Remember to Do a Cover Sheet to Tell Name of LE, Your Name, Grade, Etc

New York State Academy for Teaching and Learning Learning Experience/Information Form

Please complete the following and return this form with the learning experience.

Personal Information:

Name: Connie Kudrna

Address: 102 Pullman Avenue Buffalo NY 14217

Home Phone: 716 874-4646 Home FAX: none available

E-mail: [email protected]

Current Teaching Position: Grade level(s) First Grade Subject(s): Math

School District Name: Buffalo Public Schools

School Name: Early Childhood Center 61

School Address: 546 Leroy Street Buffalo NY 14215

School Phone: 716 816-3400 School FAX: NA

E-mail: [email protected]

Title of Learning Experience: What’s the Problem?

Standard area(s): Only list the standard area assessed through your learning experience assessment plan.

Math Science Technology 3 (MST 3) Math Standard 3

Circle the performance indicator level being assessed through this learning experience:

Elementary Beginning Level Intermediate Commencement

Alternate/Students with Disabilities

Peer Review Date(s): 11/3/05 Daemen class, 11/7/05 TAP meeting, 2/28/06 Daemen Class, 3/2/06 Daemen Class SOS New York University Conference May 19, 2006 7/18/05 TAP meeting

Connie Kudrna 1 5/22/2018 LEARNING CONTEXT Purpose: to assess students’ ability to apply basic math problem solving skills and strategies after completing a variety of practice activities. Goals: Students will be able to  understand the concepts of and become proficient with the skills of mathematics;  communicate and reason mathematically;  become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations and algebra. Enduring Understanding: There is more than one way to solve a problem. Essential Questions:  When are some strategies better than others for solving mathematical problems?  How are solutions to mathematical problems communicated?  How can I solve mathematical problems? (student friendly) Guiding questions:  Which mathematical strategies can be used to solve the problem? The objectives to be achieved are as follows: 1. To use the following steps to solve problems: 1. interpret information in a word problem by underlining known information 2. draw a picture of the known information to assist in identifying the problem 3. identify the problem 4. select and try possible strategies to solve the problem 5. use pictures, words, and numbers to communicate the solution

2. To use some or all of the following mathematical strategies to solve and communicate solutions for a mathematical word problems:  act out story problems  use physical objects to model the action in the problem  use drawings, symbols, and pictures to model the action in the problem  count by ones or grouping (tally marks)  add and subtract using number sentences  use trial and error  use process of elimination  work backwards  use a t-chart  make a graph  use an algorithm Grade Level and Ability: The students are instructed on a first grade level, however, many of the students are academically below level. There are 14 boys and one girl in a self contained class (15:1) and the breakdown of handicapping conditions is two MD (mentally disabled), three OHI (other health impaired) and ten LD (learning disabled).

Connie Kudrna 2 5/22/2018 Congruency Table Level: Elementary Grade level: First

Title of Learning Experience: What’s the Problem? New York State Learning Standard: Math Science Technology (MST) Content Standard: Standard 3 Mathematics - Students will:  understand the concepts of and become proficient with the skills of mathematics;  communicate and reason mathematically;  become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

Process Strand: Problem Solving Strand Major Understanding: Students will build new mathematical knowledge through problem solving. Performance Instructional Task Instructional Task Learning Objective Student Work Assessment Indicator (Teacher friendly) (Student Friendly) 1.PS.2 Interpret Use modeling and Read the problem Circle the known Crunchy Cookies Finding and information guided practice to independently or information. Communicating correctly, identify recognize known and with assistance Missing Squares Information Underline the unknown the problem, and unknown information from others Sweet Treats dimension on generate possible in word problems information What’s the solutions Use pencil to Circus Cents Problem? Rubric Use the plan and underline and circle Solve the problem label strategy to story information Building Blocks Teacher correctly identify the with or without Observation Math problem assistance Think-a-aloud Checklist Select a strategy and Experiment with Self-made book solve the problem solutions that Problem would solve the problem

Connie Kudrna 3 5/22/2018 Major Understanding: Students will solve problems that arise in mathematics and in other contexts. Performance Instructional Task Instructional Task Learning Objective Student Work Assessment Indicator (Teacher friendly) (Student Friendly) 1.PS.3 Act out or Use modeling and Create a play from Use What’s the Act out the play Concrete model with guided practice the book Ten Problem? to act out with Think-aloud Problem Solving manipulative to act out Black What’s the story and to find narration, choral Strategies activities involving mathematical ideas Problem? solution to word and individual dimension on mathematical from stories with problems participation What’s the content manipulatives Problem? Rubric from literature Learn and practice and/or story telling Think-aloud Teacher Observation Math Checklist Major Understanding: Students will apply and adapt a variety of appropriate strategies to solve problems. 1.PS.5 Use Use modeling and Use informal Use Plan and Label Missing Squares Abstract Problem informal counting guided practice counting to show problem solving Solving Strategies strategies to find to count and find solutions to strategy Think-aloud dimension on solutions solutions to Missing Square What’s the mathematical story problem Use informal counting Problem? Rubric problems to follow the problem solving steps Teacher Observation Math Checklist 1.PS.8 Use Use modeling and Use cubes to show Use Plan and Label Missing Squares Concrete Problem manipulatives (e.g., guided practice, solutions to problem solving Solving Strategies tiles, blocks) to use manipulatives to Missing Squares strategy Sweet Treats dimension on model the action in model solutions to a story What’s the problems word problem Use cubes and to Problem? Rubric follow the problem Teacher solving steps Observation Math Checklist

Connie Kudrna 4 5/22/2018 Performance Instructional Task Instructional Task Learning Objective Student Work Assessment Indicator (Teacher friendly) (Student Friendly) 1.PS.9 Use As guided practice: Draw pictures to Use mathematical Missing Squares Abstract Problem drawings/pictures Explain solutions to find answer to the strategies and tools to Solving Strategies to model the action word problems to questions communicate solutions Sweet Treats dimension on in problems communicate for a mathematical Self-made books What’s the mathematical problem Problem? Rubric thinking Teacher Observation Math Checklist

Process Strands: Representation Strand Major Understanding: Students will select, apply, and translate among mathematical representations to solve problems. Performance Instructional Task Instructional Task Learning Objective Student Work Assessment Indicator (Teacher friendly) (Student Friendly) 1.R.4 Connect Communicate Draw pictures, Represent word Crunchy Crackers Finding and mathematical mathematical words, numbers to problems using Communicating representations with thinking by show answers pictures, words and Missing Squares Information problem solving describing the steps numbers Sweet Treats dimension on and strategies used to What’s the solve a problem Circus Cents Problem? Rubric Building Blocks Teacher Observation Math Think-a-aloud Checklist Self-made book

Connie Kudrna 5 5/22/2018 Content Strand: Number Sense and Operations Band: Number Systems Major Understanding: Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems Performance Instructional Task Instructional Task Learning Objective Student Work Assessment Indicator (Teacher friendly) (Student Friendly) 1.N.10 Draw Use symbols and Use +, -, = or Write a number Crunchy Crackers Abstract Problem pictures or other numbers to represent numbers to make sentence using symbols Solving Strategies informal symbols to addition and/or number sentence (+, -, =) Missing Squares dimension on represent a spoken subtraction when and numbers to solve Sweet Treats What’s the number up to 20 solving problems the problem Problem? Rubric Circus Cents Teacher Building Blocks Observation Math Checklist Self-made book

Band: Operations Major Understanding: Students will understand meaning of operations and procedures and how they relate to one another 1.N.24 Develop and Develop one or more Solve a word Use a number sentence, Crunchy Crackers Abstract Problem use strategies to strategies to solve problem using words, Solving Strategies solve addition and word problems strategies: Pictures and/or Missing Squares dimension on subtraction word Plan and label manipulatives to find Sweet Treats What’s the problems Think aloud solutions for a word Problem? Rubric Act out problem Circus Cents Draw Teacher Symbols Count Building Blocks Observation Math Add and subtract Checklist Trial and error Think-a-aloud Process of elimination Physical object Self-made book Algorithm

Connie Kudrna 6 5/22/2018 What students need to know and be able to do to succeed: Prior to the Learning Experience: The Buffalo School District uses the Investigations in Numbers, Data and Space math program, developed by TERC and published by Scott Foresman. At the beginning of this math program, it is important to develop procedures and rules for all of the activities, such as for journaling and for small and whole group work. Students have also practiced: CLASSROOM MANAGEMENT  Classroom rules: We immediately follow adult directions. We keep our hands and feet to ourselves. We work safely and share classroom resources. We take turns talking.  Classroom procedures:  Large Group Procedures: Sit cross leg, in a horseshoe on rug. Students raise hands to respond to questions. Students listen quietly as others speak.  Small Group Procedures: Secure the materials that you need to complete the activity. Students are given the opportunity to select the level of difficulty of the task. Work quietly in your group. Everyone will contribute. Share your answers in large group.  Material Management: In small groups the students decide among themselves who retrieves and distributes the materials. The same person is responsible for returning the materials to the proper place. Everyone in the group is responsible for clean-up of their personal space.  Presentation Procedures: Teacher draws a craft stick (popsicle stick) with a student’s names to determine who presents. Student presenter sits in the author chair next to the teacher in the front of the room. Other students are seated in a circle on the floor and follow large group procedures. CONTENT KNOWLEDGE AND SKILLS  communicate  orally  act out story problems

Connie Kudrna 7 5/22/2018  use physical objects to model the action in the problem  use drawings, symbols, and pictures to model the action in the problem  count by ones or grouping (tally marks)  count objects (Note: students should have the prerequisite skill to count objects with one-to-one correspondence to number. If skill is absent, the task will need to be differentiated with this skill being the summative goal for that student.)

ASSESSMENT PLAN The assessment plan includes both teacher and student use of a rubric. Following each task students use the student friendly rubric to self-assess. The teacher uses the Scoring rubric and tracks student progress on a Scorecard. The teacher comments on student work detailing what each student can do and what each struggles with. While students are working the teacher observes and records their level of independence in employing math skills. A similar problem is used for pre and post assessments to document achievement of the learning standards. When solving the problems students circle the unknown, solve the problem and then circle the answer. This provides a visual connection between the problem and the solution.

The following tools are used to assess and document student progress:  What’s the Problem? Rubric to score how well students locate information and use concrete and abstract problem solving strategies (teacher-friendly, and student-friendly versions) using math journals  Teacher observation and anecdotal recording on Teacher Observation Math Checklist for classroom math instruction  Scorecard for What’s the Problem? Learning Experience for documenting teacher and student scoring of work samples.

Connie Kudrna 8 5/22/2018 Student: What’s the Problem? Scoring Rubric (teacher) Score: DIMENSIONS DISTINQUISHED 3 PROFICIENT 2 DEVELOPING 1 FINDING AND COMMUNICATING Underlines what is known without Underlines what is known with 1 or Can find known and unknown INFORMATION help from others 2 prompts from others information only if teacher provides one-on-one instruction The extent to which student: Circles what is not known Circles what is not known  Solves the problem and find without help from others with 1 or 2 prompts from others answers (1.PS.2)  Shows work of how to solve the Communicates answers by speaking Communicates answers by speaking Communicating answers requires problem (1.N.2) and writing in journal without help and writing in journal with 1 or 2 one-on-one instruction  Communicates the answers from others prompts from others (1.R.4)

Task: Journals Five Black Squares Book CONCRETE PROBLEM SOLVING Acts out the story without prompts Acts out the story with 1 or 2 Acts out the story with 3 or more STRATEGIES from others prompts from others prompts from others

The extent to which student: OR OR OR  Participates in acting out the story (1.PS.3) Uses manipulatives to find answers Uses manipulatives to find answers Uses manipulatives to find answers  Uses manipulatives to find without help from teacher or others with 1 or 2 assists from teacher only if teacher provides one-on-one answer (1.PS.8) instruction Task: Acting out story Journals Five Black Squares Book ABSTRACT PROBLEM SOLVING Can count and answer questions Can count with the use of Must use manipulatives and count STRATEGIES without manipulatives. manipulatives to find the answer with one-on-one instruction The extent to which student:  Counts to find answer (1.PS.5) Drawings contain no mistakes and Drawings contain 1 or 2 mistakes Unable to solve the problem using  Draws accurate pictures to find were reached without using and were reached with assistance an abstract problem solving answer (1.PS.9) manipulatives and without help from manipulatives and/or others strategy  Draws pictures or signs to show from others answers (1.N.10)

Task: Journals Five Black Squares Book

COMMENTS:

Connie Kudrna 9 5/22/2018 Student name: Student Rubric What’s the Problem? Score:

Connie Kudrna 10 5/22/2018 Teacher Observation Math Checklist Date: Assignment: DIMENSION Classroom DISTINQUISHEDLocates UsesPROFICIENTCommunicates DEVELOPINGCommunicates 3 2 1 Student Management, Known/Unknown Manipulatives Solutions Verbally Solutions in FINDINGName WHAT PromptingI NEED Information Writing Not needed = N Independently = I Independently = I Not needed = N Independent = I Independent - I With assistance = A With assistance = A  Underline # = times needing Assistance = A Assistance = A Unable = U Unable = U prompting Unable = U Unable = U  Circle I can do this by myself. I need help. I can’t do this.

 Act out story

 Use counters I can do this by myself. I need help. I can’t do this.

THINKING

 Drawing pictures

 Counting I can do this by myself. I need help. I can’t do this.  Adding and subtracting

COMMENTS:

Connie Kudrna 11 5/22/2018 Score Card for What’s the Problem? Learning Experience e

r Five Student o Sweet Treats Score Circus Cents Score Building Blocks *Level c Black S Name Score

i Squares t s

o Book P n

g Score Dv a i D

s Student Teacher Student Teacher Student Teacher e i k o o C

y h c n u r C

Connie Kudrna 12 5/22/2018 *D = Distinguished, 9-8 points P = Proficient, 7-5 points Dv = Developing, 5-0 points #/** = raw score/differentiated score

Connie Kudrna 13 5/22/2018 STUDENT WORK Out of 14 students, six students scored in the distinguished level, six students scored in the proficient level, and two students scored in the developing level. All students received a raw score based on the teacher’s scoring rubric. The instruction and tasks were differentiated for lower performing students based Individual Educational Plan goals. These students were given a differentiated score. Since introducing this activity, all of the students have used a variety of methods for solving problems. The activities include concrete and abstract reasoning as well as communicating solutions to others. In this manner, the class is exposed to a variety of mathematical concepts and applications. The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads the way they can see this when using concrete objects. These two students have not mastered the one-to-one correspondence between number and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre- requisite skill for this learning experience. Students who are in the proficient level can comfortably use the counters and manipulatives when they are given a longer period of time to explore written format. When given the correct tools, such as a vocabulary list of written numbers, the students can write the words. They can also explain their thinking and processing of the word problems. Drawings are more detailed and some students use tallies and simple marks to represent data. At this level the students do not always recognize that using different strategies should yield the same results. Finally, students who received a distinguished score have the ability to use multiple representations for solving the problem without assistance from others. He or she can use numbers effectively, apply a number sentence and demonstrate the skills in an abstract format. They are able to complete the examples and clearly demonstrate their understanding by communicating to others. At this level the students recognize that using different strategies should yield the same results. These students also assisted those peers who did not understand what was being asked.

OVERALL ACTION RESEARCH ANALYSIS: For scores to improve and for more students to score at the distinguished and proficient levels the following needs to occur:  Prior to teaching this learning experience, each problem solving strategy expected for the specific population of students needs to be taught in isolation, practiced, and achieved by the students at a proficient level or distinguished level.

Connie Kudrna 14 5/22/2018  For students lagging behind or unable to achieve at the necessary levels, instruction and tasks, and assessment requirements need to be modified.

TEACHER COMMENTS

Student Name______

This piece demonstrates (circle level):

Distinguished level Proficient Level Developing Level

What this student can do What this student struggles with + -

Additional Comments/Observations (optional):

Connie Kudrna 15 5/22/2018 PROCEDURE These tasks are adapted from the Mathematical Thinking for 1st Grade unit in the Investigations in Numbers, Data and Space program. Anticipatory sets reinforce counting and writing numbers. Task One: 1. Anticipatory Set: Read the story Ten Black What’s the Problem?. 2. Distribute one black dot to each of four students who will act out mathematical ideas from the story with manipulatives. 3. Child holding one dot moves to the front of the class. 4. Ask the question: How many What’s the Problem? need to be added to make a total of 2 What’s the Problem? (1 dot)? 5. Another child holding one dot comes forward and stands by the first child. 6. Together students count aloud the number of What’s the Problem? in the front of the class (2 What’s the Problem?). 7. Repeat this procedure until there are 4 What’s the Problem? total. 8. To demonstrate addition have child with first dot step forward. Have the next two children step forward and join hands with the first child to demonstrate addition of 1 + 2 = 3. Have the last child step forward and join hands with the other three children to demonstrate addition of 3 + 1 = 4. Think aloud each step of the addition procedure as a class. 9. Again identify the problem as: How many What’s the Problem? need to be added in order to make a total of 5 What’s the Problem? (adjust the number based on the level of challenge possible)? As the students think aloud the steps for solving problems and generate possible ways to solve the problem write ideas on chart paper. Ask students to identify the strategies they used to communicate the solutions. 10. Using think aloud, review steps and strategies for solving problems. Ask where in the past several activities the following occurred or could have occurred.: Steps: 1. interpret information in a word problem by underlining known information 2. draw a picture of the known information to assist in identifying the problem 3. identify the problem 4. select and try possible strategies to solve the problem 5. use pictures, words, and numbers to communicate the solution Strategies:  act out story problems  count by ones or grouping  use physical objects to (tally marks) model the action in the  add and subtract using problem number sentences  use drawings, symbols,  trial and error and pictures to model the  process of elimination action in the problem  work backwards  use a t-chart

Connie Kudrna 16 5/22/2018  make a graph  use an algorithm Task 2: Diagnostic Assessment 11. Prepare and post story problem Crunchy Cookies and questions on chart paper. 12. Give students the same story problem on Crunchy Cookies Journal worksheet and ask them to do their best to complete the worksheet. Assure them that it is ok to not know all of the answers and that they will know the answers at the end of the lesson. Explain in child-friendly terms that this is a diagnostic exercise to help you know what to teach them that they do not already know. 13. Collect the diagnostic Crunchy Cookies Journal. 14. Score the journal using the What’s the Problem? Rubric. 15. Record the score on Scorecard for What’s the Problem? Learning Experience.

Task 3: Teacher Modeling and Large Group Guided Practice 16. Anticipatory Set:  Prepare a box of pencils to be used for this lesson that is two less than the number of students in the room. Students count aloud the number of pencils, then count aloud the number of students.  Pose the problem: We have “x” number of pencils and “y” number of students. How many more pencils do we need so that each student has a pencil?  Explore ways of discovering the answer.  Place two more pencils in the box, then distribute the pencils to each student. 17. Prepare and post story problem Missing Squares and questions on chart paper. 18. Give each student a Missing Squares Journal worksheet. 19. Ask a student to read the word problem to the class. 20. Ask: #1 “What is the known information?” (5 squares). Underline the known information on the chart paper word problem, instruct students to do the same on their worksheet. 21. Guide student practice by modeling the correct response for question #2 by drawing 5 squares under the question on the chart paper. Instruct students to draw 5 squares on Missing Squares Journal. 22. Read question #3 and instructions. Ask: “What is the problem?” and circle the information that you need to know in the word problem on the chart paper (9 squares). Students circle this information as well. 23. Read the instructions in the left box: “Solve the problem by using drawings, symbols, words or pictures to communicate a solution.” Solicit ideas from the class and draw on chart paper while students draw on their worksheets. 24. Fill in the Answer on the line provided and circle the answer. 25. Model strategies for solving Missing Squares problem: by acting out, using cubes or crackers (manipulatives), and adding. 26. Ask students to complete the right box on their worksheets by choosing one of the strategies just demonstrated by the teacher. 27. Instruct students to bring journals to the floor and share their representations using a think aloud for counting, adding and subtracting. 28. Guide students in scoring their work using the What’s the Problem? rubric. 29. Collect worksheets.

Connie Kudrna 17 5/22/2018 30. Review : Steps: 1. interpret information in a word problem by underlining known information 2. draw a picture of the known information to assist in identifying the problem 3. identify the problem 4. select and try possible strategies to solve the problem 5. use pictures, words, and numbers to communicate the solution

Strategies:  act out story problems  add and subtract using  use physical objects to number sentences model the action in the  trial and error problem  process of elimination  use drawings, symbols,  work backwards and pictures to model the  use a t-chart action in the problem  make a graph  count by ones or grouping  use an algorithm (tally marks) 31. Complete Teacher Observation Checklist while students are working.

Task 4: Small Group Task 32. Anticipatory set:  Set a bowl with boxes of raisins in the front of the room.  Place students in groups of 3 to solve the problem Sweet Treats Journal.  Ask one student from each group to come forward, count and select enough boxed treats for each person in the group, return to the group and distribute to group members for snack while completing the task. 33. Instruct students to complete Sweet Treats Journal. Designate one person to record the group’s answers on the Sweet Treats Journal. 34. Facilitate small groups as needed. 35. Allow students to work for 15 minutes. 36. Students present and explain their thinking and solutions to the class using the think aloud strategy. 37. Guide the direction of the conversation by asking questions that illustrate there may be more than one strategy for solving the problem. 38. Guide students in scoring and analyzing their work using the What’s the Problem? rubric. 39. Collect Sweet Treats Journal worksheet. 40. Using think aloud, review steps and strategies for solving problems. Ask what steps and strategies the students used to solve the problem. 41. Complete Teacher Observation Checklist while students are working and Score Card for What’s the Problem? Learning Experience after examining student work.

Connie Kudrna 18 5/22/2018 Task 5: Independent Practice 42. Anticipatory Set:  Place a bowl of pennies in the front of the room.  Have each student take 4 pennies from the bowl.  Once students return to their seats, walk around the room and have them pay you 3 pennies for the Circus Cents Journal worksheet.  Collect and count the left over pennies. 43. Instruct students to complete the Circus Cents Journal worksheet. 44. Using think aloud, review steps and strategies for solving problems. Ask what steps and strategies the students used to solve the problem. 45. Students score work with the What’s the Problem? rubric. 46. Collect Circus Cents Journal worksheet. 47. Complete Teacher Observation Checklist while students are working and Score Card for What’s the Problem? Learning Experience after examining student work.

Task 6: Independent Assessment 48. Anticipatory Set: Decorate the room with blocks by letting each student build a tower along one of the classroom walls, count the number of blocks in their tower, write the number on a piece of paper and place it on the top of their tower. Pick two towers and determine the total number of blocks, and the difference between the two. 49. Instruct students to complete the Building Blocks Journal worksheet. 50. Students score work with the What’s the Problem? rubric 51. Using think aloud, review steps and strategies for solving problems. Ask what steps and strategies the students used to solve the problem. 52. Collect Building Blocks Journal worksheet. 53. Complete Teacher Observation Checklist while students are working and Score Card for What’s the Problem? Learning Experience after examining student work comparing this score with diagnostic score Crunchy Cookies Journal.

Task 7: Culminating Activity 54. Anticipatory Set:  Read the teacher’s story of Four Blue Triangles which serves as an exemplar.  Give students the task to discuss total number of stars in the book.  Groups of 3 work on generating solutions by offering ideas such as counting, using items, or other strategies for solving the task learned in the previous days. Give students blank sheets of paper or a modified worksheet based on their skill level. 55. Have students generate a list of where squares are found around them. 56. Give each student materials to create personal book of Five Black Squares where they add one more square on each page. (5 blank pages in book form, 5 black construction paper squares, crayons, pencils). 57. Students create and then read their books to the class. 58. Pose the problem: “How many squares did you put into your book?” 59. Students independently apply the strategies they just practiced to solve this problem without counting the squares. They record the strategy(ies) on a blank

Connie Kudrna 19 5/22/2018 sheet of paper or modified worksheet, then meet with the teacher to review the answers using a think aloud. 60. As a class, using think aloud, review steps and strategies for solving problems. Ask what steps and strategies the students used to solve the problem.

Closure: 61. In large group, discuss the strategies used in all the tasks and highlight innovative student approaches, variety of strategies, and emphasize enduring understanding that there is more than one way to solve a problem. 62. Pose the essential question “When are some strategies better than others for solving problems?” 63. Score the self-made book with problem solving sheet using What’s the Problem? rubric.

INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS Students are grouped with students of varied abilities to allow for collaboration among academic levels. The teacher circulates around the room to assist students and elicit higher level thinking skills. Students are given the use of manipulatives to assist in completing the activities. Instructional modifications are provided for use with students who have individual educational plans. Instructional/Environmental Modifications Modifications Type Specific Modification Rationale Benefits Environmental and Overview of class Established routines Expectations have Management procedures provide framework for been established for completion of tasks proper class behaviors. (this includes All students benefit procedures and rules) and learning can occur

Preferred seating Close to teacher or Proximity control blackboard provides provides immediate student with feedback for student immediate reinforcement and allows supportive feedback Students in groups can Use of small groups Smaller groups provide additional provide students with assistance and support support from other for students with students special needs Instructional Repeating/rephrase By providing Students are given questions instructional assistance to actively modifications, students participate in these Use of manipulatives are given the necessary activities without

Connie Kudrna 20 5/22/2018 assistance to complete being singled out as Oral responses/taped the tasks unable to complete the responses to reflection tasks questions Students explain their approach to solving a Students logically Modified worksheets problem to assist them check answers and in communicating reasoning, strategies Pictures to show solutions and skills. Struggling calculations students may gain new insights because of Student presentations peer coaching Content/Materials Use of manipulatives Students apply higher Students are able to such as Unifax level thinking skills to apply higher level Equation Connections all activities. skills in all problem solving situations Students retell actual steps for completing tasks Tasks Math Journals are Students complete Journals are created modified by using activities based on with differentiated lower numbers or academic abilities instructions higher numbers depending on ability Students work at own processing pace Time allowed for the task can be lengthened or shortened depending on ability

MATERIALS REQUIRED FOR INSTRUCTIONS Key Reference Materials include:  Crews, Donald. Ten Black What’s the Problem?. Greenwillow Books: New York. 1986  Dacey, L. and Easton, R. Show and Tell: Representing and Communicating Mathematical Ideas in K-2. Math Solutions Publications. Sausalito: CA, 2002  Dacey, L and Easton, R. Growing Mathematically in Kindergarten. Math Solutions Publications. Sausalito. CA. 2000  .Mathematical Thinking for 1st Grade unit in the Investigations in Numbers, Data and Space program published by Scott Foresman

Websites:  www.nctm.org  www.emsc.nysed.gov

Classroom Supplies:

Connie Kudrna 21 5/22/2018  Pencils  Craft Sticks (popsicle sticks) with student names  Crayons  Chart paper  Markers  Unifax Equation Connections (www.didax.com)

Materials:  Ten Black What’s the Problem? Power Point  Manipulatives (counting cubes)  Black construction paper circles and squares (1 by 1 inch)  pre-made books for creating their own books: Five Black Squares  Teacher made book: Five Blue Stars  What’s the Problem? Rubrics (teacher and student)  Teacher Observation Math Checklist  Score Card for What’s the Problem? Learning Experience  Algorithm: y = .5x2+.5x where y = total number of items, x = page number  Sample t-chart  Sample graph  Student Journal worksheets:  Crunchy Crackers for Task One  Missing Squares Journal for Task Two  Sweet Treat Journal for Task Three  Circus Cents for Task Four  Building Blocks for Task Five

TIME REQUIRED This learning experience can be implemented over three to four days. Each activity can be completed within a scheduled math block of one hour as per the Investigations Math Program. The hour is broken into whole group activity (15-25 minutes), followed by Choice Time activities 20-30 minutes). After Choice Time, students return to the whole group setting to discuss strategies employed during Choice Time.

Planning: 45 minutes for gathering manipulatives, planning, preparing chart paper stories and journals

Implementation: Task One: Anticipatory Set: 30 minutes Task Two: Diagnostic Assessment: 15 minutes

Connie Kudrna 22 5/22/2018 Task Three: Teacher Modeling and Guided Practice: 45 minutes Task Four: Small Group Practice: 40 minutes Task Five: Independent Practice 30 minutes Task Six: Independent Assessment 20 minutes Task Seven: Culminating Activity 40 minutes

Assessment: Scoring of Activity Journals: 5-10 minutes per student per worksheet Self-Made Book and problem discussion: 5-10 minutes per student

Schedule: The Buffalo Public School’s District Math Curriculum Team requires a strict sequence for math lessons. This learning experience is designed to take place at the beginning of the school year as an introduction to basic problem solving. The skills and strategies incorporated in this learning experience will be reinforced throughout the school year. After completing this unit, students move into the unit entitled Surveys and Secret Questions when they will use problem solving skills to count, add, collect and record data.

REFLECTION This learning experience is created to serve as a method of scaffolding problem solving mathematical tasks for students in my class in order to promote their success at increasing levels of difficulty. The activities align to the New York State Standards as well as to the Investigations program that has been adopted by the Buffalo City School district. My goal is to use the Standards to assess student achievement of the performance indicators as the basis for my informal observation and my formal evaluation (tasks from the Investigations Kit, teacher-made tasks). NYS Standards and Performance Indicators provide a consistent vocabulary for tasks and assessment tools making the creation of this learning experience easy to write and easier for students to understand. The methodology for communicating mathematical thinking in this learning experience is influenced by the writings of Dacey and Easton in the book, Show and Tell: Representing and Communicating Mathematical Ideas in K-12. I encourage students to express ideas, ask questions, make presentations, peer teach and listen to each other during math time. For example, students in my class who have strengths in communicating verbally assist peers by illustrating their thinking processes aloud. The conversations help me track student learning for modifying and adjusting my lesson or for selecting students needing individual attention.

Connie Kudrna 23 5/22/2018 I believe the following are key reasons why I can meet my goals for improving student mathematical understanding, and why I can assess the learning standards effectively through implementing this learning experience:  I offer multiple tasks that provide exposure to individual learning styles which increases student motivation. The collection of tasks provide kinesthetic experiences such as using physical objects and acting out solutions, verbal opportunities to explain discovery of solutions, the use of mathematical formulas that express the problem solving process in a logical-mathematical approach, and reading about everyday math situations for the linguistic preference.  The technique of planning and labeling information is vital for students to solve word problems. However, we did not focus on a single word for using this skill. Students were to circle phrases that would assist them in understanding the word problems. Many of my students could identify the known and unknown information with assistance; however since using this technique, my students have become comfortable with using Plan and Label to complete independent journal activities for math.  Many of the students were able to effectively use the rubric to monitor their progress. This actively engaged students in the learning process. For example, in the first implementation, one student could not verbally explain the process for solving the problems or use pictures. In the second implementation, this same student could draw the correct number of items as well as locate the known and unknown information with assistance. In the final implementation, the student was able to verbally explain the process for solving the problem. Watching his own progress in scoring his rubric led to motivation and cognitive changes that account for his improvement. This learning experience has undergone some changes due to the peer review process. Using feedback from other professionals assists me in making this a better product for teachers to use. The input of warm and cool comments during peer review provides a way for me to clarify those areas that are unclear for the reader and therefore maybe be unclear to the students. For example, one reviewer asked: “Is it appropriate to use the word ‘strategy’ with first grade students?” My response was “yes”. Students need to be exposed to mathematical terms from the beginning in proper context. This promotes mathematical understanding rather than the memorization of vocabulary. Digital camera photos serve as a record of how the students completed the tasks, as well as providing me a means to show others the actual implementation of this learning experience. The digital images form a Point presentation for sharing this learning experience during peer reviews. As well as feedback from other colleagues, I have had the opportunity to work in a study group with Jeff Arnold and Pat Loncto in revamping this learning experience. We examine the usability of this learning experience for other colleagues as we consider the comments from Peer Reviews. We refine the student worksheets to align with the NYS Performance Indicators, and we create scoring and grading tools for documenting the level of student performance.

Connie Kudrna 24 5/22/2018 When examining the student samples, it is clear to me that my students understand the process of applying strategies, yet many of them still need concrete materials to find the solution for word problems. The journals in this learning experience have been implemented three times with the same group of students and the students have made progress in applying some of my goals and objectives. I was surprised at how patient the students were when asked to repeat the identical task. The repeated practice provided a foundation for growth in succeeding tasks even though they were identical. Given that the students in the class are below first grade, the progress they made demonstrates learning is taking place. Translating performance indicators into classroom practice provides me with a uniform measurement for all the students. I discovered that I can adapt any lesson from my required curriculum and develop assessment tools because the performance indicators provide the language of my subject. My students are learning to solve problems independently using strategies that allow them to communicate correct answers and they are having fun too. That makes the work of this learning experience worth my efforts. All of the students enjoyed completing the activities and found that “doing Mrs. Kudrna’s homework was fun.” I learned that performance indicators are more powerful to use than they are painful to sort through. I learned how important student self-assessment is for student engagement.

Connie Kudrna 25 5/22/2018 Name: ______

Crunchy Cookies Journal

You have 3 cookies. How many cookies do you need to make a total of 6? 1. Underline the known information. 2. Draw a picture to show the known information.

3. Circle the problem you need to solve in the word story above. Solve the problem by drawing a Choose another strategy. picture. Show your work. Show your work.  act it out  use manipulative  add to find answer

Answer______Answer______Circle your answer. Circle your answer. Teacher Initials ______(act it out/use of manipulatives)

Connie Kudrna 26 5/22/2018 Name: ______

Missing Squares Journal

You have 5 square crackers. How many square crackers do you need to make a total of 9? 1. Underline the known information. 2. Draw a picture to show the known information.

Answer______Answer______Circle your answer. Circle your answer. Teacher Initials ______(act it out/use of manipulatives)

Connie Kudrna 27 5/22/2018 Name ______

Sweet Treats Journal You have 9 pieces of candy. You have 13 friends. You want to give each friend one piece of candy. How many pieces of candy will you need to make a total of 13 pieces? 1. Underline the known information. 2. Draw a picture to show the known information.

3. Circle the problem that you need to solve in the word story above. Solve the problem by using Choose another strategy. Show your manipulatives. Show the teacher. work. Draw your solution.  act it out  add or subtract to find answer

Answer______Answer______Circle your answer. Circle your answer. Teacher Initials ______(act it out/use of Teacher Initials ______(act it out/use of

Connie Kudrna 28 5/22/2018 manipulatives) manipulatives)

Name ______

Circus Cents Patrick wants to go to the circus. A ticket will cost 15 cents. He has 6 cents. How many pennies will he need to make a total 15 cents? 1. Underline the known information.

2. Draw a picture to show the known information.

3. Circle the problem that you need to solve in the word story above.

Connie Kudrna 29 5/22/2018 Solve the problem using Strategy 1 several strategies. Show your work.

Answer______Circle your answer.

Teacher Initials ______(act it out/use of manipulatives) Strategy 2Strategy 3

Teacher Initials ______(act it out/use of manipulatives)

Name: ______

Connie Kudrna 30 5/22/2018 Building Blocks Journal You have 4 blocks. How many blocks do you need to make a total of 7? 1. Underline the known information. 2. Draw a picture to show the known information.

Answer______Answer______Circle your answer. Circle your answer. Teacher Initials ______(act it out/use of manipulatives) Teacher Exemplars for Distinguished Student Work

Connie Kudrna 31 5/22/2018 Crunchy Cookies Journal

You have 3 cookies. How manyHow many cookies do you need to do you needto make to a total make of 6? a total o 1. Underline the known information. 2. Draw a picture to show the known information.

3. Circle the problem you need to solve in the word story above. Solve the problem by drawing a Choose another strategy. picture. Show your work. Show your work.

3 + 3 = 6

1+ 1 + 1 + 1 + 1 + 1 = 6

three and three is six

Answer_____3______Answer_____3______Circle your answer. Circle your answer. Teacher Initials ____CK__ (act it out/use of manipulatives)

Teacher Exemplars for Distinguished Student Work

Connie Kudrna 32 5/22/2018 Missing Squares Journal

How many do squares do you need to make You have 5 squares. How many squarenine? crackers do you need to

1. Underline the known information.

3. Circle the problem you need to solve in the word story above.

Solve the problem by drawing a Choose another strategy. Show your work. picture. Show your work.  act it out  use manipulative  add to find answer

5 + 4 = 9

9 – 5 = 4

five and four are nine

Answer______4______Answer___4______Circle your answer. Circle your answer. Teacher Initials ___CK___ (act it out/use of manipulatives)

Connie Kudrna 33 5/22/2018 Teacher Exemplars for Distinguished Student Work

Sweet Treat Journal You have 9 pieces of candy. You have 13 friends. You want to give each friend one piece of candy. How many pieces of Howcandy many will will you need you to make need a total ofto 13 pieces?make a total of 1 1. Underline the known information. 2. Draw a picture to show the known information.

3. Circle the problem that you need to solve in the word story above. Solve the problem by using Choose another strategy. Show your work. manipulatives. Show the teacher.  act it out Draw your solution.  add or subtract to find answer 9 + 4 = 13 nine and four is thirteen (adding with manipulatives) 13 - 9 = 4 thirteen take away 9 is four

Comments: child did act out. See anecdotal record

(subtracting with manipulatives)

(child crosses out 4 buttons)

Answer____4______Answer______4______Circle your answer. Circle your answer. Teacher Initials ___CK___ (act it out/use Teacher Initials __CK____ (act it of manipulatives) out/use of manipulatives)

Circus Cents Patrick wants to go to the circus. A ticket will cost 15 cents. He has 6 cents. How manyHow pennies many pennies will do you he need need to make to amake total of 15a tot cents? 1. Underline the known information.

4. Circle the problem that you need to solve in the word story above. Solve the problem using several Strategy 1 strategies. Show your work. (use of manipulatives)

Answer______9______Circle your answer.

Teacher Initials __CK____ (act it out/use of manipulatives) Strategy 2 Strategy 3 (act it out) (use of pictures, numbers and/or words) oooooo + ooooooooo 6 + 9 = 15 15 – 6 = 9 six and nine are fifteen fifteen take away six is nine Answer___9______Answer___9______Circle your answer. Circle your answer.

Teacher Initials _CK_____ (act it out/use of Teacher Initials __CK____ (act it out/use of manipulatives) manipulatives)

Building Blocks Journal

You have 4 blocks. How manyHow many blocks blocks do you need todo make youa total of 7?need 1. Underline the known information. 2. Draw a picture to show the known information.

3. Circle the problem you need to solve in the word story above. Solve the problem by drawing a Choose another strategy. picture. Show your work. Show your work.

4 and 3 is 7

4 + 3 equals 7

four and three is seven

Answer_____3______Circle your answer. Answer______3______Circle your answer. Teacher Initials _CK_____ (act it out/use of manipulatives)

Connie Kudrna 36 5/22/2018 Connie Kudrna 37 5/22/2018 Score Card for What’s the Problem? Learning Experience e

r Five Student o Sweet Treats Score Circus Cents Score Building Blocks *Level c Black S Name Score

i Squares t s

o Book P n

g Score Dv a i D

s Student Teacher Student Teacher Student Teacher e i k o o C

y h c n u r C

A 7 9 D B 5 6 P C 3 8 D D 9 9 D E 7 8 D F 4 5 P G 3 3/6** DV/P H 5 9 D I 6 8 D J 2 3/7** DV/P K 3 5 P L 4 6 P M 3 6 P

Connie Kudrna 38 5/22/2018 N 3 7 P *D = Distinguished, 9-8 points P = Proficient, 7-5 points Dv = Developing, 5-0 points #/** = raw score/differentiat

Connie Kudrna 39 5/22/2018 QUESTIONS/PROBLEM AREAS ARE ITALICS AND BOLD FOR REFERENCE. NEW PARAGRAPH IS UNDER WITH CHANGES IN BOLD AND ITALICS. ALL I NEED TO DO IS CUT AND PASTE. EACH PAGE IS NOTED FOR EASY PLACEMENT

Student work: 3rd PARAGRAPH

Confusing sentence: Drawings however are inaccurate

The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads the way they can see this when using concrete objects. These two students have not mastered the one-to-one correspondence between number and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre-requisite skill for this learning experience. New paragraph

The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads. When asked to explain their drawings, the students are unable to communicate the process of finding a solution to another individual. However, if they use manipulatives, students can explain the process using concrete objects as they complete the steps to find the solution.

Connie Kudrna 40 5/22/2018 These two students have not mastered the one-to-one correspondence between number and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre-requisite skill for this learning experience.

under RESEARCH FINDINGS…..

UNCLEAR TO MARY:  Prior to teaching this learning experience, each problem solving strategy expected for the specific population of students needs to be taught in isolation, practiced, and achieved by the students at a proficient level or distinguished level.

New statement

 Prior to teaching this learning experience, each problem solving strategy is taught in isolation, practiced and achieved by the students at the proficient or distinguished level.

Mary is unclear of this section and the steps…..

10. Using “think aloud”, review steps and strategies for solving problems. Ask where in the past several activities the following occurred or could have occurred.: Steps: 1. interpret information in a word problem by underlining known information 2. draw a picture of the known information to assist in identifying the problem 3. identify the problem select and try possible strategies to solve the problem

Connie Kudrna 41 5/22/2018 July 14, 2006 Peer Review Comments:  I DID THIS: Replace title Connecting the Dots to What’s the Problem  I DID THIS: Replace Dots to What’s the Problem  Read to see if all the replaces were correct and found.  Add to student work section a comment on how students can be inconsistent depending on how their day is going. State something about conferencing with them if you see ups and downs in their rubric self scoring  Modifications suggestions o Computer for one to one correspondence o Games see UB math for example party scene o Visual cue of plan and label worksheets with underline and circle done o Counting jar o Writing of numbers daily practice on lined paper o Create challenge problems in learning station for better students: Design a game, make a new worksheet, use higher numbers, make posters for room  Strategies suggestions: word wall  Fix numbers on page 13 of student work section  Need sample of teacher book  Use dev, Pro, DIS for the level descriptions  Student rubric level 3 add word count  Page 18 step 48 too many steps?  Page 18 Four Blue Stars  Page 20 put in new modifications from above  Page 21 Four Blue Stars  Power point of lesson instructions  Power point of book exemplar to discuss punctuation, etc….  Video tape teacher reading book and then the kids, take home story and video  Fix book page order for developing student Mary’s Comments

Connie Kudrna 42 5/22/2018 Connie Kudrna 43 5/22/2018