1 We are a team of current and former classroom teachers curriculum writers school leaders and education experts who have worked in the private public and nonprofit sectors We are dedicated to ID: 785140
Download The PPT/PDF document "February 2016 Focus & Coherence in H..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
February 2016
Focus & Coherence in High School
1
Slide2We are a team
of current and former classroom teachers, curriculum writers, school leaders, and education experts who have worked in the private, public, and non-profit sectors. We are dedicated to teacher learning and teacher growth. We know that teaching is hard work and requires excellent training, high quality materials, and meaningful support for practitioners who are continuously striving to better serve their students.We provide educators with high-quality materials and hands-on professional development to help their students achieve the learning goals set by higher standards. We empower educators to make strong instructional decisions through immersive training and access to free standards-aligned resources to adapt for their classrooms, schools, and districts.FOCUS IN HIGH SCHOOLIntroduction: Who We Are2
Slide3Name 1
Name 2
FOCUS IN HIGH SCHOOLIntroduction: Who I Am
Insert photo
Insert photo
3
Slide4Raise your hand if…
you are a math teacheryou are a math teacher coachyou hold a different roleyou teach in a district schoolyou teach in a charter schoolyou teach or work in a different type of school or organizationFOCUS IN HIGH SCHOOLIntroduction: Who You Are4
Slide5FOCUS IN HIGH SCHOOL
At a GlanceWebsite: www.standardsinstitutes.orgDayIdeasWednesday8:30-4:00Focus and CoherenceThursday8:30-4:00
Rigor and Instructional PracticeFriday8:30-4:00
Adapting Curriculum Maps &
Intro to Module 1Saturday
8:30-2:30
Adapting and Teaching Lessons in Module
1
5
Learning math content
Slide6FOCUS IN HIGH SCHOOL
We Will…Go deeper on standards and shifts but also see how they play out in schoolExamine standards-aligned resourcesDo a lot of math problemsThink about how what we are learning impacts what we will do in school
6
Slide7FOCUS IN HIGH SCHOOL
Data Collection at Standards Institute7Data CollectionPre-survey (10-15m)Knowledge Daily survey (5-10m)Feedback Knowledge
Analysis
Facilitators
Institute team
Immediate adjustment:
Content
Facilitation
Operation
Slide8FOCUS IN HIGH SCHOOL
Norms That Support Our LearningTake responsibility for yourself as a learnerHonor 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”8
Slide9FOCUS IN HIGH SCHOOL
Today’s SessionsMorning: Focus in High School Afternoon: Coherence in High School 9
Slide10FOCUS
IN HIGH SCHOOLMorning Session: Focus in High School Objectives: Participants will be able to identify the major work of the grade. Participants will be able to evaluate tasks for alignment to standards. Participants will be able to apply the focus shift to their practice.
10
Slide11FOCUS IN HIGH SCHOOL
This Session’s AgendaGetting to Know YouFraming the ChallengeTask AnalysisSummary: What is the Major Work?Application: Connect to Practice
11
Slide12FOCUS IN HIGH SCHOOL
I. Getting to Know YouShare with the people at your table:Where are you from?What do you do?What gets you up in the morning? No seriously, why do you do this work?Look at the cluster headings on your table. If you can pick only four clusters to teach, which clusters would you teach and why?12
Slide13FOCUS IN HIGH SCHOOL
II. Framing the Challenge13Are Students Ready for College-Level Math?
Slide14“A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.
By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra…Improvements like those suggested in this report promise immediate positive results with minimal additional cost.”FOCUS IN HIGH SCHOOLNational Mathematics Advisory Panel 14
Slide15What are the standards “underlying success in school algebra”?
How do you know?FOCUS IN HIGH SCHOOLLook at the Standards for Your Course15
Slide16Shift #1:
“The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom.”
Slide17FOCUS IN HIGH SCHOOL
Quick ReviewConceptual Category
Domain
Cluster
Standard
“F-IF.A.1”
Slide18FOCUS IN HIGH SCHOOL
Focus on Algebra
Slide19FOCUS IN HIGH SCHOOL
Focus on Functions
Slide20FOCUS IN HIGH SCHOOL
Content EmphasesGuidance from Student Achievement Partners and testing consortia organizes content in terms of major, supporting
, and additional content:
Major
clusters are the highest
priority
Supporting
clusters are designed to support and strengthen areas of major emphasis
Additional
clusters may not connect tightly or explicitly to the major work
Slide21FOCUS IN HIGH SCHOOL
Focus in Algebra 1
Major Clusters
Supporting Clusters
Additional Clusters
Slide22FOCUS IN HIGH SCHOOL
Focus in Geometry
Major Clusters
Supporting Clusters
Additional Clusters
Slide23FOCUS IN HIGH SCHOOL
Focus in Algebra 2
Major Clusters
Supporting Clusters
Additional Clusters
Slide24FOCUS IN
HIGH SCHOOLIII. Task Analysis24
Slide251. Do the math
2. Discuss: What grade and standard is the task aligned to and how do you know?Is this standard part of a major, supporting, or additional cluster?FOCUS IN HIGH SCHOOLProtocol25
Slide26FOCUS IN HIGH SCHOOL
Task #1
Slide27FOCUS IN HIGH SCHOOL
Task #2Judy is working at a retail store over summer break. A customer buys a $50 shirt that is on sale for 20% off. Judy computes the discount, then adds sales tax of 10%, and tells the customer how much he owes. The customer insists that Judy first add the sales tax and then apply the discount. He is convinced that this way he will save more money because the discount amount will be larger.Is the customer right?
b) Does your answer to part (a) depend on the numbers used or would it work for any percentage discount and any sales tax percentage? Find a convincing argument using algebraic expressions and/or diagrams for this more general scenario.
Slide28FOCUS IN HIGH SCHOOL
Task #3City Bank pays a simple interest rate of 3% per year, meaning that each year the balance increases by 3% of the initial deposit. National Bank pays an compound interest rate of 2.6% per year, compounded monthly, meaning that each month the balance increases by one twelfth of 2.6% of the previous month's balance.Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 15 years?Write an expression for
C(y
), the City Bank balance, y years after a deposit is left in the account. Write an expression for
N(
m), the National Bank balance,
m
months after a deposit is left in the account.
Create a table of values indicating the balances in the two bank accounts from year 1 to year 15. For which years is City Bank a better investment, and for which years is National Bank a better investment?
Slide29FOCUS IN HIGH SCHOOL
III. Small Group: Task AnalysisAt your tables, you have a set of tasks:1. Do the math
2. Discuss: What grade and standard is the task aligned to and how do you know?
Is this standard part of a major, supporting, or additional cluster?
Slide30What makes up the
major work in high school?FOCUS IN HIGH SCHOOLIV. Summary
Slide31Discuss:
What are your takeaways from this session?Look at the scope and sequence or curriculum map that you brought with you today. Does the scope and sequence appropriately focus on major content? What evidence do you have? How will the focus shift impact your work with creating and/or coaching around scope and sequences?
3. What questions do you have? What
resources do you need?
FOCUS IN HIGH SCHOOL V. Application
31
Slide32Break
Slide33COHERENCE IN HIGH SCHOOL
Today’s SessionsMorning: Focus in High School Afternoon: Coherence in High School 33
Slide34FOCUS IN
HIGH SCHOOL At a GlanceWebsite: www.standardsinstitutes.orgDayIdeasWednesday8:30-4:00Focus and CoherenceThursday8:30-4:00
Rigor and Instructional PracticeFriday8:30-4:00
Adapting Curriculum Maps &
Intro to Module 1Saturday
8:30-2:30
Adapting and Teaching Lessons in Module
1
34
Learning math content
Slide35COHERENCE IN
HIGH SCHOOL Afternoon Session: Coherence in High SchoolObjectives: Participants will be able to identify and explain the important connections between standards within a grade. Participants will be able to identify prerequisite standards for grade level standards. Participants will be able to apply the coherence shift to their practice.
35
Slide36Coherence Within the Course
Application: Connect to PracticeYou’ve Got Some Explaining to Do!Vertical Coherence ChallengeApplication: Connect to PracticeCOHERENCE IN HIGH SCHOOL This Session’s Agenda
36
Slide37COHERENCE IN HIGH SCHOOL I. Coherence Within the Course37
Slide381. Do the math
2. Discuss: What standard is the task aligned to and how do you know?Is this standard part of a major, supporting or additional cluster?COHERENCE IN HIGH SCHOOL Protocol38
Slide39COHERENCE IN HIGH SCHOOL
Algebra 1Suppose h(t)=−5t2 + 10
t + 3 is an expression giving the height of a diver above the water (in meters), t
seconds after the diver leaves the springboard.How high above the water is the springboard? Explain how you know.
When does the diver hit the water?
At what time on the diver's descent toward the water is the diver again at the same height as the springboard?
When does the diver reach the peak of the dive?
F-IF.4
F-IF.8
A.REI.4
A.SSE.3
Slide40Within-Grade Coherence:
Coherence is built into the standards for each grade through the utilization of complementary topics to support and reinforce a major topic in a grade. This also increases focus in the grade.
Slide41At your tables, you have a set of tasks.
1. Do the math2. Discuss:What standards is the task aligned to and how do you know?Why is this connection important to show to students?COHERENCE IN HIGH SCHOOL Task Analysis41
Slide42COHERENCE IN HIGH
SCHOOL GeometryIs the quadrilateral with vertices (-6, 2), (-3, 6), (9, -3), (6, -7) a rectangle? Explain.
G-CO.6G-GPE.4
G-GPE.5G-SRT.5
Slide43COHERENCE IN HIGH SCHOOL
Algebra 2F-IF.4F-IF.5F-BF.1
Mike likes to canoe. He can paddle 150 feet per minute. He is planning a river trip that will take him to a destination about 30,000 feet upstream (that is, against the current). The speed of the current will work against the speed that he can paddle.
Let s
be the speed of the current in feet per minute. Write an expression for r
(s
), the speed at which Mike is moving relative to the river bank, in terms of
s
.
Mike wants to know how long it will take him to travel the 30,000 feet upstream. Write an expression for
T
(
s
), the time in minutes it will take, in terms of
s.
What is the vertical intercept of
T
? What does this point represent in terms of Mike’s canoe trip?
At what value of
s
does the graph have a vertical asymptote? Explain why this makes sense in the situation.
For what values of
s
does
T
(
s
) make sense in the context of the problem?
Slide44At your tables, you have a set of tasks.
1. Do the math2. Discuss:What course and standards is the task aligned to and how do you know?Why is this connection important to show to students?COHERENCE IN HIGH SCHOOLTask Analysis44
Slide45Discuss:
1. What are your takeaways from this session so far?2. Look at the scope and sequence or curriculum map that you brought with you today. Does the scope and sequence appropriately reflect the idea of within-course coherence? What evidence do you have? How will within-course
coherence impact your work with creating and/or coaching around scope and sequences?
3. What further questions do you have? What further resources do you need?
COHERENCE IN HIGH SCHOOL
II. Application
45
Slide46COHERENCE
IN HIGH SCHOOL III. You’ve Got Some Explaining To Do!What does a student need to know about functions in high school mathematics?
Slide47COHERENCE IN HIGH SCHOOL
What’s the Right Order?StandardA. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x
is an element of its domain, then f(x
) denotes the output of f corresponding to the input
x.
B. Understand that a function
is a rule that assigns to each input exactly one output.
The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
C. Solve an equation of the form
f
(
x
) =
c
for
a simple function
f
that has an inverse and write an expression for the inverse.
D. Represent transformations in the plane using, e.g., transparencies and geometry software;
describe transformations as functions that take points in the plane as inputs and give other points as outputs
. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Algebra 1
Grade 8
Algebra 2
Geometry
Slide48“
A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. By the term coherent, the Panel means that the curriculum is marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.”COHERENCE IN HIGH SCHOOLCoherence is Key
48
Slide49COHERENCE
IN HIGH SCHOOLThe Progressions
Slide50Across-Grade Coherence:
Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years.
Slide51In your groups, you have
16 standards on pieces of paper. Most standards come from the high school standards—a few come from earlier!The standards are not labeled!Determine which standards are prerequisites for other standards.Note: There is more than one vertical strand.
Bonus: Can you determine which standards belong in which grade or
course?
COHERENCE
IN HIGH SCHOOL
IV. Vertical Coherence Challenge
51
Slide52Grades 5 – 7
Grade 8Algebra IGeometry Algebra II
COHERENCE IN HIGH SCHOOL A Picture of Coherence
G
5.G.2
J
6.EE.5
L
6.G.3
E
7.RP.2C
O
8.G.3
F
8.F.1
C
G-CO.7
N
F-IF.2
M
8.EE.8A
D
A-REI.7
P
A-REI.6
A
8.F.3
B
8.EE.6
I
8.G.5
H
F-BF.1C
K
F-LE.2
Slide53Discuss:
What are your takeaways from today’s session?Look at the lesson that you brought with you today. What standard does the lesson address? What evidence do you have?What are the prerequisite standards from prior grades for this standard? How do you know?How could you use these prerequisite standards to support students
who are not on grade level?
3. What questions do you have? What
resources do you need?
COHERENCE IN HIGH SCHOOL
V. Application
53
Slide54What are your takeaways from this session?
Please fill out the feedback survey.Takeaways and FeedbackPlease fill out the feedback survey!54
Slide55Submit online
via our website: www.standardsinstitutes.org
Slide56FOCUS IN HIGH SCHOOL
Reference List56SlideSource13http://www.highereducation.org/reports/college_readiness/gap.shtml14Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC, 2008. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
16http://www.corestandards.org/other-resources/key-shifts-in-mathematics/18 – 19
SAP: High School Publisher’s Criteria:
http://achievethecore.org/page/267/high-school-publishers-criteria-for-the-common-core-state-standards-for-mathematics-detail-pg
21 – 23
http://
www.parcconline.org
/resources/educator-resources/model-content-frameworks/mathematics-model-content-framework
24, 26
– 28, 39, 42 – 43
https://www.illustrativemathematics.org/
48
Foundations for Success: The Final
Report of the National Mathematics Advisory Panel
, U.S. Department of Education: Washington, DC, 2008.
http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
49
http://math.arizona.edu/~ime/progressions/
Image Credits:
Slide 16: "Your focus needs more focus" by Leland Francisco (Flickr). Slide
30:
"Needle and Thread" by Philippa
Willitts
(Flickr). Slide
32:
"Latte art smile" by Brainy J (Flickr). Slide
37:
“Coiled Rope” by Danny Fowler (Flickr). Slide
40:
Untitled by
kropekk_pl
(
Pixabay
).
Slide 46: U.S. Army RDECOM “RDECOM presents STEM
opportunties
at Edgewood High
School” (Flickr). Slide 50:
Untitled by
bogitw
(
Pixabay
). Slide
54:
Untitled by
nguyentuanhung
(
Pixabay
).