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Factoring Trinomials with Algebra Tiles Visual Guide


This scaffolded visual guide walks through 10 examples showing how to factor quadratic trinomials using algebra tiles.


This week, I worked on a visual guide for factoring quadratic trinomials using algebra tiles. It has 10 examples, and each example includes the number of tiles needed with any zero pairs, notes about the example and a common student misconception about arranging the tiles for that trinomial. 



If you have never used algebra tiles to factor trinomials and want to give them a try, I wrote this guide to make it easy to get started.



The printable guide includes 10 trinomial examples, common student misconceptions, and the correct algebra tile arrangement.


The guide covers quadratic trinomials where A=1 and where A>1, including when zero pairs are needed because of negative values. 



There are 10 factoring examples in the guide with their common misconceptions, along with 2 additional examples for simplifying a quadratic expression in vertex form and solving a quadratic equation by completing the square.



This preview slide shows the trinomial examples included, including trinomials with leading coefficients more than 1. Using algebra tiles to complete the square to solve a quadratic equation is also included.


I've been making algebra tiles factoring videos for social media and YouTube, and thought it would be nice to have a printable algebra tiles visual guide that also shows some of the misconceptions students may have about arranging the algebra tiles when factoring quadratics.


Examples in the guide include:

  • x2 + 5x + 4 
  • x2 – x – 6 
  • x2 + x – 6 
  • x2 + 5x – 6 
  • x2 – 4x + 3 
  • x2 – 9 
  • 2x2 + 7x + 3 
  • 2x2 + x – 1 
  • 3x2 + 4x + 1 
  • 3x2 + x – 2
  • Simplify (x + 3)2 – 4 
  • Solve x2 + 2x = 3 by completing the square


If you find there's an example you'd like added to the guide, please send me an email. I'm happy to add it in. You can find the guide here.


Factoring Quadratic Trinomials with Algebra Tiles Visual eBook Guide
Algebra Tiles Visual Guide


Algebra tiles connect nicely to the area (box) model of factoring trinomials for when it's time to move past these concrete models. There's a free factoring quadratics cheat sheet here for the area model, along with one for the AC grouping method. 


2 free factoring trinomials cheat sheets
factoring trinomials cheat sheets

I like to teach the AC grouping method to students who struggle with multiplication facts because it takes out all guessing, but the box method has been growing on me! It's like a puzzle for students to figure out.



Additional resources:


Algebra tiles blog posts


Algebra tiles YouTube playlist


Algebra Tiles Reels on Facebook



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