Standard #: MA.912.AR.1.2

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

• Equation

 

Vertical Alignment

Previous Benchmarks

• MA.8.AR.2 
• MA.8.GR.1

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 isolated variables in one-variable linear equations and one-variable quadratic equations in the form $x$² = $p$ and  $x$³ = $q$. In Algebra I, students isolate a variable or quantity of interest in equations and formulas. Equations and variables will focus on linear, absolute value and quadratic in Algebra I. In later courses, students will highlight a variable or quantity of interest for other types of equations and formulas, including exponential, logarithmic and trigonometric.

• Instruction includes making connections to inverse arithmetic operations (refer to Appendix D) and solving one-variable equations. 
• Instruction includes justifying each step while rearranging an equation or formula. 
  • For example, when rearranging $A$ = $P$(1 + $\frac{\text{<math><mi>r</mi></math>}}{\text{<math><mi>n</mi></math>}}$)^$n$$t$   for $P$, it may be helpful for students to highlight the quantity of interest with a highlighter, so students remain focused on that quantity for isolation purposes. It may also be helpful for students to identify factors, or other parts of the equations.

 

Common Misconceptions or Errors

• Students may not have mastered the inverse arithmetic operations. 
• Students may be frustrated because they are not arriving at a numerical value as their solution. Remind students that they are rearranging variables that can be later evaluated to a numerical value. 
• Having multiple variables and no values may confuse students and make it difficult for them to see the connections between rearranging a formula and solving a one-variable equation.

 

Strategies to Support Tiered Instruction

• Instruction includes doing a side-by-side comparison of solving a multistep equation with rearranging equations and formulas. The teacher should allow students time to understand that the steps in solving both equations are the same. 
  • For example, solve both equations and note the similarities in solving both types of equations. 
    
    
    

• Teacher provides a chart for students to use as a study guide or to copy in their interactive notebook. 
  • For example, inverse operations chart below.
    
    
    

 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.5.1) 

• Part A. Given the equation $a$$x$² + $b$$x$ + $c$ = 0, solve for $x$. 
• Part B. Share your strategy with a partner. What do you notice about the new equation(s)?

Instructional Task 2 (MTR.4.1, MTR.5.1) 

• Part A. Given the equation $A$$x$ + $B$$y$ = $C$, solve for $B$. 
• Part B. Given the equation 7$x$ − 6$y$ = 24, determine the $x$- and $y$-intercepts. 
• Part C. What do you notice between Part A and Part B?

• Solve for $x$ in the equation 3$x$ + $y$ = 5$x$ − $x$$y$. 

Instructional Item 2 

• The formula $d$ =  relating to the translational of motion, where d represents distance, $v$₀ represents initial velocity, $v$_t represents final velocity, and $t$ represents time. Rearrange the formula to isolate final velocity. 

Instructional Item 3 

• The area $A$ of a sector of a circle with radius $r$ and angle-measure $S$ (in degrees) is given by  solve for the radius $r$.

 

 

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