Cogito
Grade 7 Math · Chapter 2 · Lesson 1
The Constant of Proportionality
The number you have been multiplying by all along.
10 problems · about 18 minutes · 7.RP.A.2
What this lesson teaches
The child identifies the constant of proportionality from a table, a graph, and an equation.
- A proportional relationship has one fixed multiplier.
- It is written y = kx.
- Divide output by input to find k, and every pair must agree.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — 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.
Review — Reading a Scale: Scale 1 cm to 30 km. Real distance for 5 cm, in km?
Answer 150
Why 150 km.
Warm Up
Straightforward practice. Get the method working first.
4 problems5 pairs with 35. What is k?
Answer 7
Why 7.
How do you test whether a table is proportional?
Answer Divide each output by its input and see if they agree.
Why Every row must give the same quotient.
3 pairs with 12. What is k?
Answer 4
Why 12 ÷ 3.
6 pairs with 42. What is k?
Answer 7
Why 42 ÷ 6.
Build It Up
The same ideas with more to keep track of.
2 problemsy = 8x. What is y when x = 5?
Answer 40
Why 8 × 5.
y = 6x and y = 54. What is x?
Answer 9
Why 54 ÷ 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Petrol: 4 litres cost 6 pounds. What is the cost of 1 litre, in pounds?
Answer 1.5
Why k = 1.5.
The Rule: y = 7x. What is y when x = 9?
Answer 63
Why 63.