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Rigor & Mathematical Practices in Grades K–2. January 2018. RIGOR IN GRADES K–2 Welcome Back!. RIGOR IN GRADES K–2 Thank You for Your Feedback!. +. RIGOR IN GRADES K–2 Norms That Support Our Learning. Take responsibility for yourself as a learner.
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Rigor & Mathematical Practices in Grades K–2 January 2018
RIGOR IN GRADES K–2Norms That Support Our Learning • Take responsibility for yourself as a learner. • Honor timeframes (start, end, and 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.” • Identify and reframe deficit thinking and speaking.
RIGOR IN GRADES K–2This Week “Do the math” Equity for all Connect to our practice 5
RIGOR IN GRADES K–2 Today • Morning: Rigor in Grades K–2 • Afternoon: Rigor and the Mathematical Practices in Grades K–2
RIGOR IN GRADES K–2Morning 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. • Participants will be able to explain how attending to the shift of rigor is an equitable practice in Standards-aligned math instruction.
RIGOR IN GRADES K–2 Morning Agenda • What Is Rigor? • Why Rigor? • Deep Dive into Rigor: Conceptual Understanding • Deep Dive into Rigor: Procedural Skills and Fluency • Deep Dive into Rigor: Application • Putting It All Together
RIGOR IN GRADES K–2 Equity Equity is engaging in practices that meet students where they are and advances their learning by giving them what they need. It’s about fairness, not sameness. Equity ensures that all children—regardless of circumstances—are receiving high-quality and Standards-aligned instruction with access to high-quality materials and resources. We want to ensure that Standards-aligned instruction is a pathway to the equitable practices needed to close the gaps caused by systemic and systematic racism, bias, and poverty. All week, we will explore our learning through an equity lens, and we will capture those moments visibly here in our room. 9
RIGOR IN GRADES K–2 I. What Is Rigor? Stop & Jot: How have you heard the word “rigor” used in your school or district?
“Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
RIGOR IN GRADES K–2 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.
“Lessons for [marginalized] students commonly focus primarily on rote skills and procedures, with scant attention to meaningful mathematics learning.” • –National Council for Teachers of Mathematics, 2014 Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, linguistic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.
RIGOR IN GRADES K–2 III. Deep Dive into Rigor: Conceptual Understanding Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes conceptual understanding. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify the conceptual understanding. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Sample Task K.NBT.A.1 Decompose teen numbers using 10-frames and a number equation. Materials • Number cards 11–19 • Pencil, crayon, or marker • Attached student worksheet Action This activity can be done individually, in partners, or in small groups. The students have a teacher-made sheet and a writing implement. The cards are shuffled and placed face down. The student picks a card off of the top of the pile. The student then says the number and draws that many dots beginning with the first 10-frame. When the first 10-frame is filled, the student continues drawing the remaining dots in the next 10-frame. The student then fills in the blank equation with the corresponding numbers. Example: The student continues to pick cards and illustrate numbers in this way until all cards are used or the sheet is filled.
RIGOR IN GRADES K–2 Identifying Rigor in the Standards Conceptual Understanding K.NBT.A.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
RIGOR IN GRADES K–2 Conceptual Understanding Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes conceptual understanding. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Conceptual Understanding Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify the conceptual understanding. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Conceptual Understanding Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out Goals for This Activity: • Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.
RIGOR IN GRADES K–2 Characteristics of Conceptual Understanding in Grades K–2 • Students explain their thinking with words, drawings, and/or equations. • “Which number is greater? Which number is less? How do you know?” • “Valid Equalities?” • “Peyton and Presley Discuss Addition” • Students understand the meaning of equivalence. • “Valid Equalities?” • “What Makes a Teen Number?” • “Three Composing/Decomposing Problems” • Students use or interpret models and drawings. • “Ford and Logan Add 45 + 36” • Students compose and decompose numbers. • “Shake and Spill” • Student apply properties.
RIGOR IN GRADES K–2 IV. Procedural Skills and Fluency Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes procedural skills and fluency. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and fluency. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Procedural Skills and Fluency Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and fluency. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify procedural skills and fluency. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 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: • Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor.
RIGOR IN GRADES K–2 Characteristics of Procedural Skills and Fluency in K–2 • Students perform procedures often with the expectation of speed and accuracy: • Counting • “Choral Counting” • “Finding Equal Groups” • Adding and subtracting • “Find the Missing Number” • “Hitting the Target Number” • Recognizing and writing numbers • “Hundred Chart Digit Game”
RIGOR IN GRADES K–2 V. Application Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes application. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Application Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify application. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out
RIGOR IN GRADES K–2 Application Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out Goals for This Activity: • Chart the characteristics of the tasks that exemplify the application aspect of rigor.
RIGOR IN GRADES K–2 Characteristics of Application in K–2 • Students use addition and subtraction and other concepts to solve word problems. • “At the Park” • “High Jump Competition” • “Christina’s Candies” • “Daisies in Vases”
RIGOR IN GRADES K–2 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.”
RIGOR IN GRADES K–2 VI. Putting It All Together What would you expect to see, in terms of rigor, in a unit on addition and subtraction at your grade level?
RIGOR IN GRADES K–2Why EngageNY? The only curriculum rated fully aligned for Grades K–8, based on Gateways 1 and 2.
RIGOR IN GRADES K–2 Rigor in the Modules Independently examine the standards for these modules: Grade K: Module 1 Grade 1: Module 1 Grade 2: Module 1 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 you’d expect to see associated with each standard.
SESSION 1 (111M): WHAT IS RIGOR AT THIS GRADE LEVEL? – FORMULA FOR MATH SUCCESS K-2Share Out • Share aspects of rigor you found in the standards with a partner.
RIGOR IN GRADES K–2 Fluency and Application
RIGOR IN GRADES K–2 Concept Development and Problem Set
RIGOR IN GRADES K–2 Student Debrief and Exit Ticket
RIGOR IN GRADES K–2 Rigor at This Grade Level • Examine the tasks and activities in the lessons and problem sets within Module 1, 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?
RIGOR IN GRADES K–2 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? • How is attending to a balance of rigor in your instruction an equitable practice for all students?
