Cogito
Grade 6 Math · Chapter 6 · Lesson 3
Inequalities and Two Variables
When many numbers work, not just one.
10 problems · about 18 minutes · 6.EE.B.8, 6.EE.C.9
What this lesson teaches
The child writes and graphs simple inequalities and describes the relationship between two variables.
- An inequality is true for many values, not one.
- An open circle marks a value that is not included.
- Two linked variables have one that depends on the other.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Solving One-Step Equations: Solve 8n = 96.
Answer 12
Why n = 12.
Review — What Solving Means: What value of n makes n + 8 = 15 true?
Answer 7
Why 7.
Warm Up
Straightforward practice. Get the method working first.
4 problemsc = 6w. What is c when w = 8?
Answer 48
Why 48.
How many numbers satisfy x > 5?
Answer Infinitely many.
Why An inequality has infinitely many solutions.
c = 5w. What is c when w = 6?
Answer 30
Why 5 × 6.
Is 8 a solution of x > 8?
Answer No.
Why Strictly greater.
Build It Up
The same ideas with more to keep track of.
2 problemsIs 9 a solution of x > 8?
Answer Yes.
Why 9 is bigger than 8.
c = 4w. What is c when w = 9?
Answer 36
Why 4 × 9.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Rule: c = 3w. What is c when w = 7?
Answer 21
Why 21.
The Ride: You must be over 12 to ride. Is 12 allowed?
Answer No. "Over 12" does not include 12.
Why x > 12 excludes 12 itself.