I covered a couple of my colleague's classes yesterday so he could attend a math conference. The afternoon class was a somewhat boisterous grade 10 group. I was asked to teach students how to find the greatest common factor, and if I had time, introduce them to more general factoring techniques.

I decided that the greatest common factor is a topic students find relatively easy, and so I just showed some examples of how to do it (actually, I drew the "how to" out of the class by asking them questions, but this is my standard technique) after verifying that they understood the distributive principle. I then assigned some practice problems, which then each student wrote their solution up on the board, and we discussed. I then showed students a couple of different techniques for multiplying binomials (like (x+2)(x+3) for example).

Next, I put up the following 4 questions.

1. x^{2} + 7x + 12

2. 2x^{2} + 7x + 3

3. x^{2} - 25

4. x^{3} + 8

I asked students to try and figure out how to write these expressions as one set of brackets times another, just like with the example from before, but I suggested to them that what we are trying to do is undo the distributive rule.

I went around the room and encouraged students, gave them hints when they needed them, asked them questions to prod their thinking, and observed their problem solving strategies. Students were engaged in the problem solving activity for a good 30 minutes. Once some of the students' attentions started to wane a bit, I gave them a sheet with a description of how to do factoring by grouping and some problems to work on the back.

A group of students though really dove into question 4, which, as you may notice is actually quite a bit more difficult than the other three problems. I ended up having to give students two hints: I told them that the expression broke into two factors, one of which was (x+2) and the other of which was three terms long. The group of students worked feverishly on solving the 4th problem for a good twenty minutes, and then all of a sudden, one of the girls in the group leapt out of her seat and screamed, "I GOT IT!! YES!!" I circled around to see if she had the right answer, asked her how she was so sure it was right (she had multiplied everything back through using the distributive rule), and then gave her group x^{3}+27 to solve (which she did quickly) and then x^{3 }+ a^{3} to solve.

At 5:30pm that night, I received an email from the girl, excitedly telling me how she had an inspiration while she was on the bus home on how to solve the general question, and had then figured out the general formula for how to factor a sum of cubes.

I emailed her back and congratulated her on becoming a mathematician.

Newsletter:

Topic:

David is a Formative Assessment Specialist for Mathematics at **New Visions for Public Schools** in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his **Masters degree in Educational Technology from UBC**, and is the **co-author of a mathematics textbook**. He has been published in **ISTE's Leading and Learning**, **Educational Technology Solutions**, **The Software Developers Journal**, **The Bangkok Post** and **Edutopia**. He blogs with the **Cooperative Catalyst**, and is the **Assessment group facilitator for Edutopia**. He has also helped organize the first **Edcamp in Canada**, and **TEDxKIDS@BC**.

- Creating a WiiMote interactive white board at my school for under $50.
- 20 reasons not to use a one to one laptop program in your school (and some solutions)
- For whom are Interactive White boards Interactive?
- What is Edcamp?
- Mathematics education blogs
- Forget the future: Here's the textbook I want now
- Eight Videos to Help Teachers Get Started Using Twitter
- Why educators should blog: A helpful flowchart
- There are no aha moments
- Paper use in schools
- 15 things kids can do instead of homework
- Online Geogebra training
- The difference between instrumental and relational understanding
- What is The Effect of Technology Training for Teachers on Student Achievement?
- Why teach math?
- Using Google forms for a "Choose your own adventure" style story
- Ways to use technology in math class
- A Fundamental Flaw in Math Education
- We are homeschooling our son
- The Death of the Amateur Mathematician
- A Restitution Guide to Classroom Management
- 25 Myths About Homework
- Migrating away from Google Reader
- Free tools for math education
- The Role of Immediacy of Feedback in Student Learning

**Subscribe** to my blog

Theme by Danetsoft and Danang Probo Sayekti inspired by Maksimer

## Add new comment