Jeanne Simpson AMSTI Math Specialist March 10, 2015 DeKalb County 6-8 Math Jeanne Simpson AMSTI Math Specialist March 10, 2015

Getting to Know You Name School Grade

He who dares to teach must never cease to learn. John Cotton Dana The new COS offers many opportunities for us to learn – new content, new teaching strategies, higher expectations for students, filling in gaps during the transition.

Agenda Aspire Major Work of the Grade Wiring Diagram Standards for Mathematical Practice Content Standards

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ACT Provides the Following: a standards-based system of assessments to monitor progress toward college and career readiness from grade 3 through early high school, connecting each grade level to the next statewide assessment, data management and reporting functions for all students, districts, schools, aggregated and disaggregated groups of learners, and the individual learner alignment with the ACT College Readiness Benchmarks student outcomes aligned to the Domain and Cluster reporting categories of the Common Core State Standards capability for predicting outcomes on the ACT Quickly….point out alignment to CCSS. This is all part of the state package, according to the ACT website. If any of the following sounds like it would be helpful to you, contact your system testing coordinator. Our state may not have released some of these features to systems, or ACT may not be finished developing all of this?

Assessments assessments in summative, interim and classroom formats summative content areas of English, math, reading, science and writing multiple question types including multiple choice, constructed response and technology-enhanced items online delivery of assessments using state-of-the-art technology while also offering paper-and-pencil testing options capability to create a personal needs profile for students on an individual education plan (IEP) Quickly…anything you didn’t know?

Interim Assessments Sounds like a benchmark test. Maybe teachers can get a preview of the test here?

Classroom Assessments Wow! 5 per grade per content area. 5 items covering 2 standards, 15-20 minutes. Sounds rigorous, might be helpful to see what types of questions are asked?

Data Reporting online reporting for professionals based on approval levels capability for state downloads of data to secure district websites capability for district downloads of data to secure district sites capability for school downloads of data to secure school sites for parental review capability of paper reporting for parental review

Score Scale The high score for 3rd grade is higher than the benchmark for 10th grade. This tells me that there should be some questions on each test that a proficient student may not be able to answer.

Sustainability ongoing research, support, and validation of the system to reflect changes in college and career readiness standards flexible professional development on the state, district or school levels If the standards change, the test will change? PD!!!! Haven’t seen any of this yet.

http://www. discoveractaspire http://www.discoveractaspire.org/assessments/summative/ Content Specifications – Technical Bulletin #1 “The ACT Aspire mathematics assessments emphasize quantitative reasoning frequently applied to real-world contexts rather than memorization of formulas or computational skills. “ (p. 26) Some items give the formula(s) they need, but others do not. “Students are allowed and expected to strategically use acceptable calculators on the ACT Aspire mathematics assessments for Grade 6 and above.” (p. 27) Paper-and-pencil tests test do not have technology-enhanced items. Multiple choice items are used in their place. (p. 27) I didn’t copy this bulletin for them, but the link is on our website. I pulled out info that I thought they might find interesting.

Constructed response items are worth 4 points each. I found the information on point values in the Technical Bulletin. This chart and the times came from the link at the top of the screen. Selected response and technology enhanced items are worth 1 point each. Constructed response items are worth 4 points each.

Reporting Categories All questions are either measuring Grade Level Progress – mathematical topics new to the grade Foundation – topics learned in previous grades Some questions are also categorized as Modeling – questions that assess understanding of mathematical models and their creation, interpretation, evaluation, and improvement Justification and Explanation – giving reasons for why things work as they do, where students create a mathematical argument to justify (constructed response)

Points by category and grade.

How does ASPIRE match the CCSSM? “Through grade 7 the two are the same.” (page 5) “Across all parts of the test, students can apply Mathematical Practices to help them demonstrate their mathematical achievement.” (page 2) This is from the Exemplar packet. I copied these pages for the handout.

Justification and Explanation Level 1 – students should have a fluent command of these skills Level 2 – most closely aligned with grade level focus Level 3 – more advanced As students progress from grade to grade, expectations increase according to which JE skill belongs to which level. Some level 3 JE skills will become level 2, and some level 2 will become level 1. A full-credit response shows evidence of the required level of JE skills needed to solve the problem and applies these skills to complete the task. Evaluated by trained scorers. From exemplar packet. Page 2. See pages 3-4 for a detailed progression of JE skills.

Depth of Knowledge “…assessing new topics for the grade and whether students continue to strengthen their mathematical core. Within this structure of content comes a level of rigor represented in part by a distribution of depth of knowledge (DOK) through Webb’s level 3. The Foundation component includes only DOK level 2 and level 3 because the component is about assessing how well students have continued to strengthen their mathematical core. Across all parts of the test, students can apply Mathematical Practices to help them demonstrate their mathematical achievement.” This information is also included in Quality Core training. This seems to be new for a lot of teachers.

Webb’s Depth of Knowledge Recall and Reproduction Skills and Concepts Strategic Thinking / Reasoning Extended Thinking Handout. There is also another handout about DOK in the packet and more links on the website.

Percentage of Points by DOK 6th Grade 7th Grade 8th Grade DOK 1 7 – 15 % 8 – 15 % DOK 2 33 – 41 % 30 – 38 % DOK 3 48 – 57 % 51 – 58 % Not many Level 1’s!!!! Foundation questions are DOK 2 and 3.

Practice Test http://www.discoveractaspire.org/assessments/test-items/ UN: math PW: actaspire This is a 6-8 test with questions from multiple grade levels. I have copied selected questions for the handout. The Exemplar packet also contains these questions with a detailed explanation of correct response.

5.NBT.B MP3 N(13-15) 6-8 Foundation JE Level 3 DOK Level 3 Explain the different pieces of information given for each question. 5.NBT.B – the B at the end refers to the 2nd cluster in the 5th grade NBT standard. Grade level progress question for 5th grade. Math Practice 3 – Construct viable arguments and critique the reasoning of others. N(13-15) – ACT CCRStandards. The numbers refer to a specific score range. This is something that a student who scored 13-15 are likely to know and be able to do. 6-8 Foundation question for 6-8 Justification and explanation level DOK level

8.F.A MP -- F(20-23) 8 Grade Level Progress JE Level -- DOK Level 2 This question does not exhibit a math practice or justification and explanation.

6.G.A MP3 G(20-23) 6 Grade Level Progress JE Level 3 DOK Level 3 7-8 Foundation JE Level 3 DOK Level 3

Multiple levels Multiple problems with common information Questions are independent of each other. It is not necessary to get one correct in order to correctly answer the others. Students must extract only the information needed for a particular question.

7.EE.B MP4 A(24-27) 7 Grade Level Progress JE Level -- DOK Level 3 8 Foundation JE Level -- DOK Level 2 MP4 – I’m thinking that this will also count for modeling Different DOK levels for different grades.

6.SP.B MP-- S(16-19) 6 Grade Level Progress JE Level -- DOK Level 3 7-8 Foundation JE Level -- DOK Level 2 6th grade example

More Practice Items www.illustrativemathematics.org http://www.parcconline.org/samples/item-task-prototypes http://www.smarterbalanced.org/smarter-balanced-assessments/ https://www.engageny.org/resource/new-york-state-common-core-sample-questions More places to get rigorous problems based on the standards. These are explained and linked to on the wiki.

Major Work of the Grades

Major Work of the Grade Share your list with your table group. Individually make a list of the four topics/standards that you spend the most time on in your grade. Share your list with your table group. On a piece of chart paper list all of the topics/standards suggested by your group. Record the number of teachers who listed each one. Identify where each topic is found in the College and Career Ready Standards. How does your list compare to the “Where to focus” handout?

Major Work of Grade 6

6th Grade Major Clusters Understand ratio concepts and use ratio reasoning to solve problems. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Apply and extend previous understandings of numbers to the system of rational numbers. Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Supporting – Solve real-world and mathematical problems involving area, surface area, and volume. Additional – multi-digit computation, common factors and multiples, statistics

Major Work of Grade 7

7th Grade Major Clusters Analyze proportional relationships and use them to solve real-world and mathematical problems. Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers. Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Supporting – random sampling, probability Additional – geometry, comparative inferences

Major Work of Grade 8

8th Grade Major Clusters Work with radicals and integer exponents Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Define, evaluate, and compare functions. Use functions to model relationship between quantities. Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Supporting – patterns of association in bivariate data Additional – volume of cylinders, cones, and spheres

Fluency Expectations Grade Required Fluency K Add/subtract within 5 1 2 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division (6.NS.2) Multi-digit decimal operations (6.NS.3) 7 Solve px + q = r, p(x + q) = r

The Wire Diagram Locate a standard in your grade band that requires students to build upon previous knowledge. High school teachers locate a standard in the 8th grade. Determine what standards from earlier grades must be mastered in order for students to be successful in this new learning. 2 minutes Background Information: Jason Zimba, one of the lead writers of the new standards, gave his opinion of how he sees the standards connected within and across grades. This wire diagram can help you see where a student has been, currently is, and a path forward through standards to become College and Career Ready. Give out the Table Handout on Zimba’s wiring diagram How do you understand the placement of standards into three parts of the school year (not a trimester system)? In Zimba’s wiring diagram, how would you account for the connection and flow between the standards that he presents? Explain the specifics of how math content is both connected and builds over time for your grade and for the surrounding grades.

How can progressions in the standards within and across grades be used to inform teaching and learning? Mathematics is a subject that builds understanding and skill on previous knowledge and experience. There are various ways to look at the connections between standards from grade to grade. However, would you teach the CCR standards in the Alabama COS, Mathematics in order? Standard #1, then Standard #2, then Standard #3, … Turn and talk with your shoulder partner about your thinking for one of the questions on the slide. 3 minutes Would you teach the CCRS in the Alabama COS Mathematics in order? Standard #1, then Standard #2, then Standard #3, …

For teaching and learning in your classroom, how do you see connections between the content standards? What standard would you teach before or after another standard? When would you teach a particular standard during the year? At the beginning of the year In the middle of the year At the end of the year A B C Are some standards foundational for multiple other standards? Read the slide. 1 minute Key standards are the result of either many standards building to one, or one standard that is a launching point into many other standards. Find an example of a key standard in the wiring diagram and study the progression. The A-B-C grouping is an attempt to show prerequisite skill and knowledge preceding later content. How would you order the content throughout a school year for the grade you teach?

Why is professional peer discussion about progressions important for the teaching and learning process? “Analysis and related discussion with your team is critical to develop mutual understanding of and support for consistent curricular priorities, pacing, lesson design, and the development of grade-level common assessments.” Together you can develop a greater understanding of the intent of each content standard cluster and how the standards are connected within and across grades. (Common Core Mathematics in a PLC at Work, Kanold, 2012, pg. 67) Take a moment to read the question and quote and reflect on the implications for your role as a CCRS Team member. 2 minutes

The Standards for Mathematical Practice Mathematically proficient students: Standard 1: Make sense of problems and persevere in solving them. Standard 2: Reason abstractly and quantitatively. Standard 3: Construct viable arguments and critique the reasoning of others. Standard 4: Model with mathematics. Standard 5: Use appropriate tools strategically. Standard 6: Attend to precision. Standard 7: Look for and make use of structure. Standard 8: Look for and express regularity in repeated reasoning. Notice that each practice standard begins with the words “Mathematically proficient students:” (CLICK X 8)to bring each standard onto screen. Read each standard. Keep in mind, these standards for mathematical practice are behaviors we want to develop in our students. (CLICK)

SMP Instructional Implementation Sequence Think-Pair-Share (1, 3) Showing thinking in classrooms (3, 6) Questioning and wait time (1, 3) Grouping and engaging problems (1, 2, 3, 4, 5, 8) Using questions and prompts with groups (4, 7) Allowing students to struggle (1, 4, 5, 6, 7, 8) Encouraging reasoning (2, 6, 7, 8) Can you see evidence of this in lesson plans?

SMP Proficiency Matrix   Students: (I) Initial (IN) Intermediate Advanced 1a Make sense of problems Explain their thought processes in solving a problem one way. Explain their thought processes in solving a problem and representing it in several ways. Discuss, explain, and demonstrate solving a problem with multiple representations and in multiple ways. 1b Persevere in solving them  Stay with a challenging problem for more than one attempt. Try several approaches in finding a solution, and only seek hints if stuck. Struggle with various attempts over time, and learn from previous solution attempts. 2 Reason abstractly and quantitatively Reason with models or pictorial representations to solve problems. Are able to translate situations into symbols for solving problems. Convert situations into symbols to appropriately solve problems as well as convert symbols into meaningful situations. 3a Construct viable arguments  Explain their thinking for the solution they found. Explain their own thinking and thinking of others with accurate vocabulary. Justify and explain, with accurate language and vocabulary, why their solution is correct. 3b Critique the reasoning of others.  Understand and discuss other ideas and approaches. Explain other students’ solutions and identify strengths and weaknesses of the solution. Compare and contrast various solution strategies and explain the reasoning of others. 4 Model with Mathematics Use models to represent and solve a problem, and translate the solution to mathematical symbols. Use models and symbols to represent and solve a problem, and accurately explain the solution representation. Use a variety of models, symbolic representations, and technology tools to demonstrate a solution to a problem. 5 Use appropriate tools strategically  Use the appropriate tool to find a solution.  Select from a variety of tools the ones that can be used to solve a problem, and explain their reasoning for the selection. Combine various tools, including technology, explore and solve a problem as well as justify their tool selection and problem solution. 6 Attend to precision  Communicate their reasoning and solution to others.  Incorporate appropriate vocabulary and symbols when communicating with others.  Use appropriate symbols, vocabulary, and labeling to effectively communicate and exchange ideas. 7 Look for and make use of structure Look for structure within mathematics to help them solve problems efficiently (such as 2 x 7 x 5 has the same value as 2 x 5 x 7, so instead of multiplying 14 x 5, which is (2 x 7) x 5, the student can mentally calculate 10 x 7. Compose and decompose number situations and relationships through observed patterns in order to simplify solutions. See complex and complicated mathematical expressions as component parts. 8 Look for and express regularity in repeated reasoning Look for obvious patterns, and use if/ then reasoning strategies for obvious patterns. Find and explain subtle patterns. Discover deep, underlying relationships, i.e. uncover a model or equation that unifies the various aspects of a problem such as discovering an underlying function. Pair-Share Questioning/Wait Time Grouping/Engaging Problems Questioning/Wait Time Grouping/Engaging Problems Showing Thinking Grouping/Engaging Problems Grouping/Engaging Problems Encourage Reasoning Showing Thinking Questioning/Wait Time Grouping/Engaging Problems Pair-Share Questioning/Wait Time Grouping/Engaging Problems Grouping/Engaging Problems Questions/Prompts for Groups Showing Thinking Grouping/Engaging Problems Showing Thinking Grouping/Engaging Problems Showing Thinking Allowing Struggle Encourage Reasoning Questions/Prompts for Groups Allowing Struggle Encourage Reasoning Grouping/Engaging Problems Allowing Struggle Encourage Reasoning

Jeanne Simpson jeanne.simpson@uah.edu acos2010.wikispaces.com Contact Information Jeanne Simpson jeanne.simpson@uah.edu acos2010.wikispaces.com