Rigor & Mathematical Practices in Grades 3-5 February 2017 1 RIGOR IN GRADES 3-5 Welcome Back! 2 RIGOR IN GRADES 3-5 Thank You for Your Feedback! +

3 RIGOR IN GRADES 3-5 Norms That Support Our Learning Take responsibility for yourself as a learner Honor timeframes (start, end, activity) Be an active and hands-on learner

Use technology to enhance learning Strive for equity of voice Contribute to a learning environment in which it is safe to not know 4 RIGOR IN GRADES 3-5

This Week Day Ideas Monday Focus and Within Grade Coherence Rigor and the Mathematical Tuesday Practices Across

Grade Coherence and Wednesday Instructional Practice Thursday Adaptation and Curriculum Study Friday Do the math Connect to our practice

Adaptation and Practice 5 RIGOR IN GRADES 3-5 Today Morning: Rigor in Grades 3-5 Afternoon: Rigor and the Mathematical Practices in Grades 3-5 6 RIGOR IN GRADES 3-5 Morning Objectives

Participants will be able to define the procedural skill and fluency, conceptual understanding, and application aspects of mathematics understanding. Participants will be able to recognize signals of procedural skill and fluency, conceptual understanding, and application within language of standards. Participants will be able to identify characteristics of tasks that emphasize conceptual understanding, procedural skill and fluency, and modeling/application.

7 RIGOR IN GRADES 3-5 Morning Agenda I. What Is Rigor? II. Why Rigor? III.

Deep Dive into Rigor: Conceptual Understanding IV. Deep Dive into Rigor: Procedural Skills and Fluency V. Deep Dive into Rigor: Application VI. Bringing It All Together 8

RIGOR IN GRADES 3-5 What Is Rigor? Stop & Jot: How have you heard the word rigor used in your school or district? 9 Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades. 10

RIGOR IN GRADES 3-5 Aspects of Rigor Conceptual Understanding: The standards call for conceptual understanding of key concepts, such as place value and ratios. Procedural Skills and Fluency: The standards call for speed and accuracy in calculation. Application: The standards call for students to use math in situations that require mathematical knowledge. 11 RIGOR IN GRADES 3-5 Why Rigor?

12 RIGOR IN GRADES 3-5 From TIMSS Video Study 13 RIGOR IN GRADES 3-5 Deep Dive into Rigor: Conceptual Understanding Goals for This Activity: Protocol: time 10 min: Individual

work time 10 min: Group collaboration 10 min: Each group share out 1. Do the math for each task. 2. Identify the language/wording of the task that emphasizes conceptual understanding. 3.

Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. 4. Identify how the task aligns to the standard. 5. Chart the characteristics of the tasks that exemplify the conceptual understanding. 14

RIGOR IN GRADES 3-5 Sample Task 5.NBT.A.1 Task Kipton has a digital scale. He puts a marshmallow on the scale, and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why? Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans, and then the scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Why? Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads 312.4 grams. How much would you expect 1,000 pink erasers to weigh? Why? 15

RIGOR IN GRADES 3-5 Identifying Rigor in the Standards Conceptual Understanding 5.NBT.A.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 16 RIGOR IN GRADES 3-5 Conceptual Understanding Goals for This Activity: Protocol: time

10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out 1. Do the math for each task. 2. Identify the language/wording of the task that emphasizes conceptual understanding. 3. Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. 4. Identify how the task aligns to the

standard. 17 Transition to Group Time! RIGOR IN GRADES 3-5 Conceptual Understanding Goals for This Activity: Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group

share out 1. Determine the standard(s) aligned with each task and identify the language of the standard(s) that calls for conceptual understanding. 2. Identify how the task aligns to the standard. 3. Chart the characteristics of the tasks that exemplify the conceptual understanding. 19 Transition to Whole Group!

RIGOR IN GRADES 3-5 Conceptual Understanding Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out Goals for This Activity: 1. Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.

21 RIGOR IN GRADES 3-5 Characteristics of Conceptual Understanding in Grades 3-5 Students explain their thinking with words, drawings, and/or equations. Indias Bathroom Tiles?

Comparing Growth, Variation 2 To Regroup or Not to Regroup Students understand the meaning of equivalence. Valid Equalities? Students use or interpret models and drawings.

Fish Tank Karls Garden Students compose and decompose numbers. Are These Equivalent to 9.52? Breaking Apart Composite Solids

Student apply properties. 22 RIGOR IN GRADES 3-5 Procedural Skills and Fluency Goals for This Activity: Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out

1. Do the math for each task. 2. Identify the language/wording of the task that emphasizes procedural skills and fluency. 3. Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and fluency. 4. Identify how the task aligns to the standard. 23 Transition to Group Time! 24

RIGOR IN GRADES 3-5 Procedural Skills and Fluency Goals for This Activity: Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out 1. Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and

fluency. 2. Identify how the task aligns to the standard. 3. Chart the characteristics of the tasks that exemplify procedural skills and fluency. 25 Transition to Whole Group! RIGOR IN GRADES 3-5 Procedural Skills and Fluency Protocol: time 10 min: Individual

work time 10 min: Group collaboration 10 min: Each group share out Goals for This Activity: 1. Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor. 27 RIGOR IN GRADES 3-5 Characteristics of Procedural Skills and

Fluency in 3-5 Students perform procedures often with the expectation of speed and accuracy: Multiplication o Kiris Multiplication Matching Game o The Square Counting Shortcut o Fluency Mini-Assessment Division o Fluency Mini-Assessment Addition o Making 22 Seventeenths in Different Ways

o Fractions on a Line Plot 28 Break RIGOR IN GRADES 3-5 Application Goals for This Activity: Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out

1. Do the math for each task. 2. Identify the language/wording of the task that emphasizes application. 3. Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application. 4. Identify how the task aligns to the standard. 30 Transition to Group Time!

RIGOR IN GRADES 3-5 Application Goals for This Activity: Protocol: time 10 min: Individual work time 10 min: Group collaboration 10 min: Each group share out 1. Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application.

2. Identify how the task aligns to the standard. 3. Chart the characteristics of the tasks that exemplify application. 32 Transition to Whole Group! RIGOR IN GRADES 3-5 Application Protocol: time 10 min: Individual work time 10 min: Group

collaboration 10 min: Each group share out Goals for This Activity: 1. Chart the characteristics of the tasks that exemplify the application aspect of rigor. 34 RIGOR IN GRADES 3-5 Characteristics of Application in 3-5 Students use multiplication and division, as well as other concepts, to solve word problems:

Gifts from Grandma The Stamp Collection Karls Garden What Is 23/5? Dajuanas Homework Punch Margie Buys Apples Making Cookies

Converting Fractions of a Unit into a Smaller Unit 35 RIGOR IN GRADES 3-5 Balance of Rigor The three aspects of rigor are not always separate in materials and standards.

Nor are the three aspects of rigor always together in materials and standards. The Standards set high expectations for all three components of rigor in the major work of each grade. 36 RIGOR IN GRADES 3-5 Putting It All Together What would you expect to see, in terms of rigor, in a unit on fractions at your grade level?

37 RIGOR IN GRADES 3-5 Why EngageNY? The only curriculum rated fully aligned for Grades K8, based on Gateways 1 and 2. 38 RIGOR IN GRADES 3-5 Curriculum Map 39

RIGOR IN GRADES 3-5 Module + Topic Overviews 40 RIGOR IN GRADES 3-5 Lessons + Assessments 41 RIGOR IN GRADES 3-5 Rigor in the Modules

Independently examine the standards for these modules: Grade 3: Module 5 Grade 4: Module 5 Grade 5: Module 3 1. What are the aspects of rigor associated with each standard? (There may be more than one!) 2. Predict the kinds of problems and activities youd expect to see

associated with each standard. 42 Share aspects of rigor you found in the standards with a partner. 43 RIGOR IN GRADES 3-5 Fluency and Application

44 RIGOR IN GRADES 3-5 Concept Development and Problem Set 45 RIGOR IN GRADES 3-5 Student Debrief and Exit Ticket 46 RIGOR IN GRADES 3-5

Homework 47 RIGOR IN GRADES 3-5 Rigor at This Grade Level Examine the tasks and activities in the lessons and problem sets within Topic A. Find at least two tasks or activities that emphasize the aspect of rigor you would expect to see in a unit containing these standards. What evidence

do you have? 48 RIGOR IN GRADES 3-5 Rigor at This Grade Level Why spend so much time classifying aspects of rigor? Is there a hierarchy to the aspects of rigor?

How does understanding the different aspects of rigor affect your instruction? 49 SESSION 1 (111M): Rigor Calibrating Common Core (6 8) BREAK Lunch 50 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5

Today Morning: Rigor in Grades 3-5 Afternoon: Rigor and the Mathematical Practices in Grades 3-5 51 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Afternoon Objectives Participants will be able to identify characteristics of tasks that require students to use the Mathematical Practices to reinforce the intended procedural skills and fluency, conceptual understanding, and/or applied understandings. Participants will be able to evaluate whether a lesson or task attends to conceptual understanding, procedural skills and fluency, and/or application/modeling.

52 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Afternoon Agenda I. The Mathematical Practices II. The Mathematical Practices and Rigor III.

The Mathematical Practices in Action IV. Aligning Lessons for Rigor 53 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 The Mathematical Practices 1. 2. 3. 4. 5.

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 6. 7. 8. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. 54

RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 The Practices and Rigor Process Standards Strands of Mathematical Proficiency

Problem Solving Reasoning and Proof Communication Representation Connections -NCTM Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition

-Adding it Up: National Research Council 55 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Conceptual Understanding 3. Construct viable arguments and critique the reasoning of others. students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They justify their conclusions, communicate them to others, and respond to the arguments of others. 6. Attend to precision. students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own

reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. In the elementary grades, students give carefully formulated explanations to each other. 56 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Procedural Skills and Fluency 7. Look for and make use of structure. students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort

a collection of shapes according to how many sides the shapes have. 8. Look for and express regularity in repeated reasoning. students notice if calculations are repeated, and look both for general methods and for shortcuts. 57 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Application 2. Reason abstractly and quantitatively. students make sense of quantities and their relationships in problem situations. the ability to decontextualizeto abstract a given situation and

represent it symbolically and manipulate the representing symbols 4. Model with mathematics. students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 58 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Conceptual Understanding Task Sometimes when we subtract one number from another number, we "regroup," and sometimes we don't. For example, if we subtract 38 from 375,

we can "regroup" by converting a ten to 10 ones: Find a 3-digit number to subtract from 375 so that: 1. You don't have to use regrouping. 2. You would naturally use regrouping from the tens to the ones place. 3. You would naturally use regrouping from the hundreds place to the tens place. 4. You would naturally use regrouping in all places. In each case, explain how you chose your numbers and complete the problem. 59 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Procedural Skills and Fluency 60

RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Application A. Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend? B. Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy? C. Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get?

61 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 The Mathematical Practices in Action 62 Break RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Rigor and the Practices in Lessons Directions 1. Read Lesson 1 and identify the intended standard(s).

2. Identify the aspects of rigor reflected in the standard(s). 3. Find evidence of how the activities in the lesson align to the intended aspects of rigor. 4. Identify the mathematical practice that is most evident in the lesson. How does it support the associated aspect of rigor? 64 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Rigor and the Practices in Lessons Identify the intended standard( s).

Identify the aspects of rigor reflected in the standard(s). Find evidence of how the the activities in the lesson align to the intended aspects of rigor. how the identified practice supports rigor. If you cant find evidence, make suggestions for improving the alignment to rigor. 65

RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Aligning Lessons for Rigor and the Practices Directions 1. Identify the intended standard(s). 2. Identify the aspects of rigor reflected in the standard(s). 3. Find evidence of how the activities in the lesson align to the intended aspects of rigor. 4. Identify the mathematical practice that is most evident in the lesson. How does it support the associated aspect of rigor? 5. Make suggestions for better alignment of rigor. 66 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5

Aligning Lessons for Rigor and the Practices Identify the intended standard( s). Identify the Find evidence of aspects of how the the activities in the lesson align rigor reflected to the intended aspects of rigor. in the how the identified practice supports rigor. standard(s).

If you cant find evidence, make suggestions for improving the alignment to rigor. 67 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Aligning Lessons for Rigor and the Practices Share: What adjustments did you make to your lesson to better align it for rigor? 68

Feedback Please fill out the survey located here: www.standardsinstitutes.org Click Winter 2017 on the top of the page. Click Details on the center of the page. 49 RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Reference List Slide Source 10

www.corestandards.org/other-resources/key-shifts-in-mathematics 12 http://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics 13 http://www.timssvideo.com/sites/default/files/TIMSS%201999%20Math%20Report.pdf 15 https://www.illustrativemathematics.org/content-standards/5/NBT/A/1/tasks/1562 36

http://achievethecore.org/page/267/publishers-criteria-for-mathematics 39 41, 44 47 www.engageny.org 55 http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/What-Do-the-Standards-for-Mathematical-Practice-Mea n-to-You_/ 59 https://www.ru.ac.za/media/rhodesuniversity/content/sanc/documents/Kilpatrick,%20Swafford,%20Findell%20-%202001%20%20Adding%20It%20Up%20Helping%20Children%20Learn%20Mathematics.pdf

https://www.illustrativemathematics.org/content-standards/4/NBT/B/tasks/1189 60 https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-d-lesson-9/file/39496 61 https://www.illustrativemathematics.org/content-standards/tasks/262 62 https://www.teachingchannel.org/videos/multiplying-fractions-by-whole-numbers-lesson 70

RIGOR AND THE MATHEMATICAL PRACTICES IN GRADES 3-5 Image References Slide # Name and Photographer/Artist 2 "Welcome Mat" by Dru Bloomfield (Flickr) 9 Notes by Brady (Flickr) 10

Incomplete Bridge by Ken Scarboro (Flickr) 18, 24, 31 "Transitions" by Arjan Almekinders (Flickr) 20, 26, 33 208/365 - He's got the whole world in his hands. by Courtney Carmody (Flickr) 29 Latte Art Smile by Brainy J (Wikimedia Commons) 37

multiplication table by Denis Mihailov (Flickr) 43 Microphone by Alex Indigo (Flickr) 49 Share by GotCredit (Flickr) 50 Coffee Break by Sam Carpenter (Flickr) 63

Snack Break by IPlayHockey (Flickr) 68 Adjustments by _dali_ (Flickr) 71