Open-Ended Questions

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Open-Ended Questions

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

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