Grade 5 GT Expressions and Equations

7.EE.4

About the Math

Full Standard

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.

4a. 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?

4b. 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 $40 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.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**5th Grade Students Learning 5 G/T Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Report Card Measurement Topic: Demonstrates understanding of algebraic thinking,expressions, and equations.

Learning Targets (I can)

Write and solve equations in the form px + q = r and p(x + q) = r.
Write and solve simple equations to represent the situation with unknown values.
Write, solve, and graph inequalities to represent the situation with unknown values.

About the Math

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.A.1-3), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.A.1). Examples of Connections to Standards for Mathematical Practices: When students compare arithmetic and algebraic solutions to the same problem, they are identifying correspondence between different approaches (MP1). Solving an equation such as 4=8(x-0.5) requires students to see and make use of structure (MP7), temporarily viewing x-0.5 as a single entity.

Progression of Standard within Grade 5 GT

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Write and solve equations in the form px + q = r and p(x + q) = r. Write and solve simple equations to represent the situation with unknown values. Write, solve, and graph inequalities to represent the situation with unknown values.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade 6	Grade 8
Use variables to represent numbers and write expressions to solve problems (6.EE.6) Solve real-world problems by solving equations (6.EE.7)	Solve linear equations in one variable (8.EE.7) Analyze and solve pairs of simultaneous linear equations (8.EE.8)

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Explore the idea of double distribution. Example: (2+3)(4+5). Try replacing a number with a variable. Try replacing two numbers with the same variable. What happens? What kind of equation have you created? (Double distribution is multiplication of two binomials).
You are constructing a fort in your backyard and you want to have an area of 64 square feet. If you want to have a square fort, what is the length of one side and what is the perimeter?
If you want to tile your bathroom floor and the area is 144 square feet, what would be the length of 1 side and how many 12 inch tiles would you need to create the border?
You are raising money for a class field trip. Currently, there is $75 for each student. However, it costs $200 for each student to attend. You are selling cookie dough buckets for $5 each. How many buckets would you need to sell?
If you made $50 a week mowing lawns and an extra $15 per hour of babysitting, how many hours of extra babysitting would you need to earn a total of $150 in a week?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 11 • Inequalities

Construct Equations and Inequalities to Solve Problems:

Additional Tasks

These links provide instructional ideas connected to this standard.

Lesson 6.13 - Reintroducing Inequalities (Open-Up Resources - Illustrative Math)
Lesson 6.14 - Finding Solutions to Inequalities in Context (Open-Up Resources - Illustrative Math )
Lesson 6.15 - Efficiently Solving Inequalities (Open-Up Resources - Illustrative Math)
Lesson 6.16 - Interpreting Inequalities (Open-Up Resources - Illustrative Math)
Lesson 6.17-Modeling Inequalities (Open-Up Resources - Illustrative Math)

Gotham City Taxis (Illustrative Math)
Sports Equipment Set (Illustrative Math)
Fishing Adventures 2 (Illustrative Math)
Bookstore Account (Illustrative Math)

Lesson 6.7 - Reasoning About Solving Equations Part 1 ( Illustrative Math )
Lesson 6.8 - Reasoning About Solving Equations Part 2 ( Illustrative Math )
Lesson 6.9 - Dealing with Negative Numbers ( Illustrative Math )
Lesson 6.10 - Different Options for Solving One Equation (Illustrative Math )
Lesson 6.11 - Solving Equations to Solve Problems (Illustrative Math )
Lesson 6.12 - Solving Problems About Percent Increase or Decrease (Illustrative Math)
Expressions and Equations (Engage NY, Module 3/Topic B-lessons 12,13,14,15
Growing Staircase (Inside Mathematics, Levels D and E)
Courtney's Collection (Inside Mathematics, Levels C-E)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	6-8
Hands -On Standards Common Core	7	p. 72-79
Problem-Driven Math	6-8	p.176-178
McDougal Littell Math	Course 2	p. 366-370
Teaching the Common Core Math Standards with Hands-On Activities	6-8	p.110-113
Problem-Driven Math	6-8	p.176-178

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Assessment

Learning Targets

rubric

Write and solve equations in the form px + q = r and p(x + q) = r.
Write and solve simple equations to represent the situation with unknown values.
Write, solve, and graph inequalities to represent the situation with unknown values.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

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