• 03/09/15   |   Adjusted: 02/11/16   |   2 files

# Leapfrog Fractions

Author: Denver Public Schools

• Description
• Files

Mathematically:

• Provides students with the opportunity to use a variety of reasoning strategies about fraction equivalence to solve computation problems
• Allows for the use of visual fraction models, number lines, or equations to demonstrate thinking and solve the problem
• Builds on grade 4 understanding of fraction equivalence to add fractions with unlike denominators
• Allows for multiple solution strategies and encourages equivalent answers, without emphasizing least common denominators or lowest terms

In the classroom:

• Includes prompts and questions for the teacher to present in order to help all students engage with the mathematics of the lesson
• Provides examples of solution methods to strengthen all students' understanding of the content
• Requires students to revisit and revise their individual work
• Allows for individual, small group, and whole class work in one lesson

• Making the Shifts

How does this lesson exemplify the instructional Shifts required by CCSSM?

 Focus Belongs to the major work of fifth grade Coherence Extends students' understanding of fraction equivalence and builds on adding fractions with like denominators Rigor Conceptual Understanding: primary in this lesson Procedural Skill and Fluency: secondary in this lesson Application: not targeted in this lesson

In this lesson, students are given two fractions and must find the third fraction that will result in a sum of 1 when all three are added. The numbers chosen for each frog encourage students to apply their understanding of fractions flexibly. In one problem (Frog 4) the two given fractions already have a common denominator, allowing students to revisit their understanding of iterating unit fractions to make a whole that was developed in grade 4. Three problems (Frogs 1, 2, and 3) provide fractions in which one denominator is a multiple of the other (e.g., $\frac{3}{5}$ and $\frac{1}{10}$). For these problems, students can create equivalent fractions using the larger denominator as the common denominator. Frog 5 provides a more challenging problem by presenting fractions with denominators that are not multiples of each other, but share a common factor other than 1. Students will have to use additional reasoning about equivalence to find the missing fraction and make a whole.

In each of these examples, students are using equivalent fractions to complete the problem. Tools such as number lines and visual fraction models can be useful for students to explain their thinking. Teachers may also use those tools with students who are struggling to find common denominators using knowledge of factors and multiples.

The structure of the lesson (beginning on page 3) is one that can be used with any mathematically worthwhile task.  The cycle of giving students an opportunity to work individually, revisit and revise their work based on feedback from the teacher, and work collaboratively allows students to engage deeply with the task. Students are able to communicate their thinking to one another and combine their ideas into one, new solution. The included discussion questions facilitate this work and can easily be adapted for other tasks. Teachers and those who support teachers may find the Instructional Practice Guide: Coaching Tool useful in implementing best practices in the classroom that allow all students to master the content of the lesson.