Standard #: MA.6.AR.1.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.6.NSO.1.2
• MA.6.NSO.1.3 
• MA.6.NSO.2.1
• MA.6.NSO.2.2
• MA.6.NSO.2.3
• MA.6.AR.2.2
• MA.6.AR.2.3
• MA.6.AR.3.5
• MA.6.GR.2.2
• MA.6.GR.2.3

 

Terms from the K-12 Glossary

• Associative Property
• Absolute Value
• Coefficient
• Commutative Property of Addition
• Commutative Property of Multiplication
• Expression

 

Vertical Alignment

Previous Benchmarks

• MA.5.AR.2.1
• MA.5.AR.2.4

Next Benchmarks

• MA.7.AR.2.2

 

Purpose and Instructional Strategies

Students are focusing on appropriate mathematical language when writing or reading expressions. In earlier grade levels, students have had experience with unknown whole numbers within equations. Grade 6 extends this knowledge by focusing on using verbal and written descriptions using constants, variables and operating with algebraic expressions. In grade 7, students use this knowledge when solving equations involving mathematical and real-world contexts.

• Within this benchmark, instruction includes connections to the properties of operations, including the associative property, commutative property and distributive property. Students need to understand subtraction and division do not comply with the commutative property, whereas addition and multiplication do. Students should have multiple experiences writing expressions (MTR.2.1, MTR.5.1).
• Instruction focuses on different ways to represent operations when translating written descriptions into algebraic expressions. For translating multiplication descriptions, students should understand that multiplication can be represented by putting a coefficient in front of a variable.
  • For instance, if students were translating “six times a number $n$,” they can write the algebraic expression as 6$n$.
• For translating division descriptions, students should understand that division can be represented by using a fraction bar or fractions as coefficients in front of the variables (MTR.2.1).
  • For example, if students were translating “a third of a number $n$,” they can write the algebraic expression as $\frac{\text{1}}{\text{3}}$$n$ or $\frac{\text{<math><mi>n</mi></math>}}{\text{3}}$.
• Students are expected to identify the parts of an algebraic expression, including variables, coefficients and constants, and the names of operations (sum, difference, product and quotient).
• Variables are not limited to $x$; instruction includes using a variety of lowercase letters for their variables; however, $o$, $i$, and $l$ should be avoided as they too closely resemble zero and one.

 

Common Misconceptions or Errors

• Students may incorrectly assume that there is not a coefficient in front of a variable if there is not a number explicitly written to indicate a coefficient (MTR.2.1).
  • $x$ is the same as 1$x$
• Students may incorrectly think that terms that are being combined using addition and subtraction have to be written in a specific order and not realize that the term being subtracted can come first in the form of a negative number (MTR.2.1).
  • $x$ −3 is the same as −3 + 2$x$
• Students may incorrectly oversimplify a problem by circling the numbers, underlining the question, boxing in key words, and try to eliminate information that is important to the context. This process can cause students to not be able to comprehend the context or the situation (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1).
• Teachers and students should engage 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?

 

Strategies to Support Tiered Instruction

• Instruction includes the use of pictorial representations, tape diagrams, or algebra tiles to represent the written situation before writing an expression.
• Instruction includes identifying unknowns, constants, negative values, and mathematical operations in a written description or algebraic expression.
• Instruction includes co-creating a graphic organizer that includes words used in written descriptions for each of the operations. The graphic organizer should continue to grow as new contexts are encountered.
• 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?

 

Instructional Tasks

Instructional Task 1 (MTR.7.1) 

The amount of money Jazmine has left after going to the mall could be described by the algebraic expression 75 − 12.75s − 9.50d, where s is the number of shirts purchased and d is the number of dresses purchased.

• Part A. Describe what each of the terms represent within the context.
• Part B. What are possible numbers of shirts and dresses Jazmine purchased.

Instructional Task 2 (MTR.2.1) 

Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains. Let d represent the distance, in miles, from a student’s home to the school. Write two different expressions that represent how far a student travels by bike in a four-week period if there is one rainy day each week.

 

Instructional Items

Instructional Item 1

Rewrite the algebraic expression as a written description: 10− $\frac{\text{6}}{\text{<math><mi>x</mi></math>}}$.

 

Instructional Item 2 

Write an expression to represent the phrase “9 plus the quotient of w and 4.”

 

Instructional Item 3 

Write an expression to represent the phrase “7 fewer than the product of 3 and y.”
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.