Cogito
Grade 4 Math · Chapter 3 · Lesson 2
Remainders
What is left when it will not share evenly.
10 problems · about 14 minutes · 4.NBT.B.6
What this lesson teaches
The child finds a quotient with a remainder and checks it by multiplying.
- A remainder is what is left after sharing evenly.
- It is always smaller than the number you divided by.
- Check by multiplying and adding the remainder back.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Dividing by One Digit: 738 ÷ 6 = ?
Answer 123
Why 738 ÷ 6 = 123.
Review — Estimating Products: Estimate 38 × 21 to the nearest ten.
Answer 800
Why 40 × 20 = 800.
Warm Up
Straightforward practice. Get the method working first.
4 problems45 ÷ 7. What is the remainder?
Answer 3
Why 45 ÷ 7 = 6 remainder 3.
How big can a remainder be when dividing by 5?
Answer 4
Why The largest possible remainder is one less than the divisor.
29 ÷ 6. What is the remainder?
Answer 5
Why 4 × 6 = 24.
38 ÷ 7. What is the quotient?
Answer 5
Why 5 × 7 = 35.
Build It Up
The same ideas with more to keep track of.
2 problems38 ÷ 7. What is the remainder?
Answer 3
Why 38 − 35.
Can the remainder be 7 when dividing by 7?
Answer No. You could share one more.
Why It must be smaller than the divisor.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Sweets: 23 sweets shared among 4 children. How many does each get?
Answer 5 each
Why 5 each, with 3 left over.
The Leftover: 23 sweets shared among 4 children. How many are left over?
Answer 3 left over
Why The remainder is 3.