Maryland Math 7.AT.A.3
The Standard
Represent proportional relationships between quantities. Represent proportional relationships using equations. Explain what a point (x, y) on the graph of a proportional relationship represents in terms of the context, with special attention to the points (0, 0) and (1, r), where r is the unit rate.
Maryland College and Career Ready Standards for Mathematics (2025) · REPRESENT AND REASON ABOUT PROPORTIONAL RELATIONSHIPS TO SOLVE PROBLEMS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the amount for one unit and use it to write an equation, such as cost = 3 × pounds. They graph the relationship and explain what points mean in the problem.
What Mastery Looks Like
- A student can move between a table, equation, and graph without changing the rate. They explain why the graph includes (0, 0) and why the point where x is 1 shows the unit rate.
Common Misconceptions
- Students may switch the quantities on the graph axes or use the total for several units as the unit rate. Some draw a graph through (0, 0) even when the situation has a starting fee.
How to Assess It
- A faucet fills 4 liters per minute. Ask students to write an equation, plot (0, 0), (1, 4), and (3, 12), and explain what each point means.
Lesson moves
Ways to Teach It
Build trains with 1, 2, and 3 identical 4-cube rods, then record and graph the total cubes in each train.
Ask students to write why a $4-per-ticket graph includes (0, 0) and what (1, 4) means.
Give pairs cards showing y = 2x and y = 5x, plus matching tables and labeled graphs, to sort into sets.
Show a grocery sign reading $3 per pound, then have students write a cost equation and explain the point (1, 3).
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