8.5.F
The Standard
distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether a relationship has a constant ratio of y to x. They use tables, graphs, and equations, then justify each decision using the origin, unit rate, or starting value.
What Mastery Looks Like
- A student correctly classifies a relationship from any of the three representations. They point to a constant y/x ratio, a line through (0,0), or a nonzero starting value as evidence.
Common Misconceptions
- Students often call every straight line proportional, even when it does not pass through the origin. They may compare constant differences instead of y/x, or mistake the slope for the starting value.
How to Assess It
- Exit ticket: Classify the table x: 0, 1, 2 and y: 3, 5, 7, then classify y = 4x. Give one piece of evidence for each answer.
Lesson moves
Ways to Teach It
Students sort table, graph, and equation cards into proportional and nonproportional groups, then match cards showing the same relationship.
Ask, "Is every linear relationship proportional?" Students use one graph and one equation to defend their answer.
Display a representation, then teams hold up P or N cards and earn a point by stating correct evidence.
Compare a taxi fare with a base fee to pay earned at a fixed hourly rate, then represent and classify each relationship.
Keep exploring
Related Standards
- 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.B
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
- 8.5.A
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
- 8.5.I
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
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