Standard #: MA.912.AR.1.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.NSO.1.2
• MA.912.AR.2.2
• MA.912.AR.2.5
• MA.912.AR.2.6 
• MA.912.AR.3.1
• MA.912.AR.3.6
• MA.912.AR.3.7
• MA.912.AR.3.8 
• MA.912.AR.4.1 
• MA.912.AR.5.3
• MA.912.AR.5.6
• MA.912.FL.3.2

 

Terms from the K-12 Glossary

• Coefficient 
• Expression 
• Equation

 

Vertical Alignment

Previous Benchmarks

• MA.8.AR.2.1
• MA.8.AR.2.2

Next Benchmarks

• MA.912.AR.5.5
• MA.912.AR.5.9
• MA.912.AR.8.2 
• MA.912.T.3.2

 

Purpose and Instructional Strategies

In grade 8, students generated and identified equivalent linear expressions, and solved multi-step problems involving linear expressions within real-world contexts. In Algebra I, students generate and interpret equivalent linear, absolute value, quadratic and exponential expressions and equations. In later courses, students will identify and interpret other functional (exponential, rational, logarithmic, trigonometric, etc.) expressions and equations. 

• Instruction includes making the connection to linear, absolute value, quadratic and exponential functions.
  • Students should be able to identify factors, terms, constants, coefficients and variables in expressions and equations. 
    • Go beyond these popular parts of an expression and equation: the growth/decay factor in exponential functions, rate of change in linear functions, interest, etc. 
  • Look for opportunities to interpret these components in context – make these discussions part of daily instruction.

 

Common Misconceptions or Errors

• Students may not be able to identify parts of an expression and equation or interpret those parts within context. Ensure these are embedded throughout instruction and discussions. 
  • For example, building in questions to identify these parts and discussing their connection to the context in which they represent in a routine way will help students to make these connections.

 

Strategies to Support Tiered Instruction

• Teacher facilitates discussions which include questions and clarifications to identify the connections of expressions and equations to the context of problems. 
• Instruction provides opportunities to increase understanding of vocabulary terms. 
  • For example, instruction may include a vocabulary review using a chart shown.
    
    
    

• Teacher provides students with an expression or equation and allows them to match the parts to key vocabulary. 

• For example, teacher can provide the word bank to identify the different parts of the equation shown.
  
  
  

Instructional Tasks

Instructional Task 1 (MTR.5.1) 

• The algebraic expression ($n$ − 1)² + (2$n$ − 1) can be used to calculate the number of symbols in each diagram below. Explain what $n$ likely represents, how the parts of this expression relate to the diagrams, and why the expression results in the number of symbols in each diagram.

                         

Instructional Task 2 (MTR.3.1, MTR.7.1) 

• Last weekend, Cindy purchased two tops, a pair of pants, and a skirt at her favorite store. The equation $T$ = 1.075$x$ can be used to calculate her total cost where $x$ represents the pretax subtotal cost of her purchase. 
  • Part A. In the equation $T$ = 1.075$x$, what does the number 1 represent? Explain using the context of Cindy’s situation. 
  • Part B. In the equation $T$ = 1.075$x$, what does the number 0.075 represent? Explain using the context of Cindy’s situation.

 

Instructional Items

Instructional Item 1 

• Identify the factors in the expression 2(3$x$ − 1) + 2(2$x$ + 2).

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.