Prepare and Review for Factoring in Algebra

Published on February 2017 | Categories: Documents | Downloads: 19 | Comments: 0 | Views: 91
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Helping students to prepare and review for tests and assessments is a critical
role of the classroom teacher. Once a teacher completes a unit of study with a group
of students, allowing them opportunities to practice their math concepts before
being tested on them is very important. Not only is conceptual understanding
necessary, but knowing when to apply a particular procedure in a problem solving
situation is also essential to succeeding in the classroom. For these reasons, giving
students abundant opportunities to practice concepts before assessment is
important.
If students need to learn when to apply a particular factoring rule, they can
be introduced to the concept in a lesson that has the students filling out a Factoring
Flow Chart. For example, let’s consider the difference of two squares, factoring out a
common factor, and factoring perfect square trinomials. A good tool to use with
students to assist in the learning process is a flow chart, which provides a structure
with which to introduce students to the different ways to factor polynomials. The
flowchart provides all of the critical metacognitive questions a student must learn to
ask themselves when encountering polynomials that must be factored. The role of
the teacher is to work through the flowchart with the students, modeling for them
when and how to use each factoring pattern. After modeling the flow chart,
students must be given ample time to independently practice the concept of
factoring in a decontextualized exercise. One such activity to practice concepts in
the classroom is a factoring puzzle. Below is a screenshot of part of a puzzle that can
be used in the classroom to provide students with the opportunity to work
independently to factor polynomials.


This particular puzzle consists of a number of triangles that contain either a
polynomial or factors of a polynomial. In this example, there is no particular
organization determining if the polynomial should be factored with a particular
factoring pattern. Instead, the assortment of polynomials is random. The triangles
of the larger puzzle will be cut out and distributed to students, who are then
required to place the triangles together in such a way to create a large hexagonal
shape that correctly has a polynomial and its factors touching side to side.
Completing this puzzle requires students to practice factoring polynomials or
multiplying them in order to match the factors with the correct polynomial. They
may do this activity alone or in groups. Since this activity is completed
independently of the teacher, the teacher has the opportunity to circulate the
classroom and provide support for students that may need re-teaching or help with
this concept.
An activity to use to help students review this concept for a test is to have
students participate in a Jeopardy Tournament. The structure of the game Jeopardy
is such that the topics given can align with the concepts covered in the previous unit.
There are 5 questions under each topic for the students to review and practice
answering questions similar to those that will be on the test. For example, if the
unit that has been completed is Factoring Polynomials, the Jeopardy game would be
set up to have the main topics include; Greatest Common Factor, Difference of
Squares, Simple Trinomials, Complex Trinomials, Zero-Product Property and
Solving Quadratics.

Having the students work in groups of 4, they would play the game (a Power
Point Application) and keep track of their own scores. Students would be required
to keep track of the questions they did not answer correctly, or did not understand.
At the end of the session, a review would be held to clear up any misconceptions or
trouble a student was still having with a particular concept. In this way, students
are monitoring their own learning and identifying the areas of instruction that they
need help in. Not only does this empower students, but having them review for a
test in this way also allows them to become autonomous learners.
An activity such as this Jeopardy Game is structured so that students are
made aware of exactly what type of questions relate to each concept. Participating
in this activity gives students opportunities to practice working through problems
that are similar to those they will encounter on an assessment or test. The game is
set up with increasingly more challenging questions as one moves through the
column of questions, a $200 question is inherently more simple than the $1000
question. Working in a small group provides students with the opportunity to
practice questions as well as observe how their peers approach a problem. If a
student is unsure of how to answer a question, the opportunity to gain the points
moves to another student who will model how to solve the problem.
In all, it is important to change the modes in which students learn and apply
the skills they learn in the classroom. By offering students different methods to
interact with the material, they are not only learning one way to understand and
work with the knowledge base they are acquiring. Instead, they are being
introduced to concepts and figuring them out through different lenses and
perspectives, thus inducing true and authentic learning. By having students learn
the basics of factoring polynomials through the hexagonal puzzle, and then by
reviewing that information through the Jeopardy question game, students are
engaging with the classroom material in deep and meaningful ways.

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