Cogito
Grade 5 Math · Chapter 5 · Lesson 3
Mixed Numbers with Regrouping
Borrow a whole one and cut it up.
10 problems · about 16 minutes · 5.NF.A.1
What this lesson teaches
The child adds and subtracts mixed numbers, including regrouping a whole into parts.
- Add or subtract the wholes and the fractions separately.
- A fraction over 1 holds another whole one.
- Borrow a whole when the fraction is too small.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Adding Unlike Fractions: 2/3 + 1/4, in twelfths. What is the top number?
Answer 11
Why 11/12.
Review — Finding a Common Denominator: 2/3 written in fifteenths. What is the top number?
Answer 10
Why 10/15.
Warm Up
Straightforward practice. Get the method working first.
4 problems4 1/3 − 2 2/3. How many whole ones in the answer?
Answer 1
Why 1 2/3.
What do you do when the fraction you are taking away is too big?
Answer Borrow a whole one and cut it up.
Why A whole becomes that many parts, and the subtraction works.
1 1/2 + 2 1/2. What is the answer?
Answer 4
Why The halves make a whole.
3 1/5 − 1 3/5. How many whole ones in the answer?
Answer 1
Why Borrow a whole first.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many fifths are in one whole?
Answer 5
Why 5/5.
2 3/4 + 1 1/4. What is the answer?
Answer 4
Why The quarters make a whole.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Two Planks: 2 3/4 metres plus 1 3/4 metres. How many whole metres in the answer?
Answer 4 whole metres
Why 4 1/2 metres.
The Ribbon: 5 1/4 metres minus 2 3/4 metres. How many whole metres in the answer?
Answer 2 whole metres
Why 2 1/2 metres.