UNPACKING the CONFUSION PARRC Mathematics 6-12 - PowerPoint Presentation

Slide1

UNPACKING the CONFUSIONPARRC Mathematics 6-12NJPSA/FEA conference October 2015 presentation Room: Oceanport North10:45 a.m. – 12:15 p.m.by Judith T. Brendel, Ed.M.educational consultantedleaderk12@hushmail.coma 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/Slide2

Common Core Content vs. Math Practice Standards—a quick review of shifts and focus at each grade and in each high school course Lesson planning and instruction to help students become more independent math learnersA review of new resources for grades 6-12AGENDASlide3

3 PRINCIPALS guided the STANDARDSKnowledge, skills and understandings for all students to be CAREER and COLLEGE READYStandards must be based on EVIDENCE not just what people feel students need to succeed.Allow TIME for teachers to teach and TIME for students to practice. Slide4

An Extra Video Resource From EngageNY info for parents/students:Common Core in Mathematics: An OverviewThis 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.Slide5

WHAT are the SHIFTS?Slide6

6 SHIFTSFOCUS on the math that really mattersCOHERENCEY relates grade-to-gradeFLUENCY really mattersdeep UNDERSTANDINGAPPLICATION in new situationsDUAL INTENSITY (both: procedures with practice and meaning and application with rich set of problems)Slide7

1. 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.Grades K-2 + - Concept, skills, and problem solving related to addition and subtraction. Grades 3-5 X ÷ Concept, skills and problem solving related to multiplication and division of whole numbers and fractions. Grade-5 (decimals) 5.6 ÷ 9.04 = price w/tax = (1.07)($38.00) = Grade 6 4/8=2/4 a+2(a+3)= x+6=12 Ratios and proportional relationships, and early algebraic expressions and equationsGrade 7 5/8+2/3= ( ¼ )( ½ =) 3/4 ÷ 2/3= Ratios and proportional relationships, and arithmetic of rational numbersGrade 8 y =

mx+b

f(x) = 3x-2

Linear

algebra and linear

functions (parallel lines, perpendicular lines, systems of equations, …. )Slide8

U.S. now = FOCUS on FEWER TOPICS per gradeNumber and Operations - Fractions

3 4 5Slide9

9

K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. ApproachSlide10

10Focusing 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 SchoolSlide11

11

ALG. - 1

Focus 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

f

(x) = x

2

Slide12

12

GEOMETRY

Focus Areas in Support of Rich Instruction and

Expectations

of Fluency and Conceptual

Understanding

UNIT-1

Congruencey

(translations)

,

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-6

Applications of Probability

Focus

Areas

in Mathematics (CCSS) - HSSlide13

13

ALG. - 2

Focus 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 (statistics)**

Focus

Areas

in Mathematics (CCSS) – HSSlide14

3 CRITICAL ASPECTSFluencyUnderstandingApplicationSlide15

3. FLUENCIES expected (without a calculator)K 1.OA.5 Add/subtract within 51 1.OA.6 Add/subtract within 102 2.OA.2 Add/subtract within 20 (know single-digit sums from memory) 2.NBT.5 Add/subtract within 1003. 3.OA.7 Multiply/divide within 100 (know single-digit products from memory) 3.NBT.2 Add/subtract within 10004. 4.NBT.4 Add/subtract within 1,000,0005. 5.NBT.5 Multi-digit multiplication6. 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?Slide16

3. FLUENCIES and 4. UNDERSTANDINGSignificant Shifts grades 3-5How fractions are taught, understood and assessed:*Activity: Do one and Pass leftGr.3 Compare 2 fractions w/same denominatorGr.4 Compare 2 fractions w/different denominatorsGr.5 Add or subtract 2 fractions with unlike denominators.Slide17

4. UnderstandingPrevious and Newer Type Questions*Activity: Compare style, expectations (page 1)Slide18

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

(2004) Before NJCCCS:

Understand and apply

the Pythagorean Theorem.

(2010) After CCSS

Explain a proof

of the Pythagorean Theorem

and its converse

.

Apply

the Pythagorean Theorem to determine unknown side lengths in right triangles

in real-world and mathematical problems in two and three dimensions.

Apply

the Pythagorean Theorem to find the

distance between two points in a coordinate system. Slide19

The CCSS Difference: Grade HS Mathematics5. APPLICATIONS to NEW SITUATIONS (modeling?)Estimate how much water and food is needed for emergency relief in a devastated city of 3 million people, and how it might be distributed.Plan a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.Design the layout of the stalls in a school fair so as to raise as much money as possible.Analyzing stopping distance for a car.Modeling savings account balance, bacterial colony growth, or investment growth.Engaging in critical path analysis, e.g., applied to turnaround of an aircraft at an airport.Slide20

ONLINE TEST CHALLENGESWHAT do Common Core and online PARCC questions look like? Slide21

Where do you see difficulties?*Check off list (workbook page 2 )√ Vocabulary in directions; within the task√ Complex text: Persevering √ Manipulating on the screen√ Organizing work on/off the screen√ Diagrams: Re-drawing/labeling/details√ Writing explanations√ Other?Slide22

Screen Shot: Traditional SCR (grade-3 EOY) Student does computation on scrap paper.Student types in answer.Student knows to use ADDITION and ADDS CORRECTLYSlide23

Screen Shot: *Traditional SCR but …? (grade-3 EOY) Multiplication and division with whole numbers. (FLUENCY) Different types of equations in one question.Slide24

Screen Shot: *table Part-A Part-B(grade-4 EOY test)What computation is needed? Where does student do the computation?APPLICATION of ADDITION and DIVISION in multi-step real-life situation.Slide25

Screen Shot: *table Part-A Part-B(grade-3 EOY test) Part MC and Part SCRTraditional 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 SUBTRACTSlide26

Screen Shot: Complete Picture GraphDrag and Drop (grade-3 EOY)Each star = 5 minutesExperience READING and USING a variety of graphs is essential.Slide27

sbac a GRADE-11 Practice Test examplew/solutions and rubrics DRAG tick marks2 POINT TASKExperience CREATING and USING a variety of graphs is essential.Slide28

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.Slide29

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 and E are below C in the same format.)

Slide30

Screen Shot: *Three correct answers(grade-4 EOY test)Select the three choices that are factor pairs for the number 28.

VOCABULARY

and MULTIPLE ANSWERS.Slide31

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

Notice that the student CANNOT actually shade-in on the screen.Slide32

Screen Shot: More than one correct answers (high school)From grades 6-HS the student is NOT told how many correct answers to select.Select all that apply.How many show that … ?Which ones match … ?Slide33

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

Note: Beginning with grade-6 the questions do

NOT

specify “Select the

two

… or

three

… correct choices.”Slide34

Screen Shot: Tools to measure(grade-4 EOY)Notice “circle shape” of “bubble-in” form when there is only “one” correct answer.Slide35

Screen Shot: Tools to measure(grade-4 EOY)170˚ or 11˚ ?Slide36

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.Slide37

Screen Shot: *Tools to GraphLine t: y = -x + 5 Line s: y = 1/3x - 3Slide38

sbac GRADE-11 Practice Test w/solutions and rubrics DRAG-DROP2-POINT TASKSlide39

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: Slide40

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

Scrap paper work:

27 – 18

x

= 20 – 16x

+ 18

x

+

18x

= 20 + 2

x

-20 -20

= 2

x

7/2 =

x

Acceptable answers:

7/

2 or

x

= 7/2

3 ½

or

x

= 3 ½

3.5 or x = 3.5 Slide41

Screen Shot: Drag/Drop Part A Part B (grade-4)Part A: drag and dropPart B: fraction symbol + drag-and-drop or type.or 7/10Slide42

Screen Shot: Drag/Drop (grade-3 EOY)Slide43

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

VOCABULARY from grade-2Slide44

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

Scrolling is necessary to see the entire table.Slide45

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?Slide46

See what online looks like! HS Teachers outside of math use grade-level-appropriate math Slide47

See what online looks like! HS Teachers outside of math use grade-level-appropriate math 960192038407680Slide48

Part B

Understanding VOCABULARYSlide49

Part C

MULTIPLE correct answers.Slide50

Part D

Explain

MODELING: applying in real life Slide51

sbac GRADE-11 Practice Test w/solutions and rubrics (2 point task)http://sbac.portal.airast.org/wp-content/uploads/2014/10/Grade11Math.pdf(click or copy/paste)Performance Tasks Writing Rubrics (see rubric ex. 666)Select grade 6, 7, 8 or 11.Slide52

How should our students be learning differently?What are “new” skills our students need to be successful?Slide53

STUDENT learning strategiesTeaching student learning strategies that THEY can use to become more successful learners … more responsible for their own learning.2. COHERENCY and 4. UNDERSTANDINGlinking topics and thinking across gradesSlide54

COHERENCY3 + 5 = 5 + 3 1 dog + 3 cats + 6 dogs = 1 dog + 6 dogs + 3 cats3a + 5b + a = 5b + a + 3a

ORDER doesn’t matter in ADDITIONSlide55

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) = -24a

2

b or

3a

(-2b)(

4a

)

= -24a

2

b

ORDER doesn’t matter in MULTIPLICATIONSlide56

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! = 5 + 3 not 83 cats + 2 cats + 4 dogs = 5 cats + 4 dogs not 9cdgs3a + 2a + 3b = 5a + 3b not 8abs

COMBINE “LIKE” TERMSSlide57

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!2’x3’ = 24” x 36” = 863sq.” 20” x 38” = 760sq.”Which area is larger? 2’x3’ or 20”x38” Why?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 compareSlide58

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 = 2x -1 Correct answer: A (slope = 3) Slide59

PARENT FUNCTIONS and …

y = x y = |x| y = x

2

linear function

absolute value function quadratic function

y

=

-

x

y

=

-

|

x|

y =

-

x

2

Slide60

PARENT FUNCTIONS and …

y = x y = |x| y = x

2

y

=

-

x

y

=

-

|

x|

y =

-

x

2

y = x

+ 2

y = |x|

+ 2

y = x

2

+ 2

Pre Algebra Algebra

Algebra-I and IISlide61

VOLUME of basic SOLIDS V = b x h x l V = s3 V = πr2hV = (area base)(height) V = (area base)(height) V= (area base) (height)

V =

Bh

V =

Bh

V =

Bh

A CUBESlide62

CORRESPONDING ANGLES are EQUAL similar congruent parallel lines cut by triangles triangles transversals equilateral triangles ? ? ?

1

2

5

3

3

4

4Slide63

Recap: RULES and STRATEGIES that DON’T CHANGE K-12The 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 modifiedSee 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!Slide64

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?

5Slide65

Differentiated Tasks for UnderstandingCONCRETE – Circle foldPICTORIAL – Geometry find areaSYMBOLIC – Create equations to represent …. X + 1.07x = $2000ABSTRACT – compare f(x) = x2 with f(x) = 3(x-2)2+1Slide66

CIRCLE FOLD (CONCRETE)CIRCLE-FOLD ACTIVITY (2D – to – 3D)INTERACTIVE ONLINE RESOURCES (NCTM)http://www.nctm.org/Classroom-Resources/Interactives/Geometric-Solids/Slide67

1) "Do you agree? Disagree?” The area of this rectilinear figure is 66.75 sq. in.

12.3”

3.5”

1

.5”

15.8”

3.5”

(12.3)(3.5) =

43.05

(15.8)(1.5) =

23.7

(12.3)(5) =

61.5

(3.5)(1.5) =

5.25

2) "Does anyone have

the same answer but a different way to explain it?"

12.3”

3.5”

1

.5”

3.5”

12.3”

3.5”

1

.5”

15

.

8

”

5”

3.5”

(15.8)(5) =

79

12.25

Area = 79 –

12.25 = 66.75PICTORIALSlide68

a2 + b2

= c

2

a

b

c

3

3

9

4

16

4

a = 4

b = 3

c = ?

5

25

5

Still PICTORIAL, not concreteSlide69

SYMBOLICThe souvenir shop at …. sells balls, caps, and jerseys ….. Samantha bought a cap and five balls for $51. The four caps Carlos bought cost $12 more than the jersey his brother bought.Mr. Kurowski spent $177 on three balls and three jerseys for his grandchildren. How much does each item cost? (Assume sales tax is included.) First, list the unknown quantities and assign a variable to each. Let b represent the cost of a ball. Let c represent the cost of a cap. Let j represent the cost of a jersey. Second, use the information from the problem to write equations. (1) C + 5b = 51 (2) 4c –

j

=

12

(3) 3

b +

3

j

=

177

Equation (1) Samantha’s

purchases

translated into an algebraic equation.

Equation

(2) Information

about Carlos’s

and his brother’s purchases.

Equation (3) Mr

.

Kurowski’s

purchases.

Third

, solve the system of equations to find the values for the variables. Finally, interpret your solution. A ball costs $7, a cap costs $16, and a jersey costs $52. Slide70

ABSTRACTabstraction (noun): the process of formulating a generalized concept of a common property by disregarding the differences between a number of particular instances …Slide71

What are “new” non-math skills our students need to be successful?Slide72

Workbook page 3Slide73

More then one right answerMORE RIGORACTIVITY Student pairsGEOMETRY Same perimeter different areasSame area different perimetersSlide74

AREA with PERIMETERActivity: FIND THE AREA: Draw 3-4 different rectangles that have a perimeter of 36. Record the area of each. (Use whole numbers only.)Which shapes have the largest & smallest area?What do you observe? Perimeter(s)1 +1 + 17 + 17 = 362 + 2 + 16 + 16 = 363 + 3 + 15 + 15 = 364 + 4 + 14 + 14 = 365 + 5 + 13 + 13 = 366 + 6 + 12 + 12 = 36

7 + 7 + 11 + 11 = 36

8 + 8 + 10 + 10 = 36

9 + 9 + 9 + 9 = 36

Areas:

(1)(17) =

17

square units

(9)(9) =

81

square unitsSlide75

PERIMETER with AREAActivity:FIND THE PERIMETER: Draw 4-5 different rectangles that have a area of 36. Record the perimeter of each. (Use whole numbers only.)Which has the largest & smallest perimeter? Area = 1 x 36 = 36 (p=74) Area = 2 x 18 = 36 (p=38) Area = 3 x 12 = 36 (p=30) Area = 4 x 9 = 36 (p=26)Area = 6 x 6 = 36 (p=24)Slide76

What you SHOULD NOT see !Slide77

Z

N

x

y

>

<

Slope =

slope =

(3,6)

(3,2)Slide78

What should I see in Lesson Plans?Slide79

Math Practices Standards K-12(workbook page 4)Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structureLook for and express regularity in repeated reasoning Slide80

See in Lesson Plans(workbook pages 5-6 and on FEA website)

Standards of Math Practices

and

Student Learning Strategies Slide81

ScreenShots of PARCC examples/MP and /grade 3-Algebra II Slide82

Links: MP1 - Make Sense & Persevere in problem solving Gr.4: Bus, Vans and Cars (we solved this one) http://ccsstoolbox.agilemind.com/parcc/elementary_3775_1.htmlLink: Gr.7: Annie’s Family Trip ** Do a & b http://ccsstoolbox.agilemind.com/parcc/about_middle_3808.htmlMath Practices ExamplesWorkbook pg.7: Gr.5 “Deb has a board that measures ….” (EngageNY grade 5 test 2014)Workbook pg.7: Gr.8 “The combined volume ….”Slide83

Links: MP2 Reason Abstractly and QuantitativelyGrade 6Link: Inches and Centimeters http://ccsstoolbox.agilemind.com/parcc/about_middle_3789.html (math practices 2 and 6)Slide84

MP3 - Construct viable arguments and critique the reasoning of others. Extra Math Practices Examples:Workbook pg.8: Gr.5 “Alice draws a triangle ….”Workbook pg.8: Gr.8 “Does the equation … define a linear ….”Link: Go to http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm Select [grade 9], [Math], Scroll down and select [COMPANY LOGO]. See pages 4, 5, and 9.Slide85

MP4 - Model with mathematics Math Practices Examples: Workbook pg. 9: Grade 8 “The population growth of two towns ….” Slide86

Link: MP5 – Use appropriate tools strategicallyThe Library of Virtual Manipulativeshttp://nlvm.usu.edu/ennav/vlibrary.htmlSlide87

MP6 - Attend to precision. Math Practices Examples:Workbook pg.10: Grade 5 “A race car ….”Link: Geometry: The Inheritance (mp # 1, 6) go to this link and select [math] [grade 10] and locate this geometry task: http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htmLink: Algebra-II: Isabella’s Credit Card: *Link and see complexity of each/all parts, a, b, chttp://ccsstoolbox.agilemind.com/parcc/about_highschool_3829_align.htmlSlide88

MP7 - Look for and make use of structure Math Practices Examples:Workbook pg. 11 Grade 8: “Four tables ….” Workbook pg. 12 Grade-8: “A box contains ….”Slide89

MP8 -Look for and express regularity in repeated reasoning Math Practices Examples:Workbook pg. 13: Grade 5 “Roberto used ….”Workbook pg.14: Grade 8 Using (4-3 )(42) ….Slide90

WHAT HAVE they TRIED?WHAT HAVE they DONE DIFFERENTLY?Tell a neighborShare with a groupSlide91

What should I see in the classroom? VideosIllustrative Math (all grades: collaboration) a Smarter Balanced projecthttps://www.teachingchannel.org/videos/illustrative-mathematics-sbac*Activity: (workbook pages 1-17)List of differentiated strategies: How often do you see these being used in elementary, middle school or high school classes? (Frequently/sometimes/rarely/never)Slide92

Plan High-Level, Open-Ended Questions Plan out the questions you are going to ask prior to your lesson.The best types of questions are high-level questions; they require thought processes beyond basic rote memory. Higher-level questions compel learners to synthesize, analyze, interpret or evaluate data.  The most thought-provoking questions focus not on simple recall of facts but require engagement in open problem solving and investigation.   Slide93

LOW-LEVEL vs HIGH LEVEL QUESTIONRound the number 2.175 to the nearest hundredth. Think of three numbers that produce 2.18 when rounded to the nearest hundredth. Other types of questions in this genre might begin with,“What happens if you…” “How many ways can…” “What can you make from…." Still others might include asking students to “name a counterexample” or determine why an incorrect solution is indeed incorrect.  These types of probing questions encourage logical thought by emboldening students to mull over multiple related ideas.Slide94

The Professional Standards propose five categories of questions that teachers should ask:Category 1 questions focus on helping students work together to make sense of mathematics.   Slide95

1) "Do you agree? Disagree?”The area of this rectilinear figure is 66.75 sq. in.

12.3”

3.5”

1

.5”

15.8”

3.5”

(12.3)(3.5) =

43.05

(15.8)(1.5) =

23.7

(12.3)(5) =

61.5

(3.5)(1.5) =

5.25

2) "

Does anyone have the same answer but a different way to explain it?"

12.3”

3.5”

1

.5”

3.5”

12.3”

3.5”

1

.5”

15

.

8

”

5”

3.5”

(15.8)(5) =

79

12.25

Area = 79 –

12.25 = 66.75Slide96

Category 2 contains questions that help students rely more on themselves to determine whether something is mathematically correct. Slide97

10.25 > 6.12 + 4.20 True or False?"Does that make sense?” "How do you know? ”"What model shows that?"Slide98

Category 3 questions seek to help students learn to reason mathematically. "Does that always work?”"How could we prove that?The area of a triangle is always one-half the base times the height.Slide99

Category 4 questions focus on helping students learn to conjecture, invent, and solve problems. "What would happen if...?” The sides of a rectangle are 5 and 5. What would happen to the perimeter if we change the sides to 3 and 7?What would happen to the area if we change the sides to 3 and 7?2. “What pattern do you see?” 1, 4, 9, 16, 25 ….Slide100

Category 5 questions relate to helping students connect mathematics, its ideas, and its applications. "Have we solved a problem that is similar to this one?” How is this similar to above? 3a + 4a = ?"How does this relate to ...?”How does it relate to Slide101

How to Make Sure a Butterfly Doesn’t FlySlide102

When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.

If you try to “help” the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your “help” has destroyed the butterfly.Slide103

The butterfly can fly because it has to struggle to come out. The ‘pushing’ forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.Slide104

If the butterfly is not left to struggle to come out of the cocoon, it will never fly.We can learn an important lesson from the  butterfly.If we do not have struggles and challenges in our work, we will never grow

strong and

capable.

If life has no difficulties, we will become weak and helpless.

-- Lim

Siong

Guan,

Former Secretary, Singapore’s Ministry of EducationSlide105

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

grade

http

://www.achievethecore.corg/

Common

Core Practice

Tests

http

://parcc.pearson.com

(sample PARCC tests and tutorials)

https

://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PT

http://sbac.portal.airast.org/practice-test

/

Common

Core Resources to use with students

http://www.illustrativemathematics.org

Dana

Center Resources

http://www.ccsstoolbox.org/

http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdfCommon Core and Special Education Studentshttp://www.ode.state.or.us/search/page/?id=3741Slide106

IN CLOSING ….Slide107

Thank you for your participation.JUDITH T. BRENDEL, Ed.M.edleaderk12@hushmail.com