Names:

Miryam Casas
James Rath


Title:

Tiling Pools (Equivalent Algebraic Expressions)


Grade level:

Eighth grade honors algebra


Source:

???
CMP Eighth Grade, Equivalent Expressions, Investigation 2, pg 20-21


TEKS:

???
8.4 Patterns, relationships, and algebraic thinking.  The student
  makes connections among various representations of a numerical
  relationship.  The student is expected to generate a different
  representation given one representation of data such as a table,
  graph, equation, or verbal description.
8.5 Patterns, relationships, and algebraic thinking.  The student uses
  graphs, tables, and algebraic representations to make predictions
  and solve problems.  (A) The student is expected to: estimate, find,
  and justify solutions to application problems using appropriate
  tables, graphs, and algebraic equations.


Performance or Learner Outcomes

Students will be able to develop and evaluate/compare equivalent
algebraic expressions.  Students will be able to find an algebraic
relationship for a pattern in table data.


Overview

Working in groups, students will use tiles to compile a table of
perimeters for different sized squares.  The students will then
develop and algebraic expression for the perimeter given the
side-length of the square.  Students will also try to develop as many
equivalent expressions as they can; they will explore reasons for the
expressions' equivalence using alebraic and graphical methods.


Materials Needed

For each group, a copy of "Investigation 2: Equivalent Expressions,"
pages 20 and 21 from the CMP book; and a bag of colored tiles.


LESSON PLAN

Engagement

Introduce/review the problem of finding the perimeter of a rectangle.
Develop several expressions for the perimeter: 2(l+w), 2l+2w, l+l+w+w,
l+w+l+w.  Ask "Why are these expressions equivalent?" and "What does
it mean for two expressions to be algebraically equivalent?"  Review
associative, commutative, and distributative rules; review existence
of additive/multiplicative identities and inverses.


Exploration

Students will work in groups of three on "Investigation 2.1: Tiling
Pools."  Students will use provided tiles to compute and tabulate the
perimeters of variously sized squares.  They will then try to
formulate expressions for the perimeter using their tabular data,
graphs of the data, and abstract drawings of the pool.


Explanation

The class as a whole will collect and share their expressions for the
perimeter.  Each group will present its reasoning for believing pairs
of the expressions to be equivalent.


Elaboration

The class will answer the "Follow-Up" questions in the lab.  In
addition, we will ask such leading questions as "What if we had a
rectangular pool?", "What is the usefulness of equivalent
expressions?", and (??? others ???).


Evaluation

???
Did we succeed?