What we like about this lesson
- Addresses standards 5.NF.A.1, 5.NF.A.2
- Provides concrete examples for the need of like denominators for addition and subtraction of fractions
- Allows students to understand adding fractions with unlike denominators without going straight to the least common denominator
- Asks students to reason about how the size of units changes as they create equivalent fractions
- Encourages students to look for and make use of structure as they analyze rectangular fraction models (MP.7)
In the classroom:
- Uses concrete and pictorial models, particularly the rectangular fraction model, to make the mathematics of the lesson explicit
- Prompts students to share their developing thinking
- Allows for whole group, partner, and individual work in one lesson
- Gives formal and informal opportunities for teachers to check for understanding
Making the Shifts
How does this lesson exemplify the instructional Shifts required by CCSSM?
Focus Belongs to the major work of fifth grade Coherence Builds on key understandings of equivalent fractions (4.NF.A.1) and addition of fractions with like denominators (4.NF.B). Builds foundation toward adding and subtracting rational numbers (7.NS.A.1) Rigor
Conceptual Understanding: primary in this lesson
Procedural Skill and Fluency: secondary in this lesson
Application: secondary in this lesson
It's important to note that this sample lesson is the first in a 5-lesson series on "Making Like Units Pictorially", which is part of a 16-lesson unit on Addition and Subtraction of Fractions. It is not intended for students to meet the full expectations of the grade-level standards addressed in these lessons through only this selected lesson. This sample lesson lays a strong foundation for the work that is to come in the unit by focusing on the use of pictorial models, particularly the rectangular fraction model, to portray addition of fractions less than 1 with unlike denominators. Subsequent lessons move away from concrete and pictorial models and focus on the abstract approach to addition and subtraction of fractions both less than 1 and between 1 and 2.
This lesson develops the understanding of adding fractions with unlike denominators by requiring students to work with rectangular fraction models. Thoughtful questioning is used throughout the lesson to promote students' reasoning on the size of denominators as they create equivalent fractions and add them. Note that there is no explicit instruction or discussion of finding the least common denominator; instead, students are developing their understanding of this concept through models. For more insight on the grade-level concepts addressed in this lesson, read page 11 of the progression document, 3–5 Number and Operations – Fractions.
The structure of these lessons and the unit/curriculum overall have some interesting aspects to highlight. The units make explicit the coherence within the fully developed curriculum. Each topic (a set of lessons) is connected to prior learning and also points to the next topic (or module) that follows in the learning progression. Within individual lessons, there are a number of components that add to their strength including daily fluency practice, variety in questioning techniques, and frequent opportunities for students to debrief about their learning.