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Open-Ended Questions Presentation Transcript

  • 1. Open-Ended Questions in Math
  • 2. What Is an Open-Ended Item?
    • An open-ended math item asks students to solve a multi-step problem and explain WHY they chose each step .
  • 3. PSSA
    • Each student has 4 open ended items on the PSSA
      • 3 on the common form
      • 1 on the matrix form
  • 4. PSSA
    • Each open-ended item has a maximum value of 5 points.
    • Therefore, open-ended items account for approximately 18% of the student’s PSSA score.
    • Responses to open-ended items are graded using a rubric.
  • 5. 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 showing a correct step toward solving the problem.
  • 6. Calculator Usage
    • Calculators can be used for all open-ended items on the PSSA
    • Students need to be familiar with using the specific calculator before the test!
  • 7. The Directions
    • For full credit, you must do the following:
    • Show OR describe each step of your work, even if you did it in your head (“mental math”) or used a calculator,
    • Write an explanation stating the mathematical reason(s) why you chose each of your steps.
  • 8. Tips for Solving from Teachers
    • Make 2 columns
      • Put “work” on the left
      • Put “explanation” on the right
    work explanation
  • 9. Solving Tips from Teachers
    • Show and number each step of the work
      • Even/especially if the work was done in the student’s head or calculator.
  • 10. Explanation Tips
    • Encourage students to EXPLAIN their work - not DESCRIBE it
      • Description:
      • “ I multiplied $1.25 and 13 and got $16.25”
      • Explanation
      • “ I multiplied the price of gas per gallon and the number of gallons to get the price for the gas used.”
  • 11. Explanation Tips from Teachers
    • Make sure ALL steps are explained in words.
    • Encourage students not to use numbers in their explanations – this will stop them from describing their work.
  • 12. Explanation Tips from Teachers
    • Use “magic words”* in the explanation.
    • These are words that gear students to ‘explain’ their work rather than ‘describe’ it.
    • * Article on “Magic Words” can be found in the math assessment handbook
  • 13. What are the Magic Words?
    • To find
    • To get
    • To see
    • To figure out
    • To show
    • To determine
    • Because
    • Since
    • Therefore…….
  • 14. Explanation Tips from Teachers
    • Encourage your students
    • NOT to use the words
    • “ to find THE ANSWER”
    • The words “the answer” do not explain what the answer represents.
  • 15. The Explanation
    • 1) I multiplied the price of gas and the number of gallons TO GET the total cost of gas.
    • 2) I added the cost of gas, food and tolls together TO FIND the total cost of the trip.
    • 3) I divided the total cost of the trip by the number of miles and I FOUND the cost per mile.
    • 4) SINCE I had many decimal places, I rounded to the hundredth BECAUSE I wanted money.
  • 16. The Final Product
    • Work
    • 1) $1.25 X 13 gal = $16.25
    • 2) $16.25 + $12.84 + $6.50
    • = $35.59
    • 3) $35.59  221mi  $0.161041
    • 4) $0.16 per mile
    • Explanation
    • 1) I multiplied the price of gas and the number of gallons TO GET the total cost of gas.
    • 2) I added the cost of gas, food and tolls together TO FIND the total cost of the trip.
    • 3) I divided the total cost of the trip by the number of miles and I FOUND the cost per mile.
    • 4) SINCE I had many decimal places, I rounded to the hundredth BECAUSE I wanted money .
  • 17.