Common Core State Standards Session 2 K-5 Mathematics
Bell Work Activity • Handout #1 • The Common Core State Standards for Mathematics from A to Z • List words that begin with each letter of the alphabet that identify aspects of the Common Core State Standards for Mathematics. Handout #1 Common Core From A to Z
WELCOME Introductions Agenda The Common Core State Standards for Mathematics from A to Z Exploring the Standards for Mathematical Practice Exploring the Common Core State Standards for Mathematics Critical Areas Exploring the Mathematics Progressions • Dr. Karol Yeatts • BCI • Bethany Mathers • BEESS • Liz Conn • BEESS • Martha Gioielli • DA • Mark Drennan • SALA
“We live in a time of vast changes that include accelerating globalization, mounting quantities of information, the dominating influence of science and technology, and the clash of civilizations. Those changes call for new ways of learning and thinking in school, business, and the professions.” -Howard Gardner Five Minds for the Future (2007)
Expected Outcomes • Enhance knowledge base of the Common Core Standards for Mathematics. • 1 • Become familiar with the structure of the Common Core State Standards for Mathematics. • 2 • Enhance knowledge of the Common Core Standards for Mathematical Practice. • 3 Understand how the critical areas bring focus to key mathematical concepts for students to learn at each grade level. • 4 • 5 Consider how the learning progressions can be used to inform curriculum and guide instruction.
Digital Checkpoint Session 2 K-5 Mathematics
Digital Checkpoint • Poll Everywhere • http://www.polleverywhere.com/
How To Vote via Texting EXAMPLE Standard texting rates only (worst case US $0.20) We have no access to your phone number Capitalization doesn’t matter, but spaces and spelling do TIPS
Rate your level of understanding of the Common Core State Standards for Mathematics? • No understanding 63586 • Limited understanding 63623 • Fair understanding 63667 • Good understanding 63668 • Excellent understanding 63669 Send to: 37607 Text Code # to respond Submit response at http://PollEV.com
Virtual Parking Lot Send to: 37607 Text: 220274 plus your message Submit response at http://PollEV.com/
Digital Resources for the Common Core • Apple • http://itunes.apple.com/us/app/common-core-standards/id439424555 • Android • https://play.google.com/store/apps/details?id=com.edutater.corestandards • Common Core State Standards for Mathematics • http://www.corestandards.org/
Building Foundation Ensuring Education • CCSSO Focus Aligned Daro Coherence Clarity Developmental Level Evidenced-based Application Balanced Critical Areas Fluency Domains Clusters Habits of Mind Knowledge Guided by Principles Joint effort International Benchmarked Learner-focused Life-long skills IllustrativeMathematics McCallum Progressions Organized Robust, Relevant, Real-world National Focus NGA Quality Procedural fluency Opportunities Mathematical Practice Proficiency Research-based PARCC Rigor Teachers Whole Child Approach Standards Vision Sense-making Understanding Zimba X YOU Timeline
High School Conceptual Categories • Number and Quantity (N) • Algebra (A) • Functions (F) • Modeling (*) • Geometry (G) • Statistics and Probability (S) A-Z http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Domains for K-12 A-Z
Cluster Headings Cluster Headings Cluster Headings Domain Domain Domain Domain Cluster Headings A-Z 17
Cluster Headings Standards Domain
Florida’s Numbering ofthe Common Core State Standards MACC.K.CC.2.5 Subject Grade Domain Cluster Standard A-Z
Standards for Mathematical Practice “The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.” - Bill McCallum
Standards for Mathematical Practice Handout • Use appropriate tools strategically • Make sense of problems and persevere in solving them • 5 • 1 • Attend to precision • Reason abstractly and quantitatively • 6 • 2 • Look for and make sense of structure • Construct viable arguments and critique the reasoning of others • 7 • 3 • Look for and express regularity in repeated reasoning • Model with mathematics • 4 • 8 A-Z
Florida’s Common Core State Standards Implementation Timeline F- full implementation of CCSS for all content areas L – begin full implementation of content area literacy standards including: (1) use of informational text, text complexity, quality and range in all grades (K-12), and (2) CCSS Literacy Standards in History/Social Studies, Science, and Technical Subjects (6-12) B - blended instruction of CCSS with Next Generation Sunshine State Standards (NGSSS); last year of NGSSS assessed on FCAT 2.0 A-Z 22 http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf
Standards for Mathematical Practice Session 2 K-5 Mathematics
Poll Question How many Common Core Standards for Mathematical Practice are there? Send to: 37607 Text: 63844 plus your message Submit response at http://PollEV.com Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Standards for Mathematical Practice Overarching Habits of Mind of a Productive Mathematical Thinker • 1. Make sense of problems and persevere in solving them • 6. Attend to precision Reasoning and Explaining Modeling and Using Tools Seeing Structure and Generalizing 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning 25
Standards for Mathematical Practice • Develops dispositions and habits of mind • “Characteristic of an educated person” • Precision in thought • Precision in the use of language and terms • Precision of argument • Sense making happens through conversations http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu http://youtu.be/9pKcO9E4Flw A-Z 26
The Standards for Mathematical Practice Please locate the Common Core State Standards for Mathematics. Take a moment to examine the first three words of the narrative description for each of the 8 mathematical practices. What do you notice? Mathematically Proficient Students… Page 6 27
Digital Task Handout Your Digital Task is to: • Read your assigned Mathematical Practice. • Identify the words (verbs) that illustrate the student actions for this practice. • Text the words on one continuous line with spaces between each word. • Example: #..... create analysis model describe demonstrate….
Digital Task Text Numbers Practice #1 63946 Practice #2 31998 Practice #3 36509 Practice #4 50239 Practice #5 66363 Practice #6 66469 Practice #7 66559 Practice #8 66572 Submit responses at http://PollEV.com Send to: 37607 Text a CODE to respond followed by the verbs CODE 29
Mathematical Practice 1 - Make sense of problems and persevere in solving them. Submit responses at http://PollEV.com Text 63946 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 2 - Reason Abstractly and Quantitatively Submit responses at http://PollEV.com Text 31998 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others. Submit responses at http://PollEV.com Text 36509 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 4 - Model with mathematics. Submit responses at http://PollEV.com Text 50239 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 5 - Use appropriate tools strategically. Submit responses at http://PollEV.com Text 66363 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 6 - Attend to precision. Submit responses at http://PollEV.com Text 66469 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 7 - Look for and make sense of structure. Submit responses at http://PollEV.com Text 66559 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 8 - Look for and express regularity in repeated reasoning. Submit responses at http://PollEV.com Text 66572 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Expectations • Students planning solution pathways, monitoring and evaluating their progress and asking “Does this make sense?” 1 • Students knowing and using different properties of operations and objects and creating a coherent representation of the problem at hand. 2 • Students understanding and using definitions. Students justifying and explaining their thinking and listening to arguments of others and deciding if they make sense.. 3 • Students applying and using mathematics to solve problems connected to real-life situations. Students using models to represent, analyze and interpret results. 4
Expectations Students communicating precisely to others. Students calculating accurately and efficiently, expressing numerical answers with a degree of precision appropriate for the problem context. 6 Students being able to look closely to discern a pattern or structure. Students being able to shift perspectives. 7 • Students evaluating the reasonableness of their results. Student Maintaining oversight of the process, while attending to the details. 8 Students being familiar with tools appropriate for their grade or course and using technology tools to explore and deepen their understanding of concepts. Students being able to make sound decisions about when each of these tools might be helpful. 5
Consider the Learners • Over 240,000 ELLs in Florida • Almost every district has ELLs • 300 languages are spoken among ELLs • 79% of ELLs are in Mainstream/Inclusion model classrooms • ELLs are learning in the same classrooms as non-ELLs
Making the Content Comprehensible • Use the standards vocabulary as a teaching tool. “Generalize, develop, describe, analyze, apply, measure,” etc. are all words ELLs will hear in the classroom and need to understand. • ELLs may know how to perform the skill using their language, they just may not yet have the English vocabulary. • Use pictures, graphs, and charts whenever possible. • Make use of root words and cognates.
Classroom Strategies • Group ELLs with non-ELLs to work together. • Allow more wait time for ELLs to respond. • Silence does not necessarily mean the student does not know the answer, the ELL may be translating the answer and need more time. • Remember that ELLs from different countries may display mathematical functions in different ways.
Critical Areas and Mathematics Progressions Session 2 K-5 Mathematics
K-5 Domains and Critical Areas Handout #2 A-Z
Two critical areas in Kindergarten In Kindergarten, instructional time should focus on two critical areas: • 1. • Representing, relating, and operating on whole numbers, initially with sets of objects Page 9 • 2. • Describing shapes and space More learning time in Kindergarten should be devoted to number than to other topics. http://www.corestandards.org/the-standards/mathematics/kindergarten/introduction/ 46
Identify the Kindergarten Critical Area #1 Numbers #1 Numbers #2 Shapes #1 Numbers #2 Shapes #1 Numbers #1 Numbers #2 Shapes #2 Shapes
Four critical areas in 1st Grade • 1. developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 In Grade 1, instructional time should focus on four critical areas: • 2. developing understanding of whole number relationships and place value, including grouping in tens and ones Page 14 • 3. developing understanding of linear measurement and measuring lengths as iterating length units • 4. reasoning about attributes of, and composing and decomposing geometric shapes http://www.corestandards.org/the-standards/mathematics/grade-1/introduction/
Identify the 1st Grade Critical Areas #1 Operations #2 Base Ten #3 Measurement #1 Operations #3 Measurement #1 Operations #4 Geometry #2 Base Ten #3 Measurement #2 Base Ten #1 Operations
Four critical areas in 2nd Grade • 1. • extending understanding of base-ten notation In Grade 2, instructional time should focus on four critical areas: • 2. building fluency with addition and subtraction Page 17 • 3. • using standard units of measure • 4. describing and analyzing shapes http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/ 50