Welcome to the SCASD Elementary Math Parent Night

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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?

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Teaching and Learning Mathematics In State
College Elementary Schools
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Pennsylvania State Standards
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Characteristics of a State High Graduate
A competent problem solver who
thinks critically and creatively
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Best Practices
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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
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Mathematical Proficiency Another Model
Conceptual Understanding
Problem Solving
Skills
Phil Daro, Executive Director The Public Forum on
School Accountability
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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?
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Problem Solving - Skills - Conceptual
Understanding
Skills

• What skills could you use to solve this problem?

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Problem Solving - Skills - Conceptual
Understanding
Conceptual Understanding
What are some other ways to think about this
problem?
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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

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History of Curriculum Development

• 2002 Research and Development
• 2004 Field Testing
• 2008 Board Adoption

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A Complete Elementary Program

• Investigations Modules
• Calendar Math
• Nimble with Numbers
• Carson Dellosa
• Blackline Resource
• PSSA Warm-ups
• Eligible Content Connections

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A Fifth Graders Perspective
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Math Goals
Please take a moment and write one or two math
goals you have for your child.
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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.

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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
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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.
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Goal 1 Misunderstanding the Algorithm

• Examples

Subtraction Algorithm 65 - 131
134
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Goal 1 Misunderstanding the Algorithm

• Examples

Multiplication 4 56 x
7 202
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Goal 1 Misunderstanding the Algorithm

• Examples

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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

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Goal 2 We expect students to be
computationally fluent in all four operations
with whole numbers.

• What is computational fluency?

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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?

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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
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Goal 2 Developing Fluency With Basic Facts

• How is mastery developed?

Efficiency
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Goal 2 Developing Fluency With Basic Facts

• Quick Images

Efficiency
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Goal 2 Developing Fluency With Basic Facts

• How is mastery developed?

Grades 2 - 3

• Todays Number
• Count Around the Class
• Calendar Math

Efficiency
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Goal 2 Developing Fluency With Basic Facts

• How is mastery developed?

Grades 4 - 5

• Game Close to 100
• Game Bowl a Fact

Efficiency
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Goal 2 Developing Fluency With Basic Facts

• How is mastery developed?

_at_ Home

• Game Packet
• Math Fact Websites
• Flash Cards

Efficiency
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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.
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Goal 2 Teacher Perspective
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Goal 2 Using and Understanding Various
Strategies

• Is the algorithm always the most efficient way to
  solve a problem?

35 x 28
Flexibility
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Fifth Graders Demonstrate Their Thinking about
136 11
Goal 2 Using and Understanding Various
Strategies
Flexibility
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Building Algorithms Conceptually
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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
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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

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Goal 3 PSSA Eligible Content
Data Analysis
Number Systems
Algebra
Geometry
Measurement
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• 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.

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Goal 3 Number Systems - Rational Numbers
K - 1

• recognize fractional relationships among pattern
  blocks
• measure and compare lengths between whole number
  units

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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

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Goal 3 Number Systems - Rational Numbers
Grades 2 - 3

• compare fractions and recognize equivalencies

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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

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Goal 3 Number Systems - Rational Numbers
Grades 4 - 5

• use the operations of addition and subtraction
  with fractions and decimals

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• 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

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• 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

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

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• 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?

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• 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

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• 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

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

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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

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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
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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!
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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.
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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)

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Elementary Math Parent Handbook

• District Position Statement
• Games
• Data Collection
• Homework
• Fact Practice
• Helpful Tips
• Strategies

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Beyond State College Preparing Future Teachers
Andrea McCloskey, PhD, Penn State

• PSU educates future teachers from a conceptual
  perspective

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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

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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).
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Beyond State College How Do We Compare?
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Summing it Up A Teachers Perspective
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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