Diagnostic Fraction Tasks

Why Diagnostic Fraction Tasks?

Gauge students' understandings to increase access and opportunities for advancement in learning and understanding of fractions for ALL students!

Diagnostic fraction tasks are used to help you gain insight into your students’ thinking. This particular set of tasks is designed to help you better understand how students think about fractions as quantities (Hunt, Welch-Ptak, & Silva, 2016). There are ten different tasks for each student to complete. These tasks can be altered according to the student’s preferences (e.g., contexts; representations). Because students use their entire set of formal and informal experiences to access mathematics, you may find such task alterations useful to gain maximum insight into students’ thinking. The Learning Trajectory stages portion of the curriculum site will be helpful in guiding your instructional decisions based on your documentation of student thinking in the diagnostic tasks.

*We strongly recommend downloading the Diagnostic Fraction Tasks PDF files over opening as a Google Doc in order to maintain original content and formatting

Tasks to Uncover Students’ Thinking About Fractions


The following ten tasks are in a suggested order for your use with students. However, you may choose to adjust the sequence according to your preferences and/or student need (e.g., if a student is stuck on a task, or is unable to complete it, move on to the next one). You may also choose to come up with some of your own as you become more comfortable with the process.

Documenting Student Thinking (Individual and Small Group)


We understand that teachers work in different settings and will use the tasks in different ways. For example, some teachers may pose the tasks to individual students, while others may work with small groups of several students at one time. For that reason, we have provided several sample Teacher Noticing Guides for the tasks. The first guide is intended for working one-on-one with a single student on a single task. The second guide is intended for working one-on-one with a single student across multiple tasks. The third guide is intended for working with a small group of students on a single task. You should pick the tool that you find best aligns with how you plan to use the tasks (or feel free to create your own version).

Noticing Guide 1

Individual student, Single Task

Noticing Guide 2

Individual Student, Multiple Tasks

Noticing Guide 3

Small Group, Single Task

Note: We strongly recommend downloading the following PDF file over opening as a Google Doc in order to maintain original content and formatting

© 2021 Dr. Jessica Hunt, Fraction Activities and Assessments for Conceptual Teaching (FAACT), All rights reserved