 # Standard #: MAFS.7.EE.2.4

This document was generated on CPALMS - www.cpalms.org

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
1. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
2. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

### Clarifications

Fluency Expectations or Examples of Culminating Standards

In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students solve the equations fluently. This will require fluency with rational number arithmetic (7.NS.1.1–1.3), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1.1).

Examples of Opportunities for In-Depth Focus

Work toward meeting this standard builds on the work that led to meeting 6.EE.2.7 and prepares students for the work that will lead to meeting 8.EE.3.7.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Test Item Specifications

N/A

Assessment Limits :
Inequalities must have context. Inequalities may use ≤ or ≥. Inequalities may not be compound inequalities
Calculator :

Yes

Context :

Allowable

### Sample Test Items (4)

 Test Item # Question Difficulty Type Sample Item 1 The perimeter of a rectangular garden is 37.5 feet (ft). The width is x, and the length is 15 ft. What is the width, in feet, of the garden? N/A EE: Equation Editor Sample Item 2 A community is planning to build a rectangular garden. The width of the garden is feet (ft), and the perimeter of the garden is 37.5 ft. The community planners want to spread mulch on the entire garden. How many square feet of mulch will be needed? N/A EE: Equation Editor Sample Item 3 At her job, Jessie earns \$9.50 per hour. She also earns a \$60 bonus every month.Jessie needs to earn more than \$460 every month.A. Create an inequality that represents the situation, where h represents the number of hours that Jessie needs to work in a month in order to earn more than \$460.B. Enter the minimum whole number of hours Jessie would have to work to earn \$460 in a month. N/A EE: Equation Editor Sample Item 4 This question has three parts.Vanessa has added 40 gallons of water to her new fish pond in her backyard and wants to add more water. Her pond can hold a maximum of 256 gallons. Her garden hose can add 48 gallons of water in 2 minutes.Part A. Create an inequality to represent the number of minutes, m, Vanessa could run the garden hose to add more water to the pond without adding the maximum amount in case of rain.Part B. Drag the appropriate arrow and circle to the number line to graph the solution to the inequality from Part A.Part C. Select all the amounts of time, in minutes, that Vanessa could leave the house running. N/A GRID: Graphic Response Item Display

#### Related Courses

 Course Number1111 Course Title222 1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020 (current), 2020 and beyond) 1204000: M/J Intensive Mathematics (MC) (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200700: Mathematics for College Readiness (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current)) 7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

#### Related Access Points

 Access Point Number Access Point Title MAFS.7.EE.2.AP.4a Set up equations with one variable based on real-world problems. MAFS.7.EE.2.AP.4b Solve equations with one variable based on real-world problems.

#### Assessments

 Name Description Sample 3 - Seventh Grade Math State Interim Assessment This is a State Interim Assessment for seventh grade. Sample 4 - Seventh Grade Math State Interim Assessment This is a State Interim Assessment for seventh grade. Sample 2 - Seventh Grade Math State Interim Assessment This is a State Interim Assessment for seventh grade. Sample 1 - Seventh Grade Math State Interim Assessment This is a State Interim Assessment for seventh grade.

#### Formative Assessments

 Name Description Recycled Inequalities Students are asked to solve a real-world problem by writing and solving an inequality. Solve Equations Students are asked to solve two multistep equations involving rational numbers. Write, Solve and Graph an Inequality Students are asked to write, solve, and graph a two-step inequality. Write and Solve an Equation Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario. Squares Students are asked to write and solve an equation of the form p(x + q) = r in the context of a problem about the perimeter of a square. Gift Card Inequality Students are asked to solve a two-step inequality. Algebra or Arithmetic? Students are asked to compare an arithmetic solution to an algebraic solution of a word problem.

#### Original Student Tutorials

 Name Description Professor E. Qual Part 2: Two-Step Equations & Rational Numbers Practice solving and checking two-step equations with rational numbers in this interactive tutorial. This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1. Professor E. Qual Part 1: 2 Step Equations Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.  This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2. Balancing the Machine Use models to solve balance problems on a space station in this interactive, math and science tutorial.

#### Perspectives Video: Experts

 Name Description Improving Hurricane Scales Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale. Download the CPALMS Perspectives video student note taking guide. Water Flow Modeling for Archeology Research Submerge yourself in math as a hydrogeologist describes calculations used to investigate water flow questions related to ancient shell rings. Download the CPALMS Perspectives video student note taking guide.

#### Perspectives Video: Teaching Idea

 Name Description Programming Mathematics: Algebra, Matrices, and Variables to control Open-source Hardware If you are having trouble understanding variables, this video might help you see the light. Download the CPALMS Perspectives video student note taking guide.

 Name Description Smiles In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems. Fishing Adventures 2 Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat. Sports Equipment Set The student is asked to write and solve an inequality to match the context. Gotham City Taxis The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table. Log Ride Students are asked to solve an inequality in order to answer a real-world question.

#### Teaching Ideas

 Name Description Students Collaborate to Solve Compound Inequalities In this activity, the student teacher role is reversed using the "jigsaw activity." This is where there is an original group, and they are separated into different groups. They are then given a particular case, and solve it as a group until they understand it enough to be able to go back to their original group and teach their case to the rest of the students. Each student coming from a different group, they will all have the opportunity to do some teaching. Translating Word Problems into Equations This site shows students how to translate word problems into equations. It gives seven steps, from reading the problem carefully to checking the solution, to creating equations. The lesson moves on to a few simple exercises in which a natural language sentence is translated to an algebraic equation. It then moves on to more elaborate word problems which require students to identify the important data and follows the given seven steps to create and solve the equation. The more complex questions draw on student understanding of geometric formulae. There are six questions at the end for students to test their new knowledge of how to create and solve equations. True, False, and Open Sentences "Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions.

#### Unit/Lesson Sequences

 Name Description Drawing to Scale: Designing a Garden In this lesson (or series of lessons), students interpret and use scale drawings to plan a garden layout. Students start by producing their own layout and then work together to refine their garden design. The activity requires that students use short rules (rulers), meter rules (meter sticks), string, protractors, scissors, glue, card, plain paper, graph paper, and colored pencils. Students work individually for 20 minutes, engage in a 100-minute lesson (or two 50-minute lessons), and complete a 10-minute follow up lesson or homework. Variables and Patterns of Change: Translating Words Into Symbols; Linear Equations Lesson Plan 1: Miles of Tiles - The Pool Border Problem, students will recognize patterns and represent situations using algebraic notation and variables. Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives, students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution. Students work in teams of four. Site includes a Topic Overview, Lesson Plans, Student Work, Teaching Strategies, Resources, and a video of Workshop 1; Part 1.

#### Video/Audio/Animations

 Name Description Solving Motion Problems with Linear Equations Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance. Solving Problems with Linear Equations How do we create linear equations to solve real-world problems? The video explains the process.

#### Virtual Manipulative

 Name Description Linear Function Machine In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

#### Original Student Tutorials

 Name Description Professor E. Qual Part 2: Two-Step Equations & Rational Numbers: Practice solving and checking two-step equations with rational numbers in this interactive tutorial. This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1. Professor E. Qual Part 1: 2 Step Equations: Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.  This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2. Balancing the Machine: Use models to solve balance problems on a space station in this interactive, math and science tutorial.

 Name Description Smiles: In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems. Fishing Adventures 2: Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat. Sports Equipment Set: The student is asked to write and solve an inequality to match the context. Gotham City Taxis: The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table. Log Ride: Students are asked to solve an inequality in order to answer a real-world question.

#### Video/Audio/Animations

 Name Description Solving Motion Problems with Linear Equations: Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance. Solving Problems with Linear Equations: How do we create linear equations to solve real-world problems? The video explains the process.

#### Virtual Manipulative

 Name Description Linear Function Machine: In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.