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2011 NYS P-12 Common Core Learning Standards for Mathematics. Please visit www.engageNY.org for additional information regarding the Common Core Learning Standards. The Common Core State Standards Initiative.
Please visit www.engageNY.org for additional information regarding the Common Core Learning Standards
*Ready for first-year credit-bearing, postsecondary coursework in mathematics and English without the need for remediation.
For example: Standards from individual high-performing countries and provinces were used to inform content, structure, and language. Writing teams looked for examples of rigor, coherence, and progression.
Learning Standards for Mathematics
Test your mathematics and science knowledge by completing TIMSS items in the Dare to Compare challenge!
Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Which course is the “gatekeeper” course in high school that research indicates can be a significant predictor of college-readiness and success?
Students completing Algebra II more than double their chances of earning a four-year college degree
If only my students knew how to ….
Find the product of
(x + 1) and (x - 3).
Think-Pair-Share at your table all the different ways to solve the problem.
Can you convince me of your solution?
Write your solutions on chart paper.
Engage in a gallery walk and review the work of others.
Find the product of
(x - 2) and (x²+5x +3).
Find the product of
(x - 2) and (x²+5x +3).
Does your prior strategy work to solve this problem? Why or why not?
Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions (found in the attached list of fluencies) such as multiplication tables so that they are more able to understand and manipulate more complex concepts.
What’s your answer?
Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations. as well as writing and speaking about their understanding.
Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content.
Wikipedia reports that 8% of all Americans eat as McDonalds every day. In the U.S., there are approximately 310 million people and 12,800 McDonalds.
Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position.
Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.
“It’s what you learn after you know it all that counts.”
- John Wooden
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
Which fraction is closer to 1
4/5 or 5/4?
Same problem with Standards for
Mathematical Practice Integration
4/5 is closer to 1 than 5/4. Using a number line, explain why this is true.
The content standards are organized by domains across grade levels and each grade level begins with a narrative description of the grade level, followed by the standards for mathematical practice, a list of the “Big Ideas” for the specific grade level, and then the content standards by domain.
Because progressions are so important in the Standards, suggestions for places to begin are not a laundry list of topics but rather a menu of progressions. Experts recommend organizing implementation work according to progressions because the instructional approach to any given topic should be informed by its place in an overall flow of ideas.
They emphasize the word menu. If a curriculum provider delivers a single coherent progression of materials to a district, then that provider has added value. If a math coach helps elementary school teachers in a district better understand a single coherent progression, then that coach has added value. The quantum of improvement is not the textbook series.
“Who wants to be a Millionaire?”
Question for $16,000
Which of these square numbers also happens to be the sum of two smaller square numbers?
List strategies to help students remember square numbers
Partnership for Assessment of Readiness for College and Careers (PARCC) http://www.parcconline.org/
PARCC is a 26-state consortium working together to develop next-generation K-12 assessments in English and math.
What brought all of these states together is a shared commitment to develop an assessment system aligned to the Common Core State Standards that is anchored in college and career readiness; provides comparability across states; has the ability to assess and measure higher-order skills such as critical thinking, communications, and problem solving; and provides truly useful information for educators, parents, and students alike.
While each state has their own priorities and challenges, PARCC provides the opportunity for participating states to come together and collectively move the field forward and break new ground in assessment design. In addition, many of the PARCC states are on the leading edge of education reform, including 10 of the 12 winning Race to the Top states.
To help states measure student knowledge and skills at the lower grades, the Partnership will develop a bank of assessment resources for teachers of grades K–2 that are aligned to the Common Core State Standards, and vertically aligned to the PARCC assessment system. The tasks will consist of developmentally-appropriate assessment types, such as observations, checklists, classroom activities and protocols, which reflect foundational aspects of the Common Core State Standards. The K-2 formative assessments aim to help set a foundation for students and put them on the track to college and career readiness in the early years.
These K-2 assessments will help educators prepare students for later grades and provide information for educators about the knowledge and skills of the students entering third grade, allowing classroom teachers and administrators to adjust instruction as necessary. These tools also will help states fully utilize the Common Core State Standards across the entire K-12 spectrum.
The distributed PARCC design includes through-course and end-of-year components so that assessments are given closer in time to when instruction happens.
The 3-8 assessments will include a range of item types, including innovative constructed response, extended performance tasks, and selected response (all of which will be computer based).
The distributed PARCC design includes through-course and end-of-year components so that assessments are given closer in time to when instruction happens. PARCC states have endorsed a course-based design in math and a grade-based design in ELA/Literacy.
The high school assessments will include a range of item types, including innovative constructed response, extended performance tasks, and selected response (all of which will be computer based). In addition, there will be college-ready cut scores on high school tests in mathematics and ELA/Literacy, which will signify whether students are ready for college-level coursework. Earlier tests will be aligned vertically to ensure students are on - and stay on - the track to graduating ready for college and careers.
The Model Content Frameworks for Mathematics are designed with the following purposes in mind:
• identifying the big ideas in the Common Core State Standards for each grade level,
• helping determine the focus for the various PARCC assessment components, and
• supporting the development of the assessment blueprints.
“Coming together is a beginning, keeping together is progress, working together is success.”
- Henry Ford
“This year I am asking every teacher to try at least one Common Core-aligned unit each semester. Math teachers should select one of the priority concepts at the strategic expense of other, less critical topics and go deep in a way they haven’t before. ELA teachers will provide a thoughtful learning experience around a particular text that should result in students’ ability to make an argument about that text. Content area teachers can fulfill the “literacy” aspect of this transformation by providing similar learning experiences built around pivotal texts in their subject area. “
- What students will know, do and understand
- Evidence that will be collected to determine whether
or not desired results are achieved
- Design learning activities to align with Stage 1 and 2
- What activities and instruction will engage students
and help them better grasp the essence and the value
of this topic/content?