Mathematics 2012-2013 How will Instructional Shifts demanded of the Common Core learning standards support our children when taking state exams? CFN609 Compiled by Karen Cardinali Parent Coordinators’ Workshop February 14, 2013

The Common Core Learning Standards (CCLS) call for changes in what is expected from a teacher’s instructional approach. More specifically, the CCLS demand six key shifts in instruction in mathematics, summarized in the table below.

Teacher Team Work: Focus: Focus strongly where the standards focus (Content and Practices) Coherence: Link across grades and to major topics within grades Rigor: Requires fluency, application and deep understanding

The Grades 3–8 Mathematics New York State Testing Program (NYSTP) has been redesigned to measure student learning aligned with the instructional shifts necessitated by the CCLS. The 2013 math tests will be administered from Wednesday, April 24 – Friday, April 26. All mathematics tests will be administered over three days.

TESTING 2013

The content for all tests will be based on the Common Core Learning Standards (CCLS). The Domain Level Test blueprint (percentage of test point breakdown) will be as follows:

Standards recommended for greater emphasis that are designated for instruction after the administration of the 2013 Common Core Mathematics Test, while not tested, will be fundamental in ensuring that students are prepared for the next grade level instruction.

The Breakdown and Test Design for each day is as follows: Grade 3

Question Formats The 2013 Common Core Mathematics Test contains multiple-choice, short-response (2-Point rubric), and extended-response (3-Point rubric) questions. For multiple-choice questions, students select the correct response from four answer choices. For short- and extended-response questions, students write an answer to an open-ended question and may be required to show their work. In some cases, they may be required to explain, in words, how they arrived at their answers.

Multiple Choice Questions Are designed to assess CCLS for Mathematics. Mathematics multiple-choice questions will mainly be used to assess standard algorithms and conceptual standards. They will incorporate both Standards and Standards for Mathematical Practices, some in real-world applications. Many of these questions will require students to complete multiple steps. Likewise, many of these questions are linked to more than one standard, drawing on the simultaneous application of multiple skills and concepts. Within answer choices, distractors will all be based on plausible missteps.

Short-Response Questions Are questions are similar to past 2-Point questions, requiring students to complete a task and show their work. Like multiple-choice questions, short-response questions will often require multiple steps, the application of multiple mathematics skills, and real-world applications. Many of the short-response questions will cover conceptual and application standards.

Extended-Response Questions Are questions are similar to past 3- Point questions, asking students to show their work in completing two or more tasks or one more extensive problem. Extended-response questions allow students to show their understanding of mathematical procedures, conceptual understanding, and application. Extended-response questions may also assess student reasoning and the ability to critique the arguments of others.

Reflection of the shifts in test questions. Questions from previous tests were simpler, one or two steps, or were heavily scaffolded. The new questions will requires multiple steps involving the interpretation of operations. Questions from the past were heavy on pure fluency in isolation. The new questions require conceptual understanding and fluency in order to complete test questions. Questions from past tests isolated the math. The new problems are in a real world problem context. Questions of old relied more on the rote use of a standard algorithm for finding answers to problems. The new questions require students to do things like decompose numbers and/or shapes, apply properties of numbers, and with the information given in the problem reach an answer. Relying solely on algorithms will not be sufficient. When we compare the tests from the past with the present, we see that:

New York State Mathematics Assessments: Current vs New York State Mathematics Assessments: Current vs. Common Core-Aligned ~ Grade 3  Actual New York State Test Item - 2009 Which two number sentences below have the same answer?   2 x 8 = ? 2 x 9 = ? 3 x 7 = ? 4 x 4 = ? A 2 x 8 = ? and 4 x 4 = ? B 2 x 8 = ? and 3 x 7 = ? C 2 x 9 = ? and 4 x 4 = ? D 2 x 9 = ? and 3 x 7 = ?

Common Core Sample Test Item: Grade 3 Part A: Fill in the blanks below with whole numbers greater than 1 that will make the number sentences true.   1. 63 ÷ ___ = 7 2. 63 = 21 × ___ 3. 21 = ___ × 7 4. 7 × (___ × ___ ) = 21 × 7 5. (21 × 3) ÷ ___ = 7 Part B: If the product of two whole numbers greater than 1 is 63, what could the two whole numbers be? _______, ________

Actual New York State Test Item - 2010 New York State Mathematics Assessments: Current vs. Common Core-Aligned ~ Grade 5 Actual New York State Test Item - 2010  The total number of people who visited the Ocean Adventure Park last year was 7,040,836. What is the value of the digit 4 in this number? A four B forty C four thousand D forty thousand

Common Core-aligned Sample Test Item: Grade 5 How many times greater is the value of the digit 5 in 583,607 than the value of the digit 5 in 362,501? A 10 times B 100 times C 1,000 times D 10,000 times

Actual New York State Test Items - 2010 New York State Mathematics Assessments: Current vs. Common Core-Aligned ~ Grade 5 Actual New York State Test Items - 2010 Which number represents two million forty-five thousand five hundred five? A 2,045,055 B 2,450,505 C 2,045,505 D 2,450,055

New York State Mathematics Assessments: Current vs New York State Mathematics Assessments: Current vs. Common Core-Aligned ~ Grade 5 Heidi records the batting averages of different players on a baseball team. Which list correctly shows the batting averages in order from least to greatest? A 0.353, 0.309, 0.179, 0.172 B 0.309, 0.353, 0.179, 0.172 C 0.179, 0.172, 0.309, 0.353 D 0.172, 0.179, 0.309, 0.353 **Decimals and whole numbers were not assessed at the same time!

Common Core-aligned Sample Test Item Grade 5 1(10,000) + 2(1,000) + 4(100) + 3(10) + 2(1) + 5(1/10) + 3(1/100).   Which number below is one-tenth of the expanded form above? A 12422.53 B 1243.253 C 12432.53 D 12432.43

Grade 4 Extended-response Question 2 Candy wants to buy herself a new bicycle that cost $240. Candy has already saved $32, but she needs to make a plan so she can save the rest of the money she needs. She decides to save the same amount of money, x dollars, each month for the next four months. Write an equation that helps Candy determine the amount of money she must save each month. Equation ___________________________________________________ Solve the equation to find the amount of money she must save each month to meet her goal of buying a bicycle. Show your work. Answer $_________________________________________________ Show briefly and explain to teachers that this is a sample of a grade 4 0 – 3 point question that is aligned with Common Core learning standard 4.OA.3 – Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Move to next slide. 25

Mathematics 2-point Holistic Rubric Score Point Description 2 Points A two-point response answers the question correctly. This response demonstrates a thorough understanding of the mathematical concepts but may contain errors that do not detract from the demonstration of understanding indicates that the student has completed the task correctly, using mathematically sound procedures 1 Point A one-point response is only partially correct.   indicates that the student has demonstrated only a partial understanding of the mathematical concepts and/or procedures in the task correctly addresses some elements of the task may contain an incorrect solution but applies a mathematically appropriate process may contain correct numerical answer(s) but required work is not provided 0 Points A zero-point response is incorrect, irrelevant, incoherent, or contains a correct response arrived using an obviously incorrect procedure. Although some parts may contain correct mathematical procedures, holistically they are not sufficient to demonstrate even a limited understanding of the mathematical concepts embodied in the task. Refer participants to the 2-point Holistic Rubric in their packet. Explanation of 2-point, short-response, rubric. The 2-point rubric applies to all grade 3 – 8 short-response questions. Responses that demonstrate ‘thorough understanding’, ‘partial understanding’, ‘incorrect, irrelevant, incoherent’ and ‘insufficient for limited understanding’ are further defined by the approved guide papers. It is important to understand the differences in the language at each score point on the rubric. The Guide papers will show how the student responses are held to the criteria in the rubric.

Mathematics 3-point Holistic Rubric Score Point Description 3 Points A three-point response answers the question correctly.   This response demonstrates a thorough understanding of the mathematical concepts but may contain errors that do not detract from the demonstration of understanding indicates that the student has completed the task correctly, using mathematically sound procedures 2 Points A two-point response is partially correct. demonstrates partial understanding of the mathematical concepts and/or procedures embodied in the task addresses most aspects of the task, using mathematically sound procedures may contain an incorrect solution but provides complete procedures, reasoning, and/or explanations may reflect some misunderstanding of the underlying mathematical concepts and/or procedures 1 Point A one-point response is incomplete and exhibits many flaws but is not completely incorrect. demonstrates only a limited understanding of the mathematical concepts and/or procedures embodied in the task may address some elements of the task correctly but reaches an inadequate solution and/or provides reasoning that is faulty or incomplete exhibits multiple flaws related to misunderstanding of important aspects of the task, misuse of mathematical procedures, or faulty mathematical reasoning reflects a lack of essential understanding of the underlying mathematical concepts may contain correct numerical answer(s) but required work is not provided 0 Points A zero-point response is incorrect, irrelevant, incoherent, or contains a correct response arrived at using an obviously incorrect procedure. Although some parts may contain correct mathematical procedures, holistically they are not sufficient to demonstrate even a limited understanding of the mathematical concepts embodied in the task. Explanation of 3-point, extended-response, rubric. The 3-point rubric applies to all grade 3 – 8 extended-response questions. Responses that demonstrate ‘thorough understanding’, ‘partial understanding’, ‘limited understanding’, ‘incorrect, irrelevant, incoherent’ and ‘insufficient for limited understanding’ are further defined by the approved guide papers. It is important to understand the differences in the language at each score point on the rubric. The Guide papers will show how the student responses are held to the criteria in the rubric. 27

For additional information on citywide initiatives: For more information about the Grades 3–8 Mathematics Testing Program Guidance: September-to-April / May-to-June Common Core Learning Standards, please refer to http://www.p12.nysed.gov/assessment/math/math-ei.html. For additional information on citywide initiatives: www.schools.nyc.gov

Thank you for your attention today and your dedication every day!