Let’s Talk Essentials Grades 3-5 October 30, 2009 NCCTM State Conference
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Let’s Talk Essentials Grades 3-5
October 30, 2009 NCCTM State Conference
NCDPI’s Response to Framework For Change
SBE’s Framework For Change
Blue Ribbon Commission Report
Vision into Mandate
Mission
Our Goal:
NC public schools will produce globally compe??ve students.
The Purpose of Standards: To define and communicate the knowledge and skills a student must master to be globally compe==ve.
ES
ES ES
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Na?
onal & Interna?
onal
Standards
21st Cen
tury Skills
Revised Bloo
m’s Taxon
omy
Principles and Filters
• Enduring • Measurable
• Clear and Concise • Priori?zed and Focused • Rigorous • Relevant to the Real World
Criteria Filters Course Generalized goals Examples and processes to
achieve criteria Student Outcomes
Assessm
ent P
rototype
s
Wri?ng The Essen?al Standards
Wri=ng Teams
Instruc?onal Coaches
Higher Ed Accountability Staff
EC & Curriculum Staff
School Readiness Staff
External Business
Teachers Curriculum Directors
Administrators
Na=onal and Interna=onal Standards
Achieve
NCTM
Focal Points
Singapore & Japan
TIMSS
NAEP
Revised Bloom’s Taxonomy
• The Cognitive Processes (or verbs) in the RBT have very specific meanings.
• The RBT helps in achieving key goals:
Depth
Focus
One Taxonomy for All Content Areas
Revised Bloom’s Taxonomy
• Revised Bloom’s Taxonomy is a taxonomy of both cognitive process and knowledge.
The Cognitive Processes (or verbs) in the RBT have very specific meanings.
• Understand: construct meaning from instructional messages, including oral, written, and graphic communication.
• Explaining: requires constructing a cause-and-effect model of a system (e.g. explain the recent downturn in the global economy) grammatical principles from examples)
ES
ES ES
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Course
The Essen?al Standard is the organizing unit.
Essen?al Standard
Clarifying Objec=ves Clarifying Objectives
Clarifying Objectives
Clarifying Objectives
Essen?al Standard
Understand the value of whole numbers and decimal representations from 0.01 to 100,000.
4.N.1
Example Represent whole numbers and decimals using models, words and numbers (symbolic).
Compare sets of two to six numbers, arranging them from least to greatest or greatest to least.
Illustrate the place value structure of decimals and whole numbers when multiplying and dividing by 10.
Clarifying Objec?ves Clarifying Objectives
Clarifying Objectives
Clarifying Objectives
Essen?al Standard
Understand the structure of the Real number system.
8.N.2
Example Classify Real numbers as natural, whole, integer, rational or irrational providing a justification.
Represent Real numbers on a number line using opposites and absolute value.
Compare Real numbers.
Assessment Prototypes
Essen=al Standard
Prototypical Assessment
Prototypical Assessment
Classroom
EOC-‐EOG
WriXen with assessment in mind.
Totals:
From the individual survey on draZs On wri?ng/review teams Collabora?ve LEA Feedback
4447 165
~7500 ~12,112 stakeholders
Stakeholder Involvement
All Feedback was read and considered. Much of it improved the current drafts.
Mathematics Strands / Formatting • Number and Operations N • Algebra A • Geometry G • Measurement M • Statistics and Data Analysis S • Discrete Mathematics D
Grade level. Strand. ES. CO Example: 3.M.1.2
Timelines for Mathematics K-5 6-12
Essential Standards and Objectives
Approved Sept. 2009 Approved Sept. 2009
Field Test Year 2010 – 2011 2010 – 2011 Testing Year for 2009 Essentials
2011 – 2012 2011 - 2012
Textbooks Adoption 2008-2009 In Place 2009-2010
Adoption list 2009 Purchases—when able
• Standards reflect a more comprehensive development of ratio and proportion in response to National and International Reports.
• Standards reflect a K-12 learning progression (trajectory) in developing concepts and skills.
3-5 Essential Standards
Number Relationship Grade 3: Understand the numerical value of whole numbers 0 to
10,000. Grade 4: Understand the value of whole numbers and decimal
representation from 0.01 to 100,000. Grade 5: Understand the value of whole numbers, fractions and
decimal representations from 0.001 to 1,000,000.
Number and Operations Progressions
Operations Grade 3: Understand multiplication & division and their relationship
using facts 1-10 Use strategies to solve multi-digit addition & subtraction problems.
Grade 4: Use strategies to solve problems involving multi-digit, addition, subtraction multiplication and division of whole numbers.
Grade 5: Use combinations of whole number addition, subtraction, multiplication and division to solve multi-step problems in context.
Number and Operations Progressions
Equipartitioning and Ratios Grade 3: Understand the meaning of fractions as sharing equally
(equipartitioning) using models. Grade 4: Understand the concept of equivalence with models as it
applies to fractions, improper fractions, mixed numbers and decimals. Use models to represent addition and subtraction of fractions and
decimals. Grade 5: Use strategies to solve problems involving addition and
subtraction of fractions and decimals. Use tables and graphs to compare ratios.
Number and Operations Sample Prototype
3.N.1.3 Illustrate composing a higher-value number by multiplying by 10, and composing a lower-value number by dividing by 10.
3.N.1.3 The candy company produced 1,250 jelly beans. How many bags would you use to package them into groups of 10’s? What will happen when you package them into groups of 100’s?
solution: One hundred twenty-five bags would be needed to package all of the jelly beans. If they put them in packages of 100, they would only need 12 bags, but there would be 50 jelly beans left over.
Number and Operations Sample Prototype
3.N.4 Understand the meaning of fractions as sharing equally (equipartitioning) using models.
3. N.4.3 Show three different ways that you can decompose the 4 x 4 grid into fourths? (constructed response)
one possible solution:
Algebra Progressions Mathematical Relationship Grade 3: Illustrate the associative, commutative and the identity
properties of multiplication. Grade 4: Use mathematical properties to examine numerical
relationships and solve problems. Grade 5: Apply mathematical operations to solve equations.
Equality Grade 3: Use the concept of equality with unknown quantities.
Grade 4: Use models to write equations and inequalities with variables.
Grade 5: Apply the concept of inequality.
Patterning Grade 3: Analyze numeric and non-numeric patterns. Grade 4: Analyze patterns to identify rules. Grade 5: Analyze growing and repeating patterns to solve problems.
Algebra Sample Prototype 4.A.2.1 Use models to write multi-step equations.
4.A.2.1 What is the value of the variables in the multi-step equation below. (constructed response) solution: 10 + 10 = 20 so 10 – 10 + 0 =0
+ = 20 so
- + = 0
Geometry Progressions Shapes, Properties and Spatial Relationships Grade 3: Classify figures according to their properties.
Represent points, paths, lines and geometric figures on a rectangular coordinate grid.
Grade 5: Apply properties to classify polygons. Understand the relationship between rectangles and
rectangular prism.
Transformations Grade 4: Understand the concept of symmetry and transformations.
Geometry Sample Prototype 5.G.2 Understand the relationships between rectangles and
rectangular prisms.
5.G.2.2 Compare the area of a two-dimensional net to the surface area of its three-dimensional rectangular prism
Measurement Progressions Measurement System & Unit Selection Grade 3: Use metric units to measure length, weight, capacity and
temperature to solve problems. Grade 4: Use customary units to measure length, weight, capacity
and temperature to solve problems. Grade 5: Use a protractor to measure angles. * More properly mass, but most commonly understood as weight at this grade band.
Perimeter, Area and Volume Grade 3: Understand how to determine area. Grade 4: Understand the relationship between area and perimeter of
polygons.
Money & Time Grade 3: Use clocks to tell time. Grade 5: Use measurement of temperature and of elapsed time to solve
problems.
Measurement Sample Prototype 3.M.1.2 Apply the processes of measurement (partitioning, transitivity, iteration
and compensatory principle) to length and capacity. Partitioning: larger units can be subdivided into equivalent units. Transitivity: two objects can be compared in terms of a measurable
quality using a third object. Iteration: the same unit can be repeated to determine the measure. Compensatory Principle: the relationship between the size of the unit
and the number of the units.
Sample of Compensatory Principle- 3.M.1.2 If you were to measure an object in centimeters rather than decimeters, would you use more or fewer units? Why? What do you notice about the relationship between centimeters, decimeters and meters?
Statistics and Probability Progressions
Statistical Investigations (Distributions and Relationships) Grade 3: Interpret data from statistical investigations. Grade 4: Interpret data from investigations involving one or two sets
of data. Grade 5: Interpret trends in data from statistical investigations.
Probability Grade 3: Explain results from simple probability experiments. Grade 4: Predict the outcomes of simple probability experiments.
Statistics and Probability Sample Prototype
4.S.1.4 Understand the differences between individual-to-individual (ungrouped) comparisons and individual to group (grouped) comparisons.
Use the graphs below to answer these questions: *What are the advantages to using each representation developed? *What are the disadvantages? *What are the common features of these representations? *What are the different features of these
representations? *What can we say about our family size? *What is a typical family for us? *What is the median and mode of this data? *What does it tell us about our families? *What new questions do these results suggest? *What would you like to know next about family size?
Number of People in Families (grouped data) Number of People in Families (ungrouped data)
DPI On-line Resources
DPI Website • http://math.ncwiseowl.org/home/ K-2 or 3-5 Resources • Week-by-Week Essentials • Classroom Strategies • Indicators • Observation Profile • K-2 assessments Other DPI Resources • Glossary • Math Stars & Super Stars • Testing Link
2009 Essential Standards
Crosswalk from 2003 to 2009 Standards
Implementation Guide
Essentials with Sample Prototypes
General Purpose of MSP
To improve academic achievement of students in mathematics and science by strengthening the quality of mathematics and science instruction
To encourage partnerships between institutions of higher education and high-needs schools
Partnerships must include
• An institution of higher education science, technology, engineering, or mathematics department (STEM) at 2 or 4 year institutions.
AND • A high-need local educational agency-
district, school
Partnerships may include • Another higher education institution,
department; • Additional LEAs, charter schools, public or
private schools, or a consortium of schools;
• A business; or • An organization dedicated to improving the
quality of math/science teachers
NC MSP Projects Next Cohort:
• RFP-Sept 2009 http://math.ncwiseowl.org/resources/
mathematics___science_partnership_grants/
• Proposals Due: January 22, 2010
• Funding: June 2010-June 2013
Everly Broadway, State Program Coordinator [email protected]
NAEP Questions Tool
• Released questions from NAEP for grades 4, 8 and 12
• Highlights student responses and student performance data
Access it today for FREE at: http://www.dpi.state.nc.us/accountability/policies/naep/5
North Carolina NAEP Coordinator: Iris L. Garner, Ph.D. [email protected]
Year Who Can Apply Nomination Deadline
Application Deadline
2009 Elementary Teachers Grades K - 6
April 1, 2010 May 1, 2010
2010 Secondary Teachers Grades 7 - 12
April 1, 2011 May 1, 2011
www.paemst.org
Presidential Awards for Excellence in
Mathematics and Science Teaching
Coming Soon
• Elementary Math Certification Pilot July 9, 2009 – State Board approved proposal 18 hours of graduate level courses Ready for statewide implementation beginning
summer 2011. • K-1 Assessment Pilot • Formative Assessment
Staff Development Modules
DPI Contact Information Kitty Rutherford Elementary Mathematics Consultant 919-807-3934 [email protected]
Renee Cunningham Elementary Mathematics Consultant 919-807-3839 [email protected]
Robin Barbour Middle Grades Mathematics Consultant 919-807-3841 [email protected]
Mary Russell Middle Grades Mathematics Consultant 919-807-3618 [email protected]
Carmella Fair Secondary Mathematics Consultant 919-807-3840 [email protected]
Johannah Maynor Secondary Mathematics Consultant 919-807-3842 [email protected]
Amy Scrinzi Primary Consultant 919-807-3852 [email protected]
Susan Hart Program Assistant 919-807-3846 [email protected]
Everly Broadway K – 12 Mathematics Section Chief 919-807-3838 [email protected]
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