7.4.C
The Standard
determine the constant of proportionality (k = y/x) within mathematical and real-world problems
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the multiplicative rate connecting x and y by dividing y by x. They work from tables, graphs, equations, and real situations, then explain what the value means.
What Mastery Looks Like
- Students correctly calculate the same k from several ordered pairs in a table, graph, equation, or word problem. They label the value with units and explain it as an amount per one unit of x.
Common Misconceptions
- Students may divide x by y instead of y by x. They may use any difference between values, or assume every table and graph shows a proportional relationship.
How to Assess It
- Give students the points (3, 12) and (5, 20). Ask them to find k, show the calculation, and explain what k means.
Lesson moves
Ways to Teach It
Use linking cubes to build several red-to-blue pairs, record each pair as x and y, then calculate y divided by x.
Ask students to explain why y divided by x stays equal in a proportional table while y minus x may change.
Give groups cards showing tables, graphs, equations, and k values, then have them match representations with the same proportionality constant.
Compare grocery price labels by calculating cost per ounce, then decide which package offers the lower unit price.
Keep exploring
Related Standards
- 8.5.F
distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0
- 6.6.C
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
- 8.5.A
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
- 8.4.C
use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems
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