Area Model Matthew Cheng, Rachel Griffin, Bryant Lucas
Participants will gain an understanding of how to use area models to multiply, divide, and factor polynomials. We will discuss common student misconceptions and errors, followed by a brainstorm on interventions and responses.
What we do:
Use area models to model polynomial multiplication, division, factoring, and completing the square.
How we do it:
Participants will:
use area models to multiply, factor, and divide polynomials
implement the use of area models in Algebra 1 and Algebra 2 courses
Why it works:
The CCSS for Math shows that the distributive property (DP) is in the forefront of student understanding of multiplication, beginning in the early grades. The DP helps students understand what multiplication means, how to break down complicated problems to simple ones and how to relate multiplication to area by using array models. Mathematical ideas should not be taught in isolation. The concept of multiplication applied to finding the area of a rectangle connects with the prior understanding that students have about multiplying natural numbers. This in turn can be applied to multiplying polynomials.
Research:
Cathy J. Kinzer, & Ted Stanford. (2014). The Distributive Property: The Core of Multiplication. Teaching Children Mathematics, 20(5), 302-309. doi:10.5951/teacchilmath.20.5.0302
Ji-Eun Lee. (2014). Deciphering Multiplication Algorithms with the Area Model. Mathematics Teaching in the Middle School, 19(9), 556-563. doi:10.5951/mathteacmiddscho.19.9.0556
Küchemann, D., & Hodgen, J. (2018). Using the array model to develop multiplicative reasoning. Mathematics Teaching, (261), 11-14.
Tillema, E. (2009). CULTIVATING AN AREA MODEL. Mathematics Teaching in the Middle School, 15(3), 142-147. Retrieved from http://www.jstor.org/stable/41182979
Tsankova, J., & Pjanic, K. (2009). The Area Model of Multiplication of Fractions. Mathematics Teaching in the Middle School, 15(5), 281-285. Retrieved from http://www.jstor.org/stable/41183357
Common Core State Standards
Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity, Tall and Vinner (1981)
Faster Than a Calculator, TEDx Oxford, Benjamin (2013)
View TLP PCMI | IAS YouTube channel for an overview of the Teacher Leadership Program, ideas for your classroom, resources for you and your colleagues, and short clips of important things to think about as teachers.
