Cogito
Grade 6 Math · Chapter 4 · Lesson 6
Distance on the Coordinate Plane
Counting the gap between two points.
10 problems · about 18 minutes · 6.NS.C.8, 6.G.A.3
What this lesson teaches
The child finds the distance between two points sharing a coordinate, and draws polygons on the plane.
- Two points sharing a coordinate lie on a straight line, so the gap can be counted.
- On the same side of zero, subtract. Across zero, add the two distances.
- These gaps are the side lengths of a polygon drawn on the plane.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Ordering Negative Numbers: Which is smaller, −7 or −4?
Answer -7
Why −7.
Review — Opposites: What is −(−8)?
Answer 8
Why 8.
Review — All Four Quadrants: How far is it from (−3, 4) to (6, 4)?
Answer 9
Why 9 units.
Warm Up
Straightforward practice. Get the method working first.
3 problemsDistance from (−3, 2) to (5, 2)?
Answer 8
Why 8 units.
Distance from (2, 5) to (2, 9)?
Answer 4
Why The x values match, so count in y.
Distance from (−5, 0) to (−1, 0)?
Answer 4
Why Both are left of zero.
Build It Up
The same ideas with more to keep track of.
2 problemsDistance from (0, −3) to (0, 6)?
Answer 9
Why 3 up to zero, then 6 more.
Distance from (−6, 1) to (−2, 1)?
Answer 4
Why Subtract the smaller from the larger.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Horizontal Gap: How far is it from (1, 4) to (9, 4)?
Answer 8
Why 8 units.
Across Zero: How far is it from (−4, 2) to (3, 2)?
Answer 7
Why 7 units.