MA.6.AR.2.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.6.NSO.4.1
• MA.6.AR.1.1

Terms from the K-12 Glossary

• Additive Inverse Property
• Addition Property of Equality
• Associative Property
• Commutative Property of Addition
• Equation
• Identity Property of Addition
• Integer
• Number Line

Vertical Alignment

Previous Benchmarks

• MA.5.AR.1.1
• MA.5.AR.2.1
• MA.5.AR.2.2
• MA.5.AR.2.3
• MA.5.AR.2.4

Next Benchmarks

• MA.7.AR.2.2

Purpose and Instructional Strategies

• 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.
• Use models or manipulatives, such as algebra tiles, bar diagrams, number lines and balances to conceptualize equations (MTR.2.1).
  • Algebra Tiles
    
    $x$  − 3 = −10
    
    
  • Bar Diagrams
    
    $x$ − 4 = −13
    
    
  • Number Lines
    
    $x$ + 6 = −7
    
    
  • Balances
    
    $x$ + 3 = −9
    
    
    
    Students should understand the equal sign represents the fulcrum in the center of the balance and the scale is supposed to stay balanced even when you manipulate the expression on the pan of the balance (MTR.2.1).
• Instruction includes 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 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).

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 balances, algebra tiles, or bar diagrams to show the balance between the two sides of an equation.

Instructional Tasks

• Melvin wants to go to the school musical. The school auditorium has 1250 seats arranged in three sections. The left section has 375 seats, and the right section has 375 seats. Write an equation to find the number of seats in the center section and explain why you wrote the equation the way you did.

Instructional Items

• Given $z$ + 15 = 3, what is the value of $z$?

• Given 6 = $x$ − 13, what is the value of $x$?

• Alex has some money in his wallet. His grandmother gives him $10 for a gift in his birthday card. He now has $28 in his wallet. Write an equation to represent the problem. How much money did he originally have in his wallet?

• The width of the rectangular table top is 4 feet shorter than its length. If the length of the table top is 6 feet, write and solve an equation to determine the width of the table top.

Related Courses

Related Access Points

Related Resources

Student Resources

Parent Resources