Mathematics 2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.
a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.
b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.
c. Explain in context the meaning of a point (x,y ) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r ) where r is the unit rate.
Unpacked Content
Evidence Of Student Attainment:
Students:
Decide whether a relationship between two quantities is proportional. Recognize that not all relationships are proportional. Use equivalent ratios in a table or a coordinate graph to verify a proportional relationship.
Identify the constant of proportionality when a proportional relationship exists between two quantities. Use a variety of models (tables, graphs, equations, diagrams and verbal descriptions) to demonstrate the constant of proportionality. Explain the meaning of a point (x, y) in the context of a real-world problem. Example, if a boy charges $6 per hour to mow lawns, this relationship can be graphed on the coordinate plane. The point (1,6) means that after 1 hour of working the boy makes $6, which shows the unit rate of $6 per hour. Teacher Vocabulary:
Equivalent ratios proportional Coordinate plane Ratio table Unit rate Constant of proportionality Equation ordered pair Knowledge:
Students know:
(2a) how to explain whether a relationship is proportional.
(2b) that the constant of proportionality is the same as a unit rate. Students know: where the constant of proportionality can be found in a table, graph, equation or diagram.
(2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1. Skills:
Students are able to:
(2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane. (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
(2c) model a proportional relationship using coordinate graphing. Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality. Understanding:
Students understand that:
(2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional. (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context.
(2c) The context of a problem can help them interpret a point on a graph of a proportional relationship. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.2.1: Define proportions and proportional relationships.
M.7.2.2: Demonstrate how to write ratios as a fraction.
M.7.2.3: Define equivalent ratios and origin.
M.7.2.4: Locate the origin on a coordinate plane.
M.7.2.5 Show how to graph on Cartesian plane.
M.7.2.6: Determine if the graph is a straight line through the origin.
M.7.2.7: Use a table or graph to determine whether two quantities are proportional.
M.7.2.8: Define a constant and equations.
M.7.2.9: Create a table from a verbal description, diagram, or a graph.
M.7.2.10: Identify numeric patterns and finding the rule for that pattern.
M.7.2.11: Recall how to find unit rate.
M.7.2.12: Recall how to write equations to represent a proportional relationship.
M.7.2.13: Discuss the use of variables.
M.7.2.14: Define ordered pairs.
M.7.2.15: Show how to plot points on a Cartesian plane.
M.7.2.16: Locate the origin on the coordinate plane.
Prior Knowledge Skills:
Recall basic addition, subtraction, multiplication, and division facts.
Define ordered pair of numbers.
Define x-axis, y-axis, and zero on a coordinate.
Specify locations on the coordinate system.
Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
Label the horizontal axis (x).
Label the vertical axis (y).
Identify the x- and y- values in ordered pairs.
Model writing ordered pairs.
Define quantity, fraction, and ratio.
Reinterpret a fraction as a ratio. Write a ratio as a fraction.
Create a ratio or proportion from a given word problem, diagram, table, or equation.
Alabama Alternate Achievement Standards
AAS Standard:
