SHIFTS in MATH INSTRUCTIONCommon Core State Standards

FEA July 2015 presentation

by Judith T. Brendeledleaderk12@hushmail.com

Jbrendel2112@gmail.com

a 3-minute video (for parents or students)LEARN ABOUT THE COMMON CORE IN THREE MINUTES

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/

Description of Workshop

SHIFTS in MATH INSTRUCTION Common Core State Standards and PARCC

Learn how math teaching and learning is changing and what it should look like in your school.

• What are these shifts? • What do Common Core and online PARCC questions look like? Where

are they?• How should our students be learning differently?

– What are “new” skills our students need to be successful?• How should our teachers be teaching differently?

– … in lesson plans? What should I see in the classroom?

3 PRINCIPALS guided the STANDARDS

1. Knowledge, skills and understandings for all students to be CAREER and COLLEGE READY

2. Standards must be based on EVIDENCE not just what people feel students need to succeed

3. Allow TIME for teachers to teach and TIME for students to practice

An Extra Video Resource

From EngageNY info for parents/students:

Common Core in Mathematics: An Overview

This 14-minute video provides an overview of the Common Core State Standards in Mathematics.

NYS Commissioner of Education John B. King Jr. and contributing author David Coleman discuss the background of the Common Core State Standards, their value in the state, the principles of their development, and the changes required of schools during this transition.

WHAT are the SHIFTS?

6 SHIFTS

1. FOCUS on the math that really matters2. COHERENCEY relates grade-to-grade3. FLUENCY really matters4. deep UNDERSTANDING5. APPLICATION in new situations6. DUAL INTENSITY (both: procedures with

practice and meaning and application with rich set of problems)

Greater FOCUS on FEWER TOPICSNOT racing to cover many topics in a mile-wide, inch deep curriculum. YES, focus on the major work of each grade.

• K-2: Concept, skills, and problem solving related to addition and subtraction.

• 3-5: Concept, skills and problem solving related to multiplication and division of whole numbers and fractions.

• 6: Ratios and proportional relationships, and early algebraic expressions and equations

• 7: Ratios and proportional relationships, and arithmetic of rational numbers

• 8: Linear algebra and linear functions

9

K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach

10

Focusing Attention Within Number and Operations

Operations and Algebraic Thinking

Expressions and Equations

Algebra

→ →

Number and Operations—Base Ten →

The Number System

→

Number and Operations—Fractions

→

K 1 2 3 4 5 6 7 8 High School

11

ALG. - 1Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

UNIT-1 Relationships Between Quantities and Reasoning with Equations

UNIT-2 Linear Relationships

UNIT-3 Expressions and Equations

UNIT-4 Quadratic Functions and Modeling

UNIT-5 Functions and Descriptive Statistics

Focus Areas in Mathematics (CCSS)- MS/HS

12

GEOMETRYFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

UNIT-1 Congruence, Proof, and Constructions

UNIT-2 Similarity, Proof, and Trigonometry

UNIT-3 Extending to Three Dimensions

UNIT-4 Connecting Algebra and Geometry Through Coordinates

UNIT-5 Circles With and Without Coordinates

UNIT-6Applications of Probability

Focus Areas in Mathematics (CCSS) - HS

13

ALG. - 2Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

UNIT-1 Polynomial, Rational, and Radical Relationships

UNIT-2 Trigonometric Functions

UNIT-3 Modeling with Functions

UNIT-4 Inferences and Conclusions from Data

Focus Areas in Mathematics (CCSS) – HS

FLUENCIES expected (without a calculator)• K 1.OA.5 Add/subtract within 5• 1 1.OA.6 Add/subtract within 10• 2 2.OA.2 Add/subtract within 20 (know single-digit sums from

memory) 2.NBT.5 Add/subtract within 100

• 3. 3.OA.7 Multiply/divide within 100 (know single-digit products from memory)

3.NBT.2 Add/subtract within 1000• 4. 4.NBT.4 Add/subtract within 1,000,000

• 5. 5.NBT.5 Multi-digit multiplication• 6. 6.NS.2,3 Multi-digit division

Multi-digit decimal operations

What strategies and/or resources have you used to help your students become fluent in required skills for your grade? (in school? At home?) Have 100% of your students become fluent?

Significant Shifts grades 3-5

How fractions are taught, understood and assessed:

*Activity: Do one and Pass left

Gr.3 Compare 2 fractions w/same denominator

Gr.4 Compare 2 fractions w/different denominators

Gr.5 Add or subtract 2 fractions with unlike denominators.

The CCSS Difference: Grade 8 Mathematics(what the NJCCCS vs CCSS say)

(2004) Before NJCCCS:1. Understand and apply the Pythagorean Theorem.

(2010) After CCSS 2. Explain a proof of the Pythagorean Theorem and its converse.

3. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

4. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Previous and Newer Type Questions

*Activity: Compare style, expectations

WHAT do Common Core and

online PARCC questions look like?

Screen Shot: Traditional SCR (grade-3 EOY)

Student does computation on scrap paper.

Student types in answer.

Student knows to use ADDITION and ADDS CORRECTLY

Screen Shot: *Traditional SCR but …? (grade-3 EOY)

Multiplication and division with whole numbers. (FLUENCY) Multiple equations in one question.

Screen Shot: *table Part-A Part-B(grade-4 EOY test)

What computation is needed? Where does student do the computation?

What strategies might a student use?

APPLICATION of ADDITION and DIVISION in multi-step real-life situation.

Screen Shot: *table Part-A Part-B(grade-3 EOY test) Part MC and Part SCR

Traditional MC and SCR in one question. Partial credit; B not dependent on A answer.

Part A. Read the bar graph (between markings) then easy addition.

Part B. Know what and when to ADD and SUBTRACT

Screen Shot: Complete Picture GraphDrag and Drop (grade-3 EOY)

Each star = 5 minutes

Screen Shot: *Multiple correct answers(grade-3 EOY test)

Notice “square-like shape” of the “bubble-in” form when more than one correct answer.

DEEP UNDERSTANDING of concept of multiplication

No computation required.

Screen Shot: *Multiple correct answers(grade-3 EOY test)

Notice “square-like shape” of the “bubble-in” form when more than one correct answer.

D. ( D and E are below C in the same

format.)

E.

Screen Shot: *Three correct answers(grade-4 EOY test)

Select the three choices that are factor pairs for the number 28.

Screen Shot: *Two Correct Answers(canot shade-in on screen) (grade-4 EOY)

Notice that the student CANNOT actually shade-in on the screen.

Screen Shot: *Multiple correct answers(All graphics not given to students)

Note: in grades 3-5 the questions specify “Select the two … or three … correct choices.”

Screen Shot: Tools to measure(grade-4 EOY)

Notice “circle shape” of “bubble-in” form when there is only “one” correct answer.

Screen Shot: Tools to measure(grade-4 EOY)

170˚ or 11˚ ?

Screen Shot: Plotting on Grid(grade-5 EOY)

Point value could be: 2 points for 3 correct answers1 point for 2 correct answers0 points for 1 or no correct answers.

Screen Shot: *Tools to Graph

Line t: y = -x + 5 Line s: y = 1/3x - 3

sbac GRADE-11 Practice Test w/solutions and rubrics DRAG-DROP

2-POINT TASK

Screen Shot: *Click/Drag or Type (one correct answer) (grade-4 EOY test)

Notice the “fraction” and “mixed

number” forms.

Also note: no “work” is scored,

only the final answer.

Acceptable answers might be:

Screen Shot: *Use Symbols or Type (one correct answer; answer forms)

Scrap paper work:27 – 18 x = 20 – 16x + 18 x + 18x

27 = 20 + 2x-20 -20

28 = 2x 7/2 = x

Acceptable answers:

7/2 o r x = 7/2

3 ½ or x = 3 ½ 3.5 or x = 3.5

Screen Shot: Drag/Drop Part A Part B (grade-4)

Part A: drag and drop

Part B: fraction symbol + drag-and-drop or type.

or 7/10

Screen Shot: Drag/Drop (grade-3 EOY)

Screen Shot: Check-off Table (grade-4 EOY)

Scrolling is necessary to see the entire table.

Screen Shot: USING “EXHIBITS” (Reference sheet Grade-5)

Yes, right now, the “exhibit” sheet covers the question(s). It cannot be moved. What will students need to do?

See what online looks like! HS Teachers outside of math

use grade-level-appropriate math

See what online looks like! HS Teachers outside of math

use grade-level-appropriate math

960

1920

3840

7680

Part B

Part C

Part D

sbac GRADE-11 Practice Test w/solutions and rubrics DRAG tick marks

2 POINT TASK

sbac GRADE-11 Practice Test w/solutions and rubrics (2 point task)

sbac.portal.airast.org/practice-test/resources/#rubrics

- click on -Performance Tasks

Writing RubricsSelect grade 6, 7, 8 or 11.

How should our students be learning differently?

What are “new” skills our students need to be successful?

STUDENT learning strategies

Teaching student learning strategies that THEY can use to become more successful learners … more responsible for their own learning.

sone strategyCOHERENCY

linking topics and thinking across grades

COHERENCY

3 + 5 = 5 + 3

1 dog + 3 cats + 6 dogs = 1 dog + 6 dogs + 3 cats

3a + 5b + a = 5b + a + 3a

=

ORDER doesn’t matter in ADDITION

COHERENCYrefers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

3 x 5 = 5 x 3 or (8)(9) = (9)(8)

3a(2a) =6a2 and 2a(3a) = 6a2

2 x 3 x 5 = 2 x 5 x 3 2 x 3 x 5 = 2 x 5 x 3 6 x 5 = 30 10 x 3 = 30

4a(3a)(-2b) = -24a2b or 3a(-2b)(4a) = -24a2b

ORDER doesn’t matter in MULTIPLICATION

COHERENCY

refers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

= 5 + 3 not 8

3 cats + 2 cats + 3 dogs = 5 cats + 3 dogs

3a + 2a + 3b = 5a + 3b not 8ab

COMBINE “LIKE” TERMS

COHERENCY

refers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

2’x3’ = 24” x 36” = 863sq.” 20” x 38” = 760sq.”

1) Which area is larger? 2’x3’ or 20”x38” Why?

2) Put in order: 3.2 6/7 0.33 2/3 π 0.33 2/3=0.66 6/7=.857 π=3.14 3.2

3) Which has the greatest rate of change?equation table of x/y values a graphed line

Use “same format” to compare

Which function has the greatest rate-of-change (the greatest slope)? (A) (B) (C)

Here, “I” decided to write each as an equation and compare them.y = 3x+4 y = 1x+1 y = 3/2x -1 Correct answer: A (slope = 3)

PARENT FUNCTIONS and … y = x y = |x| y = x2

linear function absolute value function quadratic function

y = -x y = -|x| y = -x2

PARENT FUNCTIONS and … y = x y = |x|

y = x2

y = -x y = -|x| y = -x2

y = x + 2 y = |x| + 2 y = x2 + 2

Pre Algebra Algebra Algebra-I and II

VOLUME of basic SOLIDS

V = b x h x l V = s3

V = πr2h

V = (area base)(height) V = (area base)(height) V= (area base) (height) V = Bh V = Bh

V = Bh

A CUBE

CORRESPONDING ANGLES are EQUAL

similar congruent parallel lines cut by triangles triangles transversals

equilateral triangles? ? ?

1

2

5

3

3

4

4

Recap: RULES and STRATEGIES that DON’T CHANGE K-12

• The ORDER of numbers, variables or terms, does not matter in ADDITION or in MULTIPLICATION.

• COMBINE LIKE-TERMS (or LIKE-SHAPES) as a first step in solving problems.

• When COMPARING put all in the SAME FORMAT first.• See what is the SAME when certain PARENT functions are

modified• See what is the SAME about selected VOLUME formulas.• Remember CHARACTERISTICS that are the same in different

polygons.

Look for patterns; look for what you already know!

Solving unfamiliar problems.

2 2 = 4 5 5 = 25 8 ? = 722 x 2 = 4 5 x 5 = 25 8 x 9 = 72

*1 = 1 *36 = 6 *81 = 9 *25 = ?

(A) (B) (C)A liter of water was poured into each container; which is the smallest container? How do you know?

5

a2 + b2 = c2

a

b

c

3

3

9

4 16

4

a = 4

b = 3

c = ?

5

25

5

What are “new” non-math skills our students need to be successful?

What you SHOULD NOT see !

ZN

x

y

>

<

Slope =

slope =

(3,6)

(3,2)

What should I see in Lesson Plans?

Math Practices Standards K-12

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 structure8. Look for and express regularity in repeated reasoning

See in Lesson Plans

Standards of Math Practices and Student Learning Strategies

ScreenShots of PARCC examples/MP and /grade 3-Algebra II

Links: MP1 - Make Sense & Persevere in problem solving

• Gr. 2: Carol’s Numbers (mp # 1,3,6) http://schools.nyc.gov/NR/rdonlyres/CAC1375E-6DF9-475D-97EE-E94BAB0BEFAB/0/NYCDOEG2MathCarolsNumbers_Final.pdf

• Gr. 4: Bus, Vans and Cars * SOLVE THIS ONE http://ccsstoolbox.agilemind.com/parcc/elementary_3775_1.html

• Gr. 7: Annie’s Family Trip http://ccsstoolbox.agilemind.com/parcc/about_middle_3808.html

Links: MP2 Reason Abstractly and Quantitatively

• Gr. 3: Art Teacher’s Rectangular Array http://www.parcconline.org/sites/parcc/files/ArtTeacherRectangularArray_0.pdf

• Gr. 5: Mr. Edumund’s Pencil Box http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G5AreaofBoard_081913_Final.pdf

• Algebra-I: Picture Frame http://www.parcconline.org/sites/parcc/files/PARCC%20Math%20Sample%20Problems_HS-FunctionsV2.pdf

Links: MP3 - Construct viable arguments and critique the reasoning of others.

• Gr. K: Books on Shelves (mp # 1,2,3,6) http://schools.nyc.gov/NR/rdonlyres/B50F3E83-1202-4999-B14A-309F5429A82A/0/NYCDOEKMathBooksonShelves_Final.pdf

• Gr. 2: Carol’s Numbers (mp # 1,3,6) http://schools.nyc.gov/NR/rdonlyres/CAC1375E-6DF9-475D-97EE-E94BAB0BEFAB/0/NYCDOEG2MathCarolsNumbers_Final.pdf

• Geometry: Talk and Text Plans (mp # 1, 2, 3, 4, 5, 6) http://schools.nyc.gov/NR/rdonlyres/37BEA54D-7761-4BC3-B036-01889BED352D/0/NYCDOE_G8_Math_TxtandTalk_Final.pdf

Links: MP4 - Model with mathematics

• Gr. 5: The Area of a Cut Board http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G5AreaofBoard_081913_Final.pdf

• Gr. 6: Gasoline Consumption http://ccsstoolbox.agilemind.com/parcc/about_middle_3788.html

• Grade 7: Reading Three Books http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G7ReadingBooks_081913_Final.pdf

Links: MP5 – Use appropriate tools strategically

• Grade 8: Length of Line Segment AB Proportional Relationships http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G7ReadingBooks_081913_Final.pdf

• Algebra-I: Michelle’s Conjectures http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf

• Algebra-II: Temperature Change http://www.parcconline.org/sites/parcc/files/BRHSSampleItem.pdf

Links: MP6 - Attend to precision.

• Geometry: The Inheritance (mp # 1, 6) http://schools.nyc.gov/NR/rdonlyres/EDEBDBC0-DE30-4298-AB89-7CEBF566C82E/165320/G10_Math_Inheritance_NL_52814.pdf or go to this link and select [math] [grade 10] and locate this geometry task: http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm

• Algebra-II: Isabella’s Credit Card: http://ccsstoolbox.agilemind.com/parcc/about_highschool_3829_align.html

3 CRITICAL ASPECTS

• Fluency• Understanding• Application

What should I see in the classroom?

Videos• Illustrative Math (all grades: collaboration) a

Smarter Balanced projecthttps://www.teachingchannel.org/videos/illustrative-mathematics-sbac

List of differentiated strategies: How often do you see this being used in elementary, middle school or high school classes? (Frequently/sometimes/rarely/never)

Links to helpful ResourcesKey Shifts (Scholastic)http://www.scholastic.com/teachers/top-teaching/2013/03/common-core-key-shifts-mathematics

Common Core Standards_Mathematicshttp://www.corestandards.org/Math/Practice/

PowerPoint: William McCallum and Jason Zimba (two lead writers of the Common Core State Standards for Mathematics) on the background of writing the Standards.http://www.youtube.com/watch?v=dnjbwJdcPjE

Sample Assessments by gradehttp://www.achievethecore.corg/

Common Core Practice Testshttp://parcc.pearson.com (sample PARCC tests and tutorials)https://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PThttp://sbac.portal.airast.org/practice-test/

Common Core Resources to use with studentshttp://www.illustrativemathematics.org

Dana Center Resources http://www.ccsstoolbox.org/http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf

Common Core and Special Education Studentshttp://www.ode.state.or.us/search/page/?id=3741

IN CLOSING ….

Thank you for your participation.

JUDITH T. BRENDEL

edleaderk12@hushmail.com

Jbrendel20112@gmail.com