Unit Plan 14 (Grade 5 Math): Scaling with Fractions
5th graders interpret multiplication as scaling—understanding how factors less than, equal to, or greater than 1 shrink, keep, or enlarge a quantity. Students predict and compare product sizes using benchmarks, unit fractions, and reasoning without computation.
Focus: Interpret multiplication as scaling (resizing); predict and compare the size of products without computing, using benchmarks, unit fractions, and scale factors greater than 1, equal to 1, and less than 1.
Grade Level: 5
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students reframe multiplication as scaling: factors act like scale factors that shrink (fraction less than 1), preserve (factor 1), or enlarge (factor greater than 1) a quantity. Through visuals (strips, area, number lines) and reasoning, they decide whether a product is less than, equal to, or greater than the starting amount without computing. They explain why multiplying by 1/b divides by b, and multiplying by b makes b copies, connecting to unit fractions and composite scale factors.
Essential Questions
- How does multiplication change a quantity when we think of it as scaling?
- How can I tell if a product will be less than, equal to, or greater than one factor without calculating?
- Why does multiplying by 1/b give a result b times smaller, and multiplying by b give a result b times larger?
- How can I use benchmarks (0, 1/2, 1, 2) and structure to compare products?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Interpret multiplication as resizing with a scale factor and describe the effect on magnitude.
- Use benchmarks and unit fractions to determine if a product is less than, equal to, or greater than a given factor.
- Explain why multiplying by 1/b makes a value b times smaller, and why multiplying by b makes it b times larger.
- Compare two products like 3/4 × 18 and 2/3 × 18 without computing, using reasoning about the factors.
- Communicate reasoning clearly with models, comparative statements, and precise vocabulary.
Standards Alignment — CCSS Grade 5
- 5.NF.5a: Interpret multiplication as scaling (resizing); compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- 5.NF.5b: Explain why multiplying a given number by a fraction greater than 1 results in a larger product; by a fraction less than 1 results in a smaller product; and by 1 results in a product equal to the number; explain the effect of multiplying by 1/b vs b.
- Mathematical Practices emphasized: MP.1 (persevere), MP.2 (reason abstractly/quantitatively), MP.3 (justify/critique), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can name the scale factor and say whether it will shrink, keep, or grow the starting number.
- I can decide if a product is less than, equal to, or greater than a factor without computing.
- I can explain that multiplying by 1/b makes something b times smaller, and multiplying by b makes it b times larger.
- I can compare two products using benchmarks and structure, not just arithmetic.
- I can support my claim with a model or a clear comparison statement.