Mathematics CCCs - Alternate Assessments (CA Dept of ...



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CCSS, Prioritized Mathematics CCCs, and Essential Understandings

All materials in this resource have been approved for public distribution with all necessary permissions. Selected excerpts are accompanied by annotated links to related media freely available online at the time of the publication of this document.

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The National Center and State Collaborative (NCSC) is applying the lessons learned from the past decade of research on alternate assessments based on alternate achievement standards (AA-AAS) to develop a multi-state comprehensive assessment system for students with significant cognitive disabilities. The project draws on a strong research base to develop an AA-AAS that is built from the ground up on powerful validity arguments linked to clear learning outcomes and defensible assessment results, to complement the work of the Race to the Top Common State Assessment Program (RTTA) consortia.

Our long-term goal is to ensure that students with significant cognitive disabilities achieve increasingly higher academic outcomes and leave high school ready for post-secondary options. A well-designed summative assessment alone is insufficient to achieve that goal. Thus, NCSC is developing a full system intended to support educators, which includes formative assessment tools and strategies, professional development on appropriate interim uses of data for progress monitoring, and management systems to ease the burdens of administration and documentation. All partners share a commitment to the research-to-practice focus of the project and the development of a comprehensive model of curriculum, instruction, assessment, and supportive professional development. These supports will improve the alignment of the entire system and strengthen the validity of inferences of the system of assessments.

The contents of this lesson were developed as part of the National Center and State Collaborative under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, Susan.Weigert@). However, the contents do not necessarily represent the policy of the U.S. Department of Education and no assumption of endorsement by the Federal government should be made.

The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, color, creed, religion, national origin, sex, age, marital status, disability, public assistance status, veteran status, or sexual orientation.

These materials and documents were developed under the National Center and State Collaborative (NCSC) General Supervision Enhancement Grant and are consistent with its goals and foundations. Any changes to these materials are to be consistent with their intended purpose and use as defined by NCSC.

This document is available in alternative formats upon request.

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NCSC is a collaborative of 14 states and five organizations.

The states include (shown in blue on map): Arizona, Connecticut, District of Columbia, Florida, Georgia, Indiana, Louisiana, Pacific Assessment Consortium (PAC-6)[1], Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, and Wyoming.

Tier II states are partners in curriculum, instruction, and professional development implementation but are not part of the assessment development work. They are (shown in orange on map): Arkansas, California, Delaware, Idaho, Maine, Maryland, Montana, New Mexico, New York, Oregon, and U.S. Virgin Islands.

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The five partner organizations include: The National Center on Educational Outcomes (NCEO) at the University of Minnesota, The National Center for the Improvement of Educational Assessment (Center for Assessment), The University of North Carolina at Charlotte, The University of Kentucky, and edCount, LLC.

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150 Pillsbury Drive SE

207 Pattee Hall

Minneapolis, MN 55455

Phone: 612-708-6960

Fax: 612-624-0879



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CCSS, Prioritized Mathematics CCCs, and Essential Understandings

January 2014

Table of Contents

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 3 6

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 4 9

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 5 13

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 6 17

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 7 22

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 8 25

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for High School 29

National Center State Collaborative CCSS, Prioritized Mathematics CCCs, and Essential Understandings

NCSC CCSS, Prioritized Mathematics CCCs, and EUs for Grade 3

|Domain |CCSS |CCC |Essential Understandings |

|Operations & Algebraic |3.OA.A.1 Interpret products of whole numbers, e.g., |3.NO.2d3 Solve multiplication problems with neither |Create an array of sets (e.g., 3 rows of 2). |

|Thinking |interpret 5 × 7 as the total number of objects in 5 |number greater than 5. | |

| |groups of 7 objects each. For example, describe a | | |

| |context in which a total number of objects can be | | |

| |expressed as 5 × 7. | | |

|Operations & Algebraic |3.OA.D.8 Solve two-step word problems using the four |3.NO.2e1 Solve or solve and check one or two-step word |Combine (+), decompose (-), and multiply (x) with |

|Thinking |operations. Represent these problems using equations |problems requiring addition, subtraction or |concrete objects; use counting to get the answers. |

| |with a letter standing for the unknown quantity. Assess|multiplication with answers up to 100. |Match the action of combining with vocabulary (i.e., in|

| |the reasonableness of answers using mental computation | |all; altogether) or the action of decomposing with |

| |and estimation strategies including rounding. | |vocabulary (i.e., have left; take away) in a word |

| | | |problem. |

|Operations & Algebraic |3.OA.D.9 Identify arithmetic patterns (including |3.PRF.2d1 Identify multiplication patterns in a real |Concrete understanding of a pattern as a set that |

|Thinking |patterns in the addition table or multiplication |world setting. |repeats regularly or grows according to a rule; Ability|

| |table), and explain them using properties of | |to identify a pattern that grows (able to show a |

| |operations. For example, observe that 4 times a number | |pattern) (shapes, symbols, objects). |

| |is always even, and explain why 4 times a number can be| | |

| |decomposed into two equal addends. | | |

|Number & Operations in Base |3.NBT.A.1 Use place value understanding to round whole |3.NO.1j3 Use place value to round to the nearest 10 or |Identify ones or tens in bundled sets – |

|Ten |numbers to the nearest 10 or 100. |100. |Similar/different with concrete representations (i.e., |

| | | |is this set of manipulatives (8 ones) closer to this |

| | | |set (a ten) or this set (a one)?). |

|Number & Operations in Base |3.NBT.A.2 Fluently add and subtract within 1000 using |3.NO.2c1 Solve multi-step addition and subtraction |Combine (+) or decompose (-) with concrete objects; use|

|Ten |strategies and algorithms based on place value, |problems up to 100. |counting to get the answers. |

| |properties of operations, and/or the relationship | | |

| |between addition and subtraction. | | |

|Number & |3.NF.A.1 Understand a fraction 1/b as the quantity |3.NO.1l3 Identify the fraction that matches the |Identify part and whole when item is divided. Count the|

|Operations—Fractions |formed by 1 part when a whole is partitioned into b |representation (rectangles and circles; halves, |number of the parts selected (3 of the 4 parts; have |

| |equal parts; understand a fraction a/b as the quantity |fourths, and thirds, eighths). |fraction present but not required to read ¾). |

| |formed by a parts of size 1/b. | | |

|Number & |3.NF.A.3d Compare two fractions with the same numerator|3.SE.1g1 Use =, to compare two fractions with |Concrete representation of a fractional part of a whole|

|Operations—Fractions |or the same denominator by reasoning about their size. |the same numerator or denominator. |as greater than, less than, equal to another. |

| |Recognize that comparisons are valid only when the two | | |

| |fractions refer to the same whole. Record the results | | |

| |of comparisons with the symbols >, =, or |group/row at a time. |

| |5. Represent verbal statements of multiplicative |10. | |

| |comparisons as multiplication equations. | | |

|Operations & Algebraic |4.OA.A.2 Multiply or divide to solve word problems |4.PRF.1e3 Solve multiplicative comparisons with an |Identify visual multiplicative comparisons (e.g., which|

|Thinking |involving multiplicative comparison, e.g., by using |unknown using up to 2-digit numbers with information |shows two times as many tiles as this set?). |

| |drawings and equations with a symbol for the unknown |presented in a graph or word problem (e.g., an orange | |

| |number to represent the problem, distinguishing |hat cost $3. A purple hat cost 2 times as much. How | |

| |multiplicative comparison from additive comparison. |much does the purple hat cost? [3 x 2 = p]). | |

|Operations & Algebraic |4.OA.A.3 Solve multistep word problems posed with whole|4.NO.2e2 Solve or solve and check one or two step word |Select the representation of manipulatives on a graphic|

|Thinking |numbers and having whole-number answers using the four |problems requiring addition, subtraction, or |organizer to show addition/multiplication equation; |

| |operations, including problems in which remainders must|multiplication with answers up to 100. |Match to same for representations of equations with |

| |be interpreted. Represent these problems using | |equations provided (may be different objects but same |

| |equations with a letter standing for the unknown | |configuration). |

| |quantity. Assess the reasonableness of answers using | | |

| |mental computation and estimation strategies including | | |

| |rounding. | | |

|Number & Operations in Base |4.NBT.A.3 Use place value understanding to round |4.NO.1j5 Use place value to round to any place (i.e., |Identify ones, tens, hundreds in bundled sets – |

|Ten |multi-digit whole numbers to any place. |ones, tens, hundreds, thousands). |Similar/different with concrete representations (i.e., |

| | | |is this set of manipulatives (8 tens) closer to this |

| | | |set (a hundred) or this set (a ten)?). |

|Number & |4.NF.A.1 Explain why a fraction a/b is equivalent to a |4.NO.1m1 Determine equivalent fractions. |Equivalency: what is and what is not equivalent; this |

|Operations—Fractions |fraction (n × a)/(n × b) by using visual fraction | |may begin with numbers/sets of objects: e.g., 3=3 or |

| |models, with attention to how the number and size of | |two fraction representations that are identical (two |

| |the parts differ even though the two fractions | |pies showing 2/3). |

| |themselves are the same size. Use this principle to | | |

| |recognize and generate equivalent fractions. | | |

|Number & |4.NF.A.2 Compare two fractions with different |4.NO.1n2 Compare up to 2 given fractions that have |Differentiate between parts and a whole. |

|Operations—Fractions |numerators and different denominators, e.g., by |different denominators. | |

| |creating common denominators or numerators, or by | | |

| |comparing to a benchmark fraction such as 1/2. | | |

| |Recognize that comparisons are valid only when the two | | |

| |fractions refer to the same whole. Record the results | | |

| |of comparisons with symbols >, =, or , =, or ................
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