Cogito
Grade 6 Math · Chapter 6 · Lesson 6
Two Variables That Move Together
One depends on the other.
10 problems · about 19 minutes · 6.EE.C.9
What this lesson teaches
The child identifies dependent and independent variables and relates a table, an equation, and a graph.
- The independent variable is the one you choose; the dependent one follows.
- A rule can be written as an equation, a table, or a graph.
- All three say the same thing, so any one can be built from another.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Inequalities on a Number Line: Smallest whole number satisfying x > 11?
Answer 12
Why 12.
Review — Writing Equations from Stories: 7n = 63. What is n?
Answer 9
Why 9.
Review — Inequalities and Two Variables: c = 6w. What is c when w = 8?
Answer 48
Why 48.
Warm Up
Straightforward practice. Get the method working first.
3 problemsIf y = 5x, what is y when x is 8?
Answer 40
Why 40.
If m = 3h, what is m when h is 5?
Answer 15
Why 3 × 5.
If m = 3h, what is h when m is 21?
Answer 7
Why 21 ÷ 3.
Build It Up
The same ideas with more to keep track of.
2 problemsIn "money earned depends on hours worked", which is independent?
Answer Hours worked.
Why Which one do you choose freely?
If y = 4x, what is y when x is 6?
Answer 24
Why 4 × 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Taxi: At £2 a mile, what is the fare for 7 miles, in pounds?
Answer 14
Why £14.
Working Backwards: At £2 a mile, a fare of £18 covers how many miles?
Answer 9
Why 9 miles.