# Why Fact Triangles Work

When I first started teaching, way back in the year 2000, the world was a very different place. One of the first math teaching tools I found in my special ed classroom back then was a giant stack of punch out fact triangles. There were addition/ subtraction and multiplication/ division facts, and I can still feel and even smell them and the cardstock they were printed on. I remember thinking, even then, like these are SO outdated, why on earth would I use these?! It’s the year 2000, we have to have better ways of helping kids learn math facts. And like many things I thought as a 21 year old brand new teacher in NYC public schools, boy, was I super duper wrong!

## Fact triangles work for so many reasons!

### >Of course, fact families exist for a reason, and fact triangles are probably the best (or one of the best) ways for kids to consolidate their understanding of fact families.

Fact families are important concepts for kids to learn. Sure, they can spend time writing out all four facts for each family, and that’s often a valid exercise to help develop the fact family concepts. But in terms of working with them and using fact families, fact triangles are probably the best tool for doing that. Fact triangles are intuitive and help with both the concepts and the practical applications of fact families.

### >Help kids connect part/ part/ whole thinking.

In a fact triangle, the whole is at the top point of the triangle and and the parts are on the bottom two points. For addition and subtraction facts, combining the parts makes the whole. And conversely, subtracting one of the parts from the whole leaves the other part. These part/ part/ whole concepts are very important, especially in lower elementary, and fact triangles can be another tool for developing them.

### >Minimize the number of facts kids have to learn.

Any time we can reduce the amount of memorization kids actually have to do, I consider that a win. By using fact triangles instead of straight up flashcards, we automatically reduce the number of facts kids need to memorize. If we work in fact families instead of single facts (so, one family for four facts), we can cut the number of facts kids need to memorize down to 25%.

### >Fact triangles feel more fun and engaging than flash cards.

I’ve even created Halloween and winter-themed fact triangles for my students to practice with. It just makes it a little more fun (always eneded when learning math facts!). They have the added bonus that the kids can use them and practice for a season. But then, once the holiday, has passed, it seems like a more natural time to wean the kids off of the triangles. This helps them rely more on their understanding and memory and less on the physical paper.

Halloween Candy Corn addition/ subtraction fact triangles

Halloween Candy Corn multiplication/ division fact triangles

Winter Fact Family Forest addition/ subtraction fact triangles

Winter Fact Family Forest muliplication/ division fact triangles

Psst.. if you’re looking for more holiday themed content (not just cute!) information, check out this post on Holiday Activities that Review Geometry.

### >Help understand the difference between addition/ subtraction and multiplication/ division.

One of the third grade standards asks students to understand the difference between additive comparison and multiplicative comparison. While using fact triangles doesn’t really get to the heart of that concept, they can be helpful for comparing the two. Students can find patterns, such as how the 2/ 2/ 4 fact family is the same for both addition/ subtraction and multiplication/ division. They can compare facts like 6 +6 =12, 2*6 =12, and 6*6 = 36 and see how they are related, concepts which students need for harder computation and problem solving later on.

### >Provide supports for students while playing games or doing more complicated math problems.

I taught special education that first year, way back in 2000-2001. Because of that experience, I strongly believe that all teachers should teach special ed at some point, because good teaching for special education is good teaching for everyone. It left me with a deep understanding of differentiation and how to support students while still holding them accountable, and a strong appreciation for the different ways in which kids’ brains work and develop. Teaching special ed gave me a different framework for how to approach teaching general ed, and gave me the habit of constantly looking for ways to support my students.

Anyway… it turns out that fact triangles are actually a great tool for supporting students who struggle with memorization. Allowing kids to use the triangles for the fact families they didn’t yet have memorized allowed them to participate in more difficult problem solving and higher order thinking activities. Fact triangles gave them the support they needed to be able to play math games with confidence and focus on the concepts and not just the memorizing. 10/10 would recommend.

### >Build connections between the facts, rather than straight memorizing from flash cards.

If kids memorize their math facts individually, it’s harder for them to see how they all relate to each other and connect. By grouping them into fact triangles, students can easilly see the relationships, as all the related facts are right there on one triangle!

### >Students can practice writing the equations themselves.

This activity can be a little polarizing, though, so use it with care and make sure it doesn’t feel like a punishment. Some of my students loved writing out the 4 facts for each triangle, and some absolutely hated it. But even if they don’t physically write them down, coming up with the equations for a fact family can be really helpful for students. It helps them learn the vocabulary (addend, factor, product, etc.). And, it also helps them see how equations are related and develop those concepts of the relationships between addition and subtraction and multiplication and division.

Psst… Fact triangles make great centers & “I’m done” activities. Check out this blog post for more on how I use a Math Menu in my classroom. I love being able to give kids choice and engaging activities while still providing support and accountability!