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Math - Problem
Solving
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Plan Author: David Riddick
Date Created: 5/11/2003 10:03:29 AM PST
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School:
Dyer St. Elementary
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Grade Level:
5
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Students:
31 Students. 20 boys and 11 girls. 10 E0s; 10 RFP's 10 ELD4-5: 1 ELD2. GATE
class - advanced learners
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Subject Area(s):
Mathematics
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Goal(s):
Students will have an understanding of a technique to engage in mathematics
problem solving.
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Concept(s):
Students will learn estimating is a technique to engage in mathematics
problem solving.
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Standards:
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 CA- CCTC: Aligned CSTP's and TPE's
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• Standard : CSTP: Standard for Engaging and Supporting all Students
in Learning
TPE: C. Engaging and Supporting Students in Learning
CSTP Description: Teachers build on students’ prior knowledge, life
experience, and interests to achieve learning goals for all students.
Teachers use a variety of instructional strategies and resources that
respond to students’ diverse needs. Teachers facilitate challenging
learning experiences for all students in environments that promote
autonomy, interaction and choice. Teachers actively engage all students
in problem solving and critical thinking within and across subject matter
areas. Concepts and skills are taught in ways that encourage students to
apply them in real-life contexts that make subject matter meaningful.
Teachers assist all students to become self-directed learners who are
able to demonstrate, articulate, and evaluate what they learn.
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• CSTP Key Element : Engaging students in problem solving, critical
thinking and other activities that make subject matter meaningful.
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 Question : engage all students in
problem solving activities and encourage multiple approaches and
solutions?
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• Standard : CSTP: Standard for Planning Instruction and Designing
Learning Experiences for all Students
TPE: D. Planning Instruction and Designing Learning Experiences
for Students
CSTP Description: Teachers plan instruction that draws on and values
students’ backgrounds, prior knowledge, and interests. Teachers establish
challenging learning goals for all students based on student experience,
language, development, and home and school expectations. Teachers
sequence curriculum and design long-term and short-range plans that
incorporate subject matter knowledge, reflect grade-level curriculum
expectations, and include a repertoire of instructional strategies.
Teachers use instructional activities that promote learning goals and
connect with student experiences and interests. Teachers modify and
adjust instructional plans according to student engagement and
achievement.
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• CSTP Key Element : Establishing and articulating goals for student
learning.
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Question : build on the strengths,
interests, and needs of all students to establish high expectations for
learning?
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CA- California K-12 Academic Content Standards
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• Subject : Mathematics
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• Grade : Grade Five
By the end of grade five, students increase their facility with the four
basic arithmetic operations applied to fractions, decimals, and positive
and negative numbers. They know and use common measuring units to
determine length and area and know and use formulas to determine the
volume of simple geometric figures. Students know the concept of angle measurement
and use a protractor and compass to solve problems. They use grids,
tables, graphs, and charts to record and analyze data.
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• Area : Mathematical Reasoning
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• Sub-Strand 2.0: Students use strategies, skills, and concepts in
finding solutions:
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Standard 2.1: Use estimation to verify
the reasonableness of calculated results.
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Objective(s):
Cognitive: Students will learn mathematics concepts by answering a complex
thought provoking problem using estimation.
Observable behavior: Students will struggle with a thought provoking problem
and present ideas or solutions to the class.
Criteria: Given the problem, "How many small squares will fit inside a
rectangle that is 54 units in length and 36 units in width," students
will demonstrate understanding by listing each step of their explanation and
providing explanations for them with an accuracy of 75%.
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Prerequisite Background Skills/Knowledge:
Students are familiar with shape of a square and rectangle. Students know the
area of a square and rectangle is found by multiplying the width and length.
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Vocabulary / Language Skills:
Listening: Students listen to verbal instructions given in preparation for
their task. ELD students are given help by peer tutors as teacher speaks.
Speaking: Students participate in lesson by quietly responding to one another
in cooperative groups.
Writing: Students will take notes and write on math worksheet.
Reading: Students read from the math worksheet and math textbook.
Vocabulary: squares, rectangles, length, width, unit, area, perimeter
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Materials:
1) Pencil & Paper
2) Transparencies
3) Transparency pen
4) math textbook
5) Math worksheet on "Problem Solving"
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Classroom Management:
During directed lesson, students are seated in assigned seats, which are
2-person desks.
I will give out extra credit points for students who participate and
cooperate with lesson.
Extra credit points for actively engaged students
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Procedure:
Procedure: Open
As an attention getter, I call on students who have transitioned well into
Math to be the first volunteers to share what they know about the differences
between squares and rectangles.
Procedure: Body
Input:
1st: Point out the standards we are working on (posted).
2nd: Establish a sense of academia by reviewing vocabulary for this lesson,
and deepen their understanding by allowing students to demonstrate their
knowledge of the words.
3rd: Inform students this lesson will differ from the usual mathematics
lesson and reflect more of an Asian mathematics lesson. This lesson is built
around a single problem. 3 Steps to the Lesson:
1) Before - Getting Ready
2) During - Students Work
3) After - Class Discourse
4th: Before: I pose the question the students will work on - "How many
small squares will fit inside a rectangle that is 54 units in length and 36
units in width." I will make sure students understand their task and the
vocabulary of the lesson.
5th: During: Students will write down each step of their solution and explain
why they chose their steps. Students will work independently first, and then
in cooperative groups to present their ideas and solutions to the class. I
will listen and take notes to find out how different children or groups are
thinking.
6th: After: Class discourse. I will accept student solutions without
evaluation. Students will justify and evaluate their results and methods.
Student must listen to others and help decide which approaches and solutions
make the most sense and why. I will encourage reflection on solutions,
methods, and extensions.
Guided Practice:
I will explain the idea that important mathematics concepts and procedures
can best be taught through problem solving.
Much more learning occurs and much more assessment information is available
when a class works on a single problem and engages in discourse about the
validity of the solution.
Independent Practice:
Students will try to solve the problem independently at first. Students will
transition into cooperative groups to struggle with the problem.
High achieving students will be allowed to expand their knowledge by creating
similar problems and answering them.
Procedure: Close
To close the lesson students will reflect on each others solutions, methods
and extensions.
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Assessment:
Students will demonstrate understanding by listing each step of their
solution to the problem "How many small squares will fit inside a
rectangle that is 54 units in length and 36 units in width," and include
reasons for his/her steps with a proficiency of 75%.
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Assessment/Rubrics:
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Reflection:
The objective of the lesson was achieved. Students were able to list steps of
their own solution to the critical thinking problem. This is a lesson in
which I think I may learned more than my students.
I went into the lesson with an awareness that there was no
"correct" answer to the problem. However, it was not inherent. I
still had the sense that I knew the "correct" answer and that I
would direct my students to find it. During the lesson, the students were
nowhere near where I thought they should be. It appeared to be a disaster.
But I didn't interrupt. The students were actively engaged in the lesson, so
I allowed them to explain their solutions.
It wasn't until about half-way through the lesson that I had an epiphany. The
students recognized the question, "How many small squares will fit
inside a rectangle that is 54 units in length and 36 units in width,"
the problem does not state what size the small squares have to be. The
students all arrived at different estimations for how many squares will fit
inside the rectangle.
The lesson turned into a valuable learning experience for the students to
understand the concept of area. They learned the concept of
"length" as being the side of the rectangle that is vertical by
connecting it to the "L" in length. The letter L runs vertically.
Likewise, the letter "w" in "width" is wider and
represents the horizontal side of the rectangle.
This lesson has been extremely powerful to understand math concepts. The
power comes from allowing the students to attack a problem from their
understanding, not mine.
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