enVision Mathematics Topics 2-3
7th Grade; September – November (7 weeks); 1st/2nd Quarter
Embedded Files
Topic Title(s):
Analyze and Use Proportional Relationships (Topic 2)
Analyze and Solve Percent Problems (Topic 3)
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
1. Number and Quantity
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.RP.A. Ratios & Proportional Relationships: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. (CCSS: 7.RP.A.1)
Identify and represent proportional relationships between quantities. (CCSS: 7.RP.A.2)
Determine whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (CCSS: 7.RP.A.2.a)
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (CCSS: 7.RP.A.2.b)
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pm. (CCSS: 7.RP.A.2.c)
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. (CCSS: 7.RP.A.2.d)
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (CCSS: 7.RP.A.3)
Recognize when proportional relationships occur and apply these relationships to personal experiences. (Entrepreneurial Skills: Inquiry/Analysis)
Recognize, identify, and solve problems that involve proportional relationships to make predictions and describe associations among variables. (MP1)
Reason quantitatively with rates and their units in proportional relationships. (MP2)
Use repeated reasoning to test for equivalent ratios, such as reasoning that walking 1/2 mile in 1/4 hour is equivalent to walking 1 mile in 1/2 hour and equivalent to walking 2 miles in 1 hour, the unit rate. (MP8)
Inquiry Questions
How are proportional relationships related to unit rates?
How can proportional relationships be expressed using tables, equations, and graphs?
What are properties of all proportional relationships when graphed on the coordinate plane?
Coherence Connections
This expectation represents major work of the grade.
In Grade 6, students understand ratio concepts and use ratio reasoning to solve problems.
This expectation connects with several others in Grade 7: (a) solving real-life and mathematical problems using numerical and algebraic expressions and equations, (b) investigating chance processes and developing, using, and evaluating probability models, and (c) drawing, constructing, and describing geometrical figures and describing the relationships between them.
In Grade 8, students (a) understand the connections between proportional relationships, lines, and linear equations, (b) define, evaluate, and compare functions, and (c) use functions to model relationships between quantities. In high school, students use proportional relationships to define trigonometric ratios, solve problems involving right triangles, and find arc lengths and areas of sectors of circles.
Academic Vocabulary & Language Expectations:
Proportional relationship, proportion, constant of proportionality, percent equation, percent change, percent error, markup, markdown, percent markup, percent markdown, interest rate, principal, simple interest
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topics 2-3
Let's Investigate! Tasks
Let's Investigate! An Even Bigger Puzzle (TE) (relates to Lesson 2-3)
Let's Investigate! Tracking Proportionality (TE) (relates to Lesson 2-5)
Let's Investigate! Tip-Top Tippers (TE) (relates to Lesson 3-1)
Let's Investigate! Solving for Screen Time (TE) (relates to Lesson 3-4)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 2: Identify Proportional Relationships, Model Proportional Relationships, Solve Multi-Step Ratio Problems
Tier 1 Intervention Topic 3: Multi-Step Percent Problems, Find Percent Change
Coherence Map/Concept Progressions: 7.RP.A.2.a, 7.RP.A.2.b, 7.RP.A.2.c, 7.RP.A.2.d, 7.RP.A.3
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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