Multiplying a Fraction by a Whole
A 50-minute Grade 4 lesson on multiplying a fraction by a whole number, treated as repeated addition of the same unit fraction rather than as a new rule.
Multiplying a Fraction by a Whole is a free 50-minute Grade 4 maths lesson plan for Common Core standard 4.NF.B.4 — multiply a fraction by a whole number. 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 4
- Length:
- 50 minutes
- Standard:
- 4.NF.B.4
Grade 4 · Number & Operations — Fractions
4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Objective
Students will be able to multiply a fraction by a whole number and interpret the result, including when it exceeds one.
Students are successful when they can
- Writes 4 × 2/5 as repeated addition and finds the total.
- Explains why the denominator does not change.
- Converts an improper result to a mixed number.
What you need
- Fraction strips
- Number lines marked in fifths and eighths
- Word problem cards
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — jump along in fifths
6 min- On a number line marked in fifths, jump 2/5 at a time and record where you land.
- 2/5, 4/5, 6/5, 8/5. The count passes one without stopping.
Teach — the same jump, several times
15 min- Write 4 × 2/5. Read it as four lots of two fifths.
- Write it out: 2/5 + 2/5 + 2/5 + 2/5. Eight fifths.
- Ask why the denominator stayed at 5. Every jump was measured in fifths, so the total is measured in fifths too.
- Show it as 8 × 1/5, which is the same eight jumps taken one fifth at a time.
- Convert 8/5 to 1 3/5 on the number line. Five fifths made a whole, three fifths were left.
- Do a word problem: six people each drink 3/4 of a litre. Eighteen quarters, which is 4 1/2 litres.
“Multiplying by a whole number means doing the same jump several times. The size of the jump does not change, so the denominator does not either.”
Guided practice — write it out first
14 min- Pairs write each multiplication as repeated addition before calculating.
- They mark the result on a number line and convert to a mixed number.
- Then they solve two word problems using the same approach.
Independent practice
12 min- Students complete a fraction multiplication page.
- A multiplied denominator is the diagnostic error and shows as answers far too small.
Close
3 min- Give 5 × 3/8 and ask for the answer as an improper fraction and as a mixed number.
- 15/8 and 1 7/8, both correct, and knowing both matters.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Calculates 4 × 2/5 as 8/20.
Why: The whole number has been multiplied into both parts of the fraction, treating 4 as 4/4 or simply applying the operation twice.
Fix: Write it as repeated addition. Four jumps of two fifths cannot land closer to zero than one jump did, and 8/20 is smaller than 2/5.
Says the answer cannot be 8/5 because it is more than one.
Why: Fractions are still being read as parts of a single whole, so a total exceeding the whole looks like an error.
Fix: Jump along a number line past 1. The landing point exists and has a name, and converting to a mixed number gives it a second one.
Converts 8/5 to 1 3/5 by subtracting 5 from 8 and writing 1 3/5 without knowing why.
Why: The procedure has been learned as a manipulation, which happens to be correct, without the meaning attached.
Fix: Ask how many fifths make one whole. Five, so one whole is used up and three are left. The subtraction is the answer to a question, not a rule.
If they are not there yet
- Work with unit fractions first — 4 × 1/5 — where the repeated addition is a straight count.
- Use a number line marked in the relevant fraction for every calculation.
If they finish early
- Multiply a mixed number by a whole number.
- Solve a problem where the answer must be rounded to a sensible quantity.
- Explain why multiplying by a whole number greater than one always makes a fraction larger.
Exit ticket
Work out 6 × 2/3. Write it as repeated addition first, then as a mixed number.
What to look for: 2/3 six times, 12/3, and 4. An answer of 12/18 means the denominator was multiplied too; an answer left as 12/3 is correct but worth converting.
Printable practice for 4.NF.B.4
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Multiply a Fraction by a Whole NumberWork out each answer. Simplify where you can.
- Fractions of a Whole NumberWork out each answer.
Questions about Multiplying a Fraction by a Whole
How long does the Multiplying a Fraction by a Whole 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 Multiplying a Fraction by a Whole teach?
CCSS.MATH.CONTENT.4.NF.B.4 — 4.NF.B.4, Number & Operations — Fractions for Grade 4: “Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.” In plain terms, multiply a fraction by a whole number.
What do I need to teach this lesson?
Fraction strips, number lines marked in fifths and eighths, word problem cards 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: calculates 4 × 2/5 as 8/20; says the answer cannot be 8/5 because it is more than one and converts 8/5 to 1 3/5 by subtracting 5 from 8 and writing 1 3/5 without knowing why. 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: “Work out 6 × 2/3. Write it as repeated addition first, then as a mixed number.” 2/3 six times, 12/3, and 4. An answer of 12/18 means the denominator was multiplied too; an answer left as 12/3 is correct but worth converting. 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 Multiplying a Fraction by a Whole?
Yes — 2 printable 4.NF.B.4 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 Multiplying a Fraction by a Whole 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 4.NF.B.4 of the Common Core State Standards for mathematics.