# Series Engaging Students with "Productive Struggle": Collaborative Work with Proportional Relationships

Math.Practice.MP1

Common core State Standards

• Math:  Math
• Practice:  Mathematical Practice Standards
• MP1:  Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

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Math.7.RP.A.2

Common core State Standards

• Math:  Math
• RP:  Ratios & Proportional Relationships
• A:  Analyze proportional relationships and use them to solve real-world and mathematical problems
• 2:
Recognize and represent proportional relationships between quantities.
<br />
a. Decide 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.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. 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 = pn.
<br />
d. 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.

## Collaborative Work with Proportional Relationships

Lesson Objective: Work with a partner to determine proportional relationships
Grade 7 / Math / Collaboration
Math.Practice.MP1 | Math.7.RP.A.2

## Discussion and Supporting Materials

### Thought starters

1. How would you decide which students to pair for this activity?
2. Why is it important to give the students real-world problems?
3. How does each student in the pair contribute to solving the problem?

Anastasia St. Peter. This task can be found here: http://map.mathshell.org/
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1). One can take the stronger students and pair them with students who have a difficult time with assignments. By doing this will allow the stronger students to serve as a tutor and prepare each student on the importance of working in teams. 2). Real world problems can serve as a guide and can prepare the students for assignments, quizzes and exams. 3). Students work in a team to complete assignments. Students who tend to be stronger in assignments serve as a tutor for students who tend to have a harder time with assignments.
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Are any of the lesson materials available on the web?
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### School Details

Twenhofel Middle School
Independence KY 41051
Population: 816

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