Why Students Struggle with Similarity (It Starts Before Geometry)

If you’ve ever started a similarity unit in geometry and watched students struggle almost immediately, you’re not alone. It often feels like students should be ready for similarity, yet many struggle with even the first problems. In many cases, the issue is not similarity itself. The real challenge often begins much earlier, with gaps in ratios, proportions, and unit reasoning.

When we ask students to understand similarity in geometry, we are asking them to draw on years of mathematical reasoning that many of our students just don’t have.

Students need to understand ratios, proportional reasoning, and how to use and convert between different units. These are skills that we expect students to have before we begin teaching similarity—skills they should have learned in middle school—but for many of our students, this is not the case.

Because of this, many of the struggles students experience with similarity actually begin long before they encounter similarity in geometry.

When I begin my similarity unit, I often go back and teach some of these prerequisite skills. I knew I was going to need to touch on simplifying ratios, as my students had struggled throughout the year with simplifying fractions. I knew we were going to need a lesson on solving proportions, and I knew we would need some help with converting units.

What I didn’t fully realize when we began the unit was just how many prerequisite skills my students would struggle with.

Why Students Struggle with Similarity in Geometry

When we get students at the high school level, they come from many different backgrounds.

Some students have bounced around schools for years and have gaps in their knowledge. Some have struggled with math consistently and have been passed along due to retention policies. Others, like our multilingual learners, struggle with understanding the vocabulary used because they were never fully taught it.

Each student has their own unique struggles that make learning similarity in geometry difficult.

One struggle our multilingual learners face is with units and their abbreviations. These are often assumed to be prior knowledge. Different countries use different units, so even multilingual learners who understand how to convert units will need extra support with conversions involving the imperial system used in the United States.

These units are things students have never heard of.

For example, when I was teaching about units and used the word yard, my students thought I was talking about a grassy area like you would see around houses. I had to specify and demonstrate that a yard was actually a unit of measurement used in the United States.

There are many units we use in the U.S. that are not used globally and are unfamiliar to many of our multilingual learners.

Common Confusion Points When Teaching Similarity

There are several common confusion points in a similarity unit, especially for ELLs.

Students are used to seeing fractions, as they appear throughout every math course. Suddenly, we are showing them the same setup but calling it a ratio. This can be very confusing for students who are just trying to understand and make connections with the English terms.

Students are also expected to know what all of the unit abbreviations mean, even when they are units they have never encountered and are unfamiliar with.

Ratios themselves can also be confusing. They require numbers, order, and words to all be related correctly. Students must understand which quantities are being compared and how the relationship is written.

Throughout the similarity unit, students face these confusion points repeatedly. If we don’t take the time to address them, students will struggle to move forward and actually begin to understand similarity relationships and proportional figures.

Why Ratios and Proportions Are Essential for Similarity

Students require explicit instruction to build these missing skills.

Teachers need to take time to teach how to convert units and what the different abbreviations mean. This allows students to accurately solve similarity questions involving different units without losing points for not knowing what it means when a question says to include units or when values are given in different units.

Similarity also requires a solid understanding of ratios and proportions.

Without that foundation, students will struggle with setting up and solving similarity questions and with demonstrating that the sides of triangles are proportional in order to prove similarity.

By taking time to review ratios, we build the skills students need to understand how triangles relate through proportional relationships. By reviewing and reteaching how to solve proportions, we give students the skills needed to solve similarity problems.

Building Ratio Understanding Before Teaching Similarity

To help students build these needed skills, begin by making connections to real-world experiences they already have.

While our students may be missing academic knowledge, they are often rich in life skills and understanding.

To demonstrate ratios, several examples allow for visuals and connect to students’ backgrounds. To show how ratios compare things, we can complete classroom sorting activities—for example, comparing boys to girls, freshmen to sophomores, or even tennis shoes to boots to crocs.

To discuss solving ratios, we can use the idea of sharing a pizza to show that ratios represent parts of a whole. This example provides easy visual references and makes it easier to connect ratios to fractions while also discussing the slight differences between the two.

To help students prepare to solve proportions, we can talk about scaling ratios, beginning with a discussion and then moving on to using this idea as a basis for setting up proportions.

For students unfamiliar with cooking examples, money examples can also be helpful. For example:

If two bags of chips cost $3, how much would six bags of chips cost?

This is the hidden math students do every day without thinking as they interact with the world.

By making these connections, we give students the background knowledge needed to understand similarity.

Quick Ways to Strengthen Ratio Skills Before Teaching Similarity

Before beginning a similarity unit, a short review of ratio concepts can make a big difference. A few simple strategies can help students rebuild the foundation they need:

• Use sorting activities to demonstrate comparisons between groups

• Connect ratios to visual models like pizza slices or fraction diagrams

• Practice scaling ratios using everyday examples

• Use money scenarios to introduce proportional reasoning

• Review solving proportions before applying them to similarity problems

• Explicitly review unit abbreviations and conversions

These quick activities help students rebuild the ratio reasoning skills that similarity depends on.

Supporting Students Before Similarity Begins

Similarity often seems simple to teachers because they already have the background knowledge needed to understand it.

For students, however, the struggle usually does not start with similarity itself. Instead, it begins with missing ratio and proportional reasoning skills.

In order to effectively teach similarity, teachers need to recognize these gaps and be willing to put in the extra effort to help students build these foundational skills.

By meeting students where they are and strengthening their understanding of ratios, proportions, and units, we give them the tools they need to be successful when working with similar figures and similarity in geometry.