# Components of Math Lesson Plan

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```					                    Components of a Math Lesson
Focusing on Teaching Through Problem Solving
K-5:
A Three-Part Lesson Format for Instruction

Traditionally, teachers’ math lesson plans and the implementation of
those plans consisted of an explanation or review of an idea or concept
followed by lots of exercises. Lessons that follow this explain-then-practice
pattern condition students to focus on procedures rather than problem
solving. The problem solving piece came only when the teachers’
expectations turned to students’ applying the taught skills, particularly for
assessment purposes. In this production mode, the goal is to get the right
answer. We now know that there is a need to shift the focus from a
production mode to a problem solving mode. We no longer need students
focused only on procedures. They should focus on math as reasoning and
communicating so they can be successful not only on today’s high stakes
assessments but in higher education and future employment. Having said
this, how do we know what a good math lesson looks like? Well, it has three
parts. They are the before, during, and after phases as described below:
Before
   Be sure all expectations for products are clear;
During
(Students Work) – 20 minutes
   Let go!
   Listen carefully,
   Provide hints,
   Observe and assess;
After
(Class Discourse) – 20 minutes
   Accept student solutions without evaluation,
   Conduct discussion as students justify and evaluate results and
methods (reflection).
(Adapted from Elementary and Middle School
Mathematics: Teaching Developmentally
4th Ed., John Van de Walle)
Teachers in the before phase should begin with a simple version of
the task to get students engaged. These are often called warm ups. Here is
the math task I want my students to work on in 4th grade (SOL 4.13):

Fig. 1

Assume that the edge of a square (color tile) is 1 unit. Add squares (color
tiles) to this shape so that it has a perimeter of 18 units.

Warm Up 1:
The teacher uses squares (overhead color tiles) to form a 3–by-5 rectangle.
There are 15 squares (overhead color tiles). There are three rows of five
squares (overhead color tiles). If students do not mention area and
perimeter, add them to the word wall and have students write them in their
math journal. They may represent the rectangle by tracing color tiles in
their math journals and labeling it a 3-by-5 rectangle.

Fig. 2
p=16 a=15

If students need another warm up, provide this model:
-or-
Warm Up 2:
Students use color tiles (6) and grid paper (1’x1”) to make the shape that the
teacher modeled on the overhead (See Fig. 1). It has a perimeter of 12 units
(the edge of the color tile is 1 unit). After making the same shape, have
students figure out what the area of the shape is. Students may place the
grid of the shape in their math journal and write (representations – pictorial
and written) the perimeter and area (p=12 units; a=6 units).

Teachers in the during phase let students work by letting go. The
expectation is that they can solve the problem. The students are now ready
to tackle and solve the task assigned to them. They have the materials and
math language they need. Small groups may be set up for problem solving.
These groupings are beneficial because students can communicate
mathematically and share their reasoning. Students can represent their
work through journal writing and drawings. The teacher’s role is to
facilitate and actively listen. Hints and suggestions may be provided to help
students move forward in the problem solving task. A hint may be:
 Try drawing a picture or
 Try a simpler problem.

Teachers in the after phase engage students in discussion.
Student engagement is critical during this phase. Rules, hypotheses, and
future problems are shared. Students now have an opportunity to share
their knowledge of the math language (area, perimeter, square unit, etc.) and
representations they used for problem-solving. By communicating
mathematically, students can listen to how others approached the task and
what their solution was. They can question one another for depth of
understanding while the teacher guides the discourse.
 Are their other possible solutions?
 What can you find out about that?
 Would the same idea work for…?
 Is there another method for solving?
Students will initially assume their answer is wrong when asked by the
teacher for an explanation of their thinking/working process. This
assumption will pass when the students become accustomed to explaining
their solutions. This is a learning phase and it is often during this phase that
the best learning takes place. Solutions can be recorded for closure. They
may be revisited.
MATHEMATICS LESSON PLAN

Name __________________ Grade ________ *Date of Instruction _____________
*Due One Week Prior to Date of Instruction. Feedback will be provided.

1. Strand: ________________________2. SOL Number ___________________

3. Objective: ______________________

4. Assessment – Provide a statement and attach a copy: ______________________

________________________________________________________________________

________________________________________________________________________

5. Method of Instructional Process (warm up, task, discourse) in sequence:

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

6. Mathematics Language Required for Student Learning/Application/Questions to
1. ____________________________        4. ______________________________

2. ____________________________            5. ______________________________

3. ____________________________            6. ______________________________

________________________________________________________________________

________________________________________________________________________

7. Materials Required: ___________________________________________________

________________________________________________________________________

________________________________________________________________________

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