Fractions & Rational Numbers

Overview

This 90-minute interactive lesson (Lesson 9 of 17) introduces students to fractions and rational numbers focusing on visual understanding and comparison. Using pie charts, number lines, and fraction strips, students will build foundational fraction skills aligned with Common Core State Standards (CCSS) for Grades 3-5.

This lesson targets a small group of 3 students, allowing for individualized attention and rich, hands-on exploration.

Common Core Standards

CCSS.MATH.CONTENT.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
CCSS.MATH.CONTENT.3.NF.A.3
Explain equivalence of fractions and compare fractions by reasoning about their size.
CCSS.MATH.CONTENT.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
CCSS.MATH.CONTENT.4.NF.B.3.B
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce like denominators.

Learning Objectives

By the end of this lesson, students will be able to:

Define fractions using visual models such as pie charts and number lines.
Create and use fraction strips to visually represent and compare fractions.
Compare fractions using fraction strips and number lines.
Add simple fractions with like denominators using fraction strips.
Explain fraction equivalence through decomposition.

Materials Needed

Printable fraction pie charts (color-coded)
Number lines from 0 to 1 (with marks at fractional intervals)
Blank paper and colored pencils
Pre-cut fraction strips (1 whole strip divided into 2, 3, 4, and 6 parts)
Scissors and glue sticks
Whiteboard and markers

Lesson Breakdown

Time	Activity	Details & Teacher Notes
0-10 mins	Warm-up: Fraction Recall	Quick verbal Q&A: “What is a fraction?” “Where have you seen fractions before?” Use student answers to connect to prior knowledge and piques curiosity.
10-25 mins	Visual Introduction to Fractions (Pie Charts + Number Lines)	Teacher models fractions using pie charts on the whiteboard. Then shows equivalent fractions on the number line (e.g., 1/2, 2/4). Students identify fractions by shading and labeling in printable pie charts and connect visual areas to points on the number line.
25-40 mins	Hands-on: Create Fraction Strips	Each student cuts and colors fraction strips: 1/2, 1/3, 1/4, 1/6. Teacher guides students to label strips. Enables tactile engagement with fractions.
40-55 mins	Compare Fractions Using Fraction Strips & Number Lines	Students physically line up strips to see comparisons (e.g., which is longer: 1/2 or 1/3?). Teacher introduces vocabulary: greater than, less than, equal. Students place fractions on number lines to confirm comparisons visually.
55-70 mins	Fraction Addition with Like Denominators	Using fraction strips, students add fractions (e.g., 1/4 + 2/4). Teacher models addition as combining strips. Students record sum as an equation, e.g., 1/4 + 2/4 = 3/4.
70-85 mins	Equivalence Exploration	Teacher demonstrates decomposing fractions (4/6 = 2/6 + 2/6 or 1/6 + 1/6 + 1/6 + 1/6). Students try decomposing different fractions on their fraction strips and write down equations.
85-90 mins	Formative Assessment & Reflection	Students use mini-whiteboards or paper to draw a fraction using pie charts or number lines and explain the fraction verbally or in writing. Teacher offers immediate feedback. Wrap up with summary questions.

Differentiation & Support Strategies

For struggling students: Provide pre-colored fraction strips and more guided questions during fraction comparisons. Use simplified fractions like halves and fourths initially.
For advanced students: Challenge with improper fractions or mixed numbers using fraction strips. Introduce adding fractions with unlike denominators through equivalent fractions concept (preview of upcoming lessons).

Assessment

Informal observation during hands-on activities and discussions.
Fraction drawings and explanations during wrap-up.
Completed fraction strips with correct labels and demonstrated comparisons.
Ability to correctly add fractions with like denominators using fraction strips and write the addition equation.

Extensions & Home Connection

Encourage students to find real-world examples of fractions at home (cutting fruit, measuring ingredients) and bring a drawing/photo to the next class.
Create a simple fraction journal for students to draw and label fractions they encounter daily.

Teacher Reflection

Post-lesson, note which visual models best engaged students, difficulties in concept comprehension, and effectiveness of hands-on fraction strips. Adjust pacing and scaffolding based on individual student needs in subsequent lessons.

This lesson ensures a concrete understanding of fractions through visual and tactile means, preparing students for more abstract operations with fractions later in the unit, fully aligned with Common Core standards.