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Mathematical Problem Solving
Course Number: MA.PRBLSLV
Overview
This course is intended for students who have attained
proficiency in the basic mathematical skills and who have successfully
completed at least a first year Algebra or IBMP course. It is designed
to give students a firm problem-solving foundation. Students will use
finite differences to study functions and sequences, as well as matrix
logic and unit analysis. Students are expected to master a multitude of
strategies while developing confidence in their problem-solving
abilities. Students will be challenged to apply their knowledge on
real-world problems through collaboration, presenting solutions orally
to the entire class, and writing detailed solutions to problems.
Prerequisite: Algebra 1, 2 or IBMP 1, 2, and junior or senior status
Course Length: 2 Period Length: 1 Grade Level: 11-12
Credit per Semester: 1
Additional Credit Information: Credit per Semester: Algebra 1, 2 or IBMP
1, 2, and junior or senior status |
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Enduring Understandings
- important ideas that students should carry with them years beyond the
instruction received this year.
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Mathematics is a tool for communication.
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It is essential to be able to communicate the
reasoning used to solve problems.
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Proportional reasoning solves real world problems.
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Mathematics incorporates multiple problem solving
strategies.
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Informed decision-making is dependent upon the
ability to understand data.
Essential Questions
- most important “big picture” questions students should be able to answer
after completing learning activities
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How do you know what an answer looks like before
you solve the problem?
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In what ways can we use mathematical thinking to
model real world situations?
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How is math a universal language?
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How can data be used to mislead/ manipulate
people?
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How is geometry related to everything?
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How is the triangle the essential building block
for everything?
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What purposes do measurements serve?
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How can mathematical models be made of
complex topics including quantity, size, rate, and change.)
CSAP
Tested Standards
Highest Frequency
 High
Frequency
 Other
Standards and E-Skills
Standard
1: (Number Sense) Students develop number sense and use numbers and number
relationships in problem solving situations and communicate the reasoning in
solving these problems.
Demonstrate square numbers using pictures, words, and/or symbols.
Identify and use the concepts of factor, multiple, prime, composite and
square numbers
Know the divisibility rules for 2, 3, 5, 6, 9, and 10. Describe numbers by
their characteristics
Standard 2: (Algebra and Functions) Students use algebraic methods to
explore, model and describe patterns and functions involving numbers,
shapes, data, and graphs in problem-solving situations and communicate the
reasoning used in solving these problems.
Recognize and continue a geometric and/or numeric pattern.
Translate written words into algebraic form.
Translate a given pattern into a different form.
Recognize, explain and extend a linear pattern in a problem
solving situation.
Standard
3: (Probability and Statistics) Students use data collection and analysis,
statistics, and probability in problem-solving situations and communicate
the reasoning and processes used in solving these problems.
Organize
and construct a line graph, bar graph, and frequency table from a set of
data
Interpret
and draw conclusions from a variety of visual data forms
Standard 4: (Geometry) Students use geometric concepts, properties, and
relationships in problem-solving situations and communicate the reasoning
used in solving these problems.
Determine the perimeters of
polygons.
Determine the areas of squares, rectangles, parallelograms, rhombuses,
triangles.
Use a variety of methods to
find area.
Compare areas of figures
and explain their relationships.
Standard 5: (Measurement) Students use a variety of tools and techniques to
measure, apply the results in problem-solving situations, and communicate
the reasoning involved in solving these problems.
Apply
proportional reasoning skills.
Apply spatial reasoning.
Read and interpret scales.
Use the appropriate formula/procedure correctly to solve perimeter of
polygons.
Use
the appropriate formula correctly to solve problems involving area.
Standard
6: (Computation) Students link concepts and procedures as they develop and
use computational techniques, including estimation, mental arithmetic,
paper-and-pencil, calculators, and computers, in problem-solving situations
and communicate the reasoning involved.
Apply
order of operations
Add and subtract fractions and decimals in problem-solving situations. Apply
computational strategies including traditional algorithms for adding and
subtracting fractions. |
