Factoring Dale Seymour Publications

Working with Factoring Polynomials from Dale Seymour Publications Materials

Dale Seymour Publications has been around since the 1980s. Their math curriculum materials, especially the "Puzzles and Paradigms" series and the Algebra through Patterns approach, became standard in many middle school and high school classrooms. The factoring sections in their books follow a particular pedagogical structure that isn't always obvious if you're just trying to get the answer key checked quickly. I ran into this repeatedly when I was subbing for algebra classes in the early 2010s. Teachers would hand me a worksheet and say "help them with the factoring" without realizing that Dale Seymour's method doesn't always match what parents or tutors learned. The books use area models and tile representations before moving to abstract algorithms. If you try to skip straight to the AC method on a problem that's set up for manipulatives, kids get confused fast.

Factoring Dale Seymour Publications Approach: The Tile Method

The core technique in their materials is the algebra tile area model. You represent x² terms as large squares, x terms as rectangles, and constants as small unit squares. To factor something like x² + 5x + 6, you arrange tiles into a rectangle. The length and width of that rectangle give you the binomial factors. This seems tedious compared to just finding two numbers that multiply to 6 and add to 5, but it actually builds genuine understanding of why factoring works geometrically. The book sequences it carefully: perfect square trinomials first, then simple trinomials, then difference of squares. Each section uses the same visual language so students aren't learning disconnected tricks. Here's the thing nobody tells you about using these materials. The answer keys in the teacher editions don't always show the tile arrangements. They just list the final factored form. When I was grading worksheets, I had to reconstruct the tile layouts myself to verify students weren't guessing. That took considerably longer than checking a numerical answer.

For difference of squares problems, the Seymour approach cuts the rectangle into two separate pieces and rearranges them. It's elegant but time-consuming in a 50-minute period. I found that doing the tile demonstration once per unit and then letting students use the algorithm afterward was the only way to cover the material. Spending two class periods on tiles for every topic wasn't realistic.

Common Problems and What Actually Works

The most frequent issue I encountered was students mixing up the sign conventions when moving from tiles to the abstract method. The tiles make the signs visual—negative tiles are shaded differently—but translating that to "when the constant is positive and the middle term is negative, both binomials have negative signs" is a leap that some kids never make on their own. I started having students write out the tile representation next to each problem even after they could factor abstractly. It kept the connection alive and caught errors that pure algorithmic factoring missed. A student might correctly apply the AC method to x² - 4x - 12 and get (x-6)(x+2), but if they'd built the tiles, they'd see immediately that you can't arrange those tiles into a rectangle with a negative area unit in that configuration. Another edge case: the Seymour books sometimes present trinomials where the leading coefficient isn't 1 before fully establishing the tile method for monic quadratics. I've seen whole classes stall because they hadn't internalized the basic area model yet. If you're using these materials, make sure students can confidently factor x² + bx + c by tiles before moving to ax² + bx + c. Don't follow the book order blindly if your class needs more time on the foundation.

Downloading and Using the Materials

Dale Seymour Publications was acquired by Pearson and later merged into various imprints. The original print materials are still circulating in school districts, but official downloads are harder to track down. The "Algebra through Patterns" series had companion websites that have been taken down or redirected over the years. What still works reliably is finding used copies of the student editions on eBay or Amazon. The teacher editions with full answer keys and lesson plans run about $15 to $40 depending on condition. Some school districts sell their surplus curriculum directly through eBay, and those tend to have the most complete materials including the manipulatives sets. If you're a parent working through these with your kid, I'd recommend getting the student workbook plus the teacher edition even if you don't plan to use the teacher edition primarily. The extra explanation pages in the back of the teacher book clarify the pedagogical reasoning, which helps when a student gets stuck on a problem that doesn't match what they saw in class.

When This Method Falls Short

The tile approach works well for quadratics but doesn't scale to higher-degree polynomials. Once students hit cubic factoring or polynomial division, the Seymour materials don't extend the visual method naturally. You'll need to transition them to synthetic division and the rational root theorem separately. The books acknowledge this gap but don't always provide a smooth bridge. Also worth noting: standardized tests don't care about your tile method. Students need to be able to factor quickly without manipulatives for timed assessments. Building fluency with the algorithmic approaches should still be a priority even if the conceptual foundation comes from the Seymour framework. I'd suggest spending about two weeks on the tile method for each new factoring type, then shifting to speed and accuracy work for the remainder of the unit. If you're looking for supplemental practice worksheets that align with the Seymour progression, the Math-Aids.com site has free generators that let you specify the factoring type and difficulty. They don't use the tile method but they reinforce the same skill sequence. I used those as exit tickets after the tile lessons to check for transfer of understanding.