication Property of Equality
- Number Line
- Substitution Property of Equality
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 5, students wrote and evaluated numerical expressions with positive rational numbers. Students also wrote equations to determine an unknown whole number. In grade 6, students extend their understanding to solve one-step equations which include integers. In grade 7, students write and solve one-step inequalities and two-step equations involving rational numbers.- When students write equations to solve real-world and mathematical problems, they draw on meanings of operations that they are familiar with from previous grades’ work.
- Problem types include cases where students only create an equation, only solve an equation and problems where they create an equation and use it to solve the task. Equations include variables on the left or right side of the equal symbol.
- For multiplication, instruction includes the use of coefficients, parentheses and the raised dot symbol (·).
- Use models or manipulatives, such as algebra tiles, bar diagrams and balances to conceptualize equations (MTR.2.1).
- Algebra Tiles
2 = −6
- Bar Diagrams
2 = −26
- Balance
2 = −10
- Instruction includes many contexts involving negative integers, including connections to ratio, rate and percentage problems in MA.6.AR.3.4 and MA.6.AR.3.5.
- Instruction can include students identifying the properties of operations and properties of equality being used at each step toward finding the solution. Explaining informally the validation of their steps will provide an introduction to algebraic proofs in future mathematics (MTR.5.1).
- Students should be encouraged to show flexibility in their thinking when writing equations.
Common Misconceptions or Errors
- Students may incorrectly apply an operation to a single side of an equation.
- Students may incorrectly use the multiplication and division properties of equality on the same side of the equal sign while solving an equation. To address this misconception, use manipulatives such as, algebra tiles, number lines or bar diagrams to show the balance between the two sides of an equation (MTR.2.1).
Strategies to Support Tiered Instruction
- Instruction includes identifying unknowns, constants, negative values, and mathematical operations in the provided context.
- Teacher provides opportunities for students to comprehend the context or situation by engaging in questions such as:
- What do you know from the problem?
- What is the problem asking you to find?
- Are you putting groups together? Taking groups apart? Or both?
- Are the groups you are working with the same sizes or different sizes?
- 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.
- Teacher models the use of manipulatives such as, algebra tiles, number lines or bar diagrams to show the balance between the two sides of an equation.
Instructional Tasks
Instructional Task 1(MTR.4.1, MTR.7.1)- A solar panel generates 200 watts of power each hour. A warehouse wants to generate 34,000 watts of power each hour.
- Part A. Write an equation to find how many solar panels the warehouse will need on its roof to generate 34,000 watts of power each hour.
- Part B. Explain why you wrote the equation the way you did. Could you write the equation in another way?
- Part C. Find the solution to your equation.
- Part D. What does the solution to your equation mean?
Instructional Items
Instructional Item 1- An outlet mall has 4 identical lots that can hold a total of 1,388 cars. The equation 4 = 1388 describes the number of cars that can fit into each lot. How many cars can fit into each lot?
Instructional Item 2
- Given = 56, what is the value of ?
*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 Assessment
Lesson Plans
Original Student Tutorials
Problem-Solving Task
Tutorials
MFAS Formative Assessments
Students are asked to solve a real-world problem by writing and solving an equation.
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
Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation.
Computer Science Original Student Tutorials
Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
Student Resources
Original Student Tutorials
Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation.
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
Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
- MacCoder’s Farm Part 1: Declare Variables
- MacCoder's Farm Part 2: Condition Statements
- MacCoder's Farm Part 4: Repeat Loops
Type: Original Student Tutorial
Problem-Solving Task
In this task students are asked to write an equation to solve a real-world problem.
Type: Problem-Solving Task
Tutorials
Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.
Type: Tutorial
To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.
Type: Tutorial
This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.
Type: Tutorial
Parent Resources
Problem-Solving Task
In this task students are asked to write an equation to solve a real-world problem.
Type: Problem-Solving Task
