CCSS.Math.Content.4.NF.B.4b
The Standard
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students interpret a whole number times a fraction as repeated equal groups. They break each fraction into unit fractions, combine the copies, and write the product with the same denominator.
What Mastery Looks Like
- Students can use a drawing or equation to show repeated equal groups of a fraction. They correctly multiply the numerator by the whole number, keep the denominator, and explain the result using unit fractions.
Common Misconceptions
- Students may multiply both the numerator and denominator by the whole number. They may also treat 3 × 2/5 as three fifths instead of six fifths, or stop when the product is improper.
How to Assess It
- Give students this exit ticket: Draw a model for 4 × 3/8, rewrite it using unit fractions, and find the product. Explain why the denominator stays 8.
Lesson moves
Ways to Teach It
Give pairs fraction strips and have them build three groups of 2/5, then combine and label the total in fifths.
Ask students to explain in writing why 4 × 3/7 equals twelve copies of 1/7.
Play a matching game with cards showing products, repeated addition, unit-fraction sums, models, and answers.
Use a recipe with 3/4 cup of oats per batch, and have students find the amount needed for four batches.
Free download
Printable 4.NF.B.4b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.4.NF.B.4b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.4.NF.B.4a
Students must see a/b as a copies of 1/b before seeing n × a/b as n × a copies of 1/b.
- CCSS.Math.Content.3.OA.A.1
Equal-groups multiplication carries over to seeing whole-number multiples of unit fractions, such as 3 groups of 2/5.
- CCSS.Math.Content.3.NF.A.1
Multiplying a fraction by a whole number depends on seeing a/b as a copies of the unit fraction 1/b.
What This Unlocks
Mastery here sets students up for these next.
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