Students discover that when two quantities always change by the same multiple, they are proportional — described by y = kx, where k is the constant of proportionality — and that their graph is always a straight line through the origin.
Students will be able to…
If 1 ticket costs $3, then 5 tickets cost $15 and 10 cost $30 — the cost per ticket never changes. What number is doing all the work?
Project this and change the constant k. Watch the table and graph — every y is k times x, and the line always passes through (0, 0).
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Tap any phase to open the teacher moves and student actions.
$3 per ticket — what stays the same for any number of tickets?
Teacher models.
Class drives the Proportion Machine.
Students analyze relationships.
One relationship.
Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.
Recognize and represent proportional relationships between quantities.
Identify the constant of proportionality (unit rate) in tables, graphs, and equations.
Represent proportional relationships by equations (y = kx).
Model with mathematics using proportional relationships.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students test several tables to decide which are proportional (constant ratio, passes through origin) and which are not. A printable sorting sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.