Rigor Redefined in High School MathematicsNortheast Georgia RESA

2015-2016 Cohort

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Class Information Rigor Redefined in High School Mathematics is designed to

provide monthly support for teachers in increasing rigor in instruction and to better prepare students for the Georgia Milestones End-of-Course Assessments.

The overarching goal for this professional learning series is to effectively utilize the Standards for Mathematical Practice to lead planning, instruction, and assessment.

The content focus will, primarily, be the standards for Coordinate Algebra, Algebra I, Analytic Geometry, and Geometry, though middle school standards will be addressed appropriately.

Activities will include (but are not limited to) analyzing and revising tasks, reviewing and writing assessment items, and videotaping and reviewing exemplar and participant lessons. All work in the series will be directly correlated to the ten TAPS standards of the TKES.

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Class Information Sessions will be held on the following dates

9:00 AM – 3:30 PM (lunch on your own from 11:30-12:45)Session 1: August 20, 2015Session 2: September 24, 2015Session 3: October 29, 2015Session 4: November 19, 2015Session 5: January 21, 2016Session 6: February 25, 2016Session 7: March 17, 2016Session 8: April 28, 2016

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Districts Represented

Elbert CountyGreene CountyJackson CountyJefferson CityMorgan CountyOconee CountyOglethorpe County

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Standards for Mathematical Practice

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 sense

of structure.Look for and express

regularity in repeated reasoning.

Standards for Mathematical Practice6

Some specific resources suggested by the Ga DOE Assessment Division: PARCC: Evidence Tables, sample Items, and practice Tests Smarter Balanced: sample items and practice tests NAEP sample items Georgia Frameworks units (all have been updated as of July 1,

2015) Formative Assessment Lessons (FALs) and tasks from The Shell

Center Georgia Online Assessment System

**See handout for more details

Moving to Higher Levels of SMP Implementation…9

Moving to Higher Levels of SMP Implementation…

Work Place Survival Skills:•Critical Thinking and Problem Solving•Collaboration and Leadership•Agility and Adaptability•Initiative and Entrepreneurialism•Effective Oral and Written Communication•Accessing and Analyzing Information•Curiosity and Imagination

Rigor Redefined; Educational LeadershipOctober, 2008

These are the abilities that enable teachers to design and enable students to handle rigorous work!

These are the abilities that need to be promoted in order to address multiple TKES standards and LKES standards!

These are the abilities needed for ALL post-secondary training (certificated and degree programs)!

These are the abilities that are most important in ALL work places!

These are the Standards for Mathematical Practice!

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What graduates need to knowSoft Skills

Using Mathematics and Science in Manufacturing

1. Intelligence1. Attitude

3. Experience

Make Decisions Solve Problems Ask the Right Questions

Critical ThinkingObtain, Process,

Analyze Information

Plan, Organize, Prioritize Work

Work in a Team Make the Team

Better

How to Think Logically

Communicate to the Audience Verbal & Written

Sell Ideas Influence Others

Computer Software

Proficiency

Technical Knowledge

Related to Job

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A quick lesson (jot a few notes in your journal):

Moving to Higher Levels of SMP Implementation…

VOLUME SURFACE AREA

Volume is the amount of space inside a 3-D figure.

It is measured in cubic units: cm³, in³, etc. (because we are dealing with length, width, and height/depth).

The formula for the volume of a sphere is V = (4/3)r³. (Hint: Remember that 3.14 is used to approximate and r represents the radius of the sphere.)

Area is the amount of space inside a 2-D figure.

It is measured in square units: cm², in², etc. (because we are dealing with length and width).

Surface area of a 3-D object is the amount of space around the outside of the object (imagine the object sliced open and laid out flat).

The formula for the surface area of a sphere is SA = 4r². (Hint: Remember that 3.14 is used to approximate and r represents the radius of the sphere.)

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A quick lesson (work these problems in your journal):

Moving to Higher Levels of SMP Implementation…

VOLUME SURFACE AREA

The formula for the volume of a sphere is V = (4/3)r³. (Hint: Remember that 3.14 is used to approximate and r represents the radius of the sphere.)

Practice:

1. Find the volume of a sphere with radius of 2 cm.

2. Find the volume of a sphere with a radius of 3 cm.

3. Find the volume of Earth if its radius is approximately 4000 miles.

The formula for the surface area of a sphere is V = 4r². (Hint: Remember that 3.14 is used to approximate and r represents the radius of the sphere.)

Practice:

1. Find the surface area of a sphere with a radius of 2 cm.

2. Find the surface area of a sphere with a radius of 3 cm.

3. Find the surface area of Earth if its radius is approximately 4000 miles.

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A quick lesson:

Moving to Higher Levels of SMP Implementation…

SURFACE AREA AND VOLUME

The formula for the volume of a sphere is V = (4/3) r³. The formula for the surface area of a sphere is SA = 4 r².

Practice:1. Maria is trying to figure out how much paint she will need for some party decorations. She

plans to paint 5 plastic spherical containers that will be hung from the ceiling. a. Explain which formula above would help her decide how much paint to use? b. What specific information about the objects will she need to know in order to make

her calculations?c. Will Maria’s calculations give her an approximate answer or an exact answer?

Explain your thinking.

2. A sphere has the same numerical value for its volume and its surface area. a. Find the length of the radius of this sphere and show your work.b. Does this problem have more than one correct answer? Explain why or why not.

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Which question requires a deep understanding?

A.Factor the following expression:2𝑥𝑥2 − 5𝑥𝑥 − 12

B. Find three different values for the missing middle term so that the expression is factorable over the set of rational numbers. Explain how you selected the three different values.

2𝑥𝑥2 +____−12

Which question requires a deep understanding?

A. Create a rational function so that its graph has the following asymptotes. Will every student in the class create the same function? Why or why not?Horizontal asymptote: 𝑦𝑦 = 4Vertical asymptote: 𝑥𝑥 = −5

B. What are the asymptotes for the following function?

𝑦𝑦 = (𝑥𝑥2+1)(𝑥𝑥−3)𝑥𝑥2−2𝑥𝑥−3

Which question requires a deep understanding?

A. Graph the following function:𝑦𝑦 = 2 sin 3𝜃𝜃 + 5

B. The number of daylight hours in Houston is modeled by the function: 𝑓𝑓 𝑥𝑥 = 110 sin 0.02𝑥𝑥 − 0.8 + 700Explain what the amplitude, midline, and frequency mean within the context of the hours of daylight in Houston.

The big problems of the day are complex, rife with paradoxes and dilemmas. For

these problems, there are no once-and-for-all answers.

Michael FullanLeading in a Culture of Change

Moving to Higher Levels of SMP Implementation…18

SMPs are being used as the vehicle to drive content instruction. Evidence of one or more SMPs should be obvious on a dailybasis. This includes explicit references in lesson/unit plans, explicit use in classroom discussions, and explicit use on all assignments and assessments.

Explicit teaching of and emphasis on both content and process vocabulary must be a focus EVERY DAY.

In preparation for the Georgia Milestones, students must be writing on a daily basis in a journal/notebook (warm-ups, task questions, critiques of solutions, etc.). Open-ended/constructed response questions should become an integral part of assessment and instruction.

Consistency among these ideas within each school and across school levels cannot waiver if true College and Career Readiness is to be achieved.

Nonnegotiable…19

How do we connect all of the school-level, district-level, and state initiatives. Many educators still see all of these initiatives as separate entities.TKES LKES SLOS CCRPI DOK RIGOR FIP FALS

GEORGIA MILESTONES WRITING DIFFERENTIATION FRAMEWORKS MDC LDC

COMMON ASSESSMENTS POST-SECONDARY READINESS PLANNING RTI

STUDENT ACCOUNTABILITY MOTIVATION INSTRUCTIONAL STRATEGIES

STANDARDS FOR MATHEMATICAL PRACTICE ANCHOR STANDARDS FOR LITERACY

Connecting the Dots…20

The STANDARDS FOR MATHEMATICAL PRACTICE address many of the same ideas found in the ANCHOR STANDARDS FOR LITERACY.

These standards are already embedded in the FALlessons which have been embedded into the FRAMEWORKS tasks. LDC and MDC initiatives provide specific guidance on the SMPs and Anchor Standards.

Since communication is such a vital part of these standards, WRITING provides a natural support structure.

Connecting the Dots…21

These resources used with the SMPs either provide explicit DIFFERENTIATION or provide basic structures to help teachers with that process. Understanding and addressing those differences in learning is the essence of RTI.

If the SMPs are used to guide all PLANNING, choice of INSTRUCTIONAL STRATEGIES, and ASSESSMENT, teachers will be teaching and assessing at all DOK levels and will have finally achieved that seemingly nebulous idea of RIGOR that everyone continues to expect!

Connecting the Dots…22

The use of COMMON ASSESSMENTS, including SLO assessments, only serves to create uniformity and stability across the school and district and should help in identifying specific student, teacher, and administrator strengths and challenges.

When teacher and administrator challenges are identified, the FIPmodules provide self-paced individualized professional learning opportunities.

Connecting the Dots…23

Using the SMPs as a springboard for all of these initiatives turns real-world connections and STUDENT ACCOUNTABILITY into non-negotiable ideas.

This only works in our favor to increase student MOTIVATION.

Connecting the Dots…24

Teaching and assessing at this level will ultimately increase our student achievement levels on school level assessments as well as on the GEORGIA MILESTONES—increasing our CCRPI score—leading to proficient and exemplary ratings on the TKES and LKES.

Ultimately, we have more students than ever before graduating with true POST-SECONDARY READINESS.

Connecting the Dots…25

Mindset: The New Psychology of SuccessCarol Dweck Book study – 8 chapters/8 sessions

Fixed Mindset• The intelligence you’re born

with is fixed, limiting your abilities to learn.

• Nothing can be done to increase your intelligence, so don’t even try.

• This mindset is fraught with fear of failure, fear of change, fear of being wrong, fear of being found out.

Growth Mindset• Intelligence can be

increased with instruction, practice, and time.

• You can learn from your mistakes – change is positive.

• Failure is an opportunity to figure out what to do better – a learning experience.

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What does Mindset have to do with the SMPs?

What significance do the two different mindsets (fixed and growth) have to do with teacher attitudes towards their students?

What significance do the two different mindsets have to do with student attitudes towards themselves and their peers?

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Rigor Redefined in High School Mathematics Resources

http://www.negaresa.org/

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