enVision Mathematics Topic 5
7th Grade; January – February (5 weeks); 3rd Quarter
Embedded Files
Topic Title(s):
Solve Problems Using Equations and Inequalities
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
Standard(s):
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
7.EE.B. Expressions & Equations: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. (CCSS: 7.EE.B.3) (This is applied throughout Topics 1-5)
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. (CCSS: 7.EE.B.4)
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? (CCSS: 7.EE.B.4.a)
Solve word problems leading to inequalities of the form px ± q > r, px ± q > r, 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. (CCSS: 7.EE.B.4.b)
Adapt to different forms of equations and inequalities and reach solutions that make sense in context. (Personal Skills: Adaptability/Flexibility)
Use mental computation and estimation to check the reasonableness of their solutions. Make connections between the sequence of operations used in an algebraic approach and an arithmetic approach, understanding how simply reasoning about the numbers connects to writing and solving a corresponding algebraic equation. (MP1)
Represent a situation symbolically and solve, attending to the meaning of quantities and variables. (MP2)
Select an appropriate solution approach (calculator, mental math, drawing a diagram, etc.) based on the specific values and/or desired result of a problem. (MP5)
Use estimation, mental calculations, and understanding of real-world contexts to assess the reasonableness of answers to real-life and mathematical problems. (MP6)
Inquiry Questions
Do the properties of operations apply to variables the same way they do to numbers? Why?
Why are there different ways to solve equations?
In what scenarios might estimation be better than an exact answer?
How can the reasonableness of a solution be determined?
Coherence Connections
This expectation represents major work of the grade.
In Grade 6, students reason about and solve one-step, one-variable equations and inequalities.
In Grade 7, this expectation connects with analyzing proportional relationships, using them to solve real-world and mathematical problems, and applying and extending previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
In Grade 8, students work with radicals and integer exponents, analyze and solve linear equations and pairs of simultaneous linear equations, and describe functional relationships.
Academic Vocabulary & Language Expectations:
Isolate the variable
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 5 (skip Lesson 5-7)
Let's Investigate! Tasks
Let's Investigate! The Real Deal (TE) (relates to Lesson 5-1)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Solve Multi-Step Problems, Write Equations to Solve Problems, Model and Solve One-Variable Equations, Solve and Graph Linear Inequalities
Coherence Map/Concept Progressions: 7.EE.B.3, 7.EE.B.4.a, 7.EE.B.4.b
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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