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Welcome to the SCASD Elementary Math Parent Night

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Title: Welcome to the SCASD Elementary Math Parent Night


1
Welcome to the SCASDElementary Math Parent Night
  • Please take a moment to add your thoughts to the
    following two charts
  • 1. What is something you already KNOW about
    SCASD elementary math curriculum?
  • 2. What is something that youd like to LEARN
    this evening?

2
Teaching and Learning Mathematics In State
College Elementary Schools
3
Pennsylvania State Standards
4
Characteristics of a State High Graduate
A competent problem solver who
thinks critically and creatively
5
Best Practices
6
Mathematical Proficiency The Five Strands
  • Reasoning
  • Problem Solving
  • Conceptual Understanding
  • Mathematical Confidence
  • Knowledge of Procedures

Adding It Up Helping Children Learn Mathematics,
National Research Council
7
Mathematical Proficiency Another Model
Conceptual Understanding
Problem Solving
Skills
Phil Daro, Executive Director The Public Forum on
School Accountability
8
Problem Solving - Skills - Conceptual
Understanding
Problem Solving
  • If you have 1 3/4 pounds of sugar, and you want
    to make bags of 1/2 pound each, how many 1/2
    pound bags will you have?

What is the problem asking?
9
Problem Solving - Skills - Conceptual
Understanding
Skills
  • What skills could you use to solve this problem?

10
Problem Solving - Skills - Conceptual
Understanding
Conceptual Understanding
What are some other ways to think about this
problem?
11
a) the advantages for children in having a
strong start b) the mutually reinforcing
benefits of conceptual understanding,
procedural fluency, and automatic recall of
facts and c) that efforts, not just inherent
talent, count in mathematical achievement.
Foundations for Success
Use should be made of what is clearly known from
rigorous research about how children learn,
especially by recognizing.
  • The Final Report of the National Mathematics
    Advisory Panel
  • US Department of Education 2008

12
History of Curriculum Development
  • 2002 Research and Development
  • 2004 Field Testing
  • 2008 Board Adoption

13
A Complete Elementary Program
  • Investigations Modules
  • Calendar Math
  • Nimble with Numbers
  • Carson Dellosa
  • Blackline Resource
  • PSSA Warm-ups
  • Eligible Content Connections

14
A Fifth Graders Perspective
15
Math Goals
Please take a moment and write one or two math
goals you have for your child.
16
Goals of the Math Curriculum
We Expect Students To
  • be able to make sense of mathematics and see
    themselves as mathematical thinkers.
  • be computationally fluent in all four operations
    with whole numbers.
  • explore number systems, measurement, geometry,
    early algebra, and data, and make connections
    among them.
  • reason and communicate about their mathematical
    ideas.

17
Goal 1 We expect students to be able to make
sense of mathematics and see themselves as
mathematical thinkers.
Reading
  • Math

Make sense Use clues Make connections Wonder
Social Studies
Science
18
Goal 1 Generalizing Arithmetic
  • Algebra work is about developing ideas and
    concepts rather than manipulating symbols.

1 1 248 172 420
If you subtract an amount from one of the addends
and add it to the other, the sum will remain the
same.
19
Goal 1 Misunderstanding the Algorithm
  • Examples

Subtraction Algorithm 65 - 131
134
20
Goal 1 Misunderstanding the Algorithm
  • Examples

Multiplication 4 56 x
7 202
21
Goal 1 Misunderstanding the Algorithm
  • Examples

22
Goal 1 Understanding Math
  • One of the frailest of human faculties is the
    ability to remember isolated bits of information
    such as rules accepted on faith without
    understanding. The child who is made dependent
    on his ability to memorize is painfully
    vulnerable. When he forgets, he is helpless
    when he thinks he remembers he is never sure.
  • Robert Wirtz

23
Goal 2 We expect students to be
computationally fluent in all four operations
with whole numbers.
  • What is computational fluency?

24
Goal 2 Understanding Base-10 Place Value
  • 42 x 18 420, 800, 840
  • Is it more or less than 800?
  • How do you know?

Accuracy
  • Is it more or less than 8?
  • How do you know?

25
Goal 2 Developing Fluency With Basic Facts
  • SCASD Expectations

K Model with objects 1st Addition
facts to 10 Combinations of 10 2nd
Subtraction facts to 10 Addition
facts to 20 3rd Subtraction facts to 20
Multiplication facts through 5 x 9 4th
Multiplication facts through 12 x 12 5th
Multiplication and Division through 12s
Efficiency
26
Goal 2 Developing Fluency With Basic Facts
  • How is mastery developed?

Efficiency
27
Goal 2 Developing Fluency With Basic Facts
  • Quick Images

Efficiency
28
Goal 2 Developing Fluency With Basic Facts
  • How is mastery developed?

Grades 2 - 3
  • Todays Number
  • Count Around the Class
  • Calendar Math

Efficiency
29
Goal 2 Developing Fluency With Basic Facts
  • How is mastery developed?

Grades 4 - 5
  • Game Close to 100
  • Game Bowl a Fact

Efficiency
30
Goal 2 Developing Fluency With Basic Facts
  • How is mastery developed?

_at_ Home
  • Game Packet
  • Math Fact Websites
  • Flash Cards

Efficiency
31
Goal 2 Developing Fluency With Basic Facts
The State College Area School District values
having students be proficient and confident with
basic fact recall. We recognize that these basic
facts are the building blocks for success in the
study of higher level mathematics.
32
Goal 2 Teacher Perspective
33
Goal 2 Using and Understanding Various
Strategies
  • Is the algorithm always the most efficient way to
    solve a problem?

35 x 28
Flexibility
34
Fifth Graders Demonstrate Their Thinking about
136 11
Goal 2 Using and Understanding Various
Strategies
Flexibility
35
Building Algorithms Conceptually
36
Goal 2 We expect students to be
computationally fluent in all four operations
with whole numbers.
Arithmetic is about answering a question.
Mathematics is about questioning an answer.
Fred Gross
37
Goal 3 We expect students to explore number
systems, measurement, geometry, early algebra,
and data, and make connections among them.
  • Number Systems
  • Measurement
  • Geometry
  • Algebraic Concepts
  • Data Analysis and Probability

38
Goal 3 PSSA Eligible Content
Data Analysis
Number Systems
Algebra
Geometry
Measurement
39
  • http//investigations.terc.edu/curric-math/
  • Curriculum by Math Content
  • At this site you will find PDFs that elaborate on
    the development of each of the content areas from
    kindergarten through grade 5. These documents
    include Mathematical Emphases and Benchmarks for
    each grade level.

40
Goal 3 Number Systems - Rational Numbers
K - 1
  • recognize fractional relationships among pattern
    blocks
  • measure and compare lengths between whole number
    units

41
Goal 3 Number Systems - Rational Numbers
Grades 2 - 3
  • recognize fractions as equal parts of a whole and
    as equal parts of a set
  • begin to use fractional notations and
    terminology, including mixed numbers
  • compare fractions and recognize equivalencies
  • introduce decimals

42
Goal 3 Number Systems - Rational Numbers
Grades 2 - 3
  • compare fractions and recognize equivalencies

43
Goal 3 Number Systems - Rational Numbers
Grades 4 - 5
  • develop an understanding of the meaning, order
    and equivalencies of fractions and decimals
  • understand relationships among fractions,
    decimals and percents
  • use the operations of addition and subtraction
    with fractions and decimals

44
Goal 3 Number Systems - Rational Numbers
Grades 4 - 5
  • use the operations of addition and subtraction
    with fractions and decimals

45
  • K-1
  • directly compare objects
  • measure with standard objects
  • 2-3
  • understand duration of time and temperature
  • understand perimeter and area
  • 4-5
  • find perimeter, area, and volume

46
  • K-1
  • compose, decompose, identify, sort, and compare
    2-D and 3-D shapes
  • 2-3
  • explore geometric arrays, symmetry, and
    congruency
  • 4-5
  • measure and use angles
  • explore similarity

47
  • K-1
  • construct, describe, and extend repeating
    patterns
  • identify repeating units
  • identify what comes next in a pattern
  • begin work in number patterns

48
  • 2-3
  • describe and represent ratios and constant rates
    of change
  • use, interpret and create graphs and tables to
    represent change
  • predict and extend number patterns

?
  • What is the color of the 21st cube?
  • 37th? 71st? 100th?

49
  • 4-5
  • compare situations with constant rates of change
  • describe and represent situations in which the
    rate of change is not constant
  • use symbols to represent values of variables

50
  • K-1
  • sort, classify, represent, and describe data
  • 2-3
  • investigate numerical and categorical data
    sets
  • use and interpret bar graphs and line plots
  • summarize the shape of data including modes and
    outliers

51
  • 4-5
  • summarize data including median and fractional
    parts of data
  • describe the probability of events

52
Goal 4 We expect students to reason and
communicate about their mathematical ideas.
  • A mathematician has not fully understood his own
    work until he can effectively explain it to the
    first man he meets in the street.
  • Joseph L. Lagrange

53
Goal 4 Communicating in the Classroom
Write and solve a story problem about a combining
situation. Your story problem may be about
anything you can see out your window at home.
I see 28 birds eating seeds. 13 sqarls joyn in
how many birds and sqarls are there in all? I
know if I brake the 28 into 20 and 8 and 13 into
10 and 3 and add 20 10 30 8 3 11 and
then 30 11 41
54
Goal 4 Communicating in the Classroom
Marcies dad brings in cupcakes for a birthday
party. There are 16 chocolate cupcakes and 21
vanilla cupcakes. How many cupcakes did Marcies
dad bring in? Explain how you figured out using
numbers, words, or pictures.
Well I knew that the one in sixteen is really a
ten. And the two in the twenty-one is a twenty.
If I add those together they make thirty. Then I
add the other two numbers and I get 37!
55
Goal 4 Communicating in the Classroom
Look at the quadrilateral below that was made
from Power Polygons. Circle the 4 angles in this
quadrilateral. Use the polygon pieces to find
the size of each angle. Label the size of each
angle and explain how you know.
56
Goal 4 Communicating Mathematically at Home
  • Helpful Questions to Ask Your Child
  • Does this remind you of other problems?
  • What have you come up with so far?
  • Where do you think you should start?
  • What is the problem asking you to do?
  • Would drawing a picture or diagram help?
  • How can I help? (w/o giving the solution)

57
Elementary Math Parent Handbook
  • District Position Statement
  • Games
  • Data Collection
  • Homework
  • Fact Practice
  • Helpful Tips
  • Strategies

58
Beyond State College Preparing Future Teachers
Andrea McCloskey, PhD, Penn State
  • PSU educates future teachers from a conceptual
    perspective

59
Beyond State College Conceptual Instruction in
PA
  • Bloomsburg Area, Chambersburg Area, Danville
    Area, Elizabethtown Area, Lebanon, Shikellamy,
    Avon Grove Area, Avon Grove Charter, Bethlehem
    Areas, Boyertown Area, Bristol Twp, Cheltenham
    Twp, Coatesville Area, Colonial, Council Rock,
    Craig House Academy, Downingtown, East
    Stroudsburg Area, Easton Area, Great Valley,
    Kennett Consolidated, Nazareth Area, Oley Valley,
    Owen J Roberts, Upper Periomen,
    Tredyffrin-Easttown, West Chester Area,
    Wissahickon, Germantown Friends, Gladwyne
    Montessori, School of the Holy Child, Albert
    Gallatin, Allegheny Valley, Avonworth , Baldwin
    Whitehall, Corry, Deer Lakes, Elizabeth Forward,
    Ellwood City, Erie, Fox Chapel, Gateway, Hampton
    Twp, Montour, Moon Area, Mt Lebanon, Peters Twp,
    Plum, Uniontown Area, Bermudian Springs, Conewago
    Valley, Fairfield Area, Littlestown Area, Upper
    Adams, Gettysburg Area, Governor Mifflin,
    Tulpehocken Area, Wilson SD, Twin Valley, Athens
    Area, Canton Area, Northeast Bradford, Troy,
    Bensalem Twp, State College, Bristol Twp, Central
    Bucks, New Hope Solebury, Palisades, Quakertown
    Cnty, Oxford Area, Bloomsburg, Central Columbia,
    Mechanicsburg Area, Shippensburg, Central
    Dauphin, Derry Twp, Diocese of Harrisburg,
    Halifax Area, Harrisburg City, Middletown,
    Chester Upland, Southeast Delco, Radnor Twp,
    Ridley, Haverford Twp, Springfield,
    Wallingford-Swarthmore, William Penn, Riverside,
    Cocalico, Eastern Lancaster Co, Lancaster,
    Williamsport Area, Dallas, East Lycoming, Jersey
    Shore, Loyalsock Twp, Montgomery Area,
    Montoursville, S. Williamsport, Abington,
    Cheltenham, Norristown, Perkiomen Valley,
    Pottsgrove, Hatboro-Horham, Jenkintown, Lower
    Moreland Twp, Methacton, North Penn, Souderton
    Area, Spring Ford Area, Springfield, Wissahickon,
    Bangor, Pen Argyl, Saucon Valley, Shamokin,
    Warrior Run, Philadelphia City, Williams Valley,
    Mifflinburg, Wallenpaupack, Wayne Highlands,
    Dover, Northeastern, Red Lion, Eastern York,
    South Eastern, South Western, Southern York
    County, York Suburban, Clearfield, Bald Eagle,
    Bellefonte, Ferndale, Tyrone, Berlin Brothers
    Valley, Conemaugh Twp, Windber, Waynesboro,
    Pittsburgh Area

60
Beyond State College Former Parents
Perspectives
Many thanks to you and SCASD for being on the
cutting edge in math instruction- I am seeing
firsthand its benefits. Casey's math
background in Investigations has put him in the
top of the pack in math--and his conceptual
understanding is better than his sisters (who
did not have Investigations).
61
Beyond State College How Do We Compare?
62
Summing it Up A Teachers Perspective
63
Thank You
State College Elementary Math MJ Kitt,
Coordinator (mjk12_at_scasd.org) Carrie Kauffman,
Curriculum Support (ckb11_at_scasd.org) Susan
Taptich, Curriculum Support (sat12_at_scasd.org) 814.
231.1082
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