Dividing with Unit Fractions
A 50-minute Grade 5 lesson on dividing a whole number by a unit fraction and the reverse, where the answer to 'how many halves in 4' surprises everyone the first time.
Dividing with Unit Fractions is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.NF.B.7 — divide with fractions. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Grade 5
- Length:
- 50 minutes
- Standard:
- 5.NF.B.7
Grade 5 · Number & Operations — Fractions
5.NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Objective
Students will be able to divide a unit fraction by a whole number and a whole number by a unit fraction, and interpret both.
Students are successful when they can
- Finds how many thirds are in 5.
- Finds a quarter shared between 3.
- Says which situation each division describes.
What you need
- Fraction strips and circles
- Number lines
- Word problem cards of both types
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — how many fit?
6 min- Ask how many halves are in one whole, then in two, then in four.
- Two, four, eight. The answers get bigger, and that is worth noticing before it is explained.
Teach — two directions, two stories
15 min- Write 4 ÷ 1/2 and read it as 'how many halves fit in four'.
- Lay half-strips along four wholes: eight. Write 4 ÷ 1/2 = 8.
- Ask why the answer grew. You are counting small pieces, and small pieces are numerous.
- Now 1/2 ÷ 4, read as 'a half shared between four'. Fold a half-strip into four: each piece is an eighth.
- Write 1/2 ÷ 4 = 1/8. This time the answer got smaller, because you are cutting something small into pieces.
- Put both on the board and say the distinction: one asks how many fit, the other asks how big each share is.
“Dividing by a fraction asks how many of them fit, and the answer is bigger. Dividing a fraction by a whole number asks how big each share is, and the answer is smaller.”
Guided practice — model both ways
14 min- Pairs model each division with strips or a number line before writing anything.
- They sort word problem cards by which type they are before solving.
- Every answer is stated as a sentence: eight half-cups, or one eighth of a pizza each.
Independent practice
12 min- Students complete a dividing with fractions page.
- Answers that shrink where they should grow are the diagnostic and mean the two situations are still one.
Close
3 min- Ask how many quarter-hours are in three hours.
- Twelve, and the fact that dividing gave a bigger number is the thing to leave sitting.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Says 4 ÷ 1/2 is 2.
Why: Dividing has always made numbers smaller, so halving is assumed. The expression has been read as 'half of four'.
Fix: Lay half-strips along four wholes and count them. Eight is unarguable once it is on the desk.
Confuses 1/2 ÷ 4 with 4 ÷ 1/2 and gives 8 for both.
Why: The two numbers and the operation are the same, and the order has not yet been given meaning.
Fix: Read each one as a sentence before modelling it. 'How many halves in four' and 'a half shared between four' are obviously different questions.
Applies the invert-and-multiply rule without any sense of the answer's size.
Why: A procedure has been learned that works, so no model is needed until the procedure is misremembered.
Fix: Predict whether the answer will be larger or smaller before calculating. The prediction is the check the rule does not carry.
If they are not there yet
- Work with halves and quarters and small whole numbers, modelling every calculation with strips.
- Keep the two types in separate sessions before mixing them.
If they finish early
- Solve a word problem where the division type has to be identified from the context.
- Divide a non-unit fraction by a whole number and see whether the reasoning still holds.
- Explain why dividing by a number less than one gives a larger answer.
Exit ticket
How many one-third cups are in 2 cups? Then: 1/3 of a cake shared between 2 people — how much each?
What to look for: 6 and 1/6. The same answer to both means the two situations have not separated; an answer of 2/3 to the first means the division was read as a multiplication.
Printable practice for 5.NF.B.7
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Divide a Unit Fraction by a Whole NumberWork out each answer.
- Divide a Whole Number by a Unit FractionWork out each answer.
Questions about Dividing with Unit Fractions
How long does the Dividing with Unit Fractions lesson take?
50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Dividing with Unit Fractions teach?
CCSS.MATH.CONTENT.5.NF.B.7 — 5.NF.B.7, Number & Operations — Fractions for Grade 5: “Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.” In plain terms, divide with fractions.
What do I need to teach this lesson?
Fraction strips and circles, number lines, word problem cards of both types and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: says 4 ÷ 1/2 is 2; confuses 1/2 ÷ 4 with 4 ÷ 1/2 and gives 8 for both and applies the invert-and-multiply rule without any sense of the answer's size. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “How many one-third cups are in 2 cups? Then: 1/3 of a cake shared between 2 people — how much each?.” 6 and 1/6. The same answer to both means the two situations have not separated; an answer of 2/3 to the first means the division was read as a multiplication. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Dividing with Unit Fractions?
Yes — 2 printable 5.NF.B.7 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Dividing with Unit Fractions free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to 5.NF.B.7 of the Common Core State Standards for mathematics.