8.5.A
The Standard
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show the same constant-rate relationship in a table, on a coordinate graph, and with an equation. They find the unit rate and use it as the multiplier connecting x to y.
What Mastery Looks Like
- Students find the same y divided by x value for every nonzero pair. They write an equation such as y = 3x, graph a line through the origin, and explain what 3 means.
Common Misconceptions
- Students may treat any straight line as proportional, even when it does not pass through the origin. They may reverse x and y when finding the unit rate or add an unnecessary constant term.
How to Assess It
- Give the points (0, 0), (2, 6), and (5, 15). Ask students to complete a table, graph the points, write the equation, and identify the unit rate.
Lesson moves
Ways to Teach It
Use linking cubes to build groups where each x cube matches three y cubes, then record the pairs in a table and graph them.
Ask students to explain in writing how a graph shows whether a relationship is proportional and how its steepness connects to unit rate.
Give groups card sets with tables, graphs, equations, and unit rates, then have them race to make matching sets.
Use a price of $2.50 per pound to create a produce cost table, graph the costs, and write the matching equation.
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.B
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
- 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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