Rigorous Curriculum Design - dekalbschoolsga.org

Rigorous Curriculum Design—Unit Planning Organizer

Houghton Mifflin Harcourt™ is a trademark of Houghton Mifflin Harcourt Publishing Company. © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

1

DEKALB COUNTY SCHOOL DISTRICT

RIGOROUS CURRICULUM DESIGN

UNIT PLANNING ORGANIZER

Subject(s) Mathematics

Grade and Course

Kindergarten

Unit of Study Unit 2: Comparing Numbers

Pacing 9 weeks

“Unwrapped” Priority Georgia Standards of Excellence

Skills and Concepts

Know number names and the count sequence. MGSEK.CC.3 WRITE numbers from 0 to 20. REPRESENT a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Compare numbers. MGSEK.CC.6 IDENTIFY whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Work with numbers 11–19 to gain foundations for place value. MGSEK.NBT.1 COMPOSE and DECOMPOSE numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones, e.g., by using objects or drawings, and RECORD each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8) Classify objects and count the number of objects in each category. MGSEK.MD.3 CLASSIFY objects into given categories; COUNT the numbers of objects in each category and SORT the categories by count. (Limit category counts to be less than or equal to 10.)



2

“Unwrapped” Priority Standards

“Unwrapped” Skills (Students Need

to Be Able to Do)

“Unwrapped” Concepts

(Students Need to Know)

Bloom’s Taxonomy Levels

DOK (For Overall Standard)

MGSEK.CC.3

• WRITE • Numbers from 0-20 • 1 (Remember) • 2 (Skills and

Concepts)

• REPRESNT • Number of objects

with a written numeral 0-20

• 2 (Understand)

MGSEK.CC.6

• IDENTIFY

• Object in one group is greater than, less than, or equal to the number of object in another group

• 1 (Remember) • 1(Recall and

Reproduction)

MGSEK.NBT.1

• COMPOSE

• DECOMPOSE

• UNDERSTAND

• RECORD

• Numbers from 11 to 19

• Numbers from 11 to 19

• Numbers are composed of ten ones and 1-9 more ones

• Composition or decomposition by drawing or equation

• 2,3,6 - Understand, Apply, Create

• 4 - Analyze

• 2 - Understand

• 1 – Remember

1 (Recall and Reproduction)

MGSEK.MD.3

• CLASSIFY

• COUNT

• SORT

• Objects into given categories

• Numbers of objects

• Categories by count

• 2 (Understand)

• 1 (Remember)

• 1 (Remember)

1( Recall and Reproduction)

Supporting Standards



3

Count to tell the number of objects. MGSEK.CC.4 a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (one-to-one correspondence) MGSEK.CC.5 Count to answer ‘how many?” questions. Compare numbers. MGSEK.CC.7 Compare two numbers between 1 and 10 presented as written numerals.



4

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Essential Questions Corresponding Big Ideas

1. How can numbers be represented?

2. How can you compare numbers?

3. How do you know teen numbers are made of tens and ones?

4. How can you classify objects into given categories?

1. A number can be represented by a set of objects and then by a numeral.

2. Sets of objects can be compared to determine more than, fewer than or equal.

3. Each digit in a number has a place value.

4. Objects can be classified but not limited to; size, shape, and color.



5

Unit Assessments

Pre-Assessment Post-Assessment

Student Version:

GrK_Math_Unit2_Preassessment_Student

Teacher Version:

GrK_Math_Unit2_Preassessment_Teacher

Student Version:

DeKalb Benchmark Assessment

Teacher Version:



6

Performance Assessment

Engaging Scenario

Current Situation: Great news! This year our school wants to add new equipment to our playground. The best part is that you get to make the selection. First, kindergarten students must vote to decide if we get new slides, monkey bars or swings. Each student may choose which piece of equipment they would like to add. Student Challenge: Think, pair, share with your table or partner the best piece of equipment to add. Write your name on a post it and cast your vote. Next, draw each item in your math notebook, count how many people voted for each item and write the results in your math notebook. Then, determine which piece of equipment has more votes, which piece has the fewest votes and if any have the same number of votes. Lastly, circle the one with the most votes in red. Circle the one with the fewest votes in blue. Underline any that are the same in yellow.

Student Role: Complete the following task: count the number of votes, compare votes for each piece of equipment and compare equipment votes to another class.

Intended Audience: Students will present to class

Product or Performance: Math Journal

Performance Task Synopses

Task 1: MGSEK.CC.3, MGSEK.NBT.1, and MGSEK.MD.3 – Students will vote on the equipment choice and record their results using pictures, words, and numbers. Student will decompose the numbers in tens and ones. THIS TASK IS AS A SMALL GROUP AND WILL BE REPEATED FOR TASK 2. Task 2: MGSEK.CC.3, MGSEK.NBT.1, and MGSEK.MD.3 – Students will vote on the equipment choice and record their results using pictures, words, and numbers. Student will decompose the numbers in tens and ones. THIS TASK NOW A WHOLE CLASS ACTIVITY AND IS A REPEAT FOR TASK 2. Task 3: MGSEK.CC.6 – Students will compare the equipment vote data using the terms: more, less, greater, same as.



7

Performance Task 1 In Detail

Know number names and the count sequence. MGSEK.CC.3 WRITE numbers from 0 to 20. REPRESENT a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Work with numbers 11–19 to gain foundations for place value. MGSEK.NBT.1 COMPOSE and DECOMPOSE numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six , seven, eight, or nine ones, e.g., by using objects or drawings, and RECORD each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8) Classify objects and count the number of objects in each category. MGSEK.MD.3 CLASSIFY objects into given categories; COUNT the numbers of objects in each category and SORT the categories by count. (Limit category counts to be less than or equal to 10.) Circumstances of Performance: In-Class (Approximate Time 60 minutes) Note Task 1 is to be completed as a small group activity in the class. Task 1 will be repeated as Task 2 but as a whole class activity. Task 1 Student Directions: It is time to find out what equipment other students want for the new playground. In small groups:

• Select the equipment card based upon your choice for the new playground.

• Sort the equipment cards; count the number of cards for each piece of equipment.

• Write the number of votes for the three pieces of equipment using words or numbers.

• Decompose the number in tens and ones using drawings for each equipment and the winning vote.

• Record the decomposition for each equipment and the winning vote using an equation.

Swing Monkey Bar Slide

Task 1 Teacher Notes:

• Give small groups of students a set of equipment cards. Make sure the set has enough of the equipment cards so that students can select one of the three choices.

• Allow each student to record his or her choice on a sticky note or index card. Have students write their name and then their choice in words and/or pictures.

• For each small group, allow them to complete the student activity as described in the Task 1 Student Directions. Each student will need a sheet of construction paper to record his or her results of the task. Refer to the construction paper as their data sheet.



8


• Make sure each student’s construction paper records the winning vote of the group on one sheet of construction paper and their vote on another sheet of construction paper.

Performance Task 1 Scoring Guide

4 Advanced 3 Proficient 2 Basic 1 Below Basic

All Proficient criteria plus:

o Recorded the number of votes using words and numbers.

o Graphed the data from the group activity.

o Placed the data results on a number line.

o Provided a viable argument using the data for the selection of the equipment.

o Attended to precision counting the number votes for each equipment.

o Recorded the number of votes using words or numbers.

o Decomposed the number in tens and ones using a drawing.

o Recorded the decomposition using an equation.

o Recorded the number of votes inaccurately using words or numbers.

o Decomposed the number in tens and ones inaccurately using a drawing.

o Recorded the decomposition inaccurately using an equation.

o Provided explanations and/or mathematical representations that could not be clearly understood or interpreted



9


Know number names and the count sequence. MGSEK.CC.3 WRITE numbers from 0 to 20. REPRESENT a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Work with numbers 11–19 to gain foundations for place value. MGSEK.NBT.1 COMPOSE and DECOMPOSE numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six , seven, eight, or nine ones, e.g., by using objects or drawings, and RECORD each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8) Classify objects and count the number of objects in each category. MGSEK.MD.3 CLASSIFY objects into given categories; COUNT the numbers of objects in each category and SORT the categories by count. (Limit category counts to be less than or equal to 10.) Circumstances of Performance: In-Class (Approximate Time 60 minutes) Task 2 is a repeat of Task 1 but now as a whole class activity. Task 2 Student Directions: It is time to find out what equipment other students want for the new playground. As a whole class activity:

1. Select the equipment based upon your choice for the new playground. 2. Count the number of votes for each piece of equipment. 3. Write the number of votes for the three pieces of equipment using numbers.

Complete 4 and 5 for each piece of equipment and the winning vote. 4. Decompose the number in tens and ones using drawings. 5. Record the decomposition for the equipment using an equation.

Swing Monkey Bar Slide

Task 2 Teacher Notes:

• Label three areas of the room based upon the equipment choices.

• Allow students to move to the area of the room for their choice of equipment.

• Have students to share the number of votes for each equipment choice.

• Record the number on the board in words.



10


• As students return to their seats, have them complete items 3 through 5 at their seats on construction paper. Refer to the construction paper as their data sheet.

• Make sure each student’s construction paper records the winning class vote and the group vote from Task 1.



All Proficient criteria plus:

o Recorded the number of votes using words and numbers.

o Graphed the data from the group activity.

o Placed the data results on a number line.

o Provided a viable argument using the data for the selection of the equipment.

o Attended to precision counting the number votes for each equipment.

o Recorded the number of votes using words or numbers.

o Decomposed the number in tens and ones using a drawing.

o Recorded the decomposition using an equation.

o Recorded the number of votes inaccurately using words or numbers.

o Decomposed the number in tens and ones inaccurately using a drawing.

o Recorded the decomposition inaccurately using an equation.




11


Compare numbers. MGSEK.CC.6 IDENTIFY whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Circumstances of Performance: In-Class (Approximate Time 30-45 minutes) Task 3 Student Directions: Use your data-recording sheet to answer the following questions based on the data we collected from Task 1 and Task 2. Based on the whole class data:

1. Which equipment has the most votes? How do you know? 2. Which equipment has the least votes? How do you know? 3. Do any of the three choices have the same number of votes? How do you know?

Based on the individual group results, pick two group sheets:

1. Which equipment has the most votes? How do you know? 2. Which equipment has the least votes? How do you know? 3. Write a sentence using the sentence frame: I voted for the _________ equipment. My group

vote for the ________ equipment was (more than/less than, the same as) _______ group.

Task 3 Teacher Notes: Provide a data-recording sheet so that students can record the results to the activity. Use manipulatives, If some students are having difficulty with understanding quantity.



All Proficient criteria plus: o Justified all

comparison problems with multiple representations for each problem.

o Created additional comparison sentences to analyze the results from other groups.

o Attended to precision comparing numbers for the equipment activity vote for all problems.

o Justified all comparison problems with words, pictures, or symbols.

o Attended to precision with writing and completing the comparison sentence frame.

o Attended to precision comparing numbers for the equipment activity vote for all problems.

o Attended to precision with writing and completing the comparison sentence frame.




12

Instructional Strategies Instructional Strategies

Research-Based Effective Teaching Strategies

21st Century Learning Skills

Learning Objectives (posted and referenced)

Identifying Similarities and Differences

Summarizing and Note Taking

Reinforcing Effort, Providing Recognition

Homework and Practice

Nonlinguistic Representations

Cooperative Learning

Purposeful small group instruction

Increased think time

Setting Objectives, Providing Feedback

Check for Understanding

Generating and Testing Hypotheses

Cues, Questions, and Advance Organizers

Interdisciplinary Non-Fiction Writing

Teamwork and Collaboration

Initiative and Leadership

Curiosity and Imagination

Innovation and Creativity

Critical thinking and Problem Solving

Flexibility and Adaptability

Effective Oral and Written Communication

Accessing and Analyzing Information

Other



13

Intervention Strategies Intervention Strategies

(Tiers 1, 2, 3) Additional Supports in

Classroom

Specially Designed Instruction for Special

Education Students

Strategies for English Language Learners

Re-voicing

Explaining

Prompting for participation

Challenging or countering

Asking “Why?” “How?”

Reread

Practice new academic

vocab.

Assistive technology

Pre-teach & re-teach in a different way

Repetition

Use of manipulatives

Collaborative work

Direct/explicit instruction

“Chunking”

Accommodating different learning styles

Create differentiated text

sets

Providing additional guided practice

Conferencing

Additional time

Small group collaboration

Modify quantity of work

Take student’s dictation

Scaffold information

Differentiated content

process or product

Consistent reward system

Refer to students’ IEP or 504 plan

Assistive technology

Visuals/Realia

Front-loading

Echoing/Choral response

Color-coding

Multiple exposures in different media

Pair-share

Modeling

Language scaffolds: eg, sentence frames

Deconstruct complex sentences and texts

L1 support

increased opportunities for student-student talk

Strategic vocabulary

instruction

Additional think time



14

Strategies for Gifted Learners

Tier 1: Low Preparation Tier 2: Medium Preparation

Flexible-Learning Groups by Readiness, Interest,

Learning Profiles

Gifted Education Cluster Classes

Choice of Books Gifted Education Collaboration Classes

Homework Options Tiered Activities and Products

Use of Reading Buddies Use of Literature Clubs

Various Journal Prompts Multiple Testing Options

Student/Teacher Goal Setting Multiple Texts

Varied Pacing with Anchor Options Alternative Assessments

Work Alone or Together Subject Advancement within class

Flexible Seating Curriculum Compacting

Varied Scaffolding Tiered Centers

Varied Computer Programs Spelling by Readiness

Design-A-DAY Varying Organizers

Varied Supplemental Materials Community Mentorships

Computer Mentors Stations

Think-Pair-Share by Readiness, Interest, Learning Profiles

Group Investigations

Open-ended Activities Students are Assessed in Multiple Ways

Explorations by Interest Student choice in selecting learning activities.

Options for Competition Simulations

Tier 3: High Tier 4: Advanced/Autonomous

Advanced Content English/language arts, mathematics, science and/or social studies courses

Above grade level accelerated English/language arts, mathematics, science and/or social studies courses

Resource Classes Advanced Placement Classes

Independent/Directed Study International Baccalaureate Classes

Socratic Seminars Internship/Mentorships

Whole Grade Acceleration



15

Instructional Resources and Materials Suggested Resources Suggested Technology Resources

Math Tools: o Number Line/Number Charts o Rekenrek o Subitizing/Dot Cards o Five Frame/Ten Frame o Snap Cubes/Counters o Number Generator (Dice) o Counting Bears

Early Mathematics – A Resource for Kindergarten Teachers http://www.insidemathematics.org/assets/common-core-resources/dana-center-early-mathematics-tasks/early-math-kindergarten.pdf Number Sense Trajectory

o GADOE Kindergarten Framework Unit 2 Literature Resources:

o GADOE Grade Level Curriculum Overview – Kindergarten

o GADOE Kindergarten Framework Unit 2

Explanation of Standards: o GADOE Grade Level Curriculum Overview

– Kindergarten o GADOE Kindergarten Framework Unit 2

Intervention Table and Instructional Activities:

o GADOE Kindergarten Framework Unit 2

My Math Student Edition: 443–448, 449–454, 455–460, 463–468, 469–474 Tutorials needed for instruction. (i.e. rote counting practice) Suggested Read Alouds: More or Less – by Stuart Murphy (comparing numbers) Just Enough Carrots – by Stuart Murphy Mouse by Mouse: A Counting Adventure –by Julia Noonan How Many Can you See? – by Hannah Reidy

Technology Resources: o GADOE Grade Level Curriculum

Overview – Kindergarten o GADOE Kindergarten Framework Unit 2

http://abcya.com/counting_fish.htm

http://abcya.com/counting_sorting_comparing.htm

http://abcya.com/kindergarten_counting.htm

https://learnzillion.com

https://www.illustrativemathematics.org/content-standards

http://www.sheppardsoftware.com

http://www.abcmouse.com

http://www.connected mcgraw-hill.com

http://www.insidemathematics.org/assets/common-core-resources/dana-center-early-mathematics-tasks/early-math-kindergarten.pdf



http://abcya.com/counting_fish.htm



http://abcya.com/kindergarten_counting.htm

https://learnzillion.com/



http://www.sheppardsoftware.com/

http://www.abcmouse.com/



16

Unit Vocabulary

Unit Vocabulary Terms Interdisciplinary Connections

Academic/Tier 2 Unit-Specific / Domain / Tier 3

Count Classify Sort Identify Combine Efficient Estimate

Digits Few Equal Greater Less More

SSKE3 Explain how money is used to purchase goods and services. a. Distinguish goods from services.

SSKE4 Explain that people must make choices because they cannot have everything they want.

Rigorous Curriculum Design—Unit Planning Organizer Blank


17

Weekly Planner Course: Kindergarten Unit: Unit 2 Comparing Numbers

Pacing Priority and Supporting

Standards Engaging Learning

Experiences Core Instruction and additional resources

Formative Assessments

Mathematical Literacy: The ability to read, listen, think creatively, and communicate about problem situations, mathematical representations, and the validation of solutions will help students to develop and deepen their understanding of mathematics. (National Council of Teachers of Mathematics, 2000)

9 weeks Make modifications to the pacing based upon student pre-

assessment results and the daily analysis of student work.

See CAAG for a listing of all standards. Instruction should be supported with the implementation of the Standards for Mathematical Practice (SMP).

Students should complete the listed experiences to support understanding and mastery of the math standards. Students are expected to exhibit the SMP.

Teachers should implement the listed experiences to support core instruction on the math standards. Teachers should model the SMP during the 3-Part Lesson Structure.

Teachers should use the assessments to support student learning at all levels. The unit pre-assessment should be administered prior to unit instruction for diagnostic purposes.

o Differentiate instruction based upon the pre-assessment results. o Make modifications to the pacing based upon student pre-assessment results and the daily analysis of student work. o Implement the Formative Assessment Lesson (FAL) to monitor the progress of students during the instructional unit. o Introduce the learning targets on a daily basis in kid friendly language using “I Can” statements. o Provide instruction using the Concrete-Representational-Abstract (CRA) sequence of instruction. o Utilize the Gradual Release Model of Responsibility (I do, We do, You do) during instruction to support student learning of

concepts/skills. o Use UPS Check and the 3 Read Protocol for the Problem Solving Process. o Use Newman’s Prompt to diagnose the hurdles students face while problem solving. o Incorporate Mathematical Visualization to model math concepts, skills, and problem solving.

o Remind students that mistakes are respected, expected, and inspected in the mathematics classroom.

Unit Expectations o Performance Assessment (Tasks and Scoring Guide) o Formative Assessment Lessons o GADOE Instructional Tasks

Weekly core instruction should include the implementation of instructional tasks from the Georgia Department of Education (GADOE) located at www.georgiastandards.org along with other district and supplemental instructional resources. Included in the planner are possible suggestions for GADOE tasks.

Week 1

MGSEK.CC.3 MGSEK.CC.4a

Introduce Engaging Scenario

Subitizing Rekenreks Review reading and writing numbers 0-20

Pre-Assessment (Unit Pre-Assessment) GKIDS

http://www.georgiastandards.org/



18





GADOE Gr. K Unit 2: Numeral, Picture, Word (11-20)

Match a collection of items with the appropriate numeral. Counting Numeral recognition Number relationships Number Words

Discussion of the Essential Questions (throughout unit)

Week 2

MGSEK.NBT.1 MGSEK.CC.3 MGSEK.CC.4a MGSEK.CC.5

GADOE Gr. K Unit 2: “Teen” Frame Talk About (11-12)

Subitizing Rekenreks Review reading and writing numbers 0-20 Represent sets of objects with numerals. Number relationships Teen number is a group of ten and some more

GKIDS Informal progress checks I.E. Ticket out the door Four Corners Popsicle Sticks Teacher observations Discussion of the Essential Questions (throughout unit)

Week 3

MGSEK.NBT.1 MGSEK.CC.3 MGSEK.CC.4a MGSEK.CC.5 MGSEK.CC.6

Task 1: Small Group – Equipment Vote GADOE Gr. K Unit 2: “Teen” Frame Talk About (13-19)

Subitizing Rekenreks Review reading and writing numbers 0-20 Number relationships Teen number is a group of ten and some more Use various strategies to compare items in two sets.

Scoring Guide Task 1 GKIDS Discussion of the Essential Questions (throughout unit)

Week 4

MGSEK.NBT.1 MGSEK.CC.3 MGSEK.CC.4a MGSEK.CC.5

GADOE Gr. K Unit 2: Moving a Cup of 10

Subitizing Rekenreks Counting One to one correspondence Unitizing

GKIDS Discussion of the Essential Questions (throughout unit) Informal progress checks I.E. Ticket out the door Four Corners Popsicle Sticks Teacher observations



19





Week 5

MGSEK.NBT.1 MGSEK.CC.3 MGSEK.CC.4a MGSEK.CC.5 MGSEK.CC.6 MGSEK.CC.7 MGSEK.MD.3

Task 2: Whole Class – Equipment Vote GADOE Gr. K Unit 2: “Teen” Frame Talk About (13-19)

Subitizing Rekenreks Counting Unitizing

Scoring Guide Task 2 GKIDS Discussion of the Essential Questions (throughout unit) Informal progress checks I.E. Ticket out the door Four Corners Popsicle Sticks Teacher observations

Week 6 MGSEK.NBT.1 MGSEK.CC.4a MGSEK.CC.6

Formative Assessment Lesson – Counting Dots GADOE Gr. K Unit 2: Make Sets of Less/Same/More

Subitizing Rekenreks Counting Numeral recognition Number relationships Recognizing number words Develop vocabulary of greater than, less than to compare the number of items.


Formative Assessment Lesson – Counting Dots http://education.ky.gov/curriculum/conpro/Math/Pages/ElemFormAssessLessons.aspx

Week 7 MGSEK.CC.4a MGSEK.CC.5 MGSEK.CC.6

GADOE Gr. K Unit 2: One More/Less Than Dominos

Subitizing Rekenreks Comparing sets Number relationships


Week 8

MGSEK.NBT.1 MGSEK.CC.4a MGSEK.CC.5 MGSEK.CC.6

Task 3: Comparing Numbers

Subitizing Rekenreks Counting

Scoring Guide Task 3 GKIDS

http://education.ky.gov/curriculum/conpro/Math/Pages/ElemFormAssessLessons.aspx



20





GADOE Gr. K Unit 2: Race to 100 Pennies (Revisited)

One to one correspondence Skip counting Unitizing Explain reasoning to show that one set has more or less than another.

Discussion of the Essential Questions (throughout unit) Informal progress checks I.E. Ticket out the door Four Corners Popsicle Sticks Teacher observations

Week 9

MGSEK.NBT.1 MGSEK.CC.3 MGSEK.CC.4a MGSEK.CC.5 MGSEK.CC.6 MGSEK.CC.7 MGSEK.MD.3

GADOE Gr. K Unit 2: 10 and Some More

Subitizing Rekenreks Counting One to one correspondence Number relationships Comparing sets

Post-Assessment (District Benchmark) Informal progress checks I.E. Ticket out the door Four Corners Popsicle Sticks Teacher observations

Rigorous Curriculum Design - dekalbschoolsga.org

Documents

Transcript of Rigorous Curriculum Design - dekalbschoolsga.org