MPs: Math Practice Standards - PowerPoint Presentation

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MPs: Math Practice Standards and UDL planninggrades 7-8 (CCSS) SESSION #2 Judith T. Brendel, Ed.M.

Bridgeton: October 9 (gr.6); December 4 (gr.7/8) 2015 Slide2

Today’s Plan: Make UDL and MATH PRACTICES common household “math-class” wordsContent: Focus on Expressions and Equations Focus on UDL and Math Practices 1, 2 and 3Process: (Differentiate Tasks)Review Effective Questioning Techniques

Select Objective and Variety of Student TasksDesign questions, differentiated tasks and rubrics using PARCC-type materialSlide3

By the end of the PD each grade will complete one chapter_UDLFocus: one step and multi-step equationsContent: a chapter/unit/topic; use textbookStandards: Select CCSS for your grade level Process: Do/select a variety of interactivitiesContent : Do/select a variety of PARCC-like tasksTeacher Resource Page(s): createStudent Page(s), Directions: create Answer key/point value/rubric createNext year, a new teacher should be able to follow all.Slide4

LESSON PLANNING with MATH PRACTICES and UDLSlide5

Standards of Mathematical Practices (MP)

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 structure.

Look for and express regularity in repeated reasoning.

TODAY’S FOCUSSlide6

Resources Provided: gr.7/8 CCSS for Expressions and Equations Released items: PARCC PBA/EOY 2015** Released items: NYS 2015 selections Student answers and rubrics: Sample Expressions, Equations items from PARCC 2015; (two from grade 7, one from grade 8) Math Practices 1, 2, 3 packet with sample examples from various sources

Differentiated Tasks list created by J. Brendel www.njpsa.org …

. Select [FEA Programs] … scroll down to [Professional Learning Resources] … scroll to [Dec. 4 Bridgeton gr.7-8 math] … download files as needed **Slide7

UDL: Universal Design for Learning Framework Principles1: Methods of Presentation (HOW TEACHER … )To support recognition learning, provide multiple, flexible methods of presentation 2: Methods of Expression (HOW STUDENT … )To support strategic learning, provide multiple, flexible methods of expression and apprenticeship. 3: Options for Engagement (WHAT STUDENT … )To support affective learning, provide multiple, flexible options for engagement.4 Main ComponentsGoals, Materials, Methods, Assessment Slide8

Grade 7: Standardshttp://www.corestandards.org/Math/Content/7/EE/Use properties of operations +-x÷ factor/expand linear expressions w/rational coefficientsSolve real-life and mathematical problems using numerical and algebraic expressions and equationsGrade 8: Standardshttp://www.corestandards.org/Math/Content/8/EE/Expressions & equations work with radicals and integer exponentsUnderstand the connections between proportional relationships, lines and linear equationsAnalyze and solve linear equations and pairs of simultaneous linear equationsCCSS EXPRESSIONS and EQUATIONS Grades 7, 8(Content Focus Goal: Select from hardcopy packet)Slide9

CCSS EXPRESSIONS and EQUATIONS(See simplified CONTENT-AT-A-GLANCE)GRADE 7www.ixl.com/math/gade-7Slide10

CCSS EXPRESSIONS and EQUATIONS(See simplified CONTENT-AT-A-GLANCE)GRADE 8Slide11

recently released spring operational 2015 PARCC itemsSAMPLE EXAMPLES with answer key, student responses, detailed rubrics Grade 7:Example #12 “Cost of Lunch”Example #13 “Saving Twenty Dollars”Grade 8:Example #12 “Explain Solutions Conclusion”CCSS EXPRESSIONS and EQUATIONS Grades 7, 8(Content Focus Goal: Select from hardcopy packet)Slide12

PROCESS: Create DIFFERENTIATED STUDENT ACTIVITIES Options for Student Engagement21st C. Assembly line: Do one step and move right21st C. Assembly line: Do one step and pass rightWhich one doesn’t belong, and why?Carousel (different levels of difficulty; non-sequential) (tiered)Match your Partner’s Answer (tiered) samples

and templatesMatch cards (pair equivalent cards/slips)Vocabulary Ladder (paired game/ word-definition

/exampleBattle-ship type game (explain/match verbal explanation)Tic-Tac-ToeBingoJeopardy

Lab Stations

Divide into 2 groups; your rule? Easiest/most complex

Choose 2 out of 6 activities; demonstrate understandingSlide13

Tiered TasksSlide14

9 - (9-8) =

(8 x 8) x 2=

(4 x 8) + 10 =

4x(1-4) =

9x(2-2) =

8-(4-3) =

(8x8) – 8 =

(4x5) + 4 =

(8+10)-3 =

1-(7x5)-4 =

10x(6-6) + 10=

(4 + 4-1)-7=

(5-7)-(5x5) =

(4 + 5 + 6) =

(4 x 6)+(4-5)=

(5x9+2)x4 =

(5-10) x (8x8)=

(1+2)x( 3-2)=

Basic Order of Operations

Advanced Order of Operations

Tiered Skill

Based Readiness

Diane Heacox 2013 all rights reservedSlide15

Sample EXIT CARD PROMPTSPromote Student Self-AssessmentI was confused by…This reminded me of…I wonder why…I learned that…I was surprised…I predict…One thing I still need to learn…A better way for me to learn this…Slide16

Sample EXIT CARD PROMPTS continuedPromote Student Self-AssessmentDraw an illustration or make a graphic organizer of today’s lesson.The most important thing about _________ is _________.How did today’s work connect to the work we did yesterday

?Pick any task, write a similar one and explain how it compares to a concept in today’

s lesson.I want to start tomorrow

’

s class with the most important learning from today. What would it be for you?Slide17

WHAT HAVE YOU TRIED?WHAT HAVE YOU DONE DIFFERENTLY?Tell a neighborShare with a groupSlide18

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.   Slide19

LOW-LEVEL vs HIGH LEVEL QUESTIONAre these lines parallel? Write the equations of 3 other lines that are parallel.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.Slide20

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.   Slide21

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

12.3”

3.5”

1

.5”

3.5”

12.3”

3.5”

1

.5”

12.3”

3.5”

1

.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?"

Or create the larger rectangle (18.8)(5) and subtract top smaller rectangle(3.5)(3.5).Slide22

Category 2 contains questions that help students rely more on themselves to determine whether something is mathematically correct. Slide23

> True or False?"Does that make sense?” "How do you know? ”"What model shows that?"Slide24

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.Slide25

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 ….Slide26

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 Slide27

PARENT FUNCTIONS and …

y = x y = |x| y = x

2

linear function

absolute value function quadratic function

y

=

-

x

y

=

-

|

x|

y =

-

x

2

Slide28

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 IISlide29

Lesson Planning with Math Practice Standard #1

*ACTIVITY: Note suggested questions for this MP.

(See related examples in your packet; see next slide. )Slide30

Math practices 1: Make sense of problems and persevere in solving them Grade 7 See Packet: NY 2015 released gr.7 (examples: 1, 18 and 37)Anne’s Family Trip http://ccsstoolbox.agilemind.com/parcc/about_middle_3808.htmlSchool Supplies http://ccsstoolbox.agilemind.com/parcc/about_middle_3819.htmlSpicy Vegetables http://ccsstoolbox.agilemind.com/parcc/about_middle_3812.html

Grade 8 Extra Student Examples p.1: see ex. grade 5 and 8) Combine volume of all the tanks

…. (EngageNY 2014 exam) Slide31

Lesson Planning with Math Practice Standard #2*ACTIVITY: Note suggested questions for this MP. (See related examples in your packet; see next slide.)Slide32

Math practices 2: Reason abstractly and quantitatively Grade 7 See Packet: NY 2015 gr.7 example 46See Extra Student Ex. MP#2 gr.7“Cat Food” www.insdiemathemacitcs.orgTV Sales http://ccsstoolbox.agilemind.com/parcc/about_middle_3815.htmlProportional Relationships (scroll down to EngageNY, 7 RP Unit Module, then to Midyear Module and/or End Year Module)https://grade7commoncoremath.wikispaces.hcpss.org/Unit+2+Ratios+and+Proportional+

RelationshipsGrade 8 See Extra Student Examples MP.#2 grade 8 from engageNY

Talk and Text Plans Google ‘Grade 8 Math: Talk and Text Plans’ select pdf from NYCDOE Slippery Shoes Google ‘Slippery Shoes Grade 8 Math’ select pdf from NYCSlide33

Lesson Planning with Math Practice Standard #3*ACTIVITY: Select and link to a task for your grade. (See next slide for links and assignment.)Slide34

Math practices 3: Construct viable arguments and critique the reasoning of others. Grade 7 Proportional Reasoning Google: Proportional Reasoning Math Grade 7 NYC (scroll down to Performance Tasks)Leaky Faucets Google: Leaky Faucet Dan Meyer (for lesson and video)Grade 8 See Extra Student Examples MP#3 gr.8 from engageNY)

Party: Click on link and select Grade-8, “Party”http://www.insidemathematics.org/performance-assessment-tasksThe Picture Frame Problem Google “The Picture Frame Problem Grade 8 math,” select NYCDOE Grade 8 Math: The Picture Frame Problem (download the

pdf file)Justify Your Response tasks: Google “Grade 8 Math: Expressions and Equations NYCDOE;” scroll to the four examples in Assessment 1 ex.3Slide35

MATH PRACTICES: VIDEOS What it Looks Like in the Classroom MP1- Make sense of problems and persevere in solving them (grades 1-12)http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-1-make-sense-of-problems-persevere-in-solving-them  MP2- Reason abstractly and quantitatively (grades 5-12)http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-2-reason-abstractly-quantitativelySlide36

MATH PRACTICES: VIDEOS What it Looks Like in the ClassroomMP3- Construct viable arguments and critique the reasoning of others (grades 1-12)http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-3-construct-viable-arguments-critique-the-reasoning-of-othersSlide37

SHARE Thoughts and PlansSlide38

QUESTIONSSlide39
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Action Planning and Next Steps

Goals

Action Planning

Next Steps

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FEEDBACKThe three most useful things I learned today:Two things I would share with a colleague:One question that I have: (Email to edleaderk12@hushmail.com )Slide42

Sincere thanks for your participation, collaboration and dedicated efforts!!! See you again for our next session.Judy

edleaderk12@hushmail.com