The 3rd Grade Mathematics PSSA

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The 3rd Grade Mathematics PSSA

• Open-Ended Questions

Presented by Carolyn Marchetti cmarchetti_at_state.
pa.us
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Todays Agenda

• Overview of the 3rd grade math PSSA
• Open-ended questioning in math
• Open-ended math items in your classroom
• The importance of mathematics vocabulary

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Overview of the 3rd grade

• Mathematics PSSA

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The Make-up of the Test

• Common Form
• 60 multiple choice 1 point each
• 2 open-ended 5 points each
• Matrix Form (imbedded field test)
• 10 multiple choice
• 1 open-ended

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Manipulatives

• Calculators will NOT be permitted on the 3rd
  grade PSSA
• Punch-out rulers will be provided
• Customary side
• Calibrated to ¼ inch but students will only be
  asked to measure to the nearest ½ inch
• Metric side
• Calibrated to millimeters but students will only
  be asked to measure to the nearest centimeter

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Standards Assessed

• All PA Math Standards will be assessed (2.1
  2.11)
• The standards that will have the most number of
  questions will be
• 2.1 Numbers
• 2.2 Computation
• 2.3 Measurement
• 2.9 Geometry

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General Information

• If asked by students, test administrators will be
  permitted to PRONOUNCE words for them but will
  not be permitted to explain the meaning of these
  words.

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General Information

• Anything on the walls that can be of help on an
  item (ex, multiplication charts) MUST be taken
  down or covered
• The open-ended scoring rubric may be displayed

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Scratch Paper

• If students use scratch paper for open-ended
  items, make sure they transfer ALL of their work
  to the test booklet.
• It may be helpful to have students NOT use
  scratch paper for the open-ended items.

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Open-Ended Questioning
In Math
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What is Problem Solving?

• Reasoning, communication and making connections
• Why?
• How do you know?
• Explain that
• Convince me

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What Is an Open-Ended Item?
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Sample Open-ended Items

• Draw a fair and unfair spinner
• Create a story problem to fit given numbers
• Show amount of change with fewest number of coins
• Show different ways to make a given amount with
  coins

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Sample Open-ended Items

• Create a table, chart, list or graph from data
• Draw a picture to illustrate a problem
• List all possibilities
• Continue a pattern

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Sample Open-ended Items

• Show a reflection
• Draw geometric shapes
• Draw a line of symmetry
• Model right angles and right triangles
• See the 3rd grade standards for more possibilities

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Explanations

• At the 3rd and 5th grade levels, open-ended items
  may
• Require no explanation
• Require an explanation that focuses on
  mathematical concept knowledge
• Require an explanation that tells why each step
  was taken
• Required by all 8th 11th grade openended
  items

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Open-ended Items

• If an open-ended item is straight problem solving
  (computational type) it will have the following
  directions
• Show each step of your math work
• Explain WHY you chose each step

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The PSSA Rubric

• To earn all 5 points, students need to show each
  step of their work, and explain WHY they chose
  each of their steps
• They can earn at least 1 point by attempting to
  solve the problem

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Sample 3rd Grade Question

• Mr. Riveras 3rd grade class has set up a bird
  feeder
• and is collecting data about the number of birds
• eating the sunflower seeds.
• On Monday, they counted 14 birds eating sunflower
• seeds. On Tuesday, they counted 18 birds. On
• Wednesday, they counted 39 birds.
• How many more birds did they count eating
• sunflower seeds on Wednesday than on Monday and
• Tuesday together?

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The Directions

• For full credit, you must do the following
• Show each step of your math work
• AND
• Explain why you did each step.

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Tips for Solving from Teachers

• Make 2 columns
• Put work on the left
• Put explanation on the right

work
explanation

• Show and number each step of the work

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The Work (a students response)

• 14
• 18
• 32 birds
• 39
• - 32 answer
• 07 birds 7 birds

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Explanation Tips from Teachers

• Encourage students to EXPLAIN their work - not
  DESCRIBE it
• Description
• I added 14 and 18 and got 32
• Explanation
• I added the number of birds on Monday and the
  number of birds on Tuesday to find the total
  birds on those two days.

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Explanation Tips from Teachers

• Make sure ALL steps are explained in words
• If students numbered their work, they should have
  the same number of explanation steps as work
  steps
• Advise students not to use the words to find the
  answer

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Explanation Tips from Teachers

• Explain which operation was performed and what
  each number means
• Start each step with I added
• I subtracted
• I multiplied, etc
• Then explain what each number represents
• I added the number of Mondays birds to the
  number of Tuesdays birds

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If students are describing

• Encourage students to use the Magic Words in
  their explanations. These words gear students to
  an explanation
• Article on Magic Words appears in the
  Mathematics Handbook

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What are the Magic Words?

• To find
• To get
• To see
• To figure out
• To show
• Because
• Since
• Therefore.

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The Explanation(a students response)

• I took 14 18 because you had to add it because
  you had to find how many birds on both days. I
  got 32.
• 2) Then I subtracted 39 and 32 because you
  needed to find how many more birds they found on
  Wednesday than on Monday and Tuesday.

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The Final Product

• Work
• 14
• 18
• 32 birds
• 39
• - 32
• 07 birds
• Answer
• 7 birds

• Explanation
• I took 14 18 because you had to add it because
  you had to find how many birds on both days. I
  got 32.
• 2) Then I subtracted 39 and 32 because you
  needed to find how many more birds they found on
  Wednesday than on Monday and Tuesday.

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Labels

• Answers must be labeled correctly
• Especially money and measurement
• Ex) 57 cents can be written as 0.57 or 57?
• NOT 0.57? or 0.57?
• Perimeter in, cm, etc
• Area sq in, cm2, etc

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Open-Ended Math Items

• In Your Classroom

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Curriculum

• Your Goal
• Open-ended items should become a part of your
  math curriculum
• NOT just an added activity to do if you have time
  at the end of the chapter or on days before
  vacation!
• Your Districts Goal
• To develop a district-wide plan on the the
  implementation of open-ended items in math
  classrooms, kindergarten through 12th grade

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Where to Find Open-Ended Problems

• Mathematics Assessment handbook Released Items
  Handbook
• www.pde.state.pa.us
• Click on K-12 Schools
• Click on Assessment Testing
• Click on Assessment Handbooks
• Mathematics Instructional Rubrics (Primary thru
  High School)
• www.pde.state.pa.us
• Click on K-12 Schools
• Click on Curriculum Instruction
• Click on Mathematics
• Click on Whats New

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Where to Find Open-Ended Problems

• Open-ended problems created at the 2002 Math
  Governors Institutes
• www.pde.state.pa.us
• Click on K-12 Schools
• Click on Curriculum Instruction
• Click on Mathematics
• Click on Professional Education
• PSSA Practice Tests (5th, 8th 11th)

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Where to Find Open-Ended Items

• Text resource books
• Multi-step word problems from your textbook
• Teacher-made questions
• Internet resources

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Suggested Resources from Teachers

• PSSA Mathematics Coach books
• 1-800-221-9372 or www.educationaldesign.com

• Measuring Up books
• 1-800-822-1080 or www.patesthelp.com
• Continental Press PAM Prep
• 1-800-233-0759
• Exemplars www.exemplars.com

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Hints to Creating Your Own Open-Ended Problems

• Make sure problems address a standard at or near
  your grade level
• Make sure all problems require more than 1 step
  (or part) to solve
• Create problems that can be solved in more than
  one way
• Create some problems that include charts, graphs,
  spinners, pictures, etc

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Hints to Creating Your Own Open-Ended Problems

• Use the same directions that the PSSA uses at
  your level (show all your work AND explain each
  step)
• Have students write their answer in an answer box
  
• Make sure they label their answer
• Use your students names, other teachers names
  and your schools name to make the problems more
  interesting to your students

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Ways to Use Open-Ended Items in Your Classroom

• Put a problem on every test or quiz
• Homework
• Math journal
• Problem of the week
• Open-ended portfolio..
• DO NOT use only as extra credit

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Practice, Practice, Practice

• Practice should occur the entire year
• Open-ended questions should be addressed about
  once a week
• Open-ended questions should become an integrated
  part of the math curriculum at ALL grade levels
• When going over homework problems that involve
  multiple steps, have students orally explain why
  they chose their steps (even if they didnt have
  to write it)

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Tips for Beginners

• Provide time for students to solve problems
  individually
• Share answers/ideas with partners or in small
  groups
• Discuss as a class

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Lower Level Grades

• Students can solve problems in groups
• Groups can explain their answer in words
• Teachers can model the written explanation on the
  board

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Tips for Rubric Use

• Copy the rubric on the back of an open-ended item
  and circle or highlight where their score falls
• Have students correct lower scoring papers to
  make them a 5
• Have students grade their own solutions or
  another classmates solution using the rubric

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The Importance of

• Mathematics Vocabulary

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Math Vocabulary

• Numerous studies reveal that a knowledge of
  mathematics vocabulary directly affects
  achievement in arithmetic, particularly problem
  solving.
• Barton, M.L. Heidema, C. (2002)
• Teaching Reading in Mathematics 2nd Ed.

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Math Vocabulary Development

• Insist that students use correct mathematical
  vocabulary in their explanations (when
  developmentally appropriate)
• Refer to the Terms to Know in the math
  standards (all grade levels) or page 26 in the
  2000-2001 math handbook (for grade 5)
• A Grade 3 Terms to Know will be listed in the
  3rd grade Mathematics Handbook (coming soon)

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Math Vocabulary Development

• Math vocabulary bulletin board - add new words to
  it year-round
• Math Word Wall
• Student developed math vocabulary notebook
• Math word-of-the-day

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Conclusion

• Incorporating open-ended questions in your math
  curriculum will not only help improve your PSSA
  scores, but will also help improve your students
  understanding, and the ability to communicate
  that understanding

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Good luck to you and your students!!