## Section 1: Learning Objective Students will generate at least three equivalent fractions for a given base fraction using physical manipulatives. Students will correctly compare two fractions with different denominators and record the comparison using standard mathematical symbols. ## Section 2: Materials List * 6 complete sets of 51-piece plastic fraction tiles. * 24 printed individual student recording worksheets. * 6 laminated fraction comparison mats. * 6 black dry-erase markers. ## Section 3: Step-by-Step Activity Process 1. **Introduction and Distribution (5 minutes):** Distribute one set of fraction tiles, one comparison mat, one dry-erase marker, and four worksheets to each group of four students, while explicitly stating the physical boundaries and rules for handling the manipulatives. 2. **Equivalent Fraction Building (10 minutes):** Direct all groups to isolate the one-half fraction tile and use smaller denomination tiles to construct three distinct equivalent lengths, recording the corresponding fractions on their individual worksheets. 3. **Unlike Denominator Representation (10 minutes):** Assign two specific fractions with unlike denominators, such as two-thirds and three-fourths, instructing students to build both fractions side-by-side on the laminated comparison mat. 4. **Visual Comparison and Equation Formulation (15 minutes):** Require students to visually assess the length difference between the two built fractions, agree on which is greater, and write the formal mathematical comparison equation on the mat using the dry-erase marker. 5. **Peer Explanation and Review (5 minutes):** Instruct each group to rotate to an adjacent table, verbally read their comparison equation, and justify their answer by pointing to the physical tile evidence on the mat. ## Section 4: Teacher Instructions Circulate among the workstations to verify that students align the zero-edges of the fraction tiles perfectly on the comparison mats to prevent inaccurate visual measurements. Intervene if students attempt to compare fractions by counting the number of pieces rather than measuring the total length of the physical model. Expect students to physically demonstrate that three one-sixth tiles perfectly match the length of one one-half tile when prompted for equivalent fractions. Anticipate that students will verbally identify three-fourths as strictly greater than two-thirds because the tile row extends further to the right on the boundary line. ## Section 5: Assessment Method * **Criterion 1:** Accuracy of the three physically modeled and recorded equivalent fractions. * **Criterion 2:** Correct directional application of the greater-than, less-than, or equal-to symbols in the final written equation. * **Scoring Logic:** Award 2 points for each valid equivalent fraction recorded on the worksheet, yielding a maximum of 6 points. Award 4 points for a mathematically true comparison equation written with the correct symbol. Calculate the final score out of a 10-point maximum for each individual student. ## Section 6: Extension or Variation For student groups demonstrating rapid mastery, remove the physical fraction tiles from the workstation and require them to perform the exact same equivalent generation and comparison tasks using only the lowest common denominator numerical algorithm on a blank whiteboard.