Facilitator Guide: Writing in Math by dan gibson

Teaching ExtendedResponse Writing Skills: Writing in Math Connection Facilitatorâ&#x20AC;&#x2122;s Guide DANIEL J. GIBSON Instructional Technology/Design Major 10/29/2011

Gagne’s (1985) Nine Events of Instruction Gain Attention of Learners To gain student attention, students will take an ISTEP pre-test, which may be difficult for some students. However, it will provide the students with an understanding of what to expect on the ISTEP. This test will be scored with an ISTEP Extended Response rubric. In addition, web 2.0 and educational technology tools will be used to present instruction. The first web-based tool will be a Prezi presentation. There will be various stopping points for the students to engage in an activity. To encourage dynamic and interactive instruction, the presentation will be presented on a SMART board. At various points during the presentations, the interactive white board will allow teacher and learners to interact with the Indiana Statewide Testing for Educational Progress-Plus (ISTEP+) math problems. Overall, the presentation will be dynamic in nature. Inform Learners of Objectives Objectives can be stated at the beginning of each section of the instructional unit. Additionally, students will demonstrate the task being learned. Designing a Solution  Underline keywords for solving a math word problem  Determine what operation to use based on keywords  Identify the main question being asked to solve  Choose a strategy to solve a problem  Develop a plan for solving the math problem  Solve the problem Written Explanations  Identify all nouns  Restate the question  Write the steps taken to solve the problem with complete sentences  Write the solution at the end of the explanation in a complete sentence Self-Evaluations  Reread own response  Evaluate the response for clarity  Check for thoroughness in their work Stimulate Recall of Prior Knowledge Present students with an ISTEP extended-response pre-test. Discuss and list student experiences with word problems and ISTEP writing in Math. Their experiences will be listed in a KWL (know, want to know, and learned) graphic organizer, which will activate their prior knowledge. This chart will be posted in the classroom for the entire instructional unit. Lastly, students’ graded pre-tests will be handed out to discuss how to improve their extended-response writings.

Present Materials Instructional content will be presented in various ways to stimulate all learning styles. A visually motivating Prezi presentation on writing an ISTEP+ math explanation will be presented over a period of 5 or more days. Students will be given several handouts to practice the skills presented each day, and discussion will be generated from these handouts. Provide Learning Guidance During the student’s writing tasks, the teacher will conference with several students around the room. This conference should be short, and its purpose is to look for well-written examples to share. Students will write explanations on the student handout or in their math journal. The math journal is just a regular notebook used for note taking and practice problems. These handouts and journal entries will receive comment, suggestions, and/or questions from the instructor. Once students have completed a task, students will engage in classroom discussion of student writing. Students will receive “praise points”—positive reinforcement of effective writing behaviors—and their work will be shared. Elicit Performance At most points of instruction, math questions will simulate the applied skills portion of the ISTEP+. Provide Feedback After in-class assignments, the teacher will provide appropriate feedback to their writing. Students will receive written feedback in the form of comments, suggestions, and/or questions. In addition, with partner work, students will receive peer comments, suggestions, and/or questions. The teacher will also share well-written examples of writing. To analyze the student work, these examples can be shared using a document camera. Assess the Performance Learners will take tests and apply their writing skills. Some student tasks will be assessed with a rubric and others with a checklist. For instance, with a checklist, students will peer-evaluate and self-evaluate writings. Finally, student’s pre-test results will be compared to the summative test results. Students’ summative assessment will have three math ISTEP+ word problems and will be graded using the ISTEP+ extended-response rubric. Enhance Retention and Transfer Apply problem solving to real-world situations. Give students practice with old ISTEP+ questions. Complete exit slips after each lesson. What did you learn?

Preinstruction

Reading the Problem

Solve the Problem

•Complete Pretest •Complete KWL

•Locate keywords for operations •Determine operation(s) to apply •Identify Main Question

•Choose strategies for problem solving •Develop a plan •Solve the problem

Assess Learning

Self-Evaluation

Extended-Response Writing

•Complete the final column of the KWL •Complete the summative assessment

•Reread writing •Evaluate writing with rubric •Use checklists to check that the problem is completed

•Restate the question •Write the steps to solve the problem •Write the answer •Avoid pronouns usage

INSTRUCTIONAL STRATEGY/GOAL

Students will write a clear, concise explanation for a math problem using symbols, numbers, and words. Sequenced Tasks and Lessons

Preinstruction

1 Read the problem

Instructional Objectives

PerformanceContent Matrix

Initial Presentation Strategy (What the instructor does)

Generative Learning Strategy (What the learners do)

Assessment Item(s)

 Students will complete an extended response pre-test.  Students will complete the first two columns in a KWL chart.

ConceptRecall

 Provide students with ample time to take the test.  Ask: “What do you know or remember about the math ISTEP? What do you know about writing in math?’  Ask: “What do you want to learn about the math ISTEP? What do you want to learn about writing in math?”

 Students complete the test.  Students will recall their experiences with the math ISTEP and about writing in math.

 The ISTEP-Math PreTest will be assessed using the ISTEP extended-response rubric.  Students KWL contributions will be assessed with a KWL Chart checklist.

 Students will circle keywords for solving a math word problem.  Students will determine what operation to use based on keywords.

Concept and ProcedureApply

 Provide students with many word problem examples.  Discuss the importance of knowing what the word problem is asking from you.  List keywords for operations and strategies.

 List keywords in a 4square graphic organizer.  Practice circling keywords for choosing an operation within several word problems.  List keywords on chart paper in class.

 Successfully locates keywords within math questions.  Students will complete Problem Solving Planning Table and will be assessed with a Problem Solving Plan rubric.

2 Solve the problem

3 Extended Response

4 Avoid pronouns

 Students will identify the main question being asked to solve.

ProcedureApply

 Draw attention to the question in the sentence.

 Highlight the question.

 Students will choose a strategy to solve a problem.  Students will develop a plan for solving the math problem.  Students will solve the problem.

Concept and ProcedureApply

 Discuss strategies for solving the problem (whole class and partners).  List student ideas as presented.

 Students will restate the question.  Students will write the steps taken to solve the problem using complete sentences.  Students will write the solution at the end of the explanation in a complete sentence.  Students will identify all nouns.

ProcedureApply

 List strategies to choose when solving a problem.  Ask: “What is the question asking you to do?” and “How would you solve this problem?”  Provide opportunities to share plans and strategies used to solve the problem.  Present QSA acronym.  Demonstrate the basic requirements for a “good” response.  Provide models and examples for extended response questions.  Watch Extranormal video on writing extended-responses.

 Practice restating the question in a response.  Write the steps involved in solving the problem.  Write the answer at the end of the response.  Write responses in complete sentences.

 Assess students using an extended response rubric.

 Introduce the concept of pronouns

 Define all pronouns.  Check writing with a checklist to replace unwanted pronouns “it, they, or them”

 Utilize a checklist to ensure students are not using pronouns or at least limit pronoun usage (without affecting meaning). For instance, “I added it.” is not acceptable

ConceptApply

 Students complete Problem Solving Planning Table and will be assessed with a Problem Solving Plan rubric.  Students will list a strategy to solve the problem.  Accurate answers will be assessed from student problem solving.

5 Reread

6 Checking for Completeness

Evaluate Learning

 Students will reread their response.  Students will evaluate the response for clarity using a rubric.

Procedure and AttitudeApply

 Employ “write down-read up” strategy.  Demonstrate how to use a rubric and checklist with response writing.

 Students will check for thoroughness in their work.

Procedure and  Draw attention toward the various parts of an applied Attitudeskills ISTEP problem. Apply

 With individual copies, students will complete the final column of a KWL on their own.  Students will complete four extended response ISTEP-like problems.

ConceptApply

 Remind students about of the KWL we started and ask students to write down what they have learned.  Have students take a summative assessment simulating the extended response portion of the ISTEP.

 Self evaluate writing using “kid-friendly” rubric and/or checklist.  Evaluate peer writing using “kid-friendly” rubric and/or checklist.  Evaluate anchor responses.  Preview the format used on the ISTEP applied skills portion (i.e. terms, design & layout)

 Students will evaluate their writing and their peer’s writing using a “kid-friendly” rubric.

 Students complete the “what they learned” column of the KWL  Students will take the final test setup like the ISTEP.

 Students’ ISTEP posttest will be assessed using the ISTEP extended-response rubric.

 Use a checklist, students work is checked for completeness.

ISTEP--Math Pre-Test 1. Four students have to share one box of 21 markers. Can they share 21 markers equally? Draw a picture to solve.

Explain your answer on the lines below. ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ 2. On Monday, 987 tickets were sold for the third grade play to be performed in the school theatre. The theatre has 1,000 seats. Do you need an estimate or an exact answer to tell how many more tickets to the play can be sold? Explain. ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ How many more tickets can be sold to the play? Answer __________ more tickets

3. Eleanorâ&#x20AC;&#x2122;s class took a vote to choose what kind of ice cream to buy for their class party. They created the circle graph below to show their results.

Eleanorâ&#x20AC;&#x2122;s teacher will buy the 2 most popular kinds of ice cream for the party, and he put cookie dough and strawberry on his list. On the lines below use words, numbers or symbols to describe how Eleanor would explain that her teacher was incorrect. ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ How many more students in the class voted for strawberry than vanilla? Show All Work

Answer_________________ students

Lesson 1a: Introducing Writing in Math Students will be introduced to the main focus of this instructional unit. For this portion of the unit, students will recall their past experience with the Math ISTEP+ application section. Objective  Students will complete the first two columns of a KWL with the students Materials  

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ KWL (hardcopy and Power Point)

Initial Presentation Discuss and list student experiences with word problems and ISTEP+ writing in Math. Their experiences will be listed in a KWL (What they Know, what they Want to know, and what they Learned) graphic organizer, which will activate their prior knowledge. Generative Strategy Students will share past experiences with the Math ISTEP+. Their experience with the ISTEP+ will be listed under the “KNOW” column. Then, students will share what they “WANT” to learn to improve their ISTEP+ scores. The last column will be left until the end of the unit.

Tech Tip:

If the instructor has an interactive whiteboard, open a SMART Notebook slideshow and continuously save new items to the KWL chart. When finished, the KWL can be printed and students can fill in the last column at the end of the instructional unit. Checklist

KWL Chart Under the “What you Know” column, students shared three or more experiences with the ISTEP.

YES NO

Under the “Want to Learn or Know” column, students shared three or more goals to improve their ISTEP+ scores.

YES NO

Name: ____________________________ Directions: Think about the ISTEP test that you took in third grade. Then, fill in the columns below.

What you Know

What you Want to know

What you have Learned

Name: ____________________________ Lesson 1b: Read the Problem—Locating Keywords for Operations During this lesson, students will be introduced to keywords associated with the use of specific operations. Students will locate and list as many keywords as possible with a partner. Objectives  

Students will circle keywords for solving a math word problem Students will determine what operation to use based on keywords

Materials    

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ Keywords for Operations (partner worksheet) Problem Solving Planning Table Instructor Cheat Sheet for Keywords for Operations

Initial Presentation A Prezi presentation on writing an explanation will be started. An ISTEP+ problem will be displayed to activate students’ prior knowledge of the third grade ISTEP+ experience. Generative Strategy After the first ISTEP problem on the Prezi presentation is displayed, students will be asked to think of keywords to determine the appropriate operation to solve a math problem. With a partner, students will generate as many keywords as they can recall from past experience with word problems and from a list of math word problems. These 10 problems on the Locate Keywords and Choose an Operation worksheet will be handed out to students, while the students list keywords. Students will not solve these problems, but merely locate keywords to determine what operation to use. Post- Generative Strategy These examples will spark discussion about keywords. The instructor and learners will engage in a whole class discussion to review student work. If there are lingering questions, students can ask questions at this time and ask for clarification. Clarification can come from the teacher and/or peers. Lastly, student keywords can be listed on chart paper entitled Keywords for Operations, which will be an on-going list for the rest of the year.

Tech Tip:

If the instructor has an interactive whiteboard, open a SMART Notebook slideshow and

continuously save students’ finalized lists in the form of a SMART notebook document. This can take the place of chart paper and become an on-going chart to print and display in the room. Test Item 1. Locate Keywords and Choose an Operation (successful students will have circled the keyword(s) in each problem and will have chosen the correct operation with 85% accuracy) 2. Keywords for Operations (successful students will have more than five keywords in each category)

Instructor Keywords for Operations Overview

Keywords for Operation ADDITION add addend sum all together total in all plus more raise both combine additional extra ___________ ___________ ___________

SUBTRACTION difference how many left how many more less than more than decrease reduce change lost further left remain ____________ ____________ ____________ ____________ ____________

MULTIPLICATION factors product multiple of as much times lost by twice ____________ ____________ ____________ ____________ ____________ ____________ ____________

DIVISION divisor dividend quotient cut split each every average equal shared out of _________ _________ _________ _________ _________

Locate Keywords and Choose an Operation Directions: Circle keywords and write the operation you would use to solve the problem. 1. How could you share 16 marbles equally with 4 people?

2. The Eiffel Tower is 320m tall. The CN Tower is 555m tall. How much taller is the CN Tower?

3. Three oranges cost $1.29. How much would a dozen oranges cost?

4. Shawn has four marbles. Christopher has 7 times as many marbles. How many marbles does Christopher have?

5. In October, Leo ordered three books with 602 pages. Frederick ordered two books with 556 pages. How many pages did they order in all?

6. A page of stamps contains six rows of seven stamps in each row. How many stamps are there on one page?

7. After giving the cashier $10 for your lunch, you receive $3.70 back in change. How much did your lunch cost?

8. There are 6 reporters on the newspaper. Each reporter wrote three stories. How many stories did they write in all?

9. A class paid $21 for three boxes of â&#x20AC;&#x153;Smencils,â&#x20AC;? so that each student can have his or her own. How much did each box cost?

10. A school bus can hold 60 people. How many buses will be needed to take 240 students?

Keywords for Operations Directions: Think about keywords that help you decide on when to add, subtract, multiply, or divide. Use the ten questions to find keywords.

Addition

Subtraction

Multiplication

Division

Lesson 2: Planning for Problem Solving Students will read the entire problem and identify keywords for operations. The main question will be located and a plan will be developed before actually solving the problem. Objectives     

Students will identify keywords for solving a math word problem Students will determine what operation to use based on keywords Students will identify the main question being asked to solve Students will choose a strategy to solve a problem Students will develop a plan for solving the math problem

Materials      

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ Keywords for Operations (partner worksheet) Six—ISTEP practice problems without extended response section Problem Solving Planning Table Rubric and Exit Slip (hardcopy and Power Point) Highlighters (class set)

Initial Presentation During this part of the Prezi presentation, students will be introduced to several problem solving strategies. In addition, students will preview how to develop a plan for solving an ISTEP word problem. Students will be given a word problem to activate their prior knowledge. With an example problem on the Prezi, the instructor will demonstrate how to complete the Problem Solving Planning Table. Draw attention to the keywords and the main question in the sentence. Ask student, “What is the question asking you to do?” and “How would you solve this problem?” Once the ISTEP stop sign is reached, students are to attempt to develop problem solving strategies for six ISTEP problems. Generative Strategy With the Problem Solving Planning Table, students will use the six ISTEP+ practice problems. First, students will list keywords for solving the given math problems and highlight the main question. Then, students will circle the operation chosen for the plan. Finally, students will write down their plan for solving the problem. Post- Generative Strategy To review student work, the instructor and learners will engage in a whole class discussion. If there are lingering questions, students can ask questions at this time and ask for clarification. Clarification can come from the teacher and/or peers. In addition, student strategies can be listed on chart paper entitled Problem Solving Strategies, which will be an on-going list for the rest of the year.

Tech Tip:

If the instructor has an interactive whiteboard, open a SMART Notebook slideshow and

continuously save students’ finalized lists in the form of SMART notebook document. This can take the place of chart paper and become an on-going chart to print and display in the room.

Rubric

Rubric: Problem Solving Plan 3

All keywords words are listed or underlined. There arenâ&#x20AC;&#x2122;t any unimportant words underlined. All operations correctly chosen to solve the word problem.

Most of the keywords are located, but some unimportant words are listed or some keywords were missed. Some operations were overlooked, which may lead to a wrong answer.

Too many words located as a keyword or no keywords located.

Makes a plan to solve the problem

Describes a plan that will lead the student to the correct answer.

Little to no description of a plan that will solve the problem.

Main question located

The main question is highlighted for each question.

Describes a plan that may lead the student to the correct answer and/or the plan isnâ&#x20AC;&#x2122;t clear. Part of the question is highlighted.

Keywords

Operation(s) determined

The wrong operations were chosen, which resulted in a wrong answer.

The question is not highlighted.

Instructor Problem Solving Strategy Overview

Problem Solving Strategies Make a graph Make a table or chart Group items Make a list Other:_________________ Other:_________________

Make a drawing or model Continue the pattern (Skip Counting) Guess and Check Regular Algorithm Other:_________________ Other:_________________

NAME: _______________________

Problem Solving Planning Table

Directions: Use this chart with the six ISTEP practice problems you receive from you teacher. Problem #

List any keywords you underlined

Highlighted question (circle one)

Yes

What operation(s) will you use? (circle)

Addition Subtraction

Multiplication Division

Addition

Yes Subtraction No

Multiplication Division

Yes

Addition Subtraction

Multiplication Division

What is your plan for solving the problem? (Use complete sentences to describe your plan in 2-3 sentences.)

NAME: _______________________

Problem #

List any keywords you underlined

Problem Solving Planning Table

Highlighted question (circle one)

What operation(s) will you use? (circle)

Addition

Yes No

Subtraction Multiplication Division

Addition

Yes Subtraction No

Multiplication Division

Yes

Addition Subtraction

Multiplication Division

What is your plan for solving the problem?

Exit Slip This formative assessment will attempt to gauge how well students are learning to read and understand the ISTEP word problems. The Exit Slip is open-ended to glean as much information as possible from the studentsâ&#x20AC;&#x2122; perspective. This will allow the teacher to meet with small groups to clarify any misunderstandings students are having. If students are already overwhelmed from completing the Problem Solving Planning Table, plan to start the next lesson with the exit slip.

EXIT SLIP

Directions: Write what you have learned about reading word problems.

__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________

Lesson 3: Solving the Problem Students will implement their plan and solve the word problem. Objectives   

Students will choose an operation to solve a problem. Students will choose a strategy to solve a problem. Students will solve the problem.

Materials  

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ ISTEP practice problems without extended response section

Initial Presentation Start with where you left off on the Prezi. Once you reach the next ISTEP stop sign, stop for student practice. Review a few strategies listed from yesterday’s lesson. At this point, students will be given the six problems from the previous lesson, and they will be asked to carry out their plans. Again, ask the students, “What is the question asking you to do?” and “How would you solve this problem?” Then, remind students to show all work. Generative Strategy Students will solve the ISTEP word problems and show all their work. Post- Generative Strategy To review student work, the instructor and learners will engage in a whole class discussion. Students will be provided with an opportunity to share their plans and strategies used to solve the problems. New strategies can be added to the students’ on-going list of problem solving strategies. Checklist Accurate answers will be assessed from student problem solving.

Solving the Problem Student answered the question correctly.

YES NO

Student showed all work necessary for solving the problem.

YES NO

Directions: Answer the questions the following six questions and fill out the Planning Solving Table.

1. Katie is buying balloons for the guests at her party. She is having 27 guests.

Package Size Medium

BALLOONS Balloons per Package 6

Cost per Package $2

If Katie buys 4 medium packages of balloons, will she have enough so that each guest will have a balloon to take home? Answer_________________________________________________________________

2. Jason is doing his math homework. He finishes one math problem every ten minutes. Use the information to complete the chart below. Time (in minutes) 10 20 30 40 50

Number of Problems 1 2 3

How much time in MINUTES will Jason take to finish 10 math problems? Show All Work

Answer _________________minutes 3. Sara is making birthday cards. She takes 1 hour to make 5 cards. On Tuesday, Sara made 25 cards. How long did Sara spend working on the cards on Tuesday? Show All Work

Answer _______________________

4. The diagram below shows the three floors Elaine will mop for her summer job.

2 yards

3 yards

8 yards

4 yards

5 yards 7 yards What is the total area, in square yards, that Elaine will mop if she mops each floor once?

Area = length x width Show All Work

Answer _____________________ square yards

5. Mr. Nosbig has 24 students in his class. There are 4 reading groups. Each group has the same number of students. How many students are in each reading group?

Show All Work

Answer _____________________

6. Movie tickets cost $6.50 each. Corey and her younger sister Sadie go to the movies. They pay with a $20.00 bill. How much change would they get back? Show All Work

Answer _____________________

Lesson 4: Writing an Explanation Students will be introduced to the basic parts to a concisely well-written explanation. This list will become the focus of all associated explanation activities. Objectives  Students will restate the question within response using a complete sentence  Students will write the steps taken to solve the problem using complete sentences  Students will write the final answer at the end of the explanation using a complete sentence Materials    

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ ISTEP practice problems with extended response section Rubrics and checklists (hardcopy and Power Point) Extranormal video o http://www.xtranormal.com/watch/12645924/writing-in-math o http://youtu.be/5TENxtNu6_s

Initial Presentation Present the next section of the Prezi presentation. Stop at the next ISTEP “Stop” sign. Students will be given the six problems from the previous lesson, and they will be asked to write an explanation. Remind students of the basic procedures for writing an explanation. The acronym QSA may help students remember the following procedures: 1. Restate the question in a complete sentence 2. Write all the steps, operations, and strategies used to solve the problem in complete sentences 3. Write your answer at the end in a complete sentence Generative Strategy Students will write explanations to the problems solved previously. If needed, students can use the “Now you Try It!” explanation writing sheet with any word problem. This will provide students with additional practice if needed. [If more time is needed for students to finish their explanations, allow for more class time the following day. Don’t hesitate to stop students after the second or third problem. This may be an extremely difficult task for some students. Encourage student success with the task.] Post- Generative Strategy To review student work, the instructor and learners will engage in a whole class discussion. Students will be provided with an opportunity to share their writing with the class. The instructor is encouraged to locate students with well-written explanations to share with the class. Walk around while students are writing to find the best examples to share.

Tech Tip:

If a document camera is available, use this to project an image of students’ writing onto

the screen. Then, with the interactive whiteboard, the instructor can highlight the well written examples. On the contrary, with explanations that need work, the class can edit and revise writings as necessary.

Rubric Explanations will be evaluated with the following Extended Response ISTEP+ rubric.

Extended-Response ISTEP+ Rubric Content Rubric A score of three indicates a thorough understanding of the mathematical concepts embodied in the task. The response • shows algorithms, computations, and other content related work executed correctly and completely.

A score of two indicates a partial understanding of the mathematical concepts embodied in the task. The response • shows an attempt to execute algorithms, computations, and other content related work correctly and completely; computation errors or other minor errors in the content related work may be present.

A score of one indicates a limited understanding of the mathematical concepts embodied in the task. The response • contains major errors, or only a partial process. • contains algorithms, computations, and other content related work which may only be partially correct.

A score of zero indicates no understanding of the mathematical concepts embodied in the task. Problem-Solving Rubric A score of three indicates a thorough understanding of the problem-solving concepts embodied in the task. The response • shows an appropriate strategy to solve the problem, and the strategy is executed correctly and completely. • identifies all important elements of the problem and shows a complete understanding of the relationships among them. • provides clear and complete explanations and/or interpretations when required.

A score of two indicates a partial understanding of the problem-solving concepts embodied in the task. The response contains one or more of the following errors. The response • shows an appropriate strategy to solve the problem. However, the execution of the strategy lacks an essential element. • identifies some of the important elements of the problem and shows a general understanding of the relationships among them. • provides incomplete or unclear explanations and/or interpretations when required.

A score of one indicates a limited understanding of the problem-solving concepts embodied in the task. The response contains one or more of the following errors. The response • shows an appropriate strategy to solve the problem. However, the execution of the strategy is applied incorrectly and/or is incomplete. • shows a limited understanding of the relationships among the elements of the problem. • provides incomplete, unclear, or omitted explanations and/or interpretations when required.

A score of zero indicates no understanding of the problem-solving concepts embodied in the task.

Directions: Now, write an explanation for each problem. Pay attention to what is asked.

1. Katie is buying balloons for the guests at her party. She is having 27 guests.

Package Size Medium

BALLOONS Balloons per Package 6

Cost per Package $2

If Katie buys 4 medium packages of balloons, will she have enough so that each guest will have a balloon to take home? On the lines below, tell which operation is needed to solve the problem and explain why. Then solve. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

Answer_________________________________________________________________

2. Jason is doing his math homework. He finishes one math problem every ten minutes. Use the information to complete the chart below. Time (in minutes) 10 20 30 40 50

Number of Problems 1 2 3

How much time in MINUTES will Jason take to finish 10 math problems? Show All Work

Answer _________________minutes Use words, numbers or pictures to explain how you know how much time it will take Jason to finish all 10 math problems. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

3. Sara is making birthday cards. She takes 1 hour to make 5 cards. On Tuesday, Sara made 25 cards. How long did Sara spend working on the cards on Tuesday? Show All Work

Answer _______________________

Use words, numbers or pictures to explain how you found your answer. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

4. The diagram below shows the three floors Elaine will mop for her summer job.

2 yards

3 yards

8 yards

4 yards

5 yards 7 yards What is the total area, in square yards, that Elaine will mop if she mops each floor once?

Area = length x width Show All Work

Answer _____________________ square yards This week, Elaine has to mop floor B twice. At the end of the week, she thinks that she mopped a larger area by mopping floor B twice than mopping floors A and C once.

Use words, numbers, or symbols to explain why Elaine is NOT correct. Be sure to indicate the areas to support your answer. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

5. Mr. Nosbig has 24 students in his class. There are 4 reading groups. Each group has the same number of students. How many students are in each reading group?

Show All Work

Answer _____________________ Use words or numbers to explain how you found your answer. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 6. Movie tickets cost $6.50 each. Corey and her younger sister Sadie go to the movies. They pay with a $20.00 bill. How much change would they get back? Show All Work

Answer _____________________ Use words or numbers to explain how you found the amount of change they will get back. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

Story Dialog: ©2006-2011 Xtranormal Technology Inc. Student A: Man, I never know how to explain how I solved a math problem. I just do it. I can’t explain that. Tests are hard! Student B: If you solved the problem it should be easy. First, restate the question in a complete sentence. Second, write down all the steps you took to solve the problem in complete sentences. Last, write your answer for the problem down in a complete sentence. Student A: What if the problem is 2+2? That is so easy! I would just say, “I did it in my head.” Are you crazy, man? Don’t ever say you did it in your head. You will fail this test. Why? Student B: You have to explain it even if it seems simple. If the problem was 2+2=4, then you should start by restating the question like this. “I solve the problem by adding. First I wrote 2+2 and added the numbers together. Two and two more is four. If I needed to, I could make two tally marks and another two tally marks and count my total, which is four. So, the answer to two plus two is four.” I included the question, my steps, and the answer. The Q! The S! and the Ay! Student A: That seems like a lot of writing. I HATE writing! Student B: Tough, Dude. Just do it! It will make you a better thinker. It shows how smart you are. I know you are smart, but the test people want to see how smart you are. Besides, it gets easier the more you practice. Student A: Still...I just do a lot of the work in my head. Student B: The test scorer can’t read your mind. So, you have to make sure you explain all the steps, operations, and strategies you took to solve the problem. Even if it was so easy you did it in your head. Explain how you would solve it on paper. They want to check that you know what you are doing. Student A: Okay! Okay! I think I get it. First, I will restate the question in a complete sentence. Second, I will write down all the steps, operations, and strategies I took to solve the problem in complete sentences. Last, I will write my answer for the problem down in a complete sentence. Student B: Good. I’m glad you will first restate the question in a complete sentence. Then, write down all the steps, operations, and strategies you took to solve the problem in complete sentences. Last, write your answer for the problem down in a complete sentence.

Student A: Thanks for helping me. I might try to remember those letters for the question, the steps, and the answer. The Q, S, and A. Q, S, A. How did you get so smart? Student B: Get outta here! I had a great teacher. His name was Gilson or something like that. Anyway, I am happy you will try to do your best on this test. Don't forget to write with complete sentences. Student A: I am going to ace this test. Give me a Q! Give me an S! Give me an A! What does that spell? Student B: Nothing! Those letters just help you remember what to include in your writing. Restate the question. Explain the steps you took to solve the problem and end with your answer. Question, steps, and answer. I think you are ready!

Exit Slip This formative assessment will attempt to gage how well students are learning to write an explanation for an ISTEP word problem. The Exit Slip is open-ended to glean as much information as possible from the studentsâ&#x20AC;&#x2122; perspective. This will allow the teacher to meet with small groups to clarify any misunderstandings students are having. If students are already overwhelmed from writing explanation for the six ISTEP problems, plan to start the next lesson with the exit slip. EXIT SLIP

Directions: Write what you have learned about writing an explanation for a math problem you solve.

Additional Writing Opportunity

Extra practice:

Facilitate the extension of writing problem solving explanations in everyday

math instruction. Ask students to explain how they solved various problems within daily math practice. Then, share students’ writings with the class, which can provide students with immediate feedback. In addition, discussion and peer-evaluation can enhance students’ familiarity with composing clear and detailed explanations. The proceeding worksheet can provide students with a checklist, directions, and writing space for additional practice with writing explanations. This form allows the instructor to apply and extend what was learned to other math problems found within the school’s math series. It is also helpful to use this half sheet of paper for a quick review or formative assessment.

Now you try it! (Use the checklist below and include all 4 parts.)    

Use complete sentences. Restate the question in your answer. Write down all the steps for solving the problem. End with the final answer.

Use words, numbers or pictures to explain how you found your answer. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

Lesson 5: No Pronouns! Students will reread their writing and their peers’ writing. A checklist will be used to guide students in locating the basic components of a concisely well written explanation. Objectives 

Students will accurately identify all nouns within a detailed writing explanation

Materials    

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ ISTEP practice problems with extended response section Checklist (hardcopy and Power Point) Highlighters

Initial Presentation Start with the question: “what is a pronoun?” After students share their prior knowledge, present a definition for pronouns. For instance, pronouns are words that replace nouns. Then, list several subject and object pronouns for students to recall. Focus learner attention on three specific pronouns (“It, they, and them”). Tell students to stop using “it, they and them” within their explanations. List some bad examples, such as:   

“I added them.” “I multiplied it and found it equaled 10.” “The next number was 2. I knew because I subtracted it to find the answer.”

Once you reach the next ISTEP stop sign, stop for student practice. Generative Strategy While a list of pronouns is posted in the room, students will highlight all the pronouns in their writing. Then, students will be asked to replace “it, they, and them” with the defined noun. Last, students will be given a checklist to ensure the removal of unclear pronouns. Post- Generative Strategy To review student work, the instructor and learners will engage in a whole class discussion. Students will be provided with an opportunity to share their writing with the class. While learners are writing, the instructor is encouraged to locate students with well-written explanations to share with the class. Walk around while students are writing to find the best examples to share.

Tech Tip:

If a document camera is available, use this to project an image of students’ writing onto

the screen. Then, with the interactive whiteboard, the instructor can draw attention to the examples without the overuse of pronouns. Explanations that overuse pronouns can be edited and revised as necessary.

Checklist Explanations will be checked for undefined pronouns. Facilitator Checklist

Replacing Pronouns Checklist Student did not use “it, they, or them.”

YES NO

The writing’s meaning wasn’t obscured by any ambiguous pronouns.

YES NO

Student Checklist

Replacing Pronouns Checklist _____ All pronouns (except for “I”) are replaced? _____ Did not use “it, they, or them” _____ Does your writing make sense?

Lesson 6: Reread and Evaluate Explanations Students will reread and evaluate explanations. Students will assess their writing and their peers writing. A checklist will be used to guide students in locating the basic components of a concisely well written explanation. Objectives   

Students will reread their response Students will evaluate written responses for clarity using a rubric or checklist Students will check for completed sections in the ISTEP+ problem

Materials   

Prezi presentation http://prezi.com/pf6iodovwug9/writing-a-response/ Completed ISTEP practice problems with extended response section Math Explanation Checklist (hardcopy and Power Point)

Initial Presentation Present the students with the idea of rereading to check for clarity. To encourage students to reread, provide students with the “write down-read up” strategy (Smekens, 2008). This is an easy reminder to call out to the students. Demonstrate how to use a rubric and/or checklist with a student example. Lastly, draw learner attention toward the various parts of applied skills math problems. Three sections to check include: show work, answer, and writing. Generative Strategy Students reread their own writing for clarity and check if they have included the main parts of a well written explanation. Students will also read their peer’s writing and check for well-written responses. A kid-friendly rubric or checklist will be used to gage the student papers. Post- Generative Strategy T o review student work, the instructor and learners will engage in a whole class discussion. Students will be provided with an opportunity to share what they thought about other students’ writings. The instructor is encouraged to ask students:    

Who found a well-written explanation to share with the class? Who found mistakes after reading a writing? Was anyone left with questions after reading someone else’s writing? Does it make sense?

Tech Tip:

If a document camera is available, use this to project an image of the writing onto the

screen. Then, with the interactive whiteboard, the instructor can create a “kid-friendly rubric with the students. Also, student work can be displayed and evaluated. Rubric Well written explanations will be evaluated with the following Extended Response ISTEP+ rubric.

A score of zero indicates no understanding of the problem-solving concepts embodied in the task.

Math Explanation Checklist _____ Did you write in complete sentences? _____ Did you restate the question? _____ Did you include all the steps you took to solve the problem? _____ Did you include the final answer? _____ Does your writing make sense?

Peer Evaluation Rubric

Explanation

Explanation is clear and Explanation is clear but detailed. It is easy to could use more details. understand. You can still understand it, but it might be a little difficult.

Explanation is unclear and with no details. I canâ&#x20AC;&#x2122;t read the authors mind.

Complete Sentences

Each sentence is a complete thought with a capital letter and an end mark.

Some sentences are complete thoughts or some are missing a capital letter or end mark

Not many complete sentences and missing capital letters or end marks.

Question Steps Answer

The question is restated, the steps taken to solve the problem are written, and the answer is given at the end.

The Q, S, or A is missing.

Two or more parts of the Q, S, A are missing.

Completion

All parts of the problem are completed and all the directions were followed.

One or two parts of the problem are missing or some of the directions were not followed.

Several parts of the problem are missing and directions were not followed.

Checking

Two classmates have read your writing and all corrections have been made.

One classmate has read your writing and all corrections have been made.

No one has read your writing and no new corrections were made.

Directions: To make a â&#x20AC;&#x153;kid-friendlyâ&#x20AC;? rubric, make one with the students. Students provide their own terminology as the instructor guides them through constructing a rubric. Then, practice scoring examples together. Provide students with their own copy.

Explanation

Complete Sentences

Question Steps Answer Completion

Checking

Evaluating Student Learning Students will review what they have learned and take a summative assessment.

Objective  With individual copies, students will complete the final column of a KWL on their own  Students will complete four extended response ISTEP-like problems Materials  

Power Point with KWL Chart paper to remain up until finished with the instructional unit

Initial Presentation Discuss student experiences with word problems and ISTEP+ writing in Math. Pass out individual copies of the KWL chart, which was completed using SMART Notebook software. Their experiences will be listed in the “What they Learned” column of the graphic organizer. Last, the teacher will allow time for the students to take the final test on extended-response writing in math. Generative Strategy Students will share complete the last column of the KWL chart. After that, students will take the final ISTEP Writing in Math test.

Tech Tip:

If the instructor has an interactive whiteboard, open a SMART Notebook slideshow and

print the KWL chart to fill in the last column. Rubric Well written explanations will be evaluated with the following ISTEP+ rubric.

ISTEP--Math Test Directions: Answer the following questions completely.

1. The lines below represent 3 streets in Javier’s neighborhood. C A

Main Street is perpendicular to First Avenue. Pike Street is parallel to Main Street. Use the information above to label each street in Javier’s neighborhood.

A _____________________ B _____________________ C _____________________ Use words, numbers, or symbols to justify the labels for each of the streets in Javier’s neighborhood. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________

2. Mr. Walsh is planning a rectangular garden with a fence. He is considering the two plans shown in the diagram below.

8 feet 4 feet 5 feet Plan A

10 feet Plan B

Complete the table below with the perimeter and area of each garden plan. Area of rectangle = Length x Width Perimeter of rectangle = Side + Side + Side + Side Perimeter (feet)

Area (square feet)

Plan A Plan B The fence Mr. Walsh will use costs $6 for 1 foot. Use words, numbers, or symbols to explain which garden planâ&#x20AC;&#x2122;s fence will cost less money to build. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________

3. There were 18 silly bands on the table. Three friends just bought them from the school store. If they share them equally, how many silly bands will each friend get? Show Work

Answer _____________ Use words or numbers to explain how you found your answer. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ 4. Joey, Tim, and Carlos have 300 cards in all. Joey has 70 cards. Tim has 100 cards. How many cards does Carlos have? Show Work

Answer _____________ Explain who has the most cards. How do you know? __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________

Tech Tip:

If the instructor has an interactive

whiteboard, the following slides can be used with an Interactive white board to allow students the chance to finalize their thoughts after each lesson. Each slide is labeled with its associated lesson.

Directions: Use the following slides to promote discussion and finalize studentâ&#x20AC;&#x2122;s thoughts.

ISTEP Math Test (lesson 1a) What do you Know?

What do you WANT to know?

What have you LEARNED?

Keywords for Operations (lesson 1b) Addition

Subtraction

Multiplication

Division

Problem Solving Strategies (lesson 2)

Strategies

Examples

Problem Solving Strategies (cont'd)

Strategies

Examples

Exit Slip (lesson 2)

What have you learned about reading word problems?

Checklist for Writing an Explanation (lesson 4) Did you write in complete sentences?

Did you restate the question?

Did you write all steps, operations, and strategies you used to solve the problem?

Did you write your answer at the end of your explanation?

Does your writing make sense?

Replacing Pronouns Checklist (lesson 5) Except for "I," all pronouns are replaced.

"It, they or them" is not used in your writing.

Checklist for Writing an Explanation (lesson 6) Did you write in complete sentences?

Did you restate the question?

Did you write all steps, operations, and strategies you used to solve the problem?

Did you write your answer at the end of your explanation?

Does your writing make sense?

Kid-Friendly Rubric Template (lesson 6) 3 Explanation

Complete Sentences

Question Steps Answer

Completion

Checking

Exit Slip (end of unit)

What have you learned about writing in math?