8.4.B
The Standard
graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students plot ordered pairs from a proportional situation and draw the line through them. They find the slope and explain it as the amount gained per one unit.
What Mastery Looks Like
- Students accurately plot data pairs and draw a straight line through the origin. They calculate vertical change divided by horizontal change and explain the result using the quantities and units.
Common Misconceptions
- Students may divide the horizontal change by the vertical change, reversing the slope. They may ignore graph scales or choose points that are not on the line. Some think a proportional graph can have a nonzero starting value.
How to Assess It
- Give students a graph of a cyclist traveling 18 miles in 2 hours. Ask them to find the slope, label its units, and explain what it means.
Lesson moves
Ways to Teach It
Walk at a steady pace, record distance each second, graph the data, and calculate the slope in feet per second.
Show two lines through the origin and ask, “Which relationship has the greater unit rate, and how does the graph prove it?”
Play a matching game with cards showing tables, equations, graphs, and unit rates for the same proportional relationships.
Graph the cost of identical movie tickets, then explain how the slope represents the price of one ticket.
Keep exploring
Related Standards
- 8.4
The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope
- 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
- 8.4.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
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.