Thinking Proportionally
The lessons in this module build on your experiences with ratios and proportional relationships from grade 6. You will investigate special ratios to develop and connect formulas for the circumference and area of circles. You will identify and describe proportional and non-proportional mathematical and real-world situations to understand the characteristics of proportional relationships. You will then use formal strategies to solve proportion and percent problems.
The lessons in this module build on your experiences with ratios and proportional relationships from grade 6. You will investigate special ratios to develop and connect formulas for the circumference and area of circles. You will identify and describe proportional and non-proportional mathematical and real-world situations to understand the characteristics of proportional relationships. You will then use formal strategies to solve proportion and percent problems.
Standards: Mathematics, Grade 7, Ratios and Proportional Relationships
Standards: Mathematics, Grade 7, Geometry
- MGSE7.RP.1 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.
- MGSE7.RP.2 Recognize and represent proportional relationships between quantities.
- MGSE7.RP.2a 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
- MGSE7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- MGSE7.RP.2c 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.
- MGSE7.RP.2d 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
- MGSE7.RP.2a 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
- MGSE7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.
Standards: Mathematics, Grade 7, Geometry
- MGSE7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale
- MGSE7.G.4 Given the formulas for the area and circumference of a circle, use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
- MGSE7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.