February 2016 1 FOCUS IN GRADES 68 Introduction Who We Are 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: 779817
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Slide1
Focus & Coherence in Grades 6-8
February 2016
1
Slide2FOCUS IN GRADES 6-8
Introduction: Who We AreWe 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
.2
Slide3Name 1
Name 2
FOCUS IN GRADES 6-8Introduction: Who I AmInsert photoInsert photo3
Slide4Raise your hand if…
you are a math teacheryou are a math teacher coach
you hold a different role
you teach in a district schoolyou teach in a charter school
you teach or work in a different type of school or organizationFOCUS IN GRADES 6-8
Introduction: Who You Are4
Slide5FOCUS IN GRADES
6-8At a GlanceWebsite: www.standardsinstitutes.org
5
Learning math content
Day
IdeasWednesday8:30-4:00Focus and CoherenceThursday8:30-4:00Rigor and Instructional PracticeFriday8:30-4:00Adapting Curriculum Maps &
Intro to the Modules
Saturday
8:30-2:30
Adapting and Teaching Lessons
Slide6FOCUS IN GRADES 6-8
We Will…
Go deeper on standards and shifts but also see how they play out in
schoolExamine
standards-aligned resourcesDo a lot of math problems
Think about how what we are learning impacts what we will do in school6
Slide7FOCUS IN GRADES 6-8
Data Collection at Standards Institute7
Data Collection
Pre-survey (10-15m)
Knowledge
Daily survey (5-10m)Feedback KnowledgeAnalysisFacilitatorsInstitute team
Immediate adjustment:
Content
Facilitation
Operation
Slide8FOCUS IN GRADES 6-8
Norms That Support Our LearningTake responsibility for yourself as a learner
Honor timeframes (
start, end, activity)Be an active and hands-on learner
Use technology to enhance learningStrive for equity of voice
Contribute to a learning environment in which it is “safe to not know”8
Slide9FOCUS IN GRADES 6-8
Today’s Sessions
Morning: Focus in Grades 6-8Afternoon:
Coherence in Grades 6-8
9
Slide10FOCUS IN GRADES 6-8
Morning Session: Focus in Grades 6-8
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 GRADES 6-8
This Session’s Agenda
Getting to Know You
Framing the Challenge
Task AnalysisSummary: What is the Major Work?
Application: Connect to Practice11
Slide12FOCUS IN GRADES 6-8
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 GRADES 6-8
II. Framing the Challenge13
Are 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 GRADES 6-8
National Mathematics Advisory Panel 14
Slide15What are the standards “underlying success in school algebra”?
How do you know?
FOCUS IN GRADES 6-8Look at the Standards for Your Grade
15
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 GRADES 6-8
Quick Review
Domain
Grade Level
Standard
Cluster
17
Slide18Guidance
from Student Achievement Partners 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.FOCUS IN GRADES 6-8Content Emphases18
Slide19FOCUS IN GRADES
6-8
Focus in Grade 619
Slide20FOCUS IN GRADES
6-8
Focus in Grade 720
Slide21FOCUS IN GRADES
6-8
Focus in Grade 821
Slide22FOCUS IN GRADES 6-8
III. Task Analysis
22
Slide231. 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 GRADES 6-8 Protocol23
Slide24Molly runs 1/3 of a mile in 4 minutes.
If Molly continues at the same speed, how long will it take her to run one mile?
Draw and label a picture showing why your answer to part (a) makes sense.
FOCUS IN GRADES 6-8
#124
Slide25The number of siblings for a group of sixth grade students is shown below:
1, 0, 2, 1, 6, 0, 2, 0, 1, 10
Make a dot plot of the data.
Find the mean and the median of the data.
What does the mean tell you about the data?
Which measure of average (mean or median) do you think best describes the data? Why?FOCUS IN GRADES 6-8#225
Slide26This is a picture of two congruent rectangles.
Show that the rectangles are congruent by finding a translation followed by a rotation which maps one of the rectangles to the other.
Explain why the congruence of the two rectangles cannot be shown by translating Rectangle1 to Rectangle 2.Can the congruence of the two rectangles be shown with a single reflection? Explain.
FOCUS IN GRADES
6-8#326
Slide27At your tables, you have a set of tasks.
1. Do the math2. 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 GRADES 6-8Continue In Groups27
Slide28What
are the common threads in the
major work
in grades
6-8?FOCUS IN GRADES 6-8 IV. Summary
Slide29Discuss:
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 further questions do you have? What further resources do you need?FOCUS IN GRADES 6-8 V. Application29
Slide30Break
Slide31COHERENCE IN GRADES
6-8Today’s Sessions
Morning: Focus in Grades 6-8
Afternoon: Coherence in Grades 6-8
31
Slide32COHERENCE
IN GRADES 6-8At a Glance
Website: www.standardsinstitutes.org32
Learning math content
Day
IdeasWednesday8:30-4:00Focus and CoherenceThursday8:30-4:00Rigor and Instructional PracticeFriday8:30-4:00Adapting Curriculum Maps &
Intro to the Modules
Saturday
8:30-2:30
Adapting and Teaching Lessons
Slide33COHERENCE IN GRADES
6-8 Afternoon Session: Coherence in Grades 6-8
Objectives:
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.33
Slide34Coherence Within the Grade
Application:
Connect to PracticeYou’ve Got Some Explaining to Do!
Vertical Coherence
ChallengeApplication: Connect to Practice
COHERENCE IN GRADES 6-8 This Session’s Agenda34
Slide35COHERENCE IN GRADES
6-8 I. Coherence Within the Grade
35
Slide361. 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 GRADES 6-8
Protocol36
Slide37A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
6.EE.B.7
6.RP.A.3
COHERENCE IN GRADES
6-8
Grade 637
Slide38Within-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.
Slide39At 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 GRADES 6-8
Task Analysis39
Slide40The taxi fare in Gotham City is $2.40 for the first ½ mile and additional mileage is charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
7.EE.B.3
7
.EE.B.4
7.RP.A.3
COHERENCE IN GRADES 6-8 Grade 740
Slide418.G.C.9
8.G.B.7
The diagram shows three glasses (not drawn to scale). The measurements are all in centimeters.
The bowl of glass 1 is cylindrical. The inside diameter is 5 cm and the inside height is 6 cm.
The bowl of glass 2 is composed of a hemisphere attached to cylinder. The inside diameter of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 3 cm.
The bowl of glass 3 is an inverted cone. The inside diameter is 6 cm and the inside slant height is 6 cm.a) Find the vertical height of the bowl of glass 3.b) Calculate the volume of the bowl of each of these glasses.
c) Glass 2 is filled with water and then half the water is poured out. Find the height of the water.
COHERENCE IN GRADES
6-8
Grade 8
41
Slide42At your tables, you have a set of tasks.
1. Do the math2. Discuss:
What grade and standards
is the task aligned to and how do you know?
Why is this connection important to show to students?
COHERENCE IN GRADES 6-8 Task Analysis42
Slide43Discuss:
What are your takeaways from this session so far?
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-grade coherence? What evidence do you have?
How will within-grade 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 GRADES 6-8 II. Application43
Slide44COHERENCE IN GRADES 6-8
III. You’ve Got Some Explaining to Do!44
Lena paid $18.96 for 3 pounds of coffee.
How would you teach students to graph the proportional relationship between the number of pounds of coffee and the total cost?
Slide45Grade 6
Use ratio and rate reasoning to solve real-world and mathematical problems…
by making tables of equivalent ratios, finding missing values in tables, and plotting the pairs of values on the coordinate plane.
Grade 8
Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare different proportional relationships in different ways.
Grade 7Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.COHERENCE IN GRADES 6-8 What is the Right Order?
45
Slide46“
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 GRADES 6-8Coherence is Key46
Slide47COHERENCE IN GRADES
6-8 The Progressions
47
Slide48Across-Grade Coherence:
Learning
is carefully connected
across grades so that students can build new understanding onto foundations built in previous years.
Slide49In your groups, you have
13 standards on pieces of paper. Most standards come from the Ratios & Proportions
domain in grades 6-8.
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? COHERENCE IN GRADES 6-8 IV. Vertical Coherence Challenge
49
Slide50Grades 4 and 5
Grade 6Grade 7
Grade 8High School
J
4.MD.2
B5.NF.3G5.G.2
F
6.RP.2
L
6.RP.3a
D
7.RP.1
K
7.RP.2
M
7.RP.3
H
7.G.1
C
8.F.2
A
8.EE.6
I
8.EE.8
E
F
-BF.1
COHERENCE IN GRADES
6-8
A
Picture of Coherence
50
Slide51Discuss:
What are your takeaways from this session?
Look at the lesson
that you brought with you today. What
grade level 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 GRADES 6-8 V. Application
51
Slide52What are your takeaways from this session?
Please fill out the feedback survey.
Takeaways and Feedback
Please fill out the feedback
survey!
52
Slide53Submit online
via our
website:
www.standardsinstitutes.org
Slide54Focus and Coherence in Grades 6-8
Reference List54
Slide
Source13
http://www.highereducation.org/reports/college_readiness/gap.shtml14
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.pdf16http://www.corestandards.org/other-resources/key-shifts-in-mathematics/19 – 21 http://achievethecore.org/dashboard/2/search/1/2/0/1/2/3/4/5/6/7/8/9/10/11/12/page/774/focus-by-grade-level-list-pg 22, 24 – 26 , 37, 40 – 41 , 44https://www.illustrativemathematics.org/ 46Foundations 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
47
http://
math.arizona.edu
/~
ime
/progressions/
Image Credits:
Slide 16: "Your focus needs more focus" by Leland Francisco (Flickr). Slide 28: "Needle and Thread" by Philippa
Willitts
(Flickr). Slide 30: "Latte art smile" by Brainy J (Flickr). Slide 35: “Coiled Rope” by Danny Fowler (Flickr). Slide 38: Untitled by
kropekk_pl
(
Pixabay
).
Slide
48: Untitled by
bogitw
(
Pixabay
). Slide 52: Untitled by
nguyentuanhung
(
Pixabay
).