Unit Plan 19 (Grade 3 Math): Fractions as Numbers—Parts of a Whole

Focus: Understand unit fractions (1/b) and fractions (a/b) as numbers; build fraction models and place fractions on number lines with equal intervals.

Grade Level: 3

Subject Area: Mathematics (Fractions Foundations)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students develop fractions as numbers, not just pieces of shapes. They partition wholes into equal parts, name unit fractions and non-unit fractions, and represent them on number lines by marking off equal intervals from 0 to 1 (and beyond). Emphasis is on reasoning about size, units, and positions.

Essential Questions

• What does 1/b mean and how does it build a/b?
• How do I show equal parts on shapes and equal intervals on a number line?
• Why does the point for a/b belong at the end of a intervals of size 1/b starting at 0?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Define and identify unit fractions (1/b) as one of b equal parts of a whole.
2. Construct and name a/b by combining a copies of 1/b using models and number lines.
3. Partition shapes and number lines into equal parts/intervals and label endpoints and ticks accurately.
4. Explain with MP.2 reasoning why a point is located at a/b (size of each part × number of parts).

Standards Alignment — CCSS Grade 3

• 3.NF.1: Understand a fraction 1/b as one part when a whole is partitioned into b equal parts; understand a fraction a/b as a parts of size 1/b.
• 3.NF.2a–b: Understand a fraction as a number on the number line; represent fractions on a number line by partitioning the interval from 0 to 1 into b equal parts and locating a/b at the end of the ath part.
• Mathematical Practices: MP.2 (Reason abstractly and quantitatively) emphasized; MP.5/MP.6 used as needed.

Success Criteria — Student Language

• I can explain 1/b and build a/b with models or a number line.
• I can partition into equal parts/intervals and label 0, 1, ticks, and endpoints correctly.
• I can say why a/b is a steps of size 1/b from 0.