Transcript ADD - Pascack Valley Regional High School District

Overview of the K-5 CCSS
Common Core
State Standards
mathematics
by Judith T. Brendel
Math Supervisor, Pascack Valley Regional HS District
[email protected]
THINGS we shouldn’t forget!
ACTIVITY: Use the ruler on handout to
measure a writing tool you have with you.
What decisions did you make? :
1- What should I measure (shorter than the ruler)?
2- Should I use inches or centimeters?
3. Where should I start on the ruler?
4- Should I round up or down? How accurate do I need to
be? What should I round to?
CCSS: Common CORE
State standards
NOT TO BE CONFUSED WITH
CCC STANDARDS; NJ’s present
Core-Curriculum Content Standards
But, don’t throw away what you
already have!
Shocking but true?
 1985:
3,800,000 Kindergarten students
 1998:
2,810,000 High school graduates
 1998:
1,843,000 College Freshmen
 2002:
1,292,000 College Graduates
 2002:
1,50,000 STEM majors
 2006:
1,200 PhD’s in mathematics
Let me know a little bit
How familiar you are with the CCSS?
Closed fist – I know nothing.
1 finger – I know they exist.
5 fingers – I could be standing up here
doing this presentation.
Our plan for these 2 days:
• CONTENT
• ORGANIZATION
• NEW DESIGN
• IMPACT on STUDENT LEARNING
• IMPACT on how STUDENTS are
ASSESSED
• NEEDS and RESOURCES
Be Pro-active
Prepare for the change
• Timeline: implementation & assessment
• Transition Phase - Today’s Reality
• Last Year vs CCSS expectations
• Mathematical Practices
• Plan: Curriculum, Pacing, Assessments
• Align to texts
• OE Questions, Projects, Resources
WHAT’S NEW
Measure standards that are rigorous, globally
competitive, and consistent across the states.
New Jersey’s choice
The assessment consortium PARCC (Partnership for
Assessment of Readiness for College and Careers)
New assessments will replace current state
NCLB tests (NJASK, HSPA) in 2014-2015.
What We’ve Learned
during the past decades:
 Absolutely, students must know the basics, but
knowing basics not enough.
 Students learning math with understandings is
essential to enable students to solve problems.
 Students learn math primarily by doing math
rather than just by listening and memorizing.
What they’ve Learned
during the past decades:
 absolutely students must know the basics, but
knowing basics not enough
 students learning math w/understandings is
essential to enable students to solve problems
.64 is POINT 64
 students learn math primarily by doing math
rather than just by listening and memorizing
What we should do!
Start with a problem (division w/one-digit
divisors) Give to students and see what
they do with it. Let them work in pairs. Let
them talk about it.
Paulo has 39 patches from states that
he and his relatives have visited. He
wants to arrange the patches on a board
in 3 rows. How many patches will be in
each row? (from Dr. Janet Caldwell)
Characteristics of the CCSS
 Fewer and more rigorous
 Aligned with college and career expectations
 Internationally benchmarked
 Rigorous content and applications of higher-order
skills – rigor a depth, not complexity
 Research-based
 Common, coherent, fair and teachable
COMMON ADVANTAGES
 FEWER standards means that teachers and students will
have more time to focus on each knowledge & skill.
 CLEAR standards means the parents, teachers and the
general public will find it easier to understand the
expectations for students
 HIGHER standards means that all students will be fully
prepared for the future, whether they choose to further their
education or immediately enter the workforce.
 COMMON standards means that schools can compare
student test scores state-by-state or state to the national
average.
Big Things to Notice K-8
 Number is emphasized in K-5.
 Algebra is imbedded in number until grade-6.
 Less is expected in statistics and probability early;
more at later grades.
 Geometry is included in every grade but is limited in
scope in K-8.
 Length is included in grades 1-2, both other types of
measurement are postponed until grade-3.
 Some topics change grades from current NJ CCCs.
GRADE-K focus
The Common Core Standards emphasize that
instructional time in Kindergarten should focus on two
critical areas:
1. Representing and comparing whole numbers, initially
with sets of objects; and
2. Describing shapes and space.
https://sites.google.com/site/pvrsdportal/kindergartencurriculum
Grade-K questions ?
What about the calendar?
What about patterns?
What about telling time?
GRADE-1 focus
instructional time should focus on four critical areas:
1. developing understanding of addition, subtraction, and
strategies for addition and subtraction within 20;
2. developing understanding of whole number relationships
and place value, including grouping in tens and ones;
3. developing understanding of linear measurement and
measuring lengths as iterating length units; and
4. reasoning about attributes of, and composing and
decomposing geometric shapes.
Grade-1 What’s new?
New topics: what should I do?
Describe these shapes without talking
about color.
Students need to know how to add 25 +
17. Ask kids what they’d do to find out how
much 17 + 25 is.
What do you think they might do?
GRADE-2 focus
instructional time should focus on four critical areas:
1.Extending understanding of base-10 notation (multidigits to 1,000)
2.Building fluency with addition and subtraction
3.Use standard units of measure (cm., inch; use ruler)
4.Describe and analyze shapes (sides, angles; compose,
decompose; 2D and 3D) … building a foundation for area,
volume, congruency, similarity, symmetry in later grades.
TIMELINE
* CCC database but
Only CCSS questions
Curriculum
2011-12
K-2
New
Assessments
(none)
6-8,11
NJASK, HSPA
2012-13
K-2, 6-8
3-5, HS New
(none), NJASK
NJASK*, HSPA*
2013-14
6-8
New
K-5, HS
NJASK*
NJASK*, HSPA*
2014-15
K-11
NEW (PARCC)
(This year’s 8th graders)
GRADE-3 focus
instructional time should focus on four critical areas:
1. developing understanding of multiplication and division
and strategies for multiplication and division within
100;
2. developing understanding of fractions, especially unit
fractions (fractions with numerator 1);
3. developing understanding of the structure of
rectangular arrays and of area; and
4. describing and analyzing two-dimensional shapes.
Grade-3 before/after NJASK?
 Multiplication facts by memory (all of them for
NJASK … Do these all year long.)
 Fractions on number line (do after NJASK)
 Equivalent fractions (do after NJASK)
 Time (see new CCSS 3.MD.1.) see – symbol
 Areas of rectilinear figures (like an ‘L’ shape
w/right angles).
Left Out of Grade-3
 Decimals
 Estimation
 Congruence, symmetry, circles
 Coordinate geometry, transformations
 Patterns, functions
 Probability, discrete math
What’s Different in Grade-3?
 First time students use metric measuring
 Ex. What might students do?
7 x 28
We need to do more mental math to help students gain
number sense … working on pencil-paper procedures
for computation will not help students gain good
number sense.
 Ex. Pose a problem. Jose has 3 boxes of 24
crayons, how many does he have in all.
Fractions Across Grades
Grade-1
 taking squares/circles and dividing them up.
Grade-2
 Know equal shares don’t need to be the same
shape to be the same size
Grade-3
 unit numerators
 fractions on the number line
Grade-4
should focus on three critical areas:
1. developing understanding and fluency with multi-digit
multiplication, and developing understanding of dividing to
find quotients involving multi-digit dividends;
2. developing an understanding of fraction equivalence,
addition and subtraction of fractions with like denominators,
and multiplication of fractions by whole numbers; and
3. understanding that geometric figures can be analyzed and
classified based on their properties, such as having parallel
sides, perpendicular sides, particular angle measures, and
symmetry.
What are we doing? GRADE-4
FRACTIONS, FACTIONS, fractions
Don’t’ change till after NJASK
Fill in gaps fall 2012 from grades K – 3
Add new topics:
number sentences w/variables (start using letters for
unknowns)
factors and multiples
Grade-4: Do AFTER NJASK
 multiply 1 digit by 3 digits (425 x 6)
 divide 4 digits by 1 digit ( 427 ÷ 3)
 equivalent fractions (2/3 and 4/6)
 decimal notation for fractions (2/5 = 0.40)
 multiply fraction by whole number (2/3 x 6 )
Leave for next year:
 Convert units to smaller ones (2 ft = 24 inches)
 measure angles
What’s omitted in grade-4?
 Negative numbers
 Estimation
 Congruence,
 Symmetry,
 Transformations
Grade-5
Should focus on three critical areas:
1.developing fluency with addition and subtraction of
fractions, and developing understanding of the multiplication
of fractions and of division of fractions in limited cases (unit
fractions divided by whole numbers and whole numbers
divided by unit fractions);
2.extending division to 2-digit divisors, integrating decimal
fractions into the place value system and developing
understanding of operations with decimals to hundredths, and
developing fluency with whole number and decimal
operations; and
3.developing understanding of volume.
Gr.5 – Fractions, Division, Decimals
(This is going to be hard!)
Fill in gaps fall 2012 from grades K-4
Add new topics
Whole number exponents for powers of 10
3 x 102 + 2 x 101 + 1 or 100 )
Multiply fractions and mixed numbers (½ x 4 ½ )
Divide unit fractions and whole numbers (3 ÷ ½ )
Converting little units into big 24” = ___ ft.
Line plot with fractional measures (a big group)
Volume
( 321 =
Multiplcation and Division
Across Grades
 Grade-2 Intro to multiplication briefly
 Grade-3 When do you use it? (Understand and
master facts) 1 digit x multiples of 10
60 = 240
4x
 Grade-4 Use multiplication to compare (twice as
big, three times a big) and 1 digit mult. up to 4
digits, 2 digits x 2 digits, 2 digits x 3 digits
 Grade-5 Fluent with multiplication
 Grade-6 Fluent with division
Not explicitly in CCSS
 Zero as an additive identity element
 Ordinals
 Calendar-related skills
 Mode
 Recognizing when an estimate is appropriate, and
understand usefulness of an estimate.
 Know approximate equivalents between standard and metric
systems (one kilometer is about 6/10 of a mile)
 Solve problems involving different units of measure within a
measurement system (4’3” plus 7’10” = 12’1”)
New Assessments (PARCC)
K-2 ASSESSMENTS
Will not be done electronically
May be optional for districts
GRADES 3-8, 11
Will have all/part electronically
Results back to teachers in a few weeks
Technology-Availability Survey to districts this fall to
collect data about each school.
New Assessments (PARCC)
Whatever is in the CCSS for each grade-level K-8 may be assessed.
Quarterly assessments are being considered
25%
content
50%
content
75%
content
All
content
Formative
diagnostic
tool
Formative
performance
based (?)
Formative
(machine &
hand-scored)
Summative
end-yr results
before end yr
Optional
Optional
Required (?)
required
Detailed results to be received by teacher w/in a few weeks.
These will all be ‘secured’ tests (Districts will have testing
‘windows’ instead of same date for all districts and schools.)
New Assessments
The Dream !
Whatever is in the CCSS for each grade-level K-8 may be assessed.
Quarterly assessments are being considered
Computer adaptive assessments with routers and
appropriate items for stage-2
Four-week testing windows
Computer score-able constructed response items
Item banks for Formative, Benchmark AND Summative
assessments
Student, class, school, district, state and nation results
three days after the window closes
Grade K-8, 9-12 math is
divided into categories
K to 8
High School
Grade
Conceptual Category
Domain
Cluster
Standards
Domain
Cluster
Standards
Is the HSFORMAT different?
 CONCEPTUAL CATEGORY
• DOMAIN
• CLUSTER
• Standards
+ H.S.
STEM
K-8 math is divided into
4 DOMAINS
OA Operations & Algebraic Thinking
NB Number & Operations in Base 10
NBF Number & Operations - Fractions
MD Measurement and Data
G
Geometry
What does it look like? (Grade-2)
DOMAIN: 2.0A Operations & Algebraic
thinking
CLUSTER: ADD & SUBTRACT WITHIN 20
Standard 2.0A.3. Fluently add and subtract within
20 using mental strategies.
By the end of grade 2, know from memory all sums of
two one-digit numbers
2+2
9+9
8+9
See 1.OA.6 for a list of mental strategies.
5+7
What does it look like? Grade-K
DOMAIN:
Operations & Algebraic thinking
CLUSTER K.OA: Understand addition as putting together &
adding to, and understand subtraction as taking apart & taking
from.
Standard K.0A.1 Represent addition and subtraction with
objects, fingers, mental images, drawings, sounds, acting out
situations, verbal explanations, expressions, or equations.
Standard K.OA.2 Solve addition & subtraction word
problems, … add and subtract with 10
Standard K.OA.3 Fluently add and subtract
within 5.
What does it look like? Grade-1
DOMAIN:
Operations & Algebraic thinking
CLUSTER: 1.OA Represent and solve problems involving
addition and subtraction
Standard 1.0A.1 Use addition & subtraction within 20 to
solve word problems involving putting together, taking
apart, and comparing with unknowns … by using objects,
drawings & equations with a symbol for the unknown to
represent the problem.
Standard K.OA.2 Solve word problems that call for
addition of three whole numbers … sum is < 20.
What does it look like? Grade-2
DOMAIN:
Operations & Algebraic thinking
CLUSTER: 2.OA Represent and solve problems involving
addition and subtraction
Standard 2.0A.1 Use addition & subtraction within 100
to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking
apart, and comparing with unknowns … by using objects,
drawings & equations with a symbol for the unknown to
represent the problem.
What does it look like? Grade-3
DOMAIN:
Operations & Algebraic thinking
CLUSTER: 3.OA Represent and solve problems involving
multiplication and division.
Standard 3.0A.1 Interpret products of whole numbers, e.g.
interpret 5 x 7 as the total number of objects in 5 groups of 7
objects each. For example, describe a context in which a total
number of objects can be expressed as 5 x 7.
Standard 3.0A.2 Interpret whole-number quotients
Standard 3.0A.3 Use x and ÷ within 100 …
Standard 3.0A.4 Determine the unknown ..
8 x ? = 48
5=
÷ 3,
6x6=
What does it look like? Grade-4
DOMAIN:
Operations & Algebraic thinking
CLUSTER: 4.OA Use the four operations with whole
numbers to solve problems
Standard 4.0A.1 Interpret a multiplication equation as
a comparison, e.g., interpret 35 = 5 x 7 … Represent
verbal statements of multiplicative comparisons as
mutiplication equations.
Standard 4.0A.2 Multiply or divide to solve word...
Standard 3.0A.3 Solve multi-step word problems …
whole numbers … four operations … Assess the
reasonableness of answers.
What does it look like? Grade-5
DOMAIN: Operations & Algebraic thinking
CLUSTER: 5.OA Write and interpret numerical
expressions.
Standard 5.0A.1 Use parenthesis, brackets,
or braces in numerical expressions, and
evaluate expressions with these symbols. (new
to gr. 5)
Standard 5.0A.2 Write simple expressions
that record calculations with numbers, and
interpret numerical expressions without
evaluating them.
Easy to remember!
 4.0A
Operations & Algebraic Thinking
 3.MD
Measurement and Data
 5.G
 2.NBT
Number & Operations Base 10
 4.NF
Number & Operations Fractions
AN OVERVIEW
WHAT has been added?
What has been moved?
Grade- 1 (add/remove?)
ADD: Move symbols = < > from gr.-3 to gr. 1
1.NBT.3
ADD: Zero as the identity element (e.g. 7 + 0 = 7) Zero as an
additive identity element is not explicitly articulated in the
CCSS at any grade. 1.OA.3
ADD: Calculator (use of a calculator is explicitly included only
in the CCSS for Mathematical Practice. 1.NBT.4)
ADD: Weight (lb., gram, kilogram), Capacity (pint, quart, liter),
Temperature (degrees Celsius, degrees Farenheit)
ADD: Data generated from chance devices 1.MD.4
ADD: Use simple shapes to make designs, patterns, …
Grade- 2 (add/remove)
 ADD: Determine whether a whole number is ODD or
EVEN from grade-3 to 2.OA.3
 ADD: Compare two 3-Digit numbers based on
meanings of hundreds tens and ones digits using > < =
symbols to record comparisons 2.NB.4
REMOVE
 Move actual using of symbols > < = for first time
to grade-1.NBT.3
Grade- 3 (add/remove)
 ADD: Fluently multiply and divide within 100, …
3.0A.7
 ADD: Move memorize the multiplication table from
grade-4 to grade-3. By end of grade-3, know from
memory all products of two one-digit numbers.
REMOVE
 Move determining whether a whole number is odd or
even from grade-3 to grade-2.A.3
 Move actual using of symbols > < = from grade-3 to
grade-1.NBT.3
Grade- 4 (add/remove)
 ADD: Move from grade-5: Find all factor pairs of whole
numbers in the range. Recognize 1-100. 4.OA.4
 ADD: Move from grade-5: Recognize angles as
geometric shapes when … understand concept of angle
measurement. 4.MD.5
 ADD: Move from grade-5: Measure angles in wholenumber degrees using a protractor. Sketch angles of
specified measure. 4.MD.6
Move memorize the multiplication table from grade-4 to
grade-3. By end of grade-3, know from memory all
products of two one-digit numbers.
Grade- 5 (add/remove)
 ADD: EXPLAIN patterns in numbers of zeros … 5.NBT.2 (moved from
grade-6; note this includes exponents)
 ADD: + - x ÷ decimals to hundredths using concrete models .. 5.NBT.7
(moved x ÷ of decimals from grade-6)
 ADD: Solve real world problems with multiplication of fractions and
mixed numbers 5.NF.6 (moved from grade-6)
 ADD: Apply and extend previous understandings of division to divide
unit fractions by whole numbers and whole numbers by unit fractions
5.NF.7 (moved from grade-6)
Move from grade-5 to 4: Find all factor pairs of whole numbers in the range. 1100. Recognize angles as geometric shapes when … understand concept of
angle measurement. Measure angles in whole-number degrees using a
protractor. Sketch angles of specified measure. 4.OA.4, 4MD.5, 4.MD.6
Potential Challenges
When you TRANSITION to the COMMON CORE in
mathematics
See handout (tan/gray)
CCSS (June 16,2010)
Grade/Course
2–8
Algebra
Geometry
Change
SMALL-GROUP ACTIVITIES
CUT THE CAKE
FIND THE PERIMETER
(Algebra Tiles: black =“x” yellow = “1”)
MATHEMATICAL PRACTICES
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
REASONING and
SENSE MAKING
Why PROBLEM-BASED
Interactive learning
 Motivates new learning
 Recalls prior learning
 Engages students in thinking about math
 Requires students to communicate
 Introduces or develops math representations
 Fosters reasoning skills
As The Crow Flies (** Activity)
CCSS takes what seems so usual, just a bit further.
Your house
School
Friend’s
House
As The Crow Flies (activity)
CCSS takes what seems so usual, just a bit further.
Your house
School
Friend’s
House
As The Crow Flies (activity)
CCSS takes what seems so usual, just a bit further.
Your house
School
Friend’s
House
Grade-5 reasoning example
 Students write an expression for calculations
given in words such as:
and then subtract 7/8.
Divide 144 by 12,
They write (144 ÷ 12) – 7/8.
 Students recognize that 0.5 x (300 ÷ 15) is
1⁄2 of (300 ÷ 15) without calculating the quotient.
Grade 4.NF.2.
Compare two fractions ….
 Fractions with common denominators may be
compared using the numerators as a guide:
2/6
3/6
4/6
smallest to largest
 Fractions with common numerators may be compared
and ordered using the denominators as a guide.
1/10
1/5
1/3
smallest to largest
NOT JUST MEMORIZE, understand, visualize!
Grade-3 MODELING
 Models help build understanding of the commutative
property:
Example: 3 x 6 = 6 x 3
OR 3 x 2 = 2 x 3
 In the following diagram it may not be obvious that 2
groups of 3 is the same as 3 groups of 2. A student
may need to count to verify this.
Grade 2- Reasoning
 This standard calls for students to solve one- and two-step
problems using drawings, objects and equations. Students can
use place value blocks or hundreds charts, or create drawings of
place value blocks or number lines to support their work. Two
step-problems include situations where students have to add
and subtract within the same problem.
 Example: In the morning there are 25 students in the
cafeteria. 18 more students come in. After a few
minutes, some students leave. If there are 14 students
still in the cafeteria, how many students left the
cafeteria? Write an equation for your problem.
Do and Understand !
(new handouts)
The Question Changes
Processes are Open Ended
 WATER CONTAINERS
 YOU CHOOSE
 INTERNET RELAY CHAT
 POSSIBLE FLOOD
 ICE CREAM MELT (Pre Calculus)
REASONING & SENSE MAKING
http://www.nctm.org
Not the CORE only
 The Common Core State Standards identify
mathematics that ALL students should
understand and be able to do.
 The Common Core State Standards do NOT
delineate ALL of the mathematics that
students should know and be able to do.
There is more to the apple
than the core!
Bob Riehs, NJDOE Sept. 2011
BRING for TOMORROW
 Your Textbooks
 Curriculum guide or whatever you use
 Laptop if you can access the Internet in school with it.
QUESTIONS?
http://www.corestandards.org
[email protected]
http://www.state.nj.us/education/aps/cccs/math
KEEP IN TOUCH
JUDITH T. BRENDEL
[email protected]
http://www.pascack.k12.nj.us
[curriculum][mathematics][Workshop: K-5
CCSS Standards]