Planning Overview: Comparing Fractions
Brain dump for IM Unit 4.2: Fraction Equivalence and Comparison
What is a fraction? Fractions represent the parts of a whole or collection of an object (SplashLearn). They are made of two parts - numerators (equal parts taken) and denominators (total equal parts). In the image below, the pizza is broken into 8 equal parts, with 1 slice representing 1/8. Fractions with a numerator of 1 are called unit fractions.
About the Unit
Learning goals: Students generate and reason about equivalent fractions and compare and order fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100. (Illustrative Mathematics)
There are three sections: A: Size and location of fractions, B: Equivalent fractions & C: Fraction comparison
There are 16 required lessons. Students will spend about 18 or 19 days total on the material including content to address missed learning and the unit assessment.
Using Data to Plan for Fractions
Earlier this year, students took STAR and iReady benchmark tests to determine proficiency levels of 4th-grade math content. Both tests showed that students had very little mastery of fractions. In fact, based on iReady’s recommendation:
25/46 students require an in-depth review of understanding basic fraction concepts
40/46 students require an in-depth review of recognizing equivalent fractions and comparing fractions with like denominators
When it comes to decision-making for planning, I find the data mentioned above overwhelming but also helpful and informative. Overwhelming because IM Unit 4.2 assumes that students have mastered these prerequisites but more than half of my class would have trouble making sense of the pizza example above. Still, the data is helpful and informative because I can plan ahead to address missed learning and get students up to speed without frustration.
Unit Planning: Pre-Teaching, Small Group Instruction, Independent Practice
Pre-Teaching: Before jumping into 4th-grade content, all students will spend two days addressing missed learning via IM’s Adaption Pack (Adaption Packs are designed to help address missed learning). This pack utilizes Grade 3, Unit 5 Section A. Students will make their own fraction tiles to demonstrate an understanding of equal parts and unit fractions. In addition to the IM resources, I will explicitly teach basic fraction concepts and fraction equivalency to students in both whole-group and small-group instruction.
Small Group Instruction:
Grade-Level: Students who demonstrate mastery of prerequisites will work through grade-level content and problem-solving skills during small group instruction. This will include a variation of IM Practice problems and problems from other resources.
Intervention: Students who have not demonstrated mastery of basic fraction concepts will spend small group instruction addressing gaps in learning. As they demonstrate conceptual and procedural understanding, they will be moved into groups to practice grade-level skills and concepts.
Independent Practice: Students will be assigned lessons via Khan Academy and iReady to work at/above their level of proficiency. Students performing 2-3 grade levels behind will work on identifying fractions and continue to build their understanding of numbers with place value practice.
Fluency: Students will practice multiplication fluency to assist with their ability to generate equivalent fractions.
Manipulatives: Students will use fraction tiles, drawings, and other representations throughout the unit.
Scope and Sequence: Total Unit Lessons: 16 / Total Days: 18 or 19
Section A: There are 6 lessons in this section. Students should be able to demonstrate an understanding of benchmark fractions and identify fractions on a number line. Cool-downs from lessons 3 and 5 will be graded. The Section A Checkpoint will also be graded.
Section B: There are 5 lessons in this unit and students should be able to generate equivalent fractions and use reasoning to identify equivalent fractions with visual representations. Cool-downs from lessons 8 and 11 will be graded. The Section B Checkpoint will also be graded.
Section C: There are 5 required lessons in this unit. By the end, students will be able to reason about fraction comparison. Cool-downs from lessons 13 and 16 will be graded. The Section C Checkpoint will also be graded.
Upon completion of the unit, students will also receive the 4.2 End of Unit Assessment. This score will also be included in the grade book. All students will receive credit for completed teacher-assigned assignments in iReady or Khan Academy.
Resources:
Hands-On Fraction Activity [Video]
The Progression of Fractions Meaning, Equivalence, and Comparison [Video]
Khan Academy Practice Sets - Lesson 1: Equivalent Fractions Modeling, Equivalent Fractions on a Number Line, Equivalent Fractions, Fractions of Different Wholes
Khan Academy Practice Sets - Lesson 2: Common Denominators