### Examples

*Algebra 1 Example:*The Ideal Gas Law

*PV = nRT*can be rearranged as to isolate temperature as the quantity of interest.

*Example*: Given the Compound Interest formula , solve for *P*.

*Mathematics for Data and Financial Literacy Honors Example*: Given the Compound Interest formula , solve for *t*.

### Clarifications

*Clarification 1*: Instruction includes using formulas for temperature, perimeter, area and volume; using equations for linear (standard, slope-intercept and point-slope forms) and quadratic (standard, factored and vertex forms) functions.

*Clarification 2*: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## 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

Next Benchmarks

### 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 + $\frac{\text{r}}{\text{n}}$)
^{$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.

- For example, when rearranging $A$ = $P$(1 + $\frac{\text{r}}{\text{n}}$)

### 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.

- 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.

- 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 (

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?

### Instructional Items

*Instructional Item 1*

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

Instructional Item 2

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

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.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Task

## Tutorial

## Video/Audio/Animation

## STEM Lessons - Model Eliciting Activity

The topic of this MEA is work and power. Students will be assigned the task of hiring employees to complete a given task. In order to make a decision as to which candidates to hire, the students initially must calculate the required work. The power each potential employee is capable of, the days they are available to work, the percentage of work-shifts they have missed over the past 12 months, and the hourly pay rate each worker commands will be provided to assist in the decision process. Full- and/or part-time positions are available. Through data analysis, the students will need to evaluate which factors are most significant in the hiring process. For instance, some groups may prioritize speed of work, while others prioritize cost or availability/dependability.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are given three literal equations, each involving three variables and either multiplication or division, and are asked to solve each equation for a specific variable.

Students are given a literal equation involving four variables and are asked to solve for the variable in the quadratic term.

Students are given a literal linear equation and asked to solve for a specific variable.

Students are given the slope formula and the slope-intercept equation and are asked to solve for specific variables.

Students are given three literal equations, each involving three variables and either addition or subtraction, and are asked to solve each equation for a specific variable.

Students are asked to solve the formula for the surface area of a cube for *e*, the length of an edge of the cube.

## Student Resources

## Problem-Solving Task

In this task, students will use inverse operations to solve the equations for the unknown variable or for the designated variable if there is more than one.

Type: Problem-Solving Task

## Tutorial

## Video/Audio/Animation

Literal equations are formulas for calculating the value of one unknown quantity from one or more known quantities. Variables in the formula are replaced by the actual or 'literal' values corresponding to a specific instance of the relationship.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Task

In this task, students will use inverse operations to solve the equations for the unknown variable or for the designated variable if there is more than one.

Type: Problem-Solving Task