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Description
- Overview:
- This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.
- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP), Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013
- License:
-
Creative Commons Attribution-NonCommercial-NoDerivs 3.0
- Media Format:
- Downloadable docs, Text/HTML
Comments
Standards
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Recognize and represent proportional relationships between quantities.
Degree of Alignment: 3 Superior (1 user)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: 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.
Degree of Alignment: 3 Superior (2 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: 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.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: 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.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: 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.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: 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.
Degree of Alignment: Not Rated (0 users)
Cluster: Mathematical practices
Standard: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x –1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x^2 + x + 1), and (x – 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Degree of Alignment: Not Rated (0 users)
Cluster: Mathematical practices
Standard: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Recognize and represent proportional relationships between quantities.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x -1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x^2 + x + 1), and (x - 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Recognize and represent proportional relationships between quantities.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Solve multi-step real world and mathematical problems involving ratios and percentages.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Compute unit rates, including those involving complex fractions, with like or different units.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Decide whether two quantities in a table or graph are in a proportional relationship.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Represent proportional relationships with equations.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: 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.
Degree of Alignment: Not Rated (0 users)
Evaluations
Achieve OER
Average Score (3 Points Possible)| Degree of Alignment | 3 (2 users) |
| Quality of Explanation of the Subject Matter | 3 (2 users) |
| Utility of Materials Designed to Support Teaching | 3 (2 users) |
| Quality of Assessments | 3 (1 user) |
| Quality of Technological Interactivity | 3 (1 user) |
| Quality of Instructional and Practice Exercises | 3 (1 user) |
| Opportunities for Deeper Learning | 3 (1 user) |
Tags (8)
- Mathematics
- Numbers and Operations
- CCSS
- Common Core Math
- Common Core PD
- Division
- Multiplication
- Rations and Proportions
This is a lesson where students can investigate proportions and scale drawings. It is complete with student handouts, assessments, and lesson plans. It also includes a recommendation page for common errors. This addresses CCSS 7.RP.1 and 7.RP.2