8.5.E
The Standard
solve problems involving direct variation
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students recognize when two quantities have a constant ratio. They find the constant, write an equation in the form y = kx, and calculate missing values.
What Mastery Looks Like
- Students find the constant of variation from a table, graph, equation, or situation. They write y = kx and use it to find an unknown value with correct units.
Common Misconceptions
- Students may use y = mx + b with a nonzero starting value. They may divide in the wrong order when finding k or assume any increasing relationship is proportional.
How to Assess It
- Give the prompt: “A machine fills 18 bottles in 3 minutes at a constant rate. Write an equation and find how many bottles it fills in 8 minutes.”
Lesson moves
Ways to Teach It
Measure water added to identical cups, record total volume after each scoop, and write an equation connecting scoops and volume.
Ask students to explain why y = 4x shows direct variation but y = 4x + 2 does not.
Play a card match game pairing direct variation tables, graphs, equations, and situation cards with the same constant.
Compare grocery prices by using unit rates to predict the cost of different amounts of the same item.
Keep exploring
Related Standards
- 7.11.A
model and solve one-variable, two-step equations and inequalities
- 6.9.B
represent solutions for one-variable, one-step equations and inequalities on number lines
- 7.10.C
write a corresponding real-world problem given a one-variable, two-step equation or inequality
- 7.10.B
represent solutions for one-variable, two-step equations and inequalities on number lines
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