Math Coaches/Contact Meeting December 14, 2012 Course Descriptions/Learning Goals

Bureau of Curriculum & Instruction 1Florida Dept. of Education

Math Coaches/Contact MeetingDecember 14, 2012Course Descriptions/Learning Goals

Bureau of Curriculum & Instruction 2

Florida’s CCSS Implementation Plan

Florida Dept. of Education

Full Implementation Grade K

Begin Implementation of Literacy Standards in ALL Content Areas for Grades 6-12

Begin Implementation of Rich and Complex Text and Informational Text for Grades K-12

Phase 1 (2011-2012)

Full Implementation Grades K-1 (BCPS K-2)

Full Implementation of Literacy Standards in ALL Content Areas for Grades 6-12

Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12

Phase 2 (2012-2013)

Full Implementation Grades K-2

Implementation of a Blended Curriculum (CCSS and Supplemental NGSSS Aligned to FCAT 2.0 and EOCs) for Grades 3-12

Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12

Phase 3 (2013-2014)

Full Implementation Grades K-12

PARCC Assessments Aligned to CCSS

Phase 4 (2014-2015)


Course Requirements and Standards

Curriculum Mapping in Layers

“Chunks” or Big Ideas


Major Learning Goals

Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas

Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course

Progression Scales for Major Learning Goals

Describe the learning progressions and develop a scale or rubric for at least one of the major learning goals for the course

(Day 2)

Progress Monitoring AssessmentsDescribe at least one assessment item that is appropriate for each of the levels beginning with Level 2 on the learning progression scale

Draft a blueprint for future progress monitoring assessments based upon the curriculum map (or pacing guide) and anticipated learning progressions

(Day 2)


Current Way of Work

• Given the full implementation of Florida’s NGSSS what three words might we use to describe instruction in Florida?– Standards-Based Instruction

• What often guides the development of our curriculum maps or pacing guides?– Test Item Specifications

• What tools might we use to monitor the progress of our students?– Focus Mini-Assessments (Benchmark Assessments)



Florida Transitions toCommon Core State Standards

Next Generation Standards• Standards-based instruction• Test item specifications guide

development of curriculum maps

• Focus mini-assessments aligned to individual benchmarks and used to monitor student progress

• Teaching benchmarks in isolation results in long lists of tasks to master

Common Core Standards• Standards-based instruction

facilitated by learning goals• Big ideas and learning goals guide the

development of curriculum maps• Learning progressions or scales

describe expectations for student progress in attaining the learning goals

• Assessments used to monitor student progress are aligned directly to the learning progressions or scales

• Teaching big ideas narrows the focus and allows students to delve deeper for a greater depth of understanding


Common Core State Standards for Mathematics

• Domains are larger groups of related standards. Standards from different domains may sometimes be closely related

• Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.

• Standards define what students should understand and be able to do.

Domains for K-12K 1 2 3 4 5 6 7 8 HS

Counting

and Cardinality

(CC)

Number and

Quantity

Number and Operations in Base Ten (NBT) The Number System

Number and Operations-Fractions

(NF)

Ratios and Proportional Relationships

(RP)

Operations and Algebraic Thinking (OA)Functions (F)

Expressions and Equations (EE)

Algebra (A)

Geometry (G)

Measurement and Data (MD)

Statistics and Probability (SP)

High School Conceptual Categories

• Number and Quantity (N)

• Algebra (A)

• Functions (F)

• Modeling (*)

• Geometry (G)

• Statistics and Probability (S)

Florida’s Numbering ofthe Common Core State Standards

MACC.7.RP.1.1

Subject Grade Domain Cluster Standard

MACC.912.N-RN.2.3

Subject Grade Category Domain Cluster Standard

• MACC.7.RP Ratios and Proportional Relationships

• MACC.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems

• MACC.7.RP.1.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour.

Domain

Cluster

Standard

• MACC.912.N Number and Quantity

• MACC.912.N-RN The Real Number System

• MACC.912.N-RN.2 Use properties of rational and irrational numbers

• MACC.912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Domain

Cluster

Standard

Category


SAMPLE LESSONM/J MATHEMATICS 2 – RATIONAL NUMBERS

The New “Look and Feel” of Instruction with Common Core


Please refer

to sample

lesson!

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Course: M/J Math 2 (1205040) Lesson Plan SampleGoal:

Objective(s):

Essential Question:

Engaging Activity and Discussion Questions:

Formative Assessment Task:

Differentiated Instruction Strategies:


Learning Goal

Students demonstrate proficiency with addition, subtraction, multiplication, and division of rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level.



Objective

Students demonstrate fluency* when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves.


*Fluency is the ability to compute flexibly, accurately, efficiently, and appropriately.

http://youtu.be/ZFUAV00bTwA




Essential Question

Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents?



Performance Task

Jeri and Tawny were both presented with the same problem; yet, they arrived at two different answers. Their complete responses are shown below.

Jeri simply wrote ) = 1Tawny showed considerably more details and wrote 3

(0.) = (0.) + (0.) + (0.) = 0.

Who has the correct answer and why?


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Course: M/J Math 2 (1205040) Lesson Plan SampleGoal: Students demonstrate proficiency with addition, subtraction, multiplication, and division of

rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level.

Objective(s): Students demonstrate fluency when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves.

Essential Question:

Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents?

Engaging Activity and Discussion Questions:

Students should be presented with the formative assessment task shown below and the teacher should read the question aloud. Initially, students should explore their thinking independently while making notes of interesting observations and/or any questions they may have. Students should then share their thinking with others in their small group; they should take turns asking questions of others, and adjust their own notes. Once everyone has had an opportunity to share their thinking and ask all their questions, students should once again work independently to finalize their response.

Formative Assessment Task:

Differentiated Instruction Strategies:

Some students may need to explore the problem visually using grid paper or manipulatives such as Unifix cubes, fraction tiles, or a ruler.ELL students may need to use a bilingual dictionary to construct their response; they may also need to reference their glossary for this unit.Some students may need a hardcopy of the problem versus just projecting it on an overhead screen.


Discuss It!

• Based upon this lesson, how might you describe the new “look and feel” of instruction with Common Core?







Step 1 - Course Descriptions• General Information

– Course Code– Title– Credit– Graduation Requirement– Course Length

• Critical Areas of Focus or General Description• NGSSS Requirements for 2013-14 Assessments• Related Benchmarks

– Common Core Literacy Standards– Common Core Mathematical Practices– Common Core Mathematics Standards



Critical Areas of Focus


• Look at the 2013-2014 Course Description for your selected grade level/course

• Read each critical area/unit• As a group, summarize the main idea of each

critical area in 1 – 2 sentences.


Grade 7 Math - Critical Areas of Focus

1. Developing understanding of and applying proportional relationships

2. Developing understanding of operations with rational numbers and working with expressions and equations in one variable

3. Solving problems involving scale drawings and informal geometric constructions, and working with two- and three- dimensional shapes to solve problems involving area, surface area, and volume

4. Drawing inferences about populations based on samples


M/J Math 2

Course







Step 2 - “Chunking”

• Begin with the course descriptions and standards and benchmarks.

• “Chunk” the critical area into smaller major areas of focus.

• Sort the standards and/or benchmarks contained in the course description based upon these major areas of focus (there will likely be some overlapping of standards).



Algebra 1 – Critical Area #2In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students explore systems of equations and inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.



Algebra 1 “Chunking” SampleCritical Area 2: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit:1. Students will learn function notation and develop the concepts of

domain and range. They explore many examples of functions, they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.

2. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.

3. Students explore systems of equations and inequalities, and they find and interpret their solutions.



“Chunking” Standards1. Students will learn function notation and develop the concepts

of domain and range. They explore many examples of functions, they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.

– MACC.912.A-REI.4.10 MACC.912.F-IF.1.1 – MACC.912.F-IF.1.2 MACC.912.F-IF.2.4– MACC.912.F-IF.2.5 MACC.912.F-IF.2.6– MACC.912.F-IF.3.7 MACC.912.F-IF.3.8– MACC.912.F-IF.3.9 MACC.912.F-BF.1.1– MACC.912.F-BF.2.3 MACC.912.F-LE.2.5– LACC.910.RST.3.7 MACC.K12.MP.4.1– MACC.K12.MP.7.1 MACC.K12.MP.8.1







Major Learning Goals


• Learning Goals, Scales, and Learning Activities• For more information:

– https://www.floridaschoolleaders.org– https://www.floridaschoolleaders.org/resources/in

dex.aspx


https://www.floridaschoolleaders.org/

https://www.floridaschoolleaders.org/resources/index.aspx

https://www.floridaschoolleaders.org/resources/index.aspx


Step 3 - Learning Goals

The Learning Goal (Defines what students should know and be able to do.)1. Students demonstrate an understanding of function notation and the

concepts of domain and range. They interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.


The “Chunk” (Describes the integrated/related content standards students are expected to learn.)

Students will learn function notation and develop the concepts of domain and range. They explore many examples of functions, they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.


State and Map Learning Goals

• Select one learning goal to share with group and using chart paper record the learning goal and “chunked” standards.



• Learning Objectives

• •


• •




Mapping Learning Goals

Learning Goal 1

Learning Goal 2

Learning Goal 3

Learning Goal 4


State and Map Learning Goals

• Begin the mapping process to identify when these learning goals will be taught using 2013-2014 Curriculum Map.


2013-2014 M/J Mathematics 2 Curriculum Map

Week/Quarter 1 2 3 4 5 6 7 8 9

1 LG6LG7

LG5

LG1LG2

2

LG1LG2LG5LG6LG7

3 LG5LG6

4 LG5LG6

Resources • Florida Common Core

– http://www.fldoe.org/schools/ccc.asp– http://www.fldoe.org/schools/BlastOff.asp

• Common Core State Standards for Mathematics– http://www.corestandards.org

• Solution Tree– http

://files.solution-tree.com/pdfs/Reproducibles_CCMLG/repros/table%202.2mathematicalpractices--look-forsasclassroomindicators.pdf

• CPALMS– http://www.floridastandards.org

• The Teaching Channel– https://www.teachingchannel.org

• Illustrative Mathematics– http://illustrativemathematics.org/

• Inside Mathematics– http://www.insidemathematics.org/index.php/common-core-standards

• Progressions Documents – http://ime.math.arizona.edu/progressions

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http://www.fldoe.org/schools/ccc.asp



http://www.fldoe.org/schools/BlastOff.asp

http://www.fldoe.org/schools/BlastOff.asp

http://www.corestandards.org/

C:%5CUsers%5Cowner%5CDesktop%5C1%20CCSS%20Fall%20Math%20Handouts%5Ctable%202.2mathematicalpractices--look-forsasclassroomindicators.pdf

http://files.solution-tree.com/pdfs/Reproducibles_CCMLG/repros/table%202.2mathematicalpractices--look-forsasclassroomindicators.pdf




http://www.floridastandards.org/

https://www.teachingchannel.org/

https://www.teachingchannel.org/

http://illustrativemathematics.org/

http://www.insidemathematics.org/index.php/common-core-standards

http://ime.math.arizona.edu/progressions

http://ime.math.arizona.edu/progressions

Resources

• Figure This– http://figurethis.org/index.html

• New York Times– http://learning.blogs.nytimes.com/2012/09/26/n-ways-to

-apply-algebra-with-the-new-york-times/• NCTM Illuminations

• http://illuminations.nctm.org/• NCTM Navigation Series

– http://www.nctm.org/catalog/productsview.aspx?id=110

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http://figurethis.org/index.html

http://learning.blogs.nytimes.com/2012/09/26/n-ways-to-apply-algebra-with-the-new-york-times/

http://learning.blogs.nytimes.com/2012/09/26/n-ways-to-apply-algebra-with-the-new-york-times/

http://illuminations.nctm.org/

http://www.nctm.org/catalog/productsview.aspx?id=110


Objectives for Day 1 – Status Check

• Participants will:

Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas, and

Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course.



Reflections

• What are you most excited by with the transition to CCSS?

• What concerns you the most about the transition to CCSS?

• How will you try to address these concerns?
