Multiplying Fractions
A 50-minute Grade 5 lesson on multiplying fractions, where the fact to confront head-on is that multiplying by a fraction less than one makes things smaller.
Multiplying Fractions is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.NF.B.4 — multiply 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.4
Grade 5 · Number & Operations — Fractions
5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Objective
Students will be able to multiply a fraction by a whole number or by another fraction, and explain the size of the result.
Students are successful when they can
- Finds 2/3 of 12 and of 3/4.
- Models a fraction product as an area.
- Predicts whether the product will be larger or smaller than the factors.
What you need
- Squared paper for area models
- Fraction strips
- Word problem cards
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — a fraction of a whole number
6 min- Find 2/3 of 12 using counters: split into three groups of four, take two groups, eight.
- Write it as 2/3 × 12 = 8 and note that 'of' and the multiplication sign are doing the same job.
Teach — an area of a rectangle
15 min- Draw a unit square. Shade 3/4 of it going across, in one colour.
- Now shade 2/3 of it going down, in another. The overlap is 2/3 of 3/4.
- Count the overlap: 6 small pieces out of 12, which is 6/12 or 1/2.
- Write 2/3 × 3/4 = 6/12. The numerators multiplied and so did the denominators, and the grid shows why.
- Ask about the size. Half is smaller than 3/4 and smaller than 2/3. Multiplying made it smaller.
- Say why: taking a part of something gives you less than you started with, and that is what 'of' means.
“Multiplying does not always make things bigger. Two thirds of something is less than the something, and that is exactly what multiplying by two thirds does.”
Guided practice — predict, then compute
14 min- Pairs predict whether each product will be larger or smaller than the first factor, before calculating.
- They draw the area model for two of the calculations.
- Then they solve a word problem: three quarters of a two-thirds full tank.
Independent practice
12 min- Students complete a multiplying fractions page.
- Answers larger than both factors are the diagnostic and mean the prediction step was skipped.
Close
3 min- Ask whether 1/2 × 8 is bigger or smaller than 8, and why.
- Smaller, because half of something is less than the something.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Says the product of two fractions must be larger than both.
Why: Multiplication has always made numbers bigger, across every example met since Grade 2. Nothing has contradicted it until now.
Fix: Shade the area model. The overlap is visibly a small part of the square, and no argument is needed.
Adds the numerators and denominators instead of multiplying.
Why: The procedures for adding and multiplying fractions are being confused, and adding was learned first.
Fix: Go back to the area model. The grid has 12 small pieces because 3 × 4 is 12, and 6 are shaded because 2 × 3 is 6.
Multiplies 2/3 × 12 by turning 12 into 12/12.
Why: The whole number has been converted to a fraction using the nearest available denominator rather than 12/1.
Fix: Ask what 12/12 is worth. One. The conversion has changed the number, and writing 12/1 keeps it.
If they are not there yet
- Find fractions of whole numbers with counters before multiplying two fractions.
- Use pre-drawn unit squares divided into a suitable grid so the shading is the only task.
If they finish early
- Multiply two mixed numbers.
- Find the area of a rectangle with fractional side lengths.
- Explain when multiplying makes a number larger and when it makes it smaller.
Exit ticket
Work out 3/5 × 2/3. Before you calculate, say whether the answer will be more or less than 2/3.
What to look for: Less, and 6/15 or 2/5. A prediction of 'more' means the fraction-of idea has not landed; adding the parts gives 5/8 and is the other common error.
Printable practice for 5.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.
- Multiply Two FractionsWork out each answer. Simplify where you can.
Questions about Multiplying Fractions
How long does the Multiplying 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 Multiplying Fractions teach?
CCSS.MATH.CONTENT.5.NF.B.4 — 5.NF.B.4, Number & Operations — Fractions for Grade 5: “Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.” In plain terms, multiply fractions.
What do I need to teach this lesson?
Squared paper for area models, fraction strips, 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: says the product of two fractions must be larger than both; adds the numerators and denominators instead of multiplying and multiplies 2/3 × 12 by turning 12 into 12/12. 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 3/5 × 2/3. Before you calculate, say whether the answer will be more or less than 2/3.” Less, and 6/15 or 2/5. A prediction of 'more' means the fraction-of idea has not landed; adding the parts gives 5/8 and is the other common error. 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 Fractions?
Yes — 2 printable 5.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 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.4 of the Common Core State Standards for mathematics.