Unit Plan 23 (Grade 4 Math): Multiply Fractions by Whole Numbers
Multiply fractions by whole numbers using models and equations; explain a/b × n = (n × a)/b; convert improper↔mixed; solve word problems with units and reasonableness checks.
Focus: Model and solve a/b × n as repeated addition of unit fractions; represent with area and number line models; apply in word problems.
Grade Level: 4
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students interpret a/b × n as taking n copies of the fraction a/b (or a copies of 1/b repeated n times). They use visual fraction models (area/strips) and the number line to show why n × (a/b) = (n × a)/b, record equations, and express results as fractions or mixed numbers. Word problems emphasize units, a consistent whole, and reasonableness.
Essential Questions
- How does a/b × n represent n copies of a/b (and why is that the same as (n × a)/b)?
- When is an answer best shown as an improper fraction and when as a mixed number?
- How do models, equations, and units work together to explain my solution in a word problem?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Model a/b × n with area/strip and number line representations and connect to equations.
- Explain a fraction as a multiple of a unit fraction (a/b = a × 1/b) and relate this to a/b × n.
- Compute products and express results as fractions or mixed numbers, justifying equivalence.
- Solve word problems involving fraction-by-whole multiplication with accurate units and reasonableness checks.
- Use precise vocabulary (e.g., unit fraction, multiple, improper fraction, mixed number, equivalent) to explain thinking.
Standards Alignment — CCSS Grade 4
- 4.NF.4a: Understand a fraction a/b as a multiple of 1/b; use this to view a/b × n as a multiple of a/b.
- 4.NF.4b: Multiply a fraction by a whole number using visual fraction models and equations (e.g., 3 × (2/5) = 6/5); express as fraction or mixed number.
- 4.NF.4c: Solve word problems involving multiplication of a fraction by a whole number.
Success Criteria — Student Language
- I can show a/b × n with a model and write an equation that matches.
- I can explain why n × (a/b) = (n × a)/b and convert between improper fractions and mixed numbers.
- I can solve a word problem and include units, a reasonableness check, and a clear explanation.