A visual model of equivalent fractions showing 3/4 = 9/12

Using Visual Models To Compare Fractions


CCSS.MATH.CONTENT.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2

CCSS.MATH.CONTENT.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. 

Technology Required

Students will need a Mac or Windows computer or an iPad to play the Fish Lake game. Alternatively, students can play Forgotten Trail on the web using Chromebooks or any computer with a web browser.


35-45 minutes

Lesson Summary

Students play 2-3 levels of a game that teaches and assesses adding and comparing fractions with different numerators and denominators, with the context of a story from Ojibwe history. They create their own problems using visual models to compare fractions. Students discuss classmates’ problems. The lesson culminates with a video on visualization as a problem-solving strategy.


Start with a Game (10-20 minutes)

Students play the Fish Lake game through level 2. This requires installing the game on an iPad or a Mac or Windows computer. If only Chromebooks are available, students can play the Forgotten Trail Game instead. We do recommend Fish Lake if iPads are available. Although mathematics and social studies standards taught in both games overlap, the change from using Chromebooks in most lessons to a more console-level game can improve student engagement.

Students create their own problems (10 minutes)

Use slides 1-4 of this Slides presentation to explain the assignment. Optionally, for students learning at home or for homework, it can be assigned to students in Google classroom or similar system.

Discuss math problems students created (10 minutes)

Because students very often ask, “What do you mean?” or “Give me an example?” slides 5-11 of the presentation give an example.

A visual model of equivalent fractions

Watch a video (2.5 minutes)

Visualize! One way of solving a problem


This lesson includes three types of assessment. In the games, students are presented with math word problems that relate to the game narrative. Their answers are scored and data can be accessed for each student from the teacher reports. Students submit math problems they have written for teacher feedback. Also, teacher can use whole class discussion of student problems as a gauge for understanding or have students in pairs or small groups submit written discussion of their peers’ math problems.

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