UNIT 11: exploring ratios and proportional relationships
IN THIS UNIT, STUDENTS WILL BUILD UPON THEIR UNDERSTANDING IN GRADE 6:
- Rate and unit concepts
- Use graphs, tables, equations, and diagrams to recognize, represent, explain, and solve proportional relationships.
- Develop a deep understanding of the characteristics of a proportional relationship, including the exploration of similarity informally when learning about scale drawings of geometric figures, and explaining why the slope of a non-vertical line is constant.
- Demonstrate a conceptual understanding of the relationship between the slope of a line and unit rate.
- Rate and unit concepts
- Use graphs, tables, equations, and diagrams to recognize, represent, explain, and solve proportional relationships.
- Develop a deep understanding of the characteristics of a proportional relationship, including the exploration of similarity informally when learning about scale drawings of geometric figures, and explaining why the slope of a non-vertical line is constant.
- Demonstrate a conceptual understanding of the relationship between the slope of a line and unit rate.
LEARNING OBJECTIVES:
7.PAR.4 Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
7.PAR.4.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units presented in realistic problems.
7.PAR.4.2. Determine the unit rate (constant of proportionality) in tables, graphs (1, 𝑟), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.
7.PAR.4.3. Determine whether two quantities presented in authentic problems are in a proportional relationship.
7.PAR.4.4. Identify, represent, and use proportional relationships.
7.PAR.4.5. Use context to 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.
7.PAR.4 Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
7.PAR.4.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units presented in realistic problems.
7.PAR.4.2. Determine the unit rate (constant of proportionality) in tables, graphs (1, 𝑟), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.
7.PAR.4.3. Determine whether two quantities presented in authentic problems are in a proportional relationship.
7.PAR.4.4. Identify, represent, and use proportional relationships.
7.PAR.4.5. Use context to 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.
LEARNING TARGETS (I Can Statements):
- I can compute unit rates of ratios, including lengths, area, and different units.
- I can solve problems using unit rates in real-world situations.
- I can compute unit rates involving complex fractions.
- I can determine the unit rate in tables, graphs, equations, and diagrams and apply it to solve real-world problems.
- I can discover the unit rate within a verbal description.
- I can recognize what (1, r) on a graph represents, where r is the unit rate.
- I can explain what the points on a graph of a proportional relationship mean in terms of a specific situation.
- I can determine whether two quantities are proportional in given real-world contexts.
- I can identify proportional relationships.
- I can represent proportional relationships.
- I can use proportional relationships.
- I can rewrite situations from words, graphs, tables, and verbal descriptions.
- I can explain what the points on a graph of a proportional relationship mean in terms of a specific situation.
- I can contextually relate a point on the graph to the origin point and unit rate and explain its meaning.
- I can compute unit rates of ratios, including lengths, area, and different units.
- I can solve problems using unit rates in real-world situations.
- I can compute unit rates involving complex fractions.
- I can determine the unit rate in tables, graphs, equations, and diagrams and apply it to solve real-world problems.
- I can discover the unit rate within a verbal description.
- I can recognize what (1, r) on a graph represents, where r is the unit rate.
- I can explain what the points on a graph of a proportional relationship mean in terms of a specific situation.
- I can determine whether two quantities are proportional in given real-world contexts.
- I can identify proportional relationships.
- I can represent proportional relationships.
- I can use proportional relationships.
- I can rewrite situations from words, graphs, tables, and verbal descriptions.
- I can explain what the points on a graph of a proportional relationship mean in terms of a specific situation.
- I can contextually relate a point on the graph to the origin point and unit rate and explain its meaning.
TEXTBOOK CONNECTIONS:
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 1 – Proportional Relationships
Analyze multiple representations of proportional relationships (tables, graphs, and equations).
Lesson 1-1 Unit Rates Involving Ratios of Fractions
Students will find unit rates when one or both quantities are fractions.
Lesson 1-2 Understand Proportional Relationships
Students will use models and ratio reasoning to understand how a proportional relationship can exist between quantities.
Lesson 1-3 Tables of Proportional Relationships
Students will analyze the relationship between two quantities represented in tables to determine proportionality.
Lesson 1-4 Graphs of Proportional Relationships
Students will analyze the relationship between two quantities graphed on a coordinate plane to determine proportionality.
Lesson 1-5 Equations of Proportional Relationships
Students will write equations to represent proportional relationships.
Lesson 1-6 Solve Problems Involving Proportional Relationships
Students will solve problems involving proportional relationships.
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 1 – Proportional Relationships
Analyze multiple representations of proportional relationships (tables, graphs, and equations).
Lesson 1-1 Unit Rates Involving Ratios of Fractions
Students will find unit rates when one or both quantities are fractions.
Lesson 1-2 Understand Proportional Relationships
Students will use models and ratio reasoning to understand how a proportional relationship can exist between quantities.
Lesson 1-3 Tables of Proportional Relationships
Students will analyze the relationship between two quantities represented in tables to determine proportionality.
Lesson 1-4 Graphs of Proportional Relationships
Students will analyze the relationship between two quantities graphed on a coordinate plane to determine proportionality.
Lesson 1-5 Equations of Proportional Relationships
Students will write equations to represent proportional relationships.
Lesson 1-6 Solve Problems Involving Proportional Relationships
Students will solve problems involving proportional relationships.
IXL SKILLS: