Open Ended Mathematics Problems

1. Writing story problems or a story for mathematics.
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Write a story that describes (variables, figures, graphs, tables).
Illustrate your story with pictures and/or graphs.
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Write a story that describes the Jones's family's trip to the museum.
Use the graph that shows time and distance to describe the trip.
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Write a story problem that could be used to fin whole, rational,
integer operations, concepts, and formulas.
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Write a story problem for the example 52 x 36 = 1,872
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Write a detective or mystery story involving a crime where area and
perimeter are important clues to the solution.
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Write a story that includes a detailed description of our school.
Use words like perimeter, volume, area, height, triangle, etc.
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Write a children's story that would teach a first grader about geometric
shapes.
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Write a fable about mathematics. Fables usually end with a
moral. An example might be, "Practicing your math facts makes one
a speed mathematician." Think of your own mathematics moral.
Then write a fable with the moral as a lesson.
2. Student Opinions about Mathematics
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Some students think that (alternate conception, error). Explain your
thinking in pictures and in words. Example, Some students think when
you multiply you always get a larger number. What do you think?
Explain your thinking in pictures and in words.
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Explain your thinking in words and pictures.
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Some students think that 1/10 is greater than 1/2. What do
you think?
3. Writing Descriptions in Mathematics
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Describe in words and pictures how the diameter of a circle is related
to other parts of the circle.
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Describe several different ways you could measure our school cafeteria.
Then tell which way you would use and why.
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If you measured an object with five different rulers and got five
different answers, how would you decide which answer was correct.
Explain your thinking.
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Carpet is sold in square yards. The width of a carpet roll
is 12 feet. Describe how you calculate the amount of carpet you should
buy to cover the floors of three bedrooms measuring 10' x 12', 10' x 10',
and 16' x 18'.
4. Teaching Mathematics Concepts
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Write what you would say and what you would draw to teach a classmate
how to add fractions.
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Describe the error in thinking that a student has made on his math
test. Don got an answer of 15 for the example 6 + 24/2
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How would use fraction bars to teach equivalent fractions for 1/2?
5. Construct in Mathematics
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Determine the most popular flavor of ice cream in your school.
Illustrate your findings.
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Construct a line graph for the high/low temperatures for q wee.
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Construct a table that records 10 different observations you make
about weight and height relationship of people in your class.
Journal Topics for Math
Topics for Getting Started
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Describe how your mother or father uses mathematics in their job.
Use words and pictures.
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What do you like most (least) about leaning mathematics?
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Cut out pictures you like from a magazine and paste it into your
journal. Write a story problem that is related to your picture.
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Write an autobiography that describes how you have learned mathematics.
Topics that Target Conceptual Understanding
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Describe in words and pictures how fractions and decimals are alike
and how they are different.
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Tell me everything you know about this picture (a trapezoid)
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Create a pattern with two shapes of your choice. Describe your
pattern in words.
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Some people think when you divide you always get a smaller number.
What do you think?
Berenson, S. B. & Carter, G. S. (1995).
Alternative
Assessments: Practical Applications
for Mathematics and Science Teachers.
Center for Research in Mathematics and Science
Education: North Carolina State
University.