Cogito
Grade 7 Math · Chapter 2 · Lesson 2
Telling Proportional from Not
Straight through the origin, or it is not proportional.
10 problems · about 18 minutes · 7.RP.A.2
What this lesson teaches
The child decides whether a relationship is proportional from a table, graph, or equation.
- Proportional means a straight line through the origin.
- A fixed charge makes it linear but not proportional.
- Test with a table, a graph, or the equation.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — The Constant of Proportionality: 5 pairs with 35. What is k?
Answer 7
Why 7.
Review — Redrawing at a New Scale: 9 cm at 1 cm to 2 m, redrawn at 1 cm to 3 m. New length in cm?
Answer 6
Why 6 cm.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = 3x + 7. What is y when x = 6?
Answer 25
Why 25.
What must a proportional graph pass through?
Answer The origin.
Why A proportional line passes through (0, 0).
Is y = 4x proportional?
Answer Yes.
Why Nothing added.
Is y = 4x + 1 proportional?
Answer No.
Why It misses the origin.
Build It Up
The same ideas with more to keep track of.
2 problems2 pairs with 6 and 4 pairs with 12. Is it proportional?
Answer Yes, k = 3.
Why Both give 3.
y = 5x + 2. What is y when x = 4?
Answer 22
Why 20 + 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Taxi: A taxi charges 3 pounds plus 2 per mile. What is the cost of 5 miles?
Answer 13 pounds
Why 13 pounds.
The Test: Is that taxi relationship proportional?
Answer No. Zero miles still costs 3 pounds.
Why The fixed charge breaks proportionality.