Cogito
Grade 7 Math · Chapter 4 · Lesson 2
Subtraction as Distance
How far, and in which direction.
10 problems · about 18 minutes · 7.NS.A.1
What this lesson teaches
The child subtracts rational numbers and understands subtraction as distance and direction on a number line.
- Subtraction measures the gap from the second number to the first.
- Subtracting a negative is the same as adding its opposite.
- The line gives a way to check, which a sign rule does not.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Adding Signed Numbers: −9 + 4 = ?
Answer -5
Why −5.
Review — Finding the Original Price: £64 after 20% off. Original in pounds?
Answer 80
Why £80.
Warm Up
Straightforward practice. Get the method working first.
4 problems3 − (−8) = ?
Answer 11
Why 11.
What does a − b measure?
Answer The gap from b to a, with a direction.
Why Subtraction measures a signed gap.
6 − (−2) = ?
Answer 8
Why From −2 to 6.
−4 − 3 = ?
Answer -7
Why From 3 to −4.
Build It Up
The same ideas with more to keep track of.
2 problems−1 − (−6) = ?
Answer 5
Why From −6 to −1.
2 − 9 = ?
Answer -7
Why From 9 to 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Temperatures: From −5 degrees to 8 degrees. How many degrees is the rise?
Answer 13
Why 13 degrees.
The Debt: A balance of −30 has 20 taken away. What is the new balance?
Answer -50
Why −50.