Implementing the NYS P-12

Common Core Learning Standardsfor Mathematics

Turn-Key Training Guide

This turn-key training guide was developed to assist Network Teams, Principals and Teacher Leaders in the delivery of the Power Point presentation Implementing NYS P-12 Common Core Learning Standards for Mathematics created by Margaret Brady, Teri Calabrese-Gray, and Andrew Chen. This presentation may be delivered in one sitting (approximately four hours in length) or it may be broken down into smaller segments as time permits.

Please note that slides that are marked with the symbol as slides that require the support of a mathematics specialist in the delivery of the content, as they require deep mathematical knowledge and understanding.

The presentation contains links to videos and websites that will assist the presenter in demonstrating application of the Mathematical Shifts of the Common Core State Standards. These videos and websites can be accessed by double clicking on the hyperlinks on the slides.

Table of Contents

Slides 1 - 4 – The Common Core Learning Standards……………………………………………………..……………Pg 4-5

  • The CommonCoreState Standards
  • Why Common Core Standards?

Slides 5-19 – CCSS? How they were developed and who was involved?……………………….…………………Pg 5-12

  • The Mathematical Standards – Who developed them?
  • The underlying framework and the need for change.
  • A sense of urgency
  • What the research says

Slides 20-22 – Introduction to the Instructional Shifts ………………………………………………………………....Pg 12

  • Focus
  • Coherence
  • Fluency
  • Deep Understanding
  • Application
  • Dual Intensity

Slides 23-26 – Shift 1: Focus……………………………………………………………………………………………….Pg 13-14

  • The power of the eraser
  • Prioritized concepts

Slides 27-39 – Shift 2: Coherence…………………………….…………………………………………………………..Pg 14-18

  • The Structure is the Standards
  • Knowing and Teaching Elementary Mathematics

Slides 40-44 – Shift 3: Fluency…………………………….……………………………………………………………...Pg 18-19

  • Key Fluencies
  • Building on required fluencies

Slides 45-47 – Shift 4: Deep Understanding………………….………………………………………………………….Pg 19

  • Deep conceptual understanding
  • Applying to new situations

Slides 48-49 – Shift 5: Application……………………….…………………………………………………………..……...Pg 20

  • Provide opportunities at all grade levels to apply math concepts in “real world” situations

Slides 50-53 – Shift 6: Dual Intensity………………….…………………………………………………………..…….Pg 20-21

  • Practicing and understanding

Slides 54 – The Mathematical Shifts and the Standards They Require…………………………………………..….Pg 22

  • Conceptual Understanding, Procedural Fluency and Problem Solving
  • Greater focus and better coherence

Slides 55 – 57 – Assessment of Learning: The Next Shift………………………………………………………………Pg 22

  • NYS Common Core Curriculum Modules
  • PARCC Assessments

Slides 58 - 63 – Resources…………………………………………………………………………………………….……Pg 22-23

  • NYSED Mathematics Toolkit
  • EngageNY.org
  • The Tri-State Rubric for Mathematics
  • NYS CCLS for Mathematics Modules
  • Video Exemplars

References………………………..……………………….…………………………………………………………..…….Pg 24-31

Mathematics Toolkit – Presenter Notes & Directions for PowerPoint Presentation

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Slide # / Presenter Notes / Hyperlinks / Slide Timing
1 / Presenter Notes: This PowerPoint toolkit provides a brief history on the Common Core State Standards (CCSS) for Mathematics, the rationale behind the development of the CCSS, and an overview of the six instructional shifts needed to effectively implement the NYS P-12 CCLS for Mathematics.
Presenter Directions: Throughout the Power Point there are a number of hyperlinks (identified in bright blue lettering) that can be accessed by right clicking to “open hyperlink.” These movies, resources and activities can be used to support the various topics addressed in this presentation / Hyperlink:
/ 2 minutes
2 / Presenter Notes: This slide provides information of how and when the CCSS conversation began and the two organizations that oversaw the development of the Common Core State Standards (CCSS).
Presenter Directions: Open the hyperlink and show participants where the Common Core Mathematics Standards are found. Review them briefly. / Hyperlink:
is link to the National Common Core Standards website where information can be found about the development of the standards and all of the Common Core Standards in PDF format / 5 minutes
3 / Presenter Notes:“WhyCommonCoreState Standards?”
Presenter Directions: Pose this question to your audience and engage in a conversation (do not advance to the next slide or you may choose to hide the next slide of the PPT).
What to Expect: Discussion usually focuses on College and Career Readiness (CCR), global competition, states would be able to compare themselves to others states for the first time, equity for all students regardless of zip code, and focus and coherence (reduce “the mile wide, inch deep” curriculum in the United States). / 5 minutes
for total
activity
Slide # / Presenter Notes / Hyperlinks / Slide Timing
4 / Presenter Notes: This slide lists rationale as to why states agreed to collaborate and develop the CCSS. / 2 minutes
5 / Presenter Notes: The hyperlink contained is this slide is a video that explains the process on the development of the CCSS for Mathematics. Bill McCallum and Jason Zimba, two of the principal writers, share how they worked as a team with 60 writers and various professional organizations to develop the mathematics standards. There are many other Hunt Institute videos on You Tube.
Presenter Directions: Click on the hyperlink in the title to view a video. / Hyperlink:

The Hunt Institute
The Mathematics Standards: How They Were Developed and Who Was Involved
by Bill McCallum, PhD, Math Team Coordinator and Jason Zimba,PhD, Math Team Coordinator
Video Timing = 8:11 / 10 minutes
6 / Presenter Notes: Adding It Up provides a historical perspective in mathematics education and the presenter can refer participants to this document for advancing their own knowledge about how students in pre-K through 8th grade learn mathematics and it recommends how teaching, curricula, and teacher education should change to improve mathematics learning and teaching. / Hyperlink: Visit 1to read Adding It Up online, free of cost. / 2 minutes
7 / Presenter Notes: This matter is URGENT!
Presenter Directions: Emphasize that Improving K-12 Mathematics Education is an urgent matter! / 10 seconds
Slide # / Presenter Notes / Hyperlinks / Slide Timing
8 / Presenter Notes:“What is the current state of mathematical performance?”
Presenter Directions: The key questions for this activity are outlined on this slide
  • Pose these questions one at a time
  • Ask participants to discuss at their tables. Another option is to ask tables to count off by fours and discuss one of the four questions and report out.
  • Continue to the next slide and present the data
/ 6-8 Minutes
9 / Presenter Notes: This slide highlights the TIMMS study.
Presenter Directions: Ask participants if they are familiar with this study. Review the information contained on the slide and refer participants to the hyperlink for more information about this important study. / Hyperlink:
The Trends in International Mathematics and Science Study (TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. 4th- and 8th-grade students compared to that of students in other countries. TIMSS data have been collected in 1995, 1999, 2003, and 2007. In 2011, more than 60 countries and jurisdictions, including the United States, participated in TIMSS. More than 20,000 students in more than 1,000 schools across the United States took the assessment in spring 2011, joining almost 500,000 other students around the world taking part in TIMSS. / 1 minute
Slide # / Presenter Notes / Hyperlinks / Slide Timing
10 / Presenter Notes:
The 2007 Trends in International Mathematics and Science Study (TIMSS) is the fourth administration since 1995 of this international comparison. Developed and implemented at the international level by the International Association for the Evaluation of Educational Achievement (IEA)—an international organization of national research institutions and governmental research agencies—TIMSS is used to measure over time the mathematics and science knowledge and skills of fourth- and eighth-graders. This report focuses on the performance of U.S. students relative to that of their peers in other countries in 2007, and on changes in mathematics and science achievement since 1995. Thirty-six countries or educational jurisdictions participated at grade four in 2007, while 48 participated at grade eight. This report also describes additional details about the achievement of U.S. student subpopulations. All differences described in this report are statistically significant at the .05 level. No statistical adjustments to account for multiple comparisons were used.
Note: This is 8th grade math data.
Key findings from the report include the following:
• In 2007, the average mathematics scores of both U.S. fourth-graders (529) and eighth-graders (508) were higher than the TIMSS scale average (500 at both grades). The average U.S. fourth-grade mathematics score was higher than those of students in 23 of the 35 other countries, lower than those in 8 countries (all located in Asia or Europe), and not measurably different from those in the remaining 4 countries. At eighth grade, the average
U.S. mathematics score was higher than those of students in 37 of the 47 other countries, lower than those in 5 countries (all of them located in Asia), and not measurably different from those in the other 5 countries.
• Compared to 1995, the average mathematics scores for both U.S.
(Slide 10 continued)
fourth- and eighth-grade students were higher in 2007. At fourth grade, the U.S. average score in 2007 was 529, 11 points higher than the 1995 average of 518. At eighth grade, the U.S. average mathematics score in 2007 was 508, 16 points higher than the 1995 average of 492.
• In 2007, 10 percent of U.S. fourth-graders and 6 percent of U.S. eighth-graders scored at or above the advanced international benchmark in mathematics. At grade four, seven countries had higher percentages of studentsperforming at or above the advanced international mathematics benchmark than the United States:
Singapore, Hong Kong SAR, Chinese Taipei, Japan, Kazakhstan, England, and the Russian Federation. Fourth-graders in these seven countries were also found to outperform U.S. fourth-graders, on average, on theoverall mathematics scale. At grade eight, a slightly different set of seven countries had higher percentagesof students performing at or above the advanced mathematics benchmark than the United States: Chinese, Taipei, Korea, Singapore, Hong Kong SAR, Japan, Hungary, and the Russian Federation. These sevencountries include the five countries that had higher average overall mathematics scores than the UnitedStates, as well as Hungary and the Russian Federation. / Hyperlink:
8th Grade Math / 6-8 minutes
Slide # / Presenter Notes / Hyperlinks / Slide Timing
11 / Presenter Notes: Does this give us cause for alarm? / 10 seconds
12 / Presenter Notes: PISA All students take pencil-and-paper tests, with assessments lasting a total of two hours for each student. For the PISA 2009 assessment, someparticipating countries/economieshave also optedfor an assessment of the reading of electronic texts.
Presenter Directions: The link is given for reference – / Hyperlink:
PISA (Programme for International Student Assessment) / 30 seconds
13 / Presenter Notes: Please note that this is math data comparing 15 year olds. Take an interactive version of the testsonline at

You can also consult the publication'Take the Test ‘which lists all the publicly released items from the first three assessments(PISA 2000, 2003 and 2006).
The PISA test is a very rigorous test for 15 year olds and focused on mathematical application. / Hyperlink: Take the Test

PISA (Programme for International Student Assessment) / 2-3 minutes
Slide # / Presenter Notes / Hyperlinks / Slide Timing
14 / Presenter Notes: Only 4 percent of students in the combined Organization for Economic Cooperation and Development (OECD) area, but more than 8 per cent in Belgium, Japan, Korea and the partner country Hong Kong-China – can perform the highly complex tasks required to reach Level 6.
• About a third of OECD students can perform relatively difficult tasks at Levels 4, 5 or 6, but over 49 percent of students in Finland, Korea and the partner country Hong Kong-China can perform at least at Level 4.
• About three-quarters of OECD students can perform at least mathematical tasks at Level 2 (shown above the central line in the graph). However, over a quarter of students are not proficient beyond Level 1 in Italy and Portugal, over a third in Greece and over half in Mexico and Turkey. A number of partner countries also have high numbers at Level 1 or below.
• Eleven percent of students in OECD countries are not capable even of Level1 tasks. These students may still be able to perform basic mathematical operations, but were unable to utilize mathematical skills in a given situation, as required by the easiest PISA tasks. In some countries, over 20 percent are in this category
Presenter Directions: Spend time explaining theseven levels (above and below) so that participants can understanding and compare high and low performing countries. / Hyperlink: First Results from PISA 2003 Executive Summary
/ 2 minutes
Slide # / Presenter Notes / Hyperlinks / Slide Timing
15 / Presenter Notes: In 2006, the average U.S. score in mathematics literacy was 474, lower than the OECD average score of 498. Thirty-one jurisdictions (23 OECD jurisdictions and 8 non-OECD jurisdictions) scored higher, on average, than the United States in mathematics literacy in 2006. In contrast, 20 jurisdictions (4 OECD jurisdictions and 16 non-OECD jurisdictions) scored lower than the United States in mathematics literacy in 2006. When comparing the performance of the highest achieving students—those at the 90th percentile—U.S. students scored lower (593) than the OECD average (615) on the mathematics literacy scale. Twenty-nine jurisdictions (23 OECD jurisdictions and 6 non-OECD jurisdictions) had students at the 90th percentile with higher scores than the United States on the mathematics literacy scale. / 1 minutes
16 / Presenter Notes: The red bar represents some of our leading states. This graph shows the percentage of students achieving at an advanced level and how various states performed on the PISA 2006 in comparison to other states and countries. Even our best states (Massachusetts) performed considerably lower than the leading countries. The cutting edge defines a country’s ability to remain competitive. / 30 seconds
17 / Presenter Notes: The National Assessment of Educational Progress (NAEP) is the largest nationally representative and continuing assessment of what America's students know and can do in various subject areas. Assessments are conducted periodically in mathematics, reading, science, writing, the arts, civics, economics, geography, and U.S. history. In 2011, New YorkState is the only state whose 4th graders scored lower than in 2009. / Hyperlink:
National Assessment of Educational Progress (NAEP) / 30 seconds
Slide # / Presenter Notes / Hyperlinks / Slide Timing
18 / Presenter Notes: This slide depicts the 4th grade NAEP Math Results.
Presenter Directions: Review these results with participants / 2 minutes
19 / Presenter Notes: This slide depicts the 4th grade NAEP Math Results.
Presenter Directions: Review these results with participants / 2 minutes
20 / Presenter Notes: This 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. Based on the video where there any “ah-ha” moments for you?
Presenter Directions: Determine need/time to view during the presentation. The viewing of this video could be assigned as a
pre-session assignment. / Hyperlink: Common Core Math EngageNY.org
/ 15 minutes (if viewing complete video)
21 / Presenter Notes: There are six instructional shifts necessary to implement the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics. / 5 seconds
22 / Presenter Notes: The six shifts represent key areas of focus as teachers and administrators work to implement the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics. Educators are likely to be at different stages in practicing these shifts, however, focusing on these areas can help schools and districts develop a common understanding of what is needed in mathematics instruction as they move forward with implementation.
Presenter Directions: Ask participants to read the shifts, think about what the shifts mean, and what would these look like in a mathematics classroom? / 2 minutes
Slide # / Presenter Notes / Hyperlinks / Slide Timing
23 / Presenter Notes: Ask participants to read the shift, think about what the shift means, and what it would look like in a mathematics classroom. / 3-4 minutes
24 / Presenter Notes: Ask participants to paraphrase the shift. Focus involves depth, not breadth. The intent of the NYS P-12 New York State P-12 Common Core Learning Standards for Mathematics is to use the power of the eraser and get rid of a curriculum that is “a mile wide and an inch deep.” Another key word in the definition is “prioritized”. Educators need to be sure they are spending more time on those concepts critical to mathematical proficiency. Students need to have deep conceptual understanding to be able to transfer skills across concepts and grades. / 3-4 minutes
25 / Presenter Notes:
The purpose of the National Center for Education Statistics' Kids' Zone is to provide information to help visitors learn about schools; decide on a college; find a public library; engage in several games, quizzes and skill building about math, probability, graphing, and mathematicians; and to learn many interesting facts about education. Of course, all of these things have been designed to be fun too, so jump in! Dare to Compare, a part of the Kids’ Zone website, contains questions from the Trends in International Mathematics and Science Study (TIMSS), the Civic Education Study (CivEd) and National Assessment of Education Progress (NAEP).
Presenter Directions: Ask participants to engage in a math problem on the Dare to Compare site and discuss possible application in the mathematics classroom.
You could use the math questions on the Dare to Compare site as “Do Nows” or Bell Ringers, peer to peer, learning centers, and quizzesfor students to work on in teams or pairs, review, or share with parents in your newsletter. / Hyperlink: Dare to Compare

Sample TIMMS questions / 5 -8 minutes (problem and discussion)
Slide # / Presenter Notes / Hyperlinks / Slide Timing
26 / Presenter Notes:
•First-year college remediation problem: Mismatch of definitions of College Readiness between higher education and K-12
•[Teachers should] teach to greater mastery of fewer topics vs. covering more