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

MPs: Math Practice Standards grades 6-8 (CCSS)

SESSION #2 Judith T. Brendel, Ed.M.

Presenter notes for 4 MP sessions

• 6th Grade Teachers - Mathematical Practices – (also focus on Multi-digit decimal operations)

• 7th /8th Grade Teachers - Mathematical Practices - (also focus on Fluency with rational numbers/arithmetic)

• Day 1 intro all MPs w/differentiated activities & links • Day 2 focus MP1,2,3 share use MP; develop lessons • Day 3 focus MP 4,5,6 share lessons, develop lessons • Day 4 focus MP 6,7,8

Math Practice Standards session-2 Lesson Planning & Questioning

Grades 6 Focus on understanding Multi-digit decimal operations

Grades 7 and 8 Focus on fluency with rational numbers arithmetic

Today’s Plan: Make MATH PRACTICES a common household “math-class” word.

• Share MP applications used this year

• Focus on Questioning and MP 1, 2, 3 • Select CCSS/PARCC task(s) to use with your students • Create lesson activities and questions for above tasks

• Access additional online resources (videos)

• Share and Plan next steps.

Standards of Mathematical Practices (MP)

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.

LAST TIME: Reminder of Activities

1. Cut the Cake(Change process; keep topic personal, math familiar) 2. 21st.Century Assembly Line/Pass it On: “Geometry” and/or “Trip to the Zoo” pages (problem-solve, see other’s thinking, effective work habits)

1. How do you Get to School,? How do you spend Saturday? (meaningful surveys, graphs & charts) NCTM Illuminations 2. Scrambled Comics (concept with non/math puzzle) 3. Map and Trip, and blank grid (students make choices) 4. As the Crow Flies (grid location changes rigor)

1. Ski Indoors from IDE (a webquest mini-project) 2. Run Forest Run” (a webquest project, easy to update) -online- 1. EngageNY: grades 3-8 (PARCC-LIKE samples for each grade) 2. 3-HS (online: Dana Toolbox) (PARCC-Part ABC samples +) 3. Action Plan and Feedback (plans for early fall) quick review: Required Fluencies K-6 without calculators Focus Areas in Support of Rich Instruction and Grade Expectations of Fluency and Conceptual Understanding

• Add/subtract within 5/ 10/ 20 (K.OA.5, 1.OA.6, 2.OA.2) K–2 • Add/subtract within 100 (2.NBT.5) • Know single-digit sums within 20 (2.OA.2) • Multiply/divide within 100 (know single-digit products from 3 memory) (3.OA.7) • Add/subtract within 1000 (3.NBT.2) 4 • Add/subtract within 1,000,000 (4.NBT.4)

5 • Multi-digit division (5.NBT.5) • Multi-digit division (6.NS.2) 6 • Multi-digit decimal operations (6.NS.3)

WHAT HAVE YOU TRIED? WHAT HAVE YOU DONE DIFFERENTLY?

• Tell a neighbor • Share with a group

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.

LOW-LEVEL vs HIGH LEVEL QUESTION

• Round 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.

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.

1) "Do you agree? Disagree?” 2) "Does anyone have the same answer but a different way to explain it?" The area of this rectilinear figure is 66.75 sq. in.

12.3” 3.5”

1.5”

12.3” 12.3” (12.3)(3.5) = 43.05 3.5” 3.5” (12.3)(5) = 61.5 1.5” (3.5)(1.5) (15.8)(1.5) = 23.7 1.5” = 5.25 Category 2 contains questions that help students rely more on themselves to determine whether something is mathematically correct.

10.25 > 6.12 + 4.20 True or False?

1. "Does that make sense?” 2. "How do you know? ” 3. "What model shows that?"

Category 3 questions seek to help students learn to reason mathematically. 1. "Does that always work?” 2. "How could we prove that?

The area of a triangle is always one-half the base times the height.

Category 4 questions focus on helping students learn to conjecture, invent, and solve problems.

1. "What would happen if...?” The sides of a rectangle are 5 and 5. a. What would happen to the perimeter if we change the sides to 3 and 7? b. 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 ….

Category 5 questions relate to helping students connect mathematics, its ideas, and its applications. 3 4 7 + = 8 8 8 1. "Have we solved a problem that is similar to this one?” How is this similar to above? 3a + 4a = ?

1. "How does this relate to ...? 3 5 + 4 5 = ?

1. ”How does it relate to 4 x 3 + 6 x 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 LESSON PLANNING with MATH PRACTICES HANDOUT: Lesson Planning with Math Practice Standards

*ACTIVITY: Select and link to a task for your grade. (See next slide for links and assignment.) Math practices 1: Make sense of problems and persevere in solving them

Grade 6 • Proportions of Instruments http://www.parcconline.org/sites/parcc/files/PARCC_SampleIt ems_Mathematics_G6Kelvin_081513_Final.pdf

• Rational Numbers (mp # 1, 2, 3, 6) http://schools.nyc.gov/NR/rdonlyres/CE3C9B3D-609C-4F98- 84A5- DEB04A9138F1/141876/NYCDOE_G7_Math_RationalNumbers _FINAL.pdf or go to this site and select [math], [grade 6]and this task: http://schools.nyc.gov/Academics/CommonCoreLibrary/Tasks UnitsStudentWork/default.htm

SHARE Thoughts and Plans HANDOUT: Lesson Planning with Math Practice Standards

*ACTIVITY: Select and link to a task for your grade. (See next slide for links and assignment.) Math practices 2: Reason abstractly and quantitatively

Grade 6

• Fraction Model http://www.parcconline.org/sites/parcc/files/Fraction ModelFINAL.pdf

• Inches and Centimeters http://ccsstoolbox.agilemind.com/parcc/about_middle _3789.html

HANDOUT: Lesson Planning with Math Practice Standards

*ACTIVITY: Select and link to a task for your grade. (See next slide for links and assignment.) Math practices 3: Construct viable arguments and critique the reasoning of others.

Grade 6

• Company Logo (mp # 1, 3, 6) http://schools.nyc.gov/NR/rdonlyres/49162FEC-37E2- 4A96-93C1- 6671664FACD5/0/NYCDOEHSMathCompanyLogo_Fin al.pdf

• or go to this site and select [math], [grade 11], and this topic: http://schools.nyc.gov/Academics/CommonCoreLibra ry/TasksUnitsStudentWork/default.htm

QUESTIONS MATH PRACTICES VIDEOS: what it looks like in the classroom

1- 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

2- Reason abstractly and quantitatively (grades 5-12) http://www.insidemathematics.org/common-core-resources/mathematical- practice-standards/standard-2-reason-abstractly-quantitatively

3- 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-others Links to Model Math Curriculum Sites

• Sample Assessments by grade: http://achievethecore.org/dashboard/300/search/1/2/0/1/2/3/4/5/6/7/ 8/9/10/11/12

• Common Core and PARCC Accommodation Features http://www.parcconline.org/parcc-accessibility-features-and- accommodations-manual

• Common Core Resources to use with students http://www.illustrativemathematics.org

• Dana Center Resources http://ccsstoolbox.agilemind.com/resources_samples.html

Action Planning and Next Steps

• Goals • Action Planning • Next Steps

Questions? Concerns (silly question)?

Discussion/Debrief

FEEDBACK

The three most useful things I learned today:

Two things I would share with a colleague:

One question that I have: (Email to [email protected] ) Sincere thanks for your participation, collaboration and dedicated efforts!!!

See you again for our next session.

Judy [email protected]