### Examples

*Algebra 1 Example:*Derrick is using the formula to make a prediction about the camel population in Australia. He identifies the growth factor as (1+.1), or 1.1, and states that the camel population will grow at an annual rate of 10% per year.

*Example*: The expression can be rewritten as which is approximately equivalent to . This latter expression reveals the approximate equivalent monthly interest rate of 1.2% if the annual rate is 15%.

### Clarifications

*Clarification 1:*Parts of an expression include factors, terms, constants, coefficients and variables.

*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

- Coefficient
- Expression
- Equation

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### 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.

- Students should be able to identify factors, terms, constants, coefficients and
variables in expressions and equations.

### 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.

- 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.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## 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.

The Turning Tires MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best tire material for certain situations. The main focus of the MEA is applying surface area concepts and algebra through modeling.

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 asked to explain how parts of an algebraic expression relate to the number and type of symbols in a sequence of diagrams.

Students are asked to interpret the parts of an equation used to calculate the total purchase price including tax of a set of items.

Students are asked to determine how the volume of a cone will change when its dimensions are changed.

## Original Student Tutorials Mathematics - Grades 9-12

Identify parts of quadratic equations in vertex form and interpret them in terms of the context they represent in this interactive tutorial.

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

## Student Resources

## Original Student Tutorials

Identify parts of quadratic equations in vertex form and interpret them in terms of the context they represent in this interactive tutorial.

Type: Original Student Tutorial

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students explore the structure of the operation *s*/(v*n*). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of *n*, then dividing the result of that operation into *s*.

Type: Problem-Solving Task

This task provides an interesting context to ask students to estimate values in an exponential function using a graph.

Type: Problem-Solving Task

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

## Parent Resources

## Perspectives Video: Professional/Enthusiast

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students explore the structure of the operation *s*/(v*n*). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of *n*, then dividing the result of that operation into *s*.

Type: Problem-Solving Task

This task provides an interesting context to ask students to estimate values in an exponential function using a graph.

Type: Problem-Solving Task

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task