Rigor amp Mathematical Practices in High School 1 RIGOR IN HIGH SCHOOL Welcome Back 2 RIGOR IN HIGH SCHOOL Thank You for Your Feedback 3 Take responsibility for yourself as a learner ID: 575151
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July 2016
Rigor & Mathematical Practices in High School
1Slide2
RIGOR IN HIGH SCHOOL
Welcome Back!2Slide3
RIGOR IN HIGH SCHOOL
Thank You for Your Feedback!+ 3Slide4
Take responsibility for yourself as a learner
Honor timeframes (start, end, activity)Be an active and hands-on learnerUse technology to enhance learningStrive for equity of voiceContribute to a learning environment in which it is “safe to not know”RIGOR IN HIGH SCHOOLNorms That Support Our Learning4Slide5
RIGOR IN HIGH SCHOOL
This WeekDayIdeasMonday
Focus and Within Grade Coherence
Tuesday
Rigor and the
Mathematical Practices
Wednesday
Across Grade Coherence and Instructional Practice
Thursday
Adaptation
and
Curriculum Study
Friday
Adaptation and Practice
5
“Do the math”
Connect to our practiceSlide6
RIGOR IN HIGH SCHOOL Today
Morning: Rigor in High SchoolAfternoon: Rigor and the Mathematical Practices in High School6Slide7
RIGOR IN HIGH SCHOOL Morning Objectives
Participants will be able to describe the three aspects of the “Rigor” shift as conceptual understanding, procedural skill and fluency, and application.Participants will be able to describe the rationale for the “Rigor” shift.Participants will be able to identify aspects of rigor called for by the standards in their grade. Participants will be able to identify characteristics of tasks and accompanying student work
that call for/demonstrate conceptual understanding, procedural fluency, and application. 7Slide8
RIGOR IN HIGH SCHOOL Morning Agenda
What is Rigor?Why Rigor?Deep Dive into Rigor: Conceptual UnderstandingDeep Dive into Rigor: Procedural Skills and FluencyDeep Dive into Rigor: ApplicationBringing It All Together8Slide9
RIGOR IN HIGH SCHOOL
What is Rigor? Stop & Jot: How have you heard the word “rigor” used in your school or district?9Slide10
“Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
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RIGOR IN HIGH SCHOOL
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.11Slide12
RIGOR IN HIGH SCHOOL
Why Rigor?12Slide13
RIGOR IN HIGH SCHOOL
From TIMSS Video Study13Slide14
RIGOR IN HIGH SCHOOL
Deep Dive into Rigor: Conceptual Understanding14
Protocol: time 10 min: Individual work time10 min:
Group collaboration10 min: Each group share out
Goals for this activity:
Do the math for each task.For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Record the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.
For each standard, identify the language that embodies the conceptual understanding aspect of rigor.Slide15
RIGOR IN HIGH SCHOOL
Sample TaskG-CO.B.8If two triangles satisfy the SAS criteria, describe the rigid motion(s) that would map one onto the other in the following cases. The two triangles share a single common vertex.The two triangles are distinct from each other. The two triangles share a common side.Slide16
RIGOR IN HIGH SCHOOL
Identifying Rigor in the StandardsConceptual UnderstandingG-CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.16Slide17
Protocol:
time 10 min: Individual work time10 min: Group collaboration10 min: Each group share outRIGOR IN HIGH SCHOOL Conceptual UnderstandingGoals for this activity:Do the math for each task.For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor. For each standard, identify the language that embodies the conceptual understanding aspect of rigor.
17Slide18
Transition to Group Time!
18Slide19
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLConceptual Understanding
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
For each standard, identify the language that embodies the conceptual understanding aspect of rigor.
Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.
19Slide20
Transition to Whole Group!
20Slide21
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLConceptual Understanding
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
For each standard, identify the language that embodies the conceptual understanding aspect of rigor.
Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.
21Slide22
RIGOR IN HIGH SCHOOL
Characteristics of Conceptual Understanding in High SchoolStudents explain their thinking with words, drawings, and/or equations. “Animal Populations”“Skeleton Tower”“Margin of Error for Estimating a Population MeanStudents compare quantities and expressions.“Powers of 11”“Animal PopulationsStudents interpret written descriptions of mathematical relationships.“Buying a Car” “Pizza Place Promotion”
Students apply and analyze geometric relationships.“Dilating a Line”
“Building a Tile Pattern by Reflecting Octagons”“Congruent Angles in Isosceles Triangles”
22Slide23
Protocol:
time 10 min: Individual work time10 min: Group collaboration10 min: Each group share outRIGOR IN HIGH SCHOOL Procedural Skills and FluencyGoals for this activity:Do the math for each task.For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor. For each standard, identify the language that embodies the procedural skills and fluency aspect of rigor.
23Slide24
Transition to Group Time!
24Slide25
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLProcedural Skills and Fluency
25
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor.
For each standard, identify the language that embodies the procedural skills and fluency aspect of rigor.Slide26
Transition to Whole Group!
26Slide27
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLProcedural Skills and Fluency
27
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor.
For each standard, identify the language that embodies the procedural skills and fluency aspect of rigor.Slide28
RIGOR IN HIGH SCHOOL
Characteristics of Procedural Skills and Fluency in High SchoolStudents perform procedures often with the expectation of speed and accuracy:Computing and Manipulating“Non-Negative Polynomials” “A Midpoint Miracle”“Finding the Area of an Equilateral Triangle”“A Cubic Identity”Writing Equations“Sum of Angles in a Polygon” “Solution Sets”
Drawing and Labeling“A Midpoint Miracle” Applying Geometric Properties
“Bank Shot” Reading Graphs
“A Sum of Functions” “Solution Sets”
28Slide29
BreakSlide30
Protocol:
time 10 min: Individual work time10 min: Group collaboration10 min: Each group share outRIGOR IN HIGH SCHOOL ApplicationGoals for this activity:Do the math for each task.For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the application aspect of rigor. For each standard, identify the language that embodies the application aspect of rigor.
30Slide31
Transition to Group Time!
31Slide32
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLApplication
32
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the application aspect of rigor.
For each standard, identify the language that embodies the application aspect of rigor.Slide33
Transition to Whole Group!
33Slide34
Protocol:
time
10 min: Individual work time10 min: Group collaboration10 min: Each group share out
RIGOR IN HIGH SCHOOLApplication
34
Goals for this activity:
Do the math for each task.
For each task, identify the standard(s) aligned with each task and whether it’s major work of the course.
Chart the characteristics of the tasks that exemplify the application aspect of rigor.
For each standard, identify the language that embodies the application aspect of rigor.Slide35
RIGOR IN HIGH SCHOOL
Characteristics of Application in High SchoolStudents investigate science and technology“Model Airplane Acrobatics” “The Lighthouse Problem” “Satellite”Students model natural phenomena“Eratosthenes and the Circumference of the Earth”“Logistic Growth Model, Abstract Version”“Lake Algae”Students examine real-world constraints“The Restaurant”
“The Marble Jar”Students think through legitimate life tasks“Used Subaru Forester II”
35Slide36
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 HIGH SCHOOL Balance of Rigor36Slide37
What would you expect to see, in terms of rigor, in a unit on properties (of numbers, functions, polygons, etc.) at your grade level?
RIGOR IN HIGH SCHOOLPutting It All Together37Slide38
RIGOR IN HIGH SCHOOL
Why EngageNY?The only curriculum rated fully aligned for Grades K – 8, based on Gateways 1 and 2. 38Slide39
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Curriculum Map39Slide40
RIGOR IN HIGH SCHOOL
Module + Topic Overviews40Slide41
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Lessons + Assessments41Slide42
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Rigor in the Modules
Independently examine
the standards for these modules:
Algebra I: Module 1
Geometry: Module 1
Algebra II
: 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.
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SESSION 1 (111M): WHAT IS RIGOR AT THIS GRADE LEVEL? – FORMULA FOR MATH SUCCESS K-2Share Out
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Share aspects of rigor you found in the standards with a partner.Slide44
RIGOR IN HIGH SCHOOL
Teacher Version
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RIGOR IN HIGH SCHOOL
Student Version 45Slide46
RIGOR IN HIGH SCHOOL
Student Outcomes
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RIGOR IN HIGH SCHOOL
Exploratory Challenge47Slide48
RIGOR
IN HIGH SCHOOLExercises 48Slide49
RIGOR IN HIGH SCHOOL
Problem Set49Slide50
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Exit Ticket50Slide51
RIGOR IN HIGH SCHOOL
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?51Slide52
RIGOR IN HIGH SCHOOL
Rigor at this Grade Level52How does understanding the different aspects of rigor affect your instruction?Slide53
SESSION 1 (111M): Rigor– Calibrating Common Core (6 – 8)
BREAKLunch53Slide54
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Today
Morning: Rigor in High SchoolAfternoon: Rigor and the Mathematical Practices in High School54Slide55
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Afternoon Objectives
Participants will be able to explain 2 ways in which the Mathematical Practices support the aspects of rigor called for in the standards.Participants will be able to evaluate and revise a lesson plan for alignment to the rigor shift by determining whether the objectives and important activities within the lesson develop the aspects of rigor called for in the relevant standards. 55Slide56
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Afternoon Agenda
The Mathematical PracticesThe Mathematical Practices and RigorThe Mathematical Practices in ActionAligning Lessons for Rigor56Slide57
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL The Mathematical Practices
57Make 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.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.
Slide58
RIGOR AND THE MATHEMATICAL PRACTICES IN
HIGH SCHOOL 583. 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.
Conceptual UnderstandingSlide59
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
597. 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. Slide60
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
602. Reason abstractly and quantitatively.…students make sense of quantities and their relationships in problem situations. …the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols4. 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.
ApplicationSlide61
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL The Practices and Rigor
61Process StandardsProblem SolvingReasoning and ProofCommunicationRepresentationConnections-NCTMStrands of Mathematical Proficiency
Adaptive ReasoningStrategic CompetenceConceptual Understanding
Procedural FluencyProductive Disposition
-Adding it Up: National Research CouncilSlide62
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Conceptual Understanding
62Slide63
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Procedural Skills and Fluency
63Slide64
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Application
64Slide65
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL The Mathematical Practices in Action
65Slide66
Break
BreakSlide67
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Rigor and the Practices in Lessons
67DirectionsRead Lesson 1 and 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.Identify the mathematical practice is most evident in the lesson. How does it support the associated aspect of rigor?Slide68
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Rigor and the Practices in Lessons
68Identify 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 can’t find evidence, make suggestions for improving the alignment to rigor.Slide69
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL Aligning Lessons for Rigor and the Practices
69DirectionsIdentify 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.Identify the mathematical practice is most evident in the lesson. How does it support the associated aspect of rigor?Suggestions for better alignment of rigor.Slide70
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
Aligning Lessons for Rigor and the Practices70Identify 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 can’t find evidence, make suggestions for improving the alignment to rigor.Slide71
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
Aligning Lessons for Rigor and the Practices71Share: What adjustments did you make to your lesson to better align it for rigor.Slide72
Feedback
Please fill out the survey located here: www.standardsinstitutes.orgClick “Summer 2016” on the top of the page.Click “Details” on the center of the page.
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RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
Reference List73SlideSource10www.corestandards.org/other-resources/key-shifts-in-mathematics/ 12http://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
15EngageNY Geometry Module 1, Lesson 22, Exit ticket
https://www.engageny.org/resource/geometry-module-1-topic-d-lesson-22/file/57766
36
http://achievethecore.org/page/267/publishers-criteria-for-mathematics
39 – 41, 44 – 50
www.engageny.org
61
http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/What-Do-the-Standards-for-Mathematical-Practice-Mean-to-You_/
https://www.ru.ac.za/media/rhodesuniversity/content/sanc/documents/Kilpatrick,%20Swafford,%20Findell%20-%202001%20-%20Adding%20It%20Up%20Helping%20Children%20Learn%20Mathematics.pdf
62
https://www.illustrativemathematics.org/content-standards/HSA/APR/A/1/tasks/1654
63https://www.illustrativemathematics.org/content-standards/HSA/SSE/B/3/tasks/919 64https://www.illustrativemathematics.org/content-standards/HSG/MG/A/3/tasks/416 65http://commoncore.americaachieves.org/module/9 Slide74
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Slide #Name and Photographer/Artist2
"Welcome Mat" by Dru Bloomfield (Flickr)
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“Notes” by Brady (Flickr)
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“’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 Smile” by Brainy J (Wikimedia Commons)37“Blue Legos” by David Lofink (Flickr)43“Microphone” by Alex Indigo (Flickr)52“Share” by GotCredit (Flickr)53“Coffee Break” by Sam Carpenter (Flickr)66“Snack Break” by IPlayHockey
(Flickr)
71“Adjustments” by _dali
_ (Flickr)
RIGOR AND THE MATHEMATICAL PRACTICES IN HIGH SCHOOL
Image References