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The 3rd Grade Mathematics PSSA

- Open-Ended Questions

Presented by Carolyn Marchetti cmarchetti_at_state.

pa.us

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

Overview of the 3rd grade

- Mathematics PSSA

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

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

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

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.

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

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.

Open-Ended Questioning

In Math

What is Problem Solving

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

What Is an Open-Ended Item

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

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

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

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

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

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

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

The Directions

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

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

The Work (a students response)

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

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.

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

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

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

What are the Magic Words

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

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.

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.

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

Open-Ended Math Items

- In Your Classroom

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

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

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)

Where to Find Open-Ended Items

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

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

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

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

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

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)

Tips for Beginners

- Provide time for students to solve problems

individually - Share answers/ideas with partners or in small

groups - Discuss as a class

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

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

The Importance of

- Mathematics Vocabulary

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.

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)

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

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

Good luck to you and your students!!

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