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Common Core Aligned 3-8 State Assessments W H AT A R E T H E C H A N GE S F O R M AT HE MAT I C S? H O W A R E W E P R E PA R I N G O U R STUDENTS FOR THEM? Common Core Standards Overview Fewer, clearer, and higher “What” not “How” of instruction—end year expectations, not a program Aligned with college and work expectations Expectations are consistent for all – and not dependent on a student’s state or zip code. Include rigorous content and application of knowledge through higher order skills Internationally benchmarked, so that all students are prepared to succeed in our global economy and society 2 KEY DIFFERENCES IN MATH Fewer topics; more generalizing and linking of concepts Well-aligned with the way high-achieving countries teach math Emphasis on both conceptual understanding and procedural fluency starting in the early grades More time to teach and reinforce core concepts from K-12 Some concepts will now be taught later Focus on mastery of complex concepts in higher mathematics (e.g., algebra and geometry) via hands-on learning Emphasis on mathematical modeling in the upper grades Math Standards 1. Mathematical Performance What students should be able to do… 2. Mathematical Understanding Understand is used in these standards to mean that students can explain the concept with mathematical reasoning, including concrete illustrations, mathematical representations, and example applications. 3. Mathematical Practices Proficient students of all ages expect mathematics to make sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to continue. They are experimenters and inventors, and can adapt known strategies to new problems. They think strategically.” Common Core State Standards Six Shifts in Mathematics Instruction Shift 1: Focus *** Prioritized concepts leading to strong foundational knowledge and understanding will be the focus of instruction and assessments. Other standards will be deemphasized. Shift 2: Coherence *** Carefully reflect the progression of content and concepts as depicted in the standards on and across grade levels. Shift 3: Fluency It is expected that students possess the required fluencies as articulated through grade 8 with building understanding and an ability to manipulate complex concepts. Shift 4: Deep Understanding Ability to access and apply concepts from a number of perspectives in both speaking and writing rather than as a right answer. Shift 5: Application Connecting content with fluency to employ to solve real-world problems. Shift 6: Dual Intensity Practice and understanding both occur with intensity. Shifts 3, 4, 5 combined make rigor Speed and Accuracy Think Fast/Solve Problems Students must … Be able to use core math facts fast Understand and talk about why the math works— prove it! Be able to persevere in solving multi-step/nonroutine problems…productive struggle is a good thing. Be able to apply math in the real world New York State Tests 2012-2013 Content: ELA and math tests for all grades will change to align to the Common Core Structure: ELA and math tests will remain similar to 20112012 (administration time, paper/pencil format) The math test will be administered over 3 days from April 24-April 26. 3rd grade students will be given 70 each day for testing, 4th graders will be given 70 minutes for the first 2 days and 90 minutes for the 3rd day; 5th graders will be given 90 minutes each day for testing The first 2 days for all grades will be multiple choice questions, followed by day 3 with a combination of short answer and extended response questions. 2012-2013 Math Question Types Multiple Choice Designed to incorporate mathematical content and practices in real-world applications Assess both procedural and conceptual standards Require the use of multiple skills and concepts All distractors will be based on plausible mistakes and misunderstandings Short Constructed Response Complete a task and show your work All descriptors for multiple choice apply to short response questions Extended Constructed Response Show your work in completing 2 or more tasks or one more extensive problem Give students the opportunity to show their understanding of math procedures, conceptual understanding, and applications What’s New for the 2012-2013 Math Tests? New tests will mirror the Works) for each grade math content emphases (Major Major clusters will make up the majority of the assessments Supporting and additional clusters will also be assessed New assessment questions will require students to: Take multiple steps to solve Apply skills based on their understanding of mathematical vocabulary RATHER than simply being tested on that vocabulary Choose that appropriate tool (e.g., ruler, protractor) AND apply mathematical concepts in using that tool Information can be found on EngageNY http://engageny.org/resource/math-content-emphases/.} Comparing samples from past math tests with samples aligned to the Common Core 3rd Grade 2010 There were 9 people fishing in a lake. Each person caught 6 fish. What was the total number of fish caught by the 9 people? A. 15 B. 48 C. 54 D. 62 CCLS aligned There were 54 apples set aside as a snack for 3 classes of students. The teachers divided up the apples and placed equal amounts on 9 separate trays. If each of the 3 classes received the same number of trays, how many apples did each class get? A. 2 B. 6 C. 18 D. 27 4th Grade 2010 Ms. Clark has a total of 42 bananas. There are 6 bananas in each bunch. Which step can be used to find how many bunches of bananas Ms. Clark has? A. Add 6 and 42. B. Divide 42 by 6. C. Multiply 42 by 6 D. Subtract 6 from 42 CCLS aligned The area of Ken’s rectangular garden is 480 square feet. The garden is 24 feet wide. What is the length of fencing Ken will need to buy in order to fence in the garden completely on all four sides? Show your work. 5th Grade 2010 Rhonda ate 3/8 of a pizza, and Marvin ate 1/8 of the same pizza. What fraction of the pizza did Rhonda and Marvin eat? A. 5/8 B. 3/8 C. 1/4 D. 1/2 5th Grade CCLS aligned Half of a school auditorium is needed to seat 3 equalsized fifth grade classes. Part A: Make a visual fraction model to represent the whole auditorium when each class is seated in separate sections. Part B: Write an expression to determine what fractional part of the auditorium one fifth grade class will need. Part C: What fraction of the auditorium will one of the fifth grade classes need? Key Differences The samples from the past tests ask students to remember, demonstrate, solve problems and calculate. Limited cognitive rigor The samples that are aligned to the new standards ask students Solve problems, calculate, complete, construct, demonstrate use of knowledge, compile, illustrate, think deeply, compare and formulate Cognitively rigorous, demonstrating use of math facts conceptual understanding and application. What are we doing to prepare our students? Close study of Common Core Learning Standards Professional study of implications for teaching practice and content Intensive work with math consultants Pre- and Post-Unit Performance Assessments Differentiated planning of customized units from multiple sources Early bird and after school support Building skill, fluency and stamina Strategies to Support Your Child in Math Have conversations that relate to everyday life and incorporate math questions (e.g., How many more streets/stops until we get off the bus?). Involve your child in math-related activities (e.g., cooking). Become familiar with the new math standards. Practice telling time everyday. Practice their facts so they are known with automaticity. Reason through questions with your child. Think of multiple ways with your child to solve problems Have your child explain what s/he is doing. Play board games.