State Testing Writing in Math by dan gibson

Teaching Extended-Response Writing Skills for State Testing: Writing in Math Connection By Dan Gibson EDCI 572: Fall Semester November 30, 2011

Executive Summary: Jane H. Ball Elementary has requested Dan Gibson, as an instructional designer, to research and purpose a solution for improving fourth grade students‟ standardized testing results. Since 2009, Jane Ball‟s test scores have displayed an achievement gap—specifically within math. Each year, less than 5% of students are recommended for retention, which would have resulted from failing grades in Mathematics or English/Language Arts. Nevertheless, for the last two years, close to 30% of fourth grade students have not passed the Mathematics Indiana Statewide Testing for Educational Progress (ISTEP). To be exact, 28% of fourth grade students did not pass the 2011 Mathematics ISTEP at Jane Ball Elementary. After further examination, it was discovered that students scored poorly on the extended-response section of the ISTEP. Around 61% of Jane Ball‟s fourth grade students received failing scores on the extended-response questions for math testing. In addition, about 70% of students, tested during a needs analysis, provided limited responses to extended-response math problems. Consequently, the instructional designer has suggested the implementation of an instructional unit aimed at developing writing skills for state testing. During ISTEP testing, students are given four applied-skills math problems. These extendedresponse questions are considered more complex, and students receive more time. Additionally, these questions require students to provide an explanation using words, numbers, or symbols. Nevertheless, students skip or limit their responses to the applied-skills portion of the math ISTEP. These extended-response problems are usually worth multiple points and can easily lower a student‟s score if skipped. The needs analysis provided several possible causes for the instructional problem:   

Students do not understand entry-level math concepts prior to taking the ISTEP+. Students do not completely understand the various parts of the word problem Students do not know how to explain the solution to a math problem.

From this, an instructional unit was created to develop students‟ ability to write effective responses in math. Through the implementation of this instructional unit, fourth grade students at Jane Ball can develop their ability to explain a mathematical solution. To facilitate students‟ succinct writing skills, a set of procedures were created for writing responses. These procedures will be presented to the students using various learning tools. This program utilizes a Facilitator Guide, Student Guide, Power Point, Extranormal video (online), and Prezi presentation (online). Each component within the unit of instruction can be implemented by the fourth grade teachers without much expense. The largest cost to the school would be from copying student materials. This program provides a cost effective, well-designed solution that meets Jane Ball‟s instructional goal.

Table of Contents Introduction to Instructional Problem .......................................................................................................... 4 Purpose and Process ..................................................................................................................................... 5 Data Collection for Needs Analysis ............................................................................................................... 7 Data Collection for Learner Analysis ........................................................................................................... 10 Learning Styles .............................................................................................................................. 10 Learners with Disabilities ............................................................................................................... 11 Data Collection for Contextual Analysis ...................................................................................................... 12 Orienting Context........................................................................................................................................ 12 Instructional Context ..................................................................................................................... 13 Implications for Learning ........................................................................................................................... 14 Task Analysis .............................................................................................................................................. 15 Topic Analysis ................................................................................................................................ 16 Procedural Analysis ....................................................................................................................... 18 Objectives ................................................................................................................................................... 19 Facilitator’s Guide ...................................................................................................................................... 22 Gagne’s Nine Events of Instruction ............................................................................................... 23 Lesson Sequence Overview ........................................................................................................... 25 Lesson 1a: Introducing Writing in Math ....................................................................................... 26 Lesson 1b: Read the Problem-Locating Keywords for Operations ............................................... 27 Lesson 2: Planning for Problem Solving ........................................................................................ 29 Lesson 3: Solving the Problem ..................................................................................................... 32 Lesson 4: Writing an Explanation .................................................................................................. 33 Xtranormal Video Script ................................................................................................................ 35 Lesson 5: No Pronouns! ................................................................................................................ 39 Lesson 6: Rread and Evaluate Explanations .................................................................................. 41 Evaluating Student Learning ......................................................................................................... 46 Student’s Guide .......................................................................................................................................... 47 Pretest ........................................................................................................................................... 48 KWL ............................................................................................................................................... 49 Problem Solving Planning Table ................................................................................................................. 53 Summative Assessment ................................................................................................................ 68 Formative Evaluation ................................................................................................................................. 71 SME Questions .............................................................................................................................. 73 One-to-One Questions .................................................................................................................. 74 References ................................................................................................................................................. 75 Appendices.................................................................................................................................................. 76

Introduction to Instructional Problem: Math Extended-Response On the Indiana Statewide Testing for Educational Progress (ISTEP), students lost points or did not pass the Math application section of this test. On the applied-skills test, questions were openended and required students to provide a written explanation for their math work. The extendedresponse problems were worth multiple points and lowered some students‟ scores below passing. Many students provided a limited response to these explanation-based questions. Overall, students lacked the ability to explain the steps taken to solve a math problem. Therefore, they need to be taught how to respond to these questions. Condition: Students provided extremely limited or no response to math questions geared toward explaining their solution. Students did not explain the steps to solve a math problem briefly but effectively.

Criterion: Students must write the steps taken to solve a math problem. This writing should be organized, concise, and easily understood.

Causes:  Students did not recognize the ISTEP+ as a valuable or meaningful assessment.  Students did not know how to explain the steps to solve a math problem.  Students did not practice explanation skills enough.  Students did not see a connection between writing and math.  Students did not understand entry-level math concepts prior to taking the ISTEP+.  Students misread the directions. 

Symptoms:  Students performed poorly on the Math application portion of the ISTEP.  Students did not pass the Mathematics portion of the ISTEP test.  Students skipped the explanation section of the ISTEP test.  Students received partial credit for an incomplete answer.  Students provided confusing, rambling explanations.

Purpose As a fourth grade teacher and the proctor during the test, I noticed several students demonstrating limited to no written-response on the applied skills portion of the mathematics ISTEP+. Through this informal assessment, I gleaned a need for additional instruction. However, I needed more data to analyze this “felt need” (Morrison, 2011, pg. 35). My suspicions were confirmed with CTB-McGraw-Hill‟s (2011) Applied Skills Frequency Distribution. For the 2011 Mathematics ISTEP+, several fourth grade students received scores of zero on the extended response questions, which includes an area to explain their thoughts and work. For instance, out of the 122 fourth grade students, 57% (IDOE, 2011) received a score of zero on an extended response question. Another question displayed 46% (IDOE, 2011) of the students received a zero score. If these scores are improved to receive “limited” or “partial” credit, it is expected that more students would pass at least the math portion. In summation, the goal of this analysis is to discover why a performance gap exists on the Fourth Grade ISTEP+. Process Data was collected utilizing various methods. First, ISTEP+ data was collected from the Indiana Department of Education‟s website. CTB-McGraw-Hill‟s Applied Skills Frequency Distribution and Disaggregation Summary spreadsheets were used to determine if there is a gap in actual and expected performance. Both spreadsheets provided great information about third and fourth grade‟s 2011 ISTEP+ performance. The second source of data involved a brief three problem pre-test. This assessment was administered to current fourth grade students at the beginning of the school year. The content was adapted from an ISTEP Sampler provided by the Indiana Department of Education (2011). It included three questions that simulated ISTEP+ questions. Each question had a section to write an extended response. In all, this test was used to gauge how well students can provide a clear, concise, and complete explanation of their method. To analyze the students‟ learning styles, I provided a questionnaire I adapted from the University of South Dakota (2009). With this, there were eleven questions with three choices. Each choice (A, B, and C) represented a choice associated with auditory, visual, or kinesthetic learners. A copy of this question inventory is attached to end of this document. The test is entitled What’s your Learning Style? Once finished, the students totaled their choices, which let me know their learning preferences. For information specific to the learners and their feelings toward school subjects and the ISTEP+, they were given a simple survey with a few open-ended questions, multiple choice questions, and likert scales. The survey was distributed using the Qualtrics online software. These questions were used to evaluate students‟ opinion of school. A small sample of students was surveyed, and students ranged in ability levels, ISTEP+ scores, and motivation toward school. As result, the sample represented the larger population of current fourth grade students. Lastly, I utilized various ISTEP+ spreadsheets from the Department of Education‟s website. This data provided a brief overview of the 518 students that attended Jane Ball during the 20092010 school year.

Data Collection for Needs Analysis Over the past three years, fourth grade students have gradually increased their ISTEP+ scores. The following table displays the ISTEP+ data for Jane Ball‟s fourth grade math performance. 4th Grade Mathematics ISTEP+ Data 2009-2011 Year Passing Not Passing 2009 52% 44% 2010 72% 28% 2011 72% 28% Although the pass rate has improved, the state average displayed that 79% of students passed for mathematics. Therefore, Jane Ball‟s fourth graders scored 7 percentage points lower than the state average. 2011 ISTEP for 4th Grade Mathematics 80%

79%

60%

72% State Average

40%

Jane Ball

20%

21%

28%

0% Passing

Not Passing

Many students perform poorly on the applied skills portion of the mathematics ISTEP+. For the applied skills test, student responses were scored using a rubric. Simply put, one rubric follows a basic 0-3 point scale, and the other uses a 0-2 point scale. The latter rubric is used with easier “constructed response” questions, while the former is used with “extended-response” questions (IDOE, 2011). The extended-response questions are considered slightly more complex and may require more time (IDOE, 2011). These questions require students to perform multiple steps and provide an explanation using words, numbers, or symbols. The following table is a simplified version of the actual rubric used. Score 0 1 2 3

Summary No Understanding Limited Understanding Partial Understanding Thorough Understanding

According to the CTB-McGraw-Hill‟s (2011) Applied Skills Frequency Distribution report, more than 50% of last year‟s third graders received a score of 0 or 1 on the extended-response 6

question. A problem solving and content rubric were used to assess the students work. For the problem solving rubric, students‟ explanations and problem solving methods were assessed. Then, the content rubric assessed the students‟ algorithms, content related work, and their answers. The following circle graphs display both scores from last year‟s third graders. Measurement (Content Rubric)

26%

36%

23% 15%

Explanation and Method (Problem Solving Rubric)

Scored 0 points Scored 1 point Scored 2 points Scored 3 points

20%

25%

19% 36%

Scored 0 points Scored 1 point Scored 2 points Scored 3 points

The Measurement (content rubric) graph displays 51% of the students with failing scores of 0 or 1. The second graph (problem solving rubric) demonstrates that 61% of the students received a 0 or 1. Therefore, the majority of students need to develop the ability to explain their problem solving method. For more current data, twenty-four students were given an applied-skills pretest. The test contained three questions and was setup to imitate ISTEP. Each question had an area to show all work, provide an explanation, and indicate a final answer. The questions were taken from an ISTEP Sampler (2011) developed by the Indiana Department of Education. Student results confirmed several instructional needs. The highlighted sections indicate problematic responses. Pre-Test Errors Limited explanation Confusing explanation Skipped the explanation section Skipped “Show All Work” section Limited to no understanding of content Fragment sentences Misread or misunderstood question (wrong response) Just showing work on the lines

Frequency 16 9 3 4 6 8 4 2

Percentage 70% 39% 13% 17% 26% 35% 17% 9%

The following table lists concerning quotes from students. All grammatical mistakes were taken directly from the test results. Quotes from Explanations “I got the answer because I learned this trick last year from division.” 1

Question Number

“I would like the cookie dough and the strawberry for the party.”

“Four more we had 2 and 6 six is big so you don‟t start from there. You start from 2 and add to six 6 three „four, five, six‟ that make four more.” “A hundred” “add up till you get the write answer.”

“I use my brain and to be actley right I used my fignar‟s”

2 2

In all, there were seven students that answered the questions clearly; however, students were not always succinct. Some students‟ explanations were repetitive. Therefore, even these seven students could benefit from instruction in writing concise explanations and rereading their writing. Overall, the data displayed a need for instruction. Clearly there is a gap in student performance. Students need additional writing instruction to improve ISTEP+ scores.

Data Collection for Learner Analysis Current fourth grade students performed 2% points above last year‟s fourth graders. The following graph displays last year‟s third grade ISTEP results.

2011 Math ISTEP+ Results 3rd Grade

26%

24% PASS+ PASS NOT PASSING

50.0%

Overall, only 26% of the current fourth graders failed the math 2011 ISTEP and 74% received a passing score. As a result, this group performed slightly better than last year‟s fourth grade students; nevertheless, the applied skills portion of the test has proven to be problematic for most students. Learning Styles In terms of learning styles, students were given an eleven question inventory, which assessed their sensory preference for learning. Although only 24 students took the quiz, the results displayed more responses. This is resulted from ties between learning styles. Seven students had a tie between two learning styles. However, the majority of the students are visual learners.

Learning Styles 16 14

12 10 8

6 4 2 0

Visual

Auditory Kinesthetic

student numbers

Learners with Disabilities Two students in the classroom have Section 504 plans. A 504 plan is written for students with medical disabilities. In this case, both students were diagnosed with either Attention Deficient Disorder (ADD) or Attention Deficient Hyperactivity Disorder (ADHD). These accommodations include:  Repeated directions,  Preferential seating,  Shortened assignments (when appropriate),  Avoided time constraints when testing  Directions read to them on the ISTEP+, and  Extra time on the ISTEP+ test. Basically, accommodations and modifications were developed to assist students within the classroom. Although it is not a disability, there are five students in my class that receive Title I instruction for reading. These students reading levels are below average and may have a difficult time reading the word problems. On the pre-test, most of the Title I students misread the questions and subsequently answered the questions incorrectly. So, it could benefit these students to meet within a small group for additional instruction. Key vocabulary and comprehension assistance can be provided during small-group work.

Data Collection for Contextual Analysis Orienting Context To assess student feelings about school, certain subjects, and the ISTEP+, seven students were surveyed. The following bar graph represents students‟ responses on a likert scale. The question asked, “How much do you like or dislike the ISTEP?”

Like or Dislike the ISTEP+ 3.5 3 3

2.5 2 1.5

Number of Students

0.5 0 Dislike Extremely

Dislike

Like Extremely

The next graph displays what section of the ISTEP was perceived to be the most difficult. The survey question asked, “What's the hardest part about the ISTEP?” As you can see, 57% of the students chose “Explaining you answer.”

What's the Hardest Part of the Math ISTEP? 4.5 4

3.5 3 2.5 2

Student Numbers

1.5 1 0.5 0

1 0

Multiple Showing Explaining Word Running Choice your work your Problems out of answer time

The next question asked the students about their feelings toward writing. Three of the seven students expressed they disliked writing, which could explain why there was little attempt to write an explanation.

Like or Dislike Writing 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

4 3 Number of students

Dislike Extremely

Dislike

Like Extremely

The final question asked students to about their feelings toward reading. Surprisingly, all the students chose like or like extremely for reading. However, they do not always comprehend what was read, which can affect their math ISTEP+. Instructional Context: Within the classroom the students have access to a SMART Board and ELMO visual presenter. The presenter easily displays student work on SMART Board in real-time. In addition, there is a computer lab across the hallway from the classroom. So in terms of technology, it is available. Conversely, with limited resources and many other classrooms within the school, access to certain technologies can sometimes unexpectedly become unavailable. Other than technology, students will always have access to writing materials and each other to develop their problem solving abilities. With a variety of instructional strategies, students can practice ISTEP+ extended response questions. Students need to be able to communicate their understanding of math concepts prior to writing them down. So, whole group, partner work, and group work strategies should be made readily available to them.

Implications for Instruction After reviewing the data, I deduct many of the students have had little experience with written explanations. Student responses were limited, at times confusing, and sometimes unrelated to the problems. First and foremost, the current fourth graders need to develop their understanding of Indiana state standards for fourth grade. From there, students will need ample opportunities to apply this content-knowledge to problematic math situations. However, it is critical to utilize the design and feel of the ISTEP+ format. Then, students will be prepared and familiar with the applied-skills test. The following list displays the major implications for instruction:  Improve students‟ word problem analysis skills  Develop students‟ ability to use words, numbers, and symbols to provide an explanation o Construct a set of procedures for writing short-responses o Express solutions clearly and logically o Use complete thoughts o Use appropriate mathematical terminology o Justify reasoning with explanation o Make contextures  Promote rereading and self-evaluation of their writing  Practice ISTEP+ extended-response questions Many of these implications for instruction will have to take place over the entire year. Without practicing extended responses orally and in writing, a majority of the students will not pass the applied skills portion of the ISTEP+ exam. Through the strategic development of an instructional plan to improve students‟ written explanation skills and analysis of word problems, the students will improve their performance on constructed-response and extended-response questions.

Task Analysis: Instructional Goal Students will write a clear, concise explanation for a math problem using symbols, numbers, and words. Introduction to Task During the Indiana Statewide Testing for Education Progress Plus (ISTEP+), students were given an applied skills tests to evaluate their understanding of mathematic concepts. Within this test, there were only a few questions but each question was worth several points. This portion of the test did not include multiple choice questions. Instead, these questions required the students to provide computations, a final answer, and sometimes a detailed explanation for their solution. Because there were multiple steps, many students lost points for not completing the entire problem, which resulted in ISTEP+ failure for some. Students struggled with the extendedresponse portion of the test. Last year, over 50% of the students received a failing score on the extended-response section. As a result, students can benefit from additional instruction with writing extended-responses for math solutions.

Topic Analysis

Procedural Analysis

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

Performanc e-Content 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

 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.  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.

Concept and 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.

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

ProcedureApply

 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.

 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.

 Assess students using an extended response rubric.

4 Avoid pronouns

5 Reread

6 Checking for Completeness

Evaluate Learning

 Students will identify all nouns.

ConceptApply

 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

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

 Students will check for thoroughness in their work.

Procedure and AttitudeApply

 Draw attention toward the various parts of an applied skills ISTEP problem.

 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)

 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.

 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.

Teaching ExtendedResponse Writing Skills: Writing in Math Connection Facilitator Guide BY DANIEL J. GIBSON

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 extendedresponse 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

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

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

MULTIPLICATION

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

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

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

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. 28

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:_________________

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 YES

Student answered the question correctly.

Student showed all work necessary for solving the problem.

YES NO

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. 32

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. 33

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 YES

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

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

Student Checklist

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

YES NO

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. 40

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 detailed. It is easy to understand.

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

Explanation is unclear and with no details. I canâ&#x20AC;&#x;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 KWL on chart paper or printed to finish the instructional unit o This KWL was started at the beginning of the 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.

Teaching ExtendedResponse Writing Skills: Writing in Math Connection Student Guide BY DANIEL J. GIBSON

Name: ____________________________ 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

Name: ____________________________ Directions: Think about the ISTEP test that you took in third grade. Then, fill in the “K” and “W” columns below. Leave “L” alone.

What you Know

What you Want to know

What you have Learned

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 six 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 on 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

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 What question operation(s) (circle one) will you use? (circle) Addition

Yes No

Subtraction Multiplication Division

Yes

Addition Subtraction

Multiplication Division

Addition

Yes No

Subtraction Multiplication Division 52

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 What question operation(s) (circle one) will you use? (circle) Addition

Yes Subtraction No

Multiplication Division

Yes

Addition Subtraction

Multiplication Division

Addition

Yes No

Subtraction Multiplication Division 53

What is your plan for solving the problem?

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

Problem Solving Planning Questions (without explanation) 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 _______________________ 55

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 _____________________

Problem Solving Planning Questions (with explanation) 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 _______________________

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. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 61

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

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. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

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. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

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

Extended-Response Rubric

Explanation

Explanation is clear and detailed. It is easy to understand.

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

Explanation is unclear and with no details. I canâ&#x20AC;&#x;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.

Questions 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.

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. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ 68

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? __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ 69

Formative Evaluation Report Summary The purpose of evaluating The Teaching Extended-Response Writing Skills Instructional Unit was to improve the final product prior to its implementation. Objectives, tasks, instructional strategies, and assessments were evaluated by a subject matter expert (SME) and two fourth grade students. All three formative evaluation trails provided information to improve the overall quality of the instructional unit. Of course, this program is far from perfect, but a few overlooked issues were corrected. With additional evaluation trails, this prescriptive program can be refined further. Methodology To evaluate the Facilitator Guide, a fourth grade teacher was used as the Subject Matter Expert (SME). She has taught fourth grade for eight years, and experienced the Indiana Statewide Testing for Educational Progress-Plus (ISTEP+). As a result, she has had training according to the Jane Ball‟s School Improvement Plan for writing and she has experience administering the ISTEP+. The SME received a facilitator‟s guide accompanied with a brief summary and questionnaire. The questionnaire she received is attached later in this document and is entitled Subject Matter Experts Questions. Because of time constraints, the SME was given The Facilitator Guide ahead of time. Then, after the SME reviewed the material, she and I discussed all concerning issues with the instructional unit. For the one-to-one trails, two fourth grade students reviewed the material with me individually. Student A was chosen because he did not pass the math portion of the ISTEP+. Specifically, he received a 0 out of 3 score on the applied skills portion of the Mathematics ISTEP+. Student B was chosen to represent the upper end of the student performance gamut. She was not the highest overall scoring student, but she did receive a 3 out of 3 score on her math explanation question. From these trials, students were asked several questions to evaluate the effectiveness of the instructional product. Results From these evaluation methods and tools, I was able to correct issues concerning editing, formatting, and design. The following tables provide the recommendations and modifications made to address the issues brought to light. SME Evaluation Recommendations

Modifications

“No periods with bulleted points.”

I removed periods from bulleted points and attempted to standardize the whole document. So, I took my SMART Board Notebook document and transferred the graphic organizers into a Power Point document, which can then be used on other interactive whiteboards. In addition, the teacher could merely present the graphic organizers for students to copy. The Instructional Strategy/Goal table confused the

“Not everyone has a SMART Board.”

Table was large and confused her the most. She 70

asked that I modify the table.

SME the most. She did not like or understand the section explaining each column. As a result, I took out the row that confused her most. This row was used to explain each column, but it was formatted differently from the other columns. Various spelling and grammar mistakes were located by the SME.  Corrected misspelled words  Corrected verb agreements  Corrected missing words  Corrected possessive apostrophes So, I specified the exact problems to use within the generative strategies. The rubric was labeled and received a brief explanation on its use.

Minor editing issues

Confused about which problems to use with The Problem Solving Table. There was an unlabeled Extended-Response rubric, which left the SME wondering what the rubric was.

Student

One-to-One Evaluation Recommendations

Modifications

Locate Keywords and Choose an Operation worksheet‟s problem confused Student A with 6 rows with 6 in each.

The wording of this problem was changed to six rows with seven in each row. From what I understood, the student was confused by the repeated six. To help guide students, I added brief directions for each sheet, but it is expected the facilitator explain each student handout as needed. I left this suggestion alone. I thought about adding problems, but I didn‟t want to overwhelm most students. To be given to multiple students, I explained these would be cut and distributed to each student. To further illustrate the separation of these checklists and exit slips, I chose to put dashed lines in between each duplicate.

A&B

Both students asked for directions to certain tables and graphic organizers.

Student B didn‟t like how there was too much space after question 6.

Student A was confused by the repeating work provided on one page.

Conclusion As the author of the instructional unit, it is easy to overlook confusing sections and other mistakes. Each recommendation was dealt with, and the table above describes the specific actions taken. After making the recommended changes, The Teaching Extended-Response Writing Skills Instructional Unit is ready to implement within a small-group trial. The first small-group trail will be completed with my classroom after my districts winter break. Once completed, I will ask the remaining fourth grade teachers to use the instructional unit for their class. From this, I would like to see an overall improvement in the extended-response section of the math ISTEP+.

Because you are so intelligent, your expertise is requested. Please help me by reviewing the enclosed materials. This instructional unit deals with teaching students how to write explanations for math work problems on the Indiana Statewide Testing for Educational ProgressPlus (ISTEP+). Please mark any mistakes and provide me feedback to the following questions. All you help is appreciated and confidential. 1. Do you notice any unclear sections within the Facilitatorâ&#x20AC;&#x2122;s Guide? 2. Do the objectives make sense? 3. Would you be to implement this instructional unit without guidance? 4. Do you feel like there are any gaps in the instructional unit? 5. Do you notice any reoccurring mistakes that may impede instruction? 6. Any comments for revision purposes are welcome?

These questions will be asked as the students are looking through the materials. 1. Do you notice any unknown words? 2. Can you find any mistakes? 3. After looking at all these sheets, what looks the most confusing to you?

4. Does this make sense to you? (ask at various point throughout the review)

5. How do you think the sheets look?

6. What would you change?

7. What donâ&#x20AC;&#x2122;t you like?

References CTB/McGraw-Hill (2011). Applied Skills Frequency Distribution. TurnLeaf database. Indiana Department of Education (2011). Constructed Response Rubric. Retrieved from http://www.doe.in.gov/assessment/docs/Math-Rubric.pdf Indiana Department of Education (2011). Corporation and School Disaggregated by Grade and Socioeconomic Status. Retrieved from http://www.doe.in.gov/assessment/2011/ Indiana Department of Education (2011). DOE Compass. Retrieved from http://compass.doe.in.gov/Dashboard.aspx?view=SCHOOL&val=3781&desc=Jane%20B all%20Elementary%20School Indiana Department of Education (2011). ISTEP 2011 to 2010 comparison. Retrieved from http://www.doe.in.gov/assessment/2011/ Indiana Department of Education (2011). 2010 ISTEP+ Results Overview: Statewide by Grade Level. Retrieved from http://www.doe.in.gov/assessment/2011/docs/2010_istep_scores_one_pagerwithout_und.pdf Indiana Department of Education (2011). 2011 ISTEP+ Results Overview: Statewide by Grade Level. Retrieved from http://www.doe.in.gov/assessment/2011/docs/2011_istep_results_overview.pdf Indiana Department of Education (2011). ISTEP Sampler. Retrieved from http://www.doe.in.gov/assessment/docs/Math-Grades3-5.pdf Morrison, Ross, Kalman, & Kemp (2011). Designing Effective Instruction 6th Edition. Hoboken, NJ: John Wiley & Sons, Inc. James, B. (2009). Whatâ&#x20AC;&#x;s Your Learning Style? Adapted from Instructor Magazine. Retrieved from http://people.usd.edu/~bwjames/tut/learning-style/stylest.html Qualtrics (2011). Qualtrics Survey Software. Retrieved from http://www.itap.purdue.edu/learning/tools/qualtrics/index.cfm

Name: _______________ What's Your Learning Style? For these questions, choose the first answer that comes to mind and circle “A, B, or C.” Don't spend too much time thinking about any one question. When you study for a test, would you rather… a) Read notes, read headings in a book, and look at diagrams and illustrations. b) Have someone ask you questions, or repeat facts silently to yourself. c) Write things out on index cards and make models or pictures. When you work at solving a math problem do you… a) Read the problem again, and look at the graphs, tables, or numbers. b) Talk to friends or the teacher about the problem. c) Make a drawing or use objects to solve the problem. When you read for fun, which do you like best… a) A book with a lot of pictures in it. b) A book with a lot of conversation or talking with characters. c) A book where you answer questions and solve problems To learn how a computer works, would you rather… a) Watch a video or movie about it b) Listen to someone explain it c) Take the computer apart and try to figure it out for yourself You have just entered a science museum, what will you do first? a) Look around and find a map showing the locations of the various exhibits. b) Talk to a museum guide or parents and ask about exhibits. c) Go into the first exhibit that looks like you can play with things.

Would you rather go toâ&#x20AC;Ś a) An art class? b) A music class? c) An exercise or gym class? What are you most likely to do when you are happy? a) Grin b) Shout with joy c) Jump for joy When you tell a story, would you ratherâ&#x20AC;Ś a) Write it? b) Tell it out loud? c) Act it out? What is most distracting for you when you are trying to concentrate? a) Visual distractions b) Noises c) Feelings like, hunger, tight shoes, or worry When you aren't sure how to spell a word, which of these are you most likely to do? a) write it out to see if it looks right b) sound it out c) write it out to see if it feels right Which are you most likely to do when standing in a long line? a) look at posters advertising other movies b) talk to the person next to you c) tap your foot or move around in some other way When you finish, count how many times you circled A, B, or C. Then, put your totals in the chart below

Total Number of Times you Circled A, B, or C Choice A Choice B Choice C 76

Slide 1

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

Slide 2 ISTEP Math Test (lesson 1a) What do you Know?

What do you WANT to know?

What have you LEARNED?

Slide 3 Keywords for Operations (lesson 1b) Addition

Subtraction

Multiplication

Division

Slide 4 Problem Solving Strategies (lesson 2)

Strategies

Examples

Slide 5 Problem Solving Strategies (cont'd)

Strategies

Examples

Slide 6 Exit Slip (lesson 2)

What have you learned about reading word problems?

Slide 7 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?

Slide 8

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

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

Slide 9

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?

Slide 10 Kid-Friendly Rubric Template (lesson 6) 3

Explanation

Complete Sentences

Question Steps Answer

Completion

Checking

Slide 11 Exit Slip (end of unit)

What have you learned about writing in math?