Generate fractions between any two quantities
Generating Fractions between Two Numbers (Fraction Density)
Description This is a set of progressive prompts that will elicit the use of various strategies used to find fractions between two numbers. The prompts, when used in sequence, support students in choosing a strategy based upon the fractions being considered. Encourage students to build models/representations and create contexts to aid in visualization. This series of prompts can be used for a variety of grades and purposes. The time required will vary depending on the grade level and student readiness. 

Mathematics Density of fractions refers to the important mathematical idea that between any two fractions there are infinite number of fractions. Understanding this mathematical fact is a crucial stage in the development of fraction sense. This is a novel concept for students, since it is not encountered in the whole number system (there are not any whole numbers between any two whole numbers). Students are encouraged to develop a range of different strategies and to use them strategically, based on the situation. Research shows that it is beneficial to spread fraction learning throughout the year and embed it in other strands. Density is also a key concept in measurement. 

Curriculum Connections Students will:


Instructional sequence


Highlights of student thinking Students may:

Key questions


Materials Make tools available such as paper and markers, grid paper, paper strips for folding, and/or manipulatives such as relational rods. 