Cogito
Grade 7 Math · Chapter 5 · Lesson 2
Rational Numbers in Problems
All four operations, with signs.
10 problems · about 18 minutes · 7.NS.A.3, 7.EE.B.3
What this lesson teaches
The child solves multistep problems with the four operations on rational numbers.
- The order of operations still applies with signs.
- A rational number can be a fraction, a decimal, or an integer.
- Predict the sign before calculating.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
1 problemReview — Why a Negative Times a Negative Is Positive: (−9) × (−3) = ?
Answer 27
Why 27.
Warm Up
Straightforward practice. Get the method working first.
4 problems−4 + 5 × (−3) = ?
Answer -19
Why −19.
What is worth doing before calculating?
Answer Decide whether the answer should be positive or negative.
Why Predicting the sign is a cheap check.
−5 + 3 × (−2) = ?
Answer -11
Why −6 first.
(−12) ÷ 4 + 5 = ?
Answer 2
Why −3 + 5.
Build It Up
The same ideas with more to keep track of.
2 problems2 × (−7) + 10 = ?
Answer -4
Why −14 + 10.
(−3) × (−4) − 5 = ?
Answer 7
Why 12 − 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsThe Dive: A diver at −12 m descends 4 m more, then rises 7. What is the depth now?
Answer -9
Why −9 m.
The Debt: Five people each owe 8 pounds. What is the total, as a negative?
Answer -40
Why −40 pounds.
The Cooling: The temperature falls 2 degrees an hour for 6 hours from 4 degrees. What is it now?
Answer -8
Why −8 degrees.