Nick's Trick to Find Integer Factors

Students usually struggle with factoring trinomials of the form x^2 + bx + c. But I learned that, most of the time, the problem is in the failure to include the right pair of factors in their list.

As their teacher, I've always asked my Algebra 1 students to list down the integer factors from memory, which needless to say, didn't help everybody.

One day, as I showed my frustration for my students' incapability (Shame on me!), Nick Schaaf, one of my stronger students in his class, grabbed his TI 84 calculator, jumped out of his seat, and volunteered to show his unique method of finding the right pair of factors.

To find all the possible integer factors of, say, -36, all Nick did was enter the equation y= -36/x on his graphing calculator, and then he proceeded to look at the resulting table of values. He scrolled up and down the table, ignoring the pairs of factors that involved non-integers. From his integer factors, he picked the pair whose sum equalled the numerical coefficient of the middle term (bx) of the given trinomial.

Nick was an instant hero. His classmates really appreciated his method, and I started liking the test scores that immediately followed.

As a result of that experience, I have made it a point to facilitate and encourage classroom talk and collaborative group work whenever possible and whenever appropriate.

I still look forward to learning from my students.

A Classifying Triangles Activity

Here's an activity that I have been using to help my students achieve mastery on classifying triangles by side lengths and angle measures.

The primary objectives of this activity are (1) to master vocabulary, and (2) be able to correctly relate the different triangle classifications with each other.

The activity involves a 4 X 5 table. The top row will feature the triangle classifications based on angle measures: acute, right, obtuse, and equiangular. The left column will feature the triangle classifications based on side lengths: scalene, isosceles, and equilateral.

In this activity, the students, individually or in groups, will determine if triangles can fall under two such classifications. For example: Is it possible to draw a triangle that is both acute and scalene? If so, the students will draw that triangle and label it appropriately. If not, then they may write NP for not possible.

I find this activity great for reviewing vocabulary (scaffolding). It is also great for classroom talk and more questioning.

What I like the most about this activity is its "friendliness" to diverse learners, from the learning-challenged to the gifted, and from the color-blind to the most artistic.

This poster was created by Kendra Cobos, Edgar Devora,

Vincent Grimaldo and Rey de Leon in my Geometry class.

Freshmen Irma Mata, Alex Tenopala, Kaela Garcia and Amber

Hernandez created this poster in my Geometry class.

Poster created by Dalia Gutierrez, Victoria Gomez and Berenice Pacheco.