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Project ACCESS Final Report Outline

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Project ACCESS Final Report Outline

    Common Core State Standards (CCSS) for Mathematics

    2007 Mississippi Mathematics Framework Revised (MMFR)

    Alignment Analysis

    Mississippi Department of Education

    Tested Grades and Transitions to Algebra

    Program Associates:

    María E. Torres, MA, Lead

    Camille Chapman, MEd

    September 14, 2010

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    CCSS/MS Framework Alignment Analysis

    Table of Contents

     Introduction 3

     Tested Grades 5

     Grade 3 6

     Grade 4 14

     Grade 5 24

     Grade 6 33

     Grade 7 44

     Grade 8 Pre-Algebra 56

     Algebra I 66

     Non-Tested Grade 75

     Transitions to Algebra 76

    SECC | Mathematics 2

    CCSS/MS Framework Alignment Analysis

    Introduction

Purpose of the Work:

    The purpose of the alignment analysis of the 2007 Mississippi Mathematics Framework Revised (MMFR) with the June 2010, Common Core

    State Standards (CCSS) for Mathematics is to provide guidance to the Mississippi Department of Education (MDE) in the possible implementation

    of the CCSS for 20112012. The analysis will assist MDE in identifying the objectives in the MMFR that will remain or be modified. MDE will conduct a stakeholders meeting in Fall 2010, to obtain input regarding modifications to the existing Mississippi objectives.

Caveats:

    To perform this task, the staff of the Southeast Comprehensive Center (SECC) recognized the following situations:

     There are many inherent concepts and skills that are not stated explicitly that students need to have to fulfill the objectives of the MMFR

     Technical terms may have different names but still may have the same meaning.

To this end, SECC staff included the MMFR objective that best matched the CCSS, even though the alignment was not necessarily a perfect

    match due to terminology, inclusion, and/or focus.

The notations used in this alignment analysis are taken from both of the documents used, the CCSS for mathematics and the 2007 MMFR. Some

    of the footnotes referenced in the alignment analysis indicate the use of the CCSR glossary and tables that are not included here but are found at

    the indicated uniform resource locators (URLs), cited in the references.

Reading the CCSS for Mathematics:

    Each CCSS for mathematics denotes what students should know and be able to do and are found by grade level.

Within each grade level, standards are found in large groups called domains. For example, 6-SP denotes the grade level six and the domain

    Statistics and Probability. Grade 6 has five domains.

Within each domain are clusters of related standards. The domain of Statistics and Probability in grade six has two clusters, develop

    understanding of statistical variability and summarize and describe distributions.

Reading the 2007 Mississippi Mathematics Framework Revised

    The MMFR is organized by grade level (K8) and by secondary courses (grades 912). The five process standards (problem solving,

    communication, reasoning and proof, connections, and representation) should permeate all instructional practices.

The framework is comprised of five content strands Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and

    Probability.

SECC | Mathematics 3

    CCSS/MS Framework Alignment Analysis

Beneath each content strand are competencies. The competencies are presented in outline form for consistency and for easy reference

    throughout the framework. Competencies are intentionally broad in order to allow school districts and teachers the flexibility to create a curriculum that meets the needs of their students.

    Beneath each competency are objectives. The objectives indicate how competencies can be fulfilled through a progression of content and concepts at each grade level and course. Many of the objectives are interrelated rather than sequential, which means that objectives are not necessarily taught in the specific order in which they are presented. Multiple objectives can and should be taught at the same time.

    For matching purposes, the alignment analysis will be done at the CCSS standard level to the MMFR objective level only.

    The Format of the Mathematics Alignment Analysis rdthThis alignment analysis includes the grade levels that are tested in the state of Mississippi, 3 through 8 grade and Algebra I. For each grade level, SECC staff started with a key describing the numeration systems used by the CCSS and MMFR and then used a three-column table, with the first column containing the CCSS for that grade level, the second column containing the matching MMFR objective, if any for that grade level, and the third column containing comments about observations and other information. The last section in the table includes the MMFR objectives that did not match with any CCSS at that grade level.

References

    Mississippi State Department of Education. (2007). Mississippi mathematics framework revised. Jackson, MS: Author. Retrieved from http://www.mde.k12.ms.us/acad/id/curriculum/Math/index.htm

    National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010, June 2). K12 common core state standards for mathematics. Washington, DC: Author. Retrieved from http://corestandards.org/the-standards/mathematics

    SECC | Mathematics 4

CCSS/MS Framework Alignment Analysis

TESTED GRADES

SECC | Mathematics 5

    CCSS/MS Framework Alignment Analysis

    COMMON CORE STATE STANDARDS (CCSS) FOR MATHEMATICS

    2007 MISSISSIPPI MATHEMATICS FRAMEWORK REVISED (MMFR)

    ALIGNMENT ANALYSIS

    Grade 3

CCSS Key: MMFR Content Standards Key:

    Operations and Algebraic Thinking (OA) Numbers and Operations (1) Number and Operations in Base Ten (NBT) Algebra (2)

    Numbers and OperationsFractions (NF) Geometry (3)

    Measurement and Data (MD) Measurement (4)

    Geometry (G) Data Analysis and Probability (5)

     Depth of Knowledge (DOK)

Common Core State Standards for Mathematics Comments 2007 MS Mathematics Framework Revised

    3.OA.1. 3.1.f. Interpreting products and modeling Interpret products of whole numbers, e.g., interpret Model multiplication using arrays, equal-sized multiplication are not synonymous. 5 × 7 as the total number of objects in 5 groups of 7 groups, area models, and equal-sized moves However, in modeling multiplication, a objects each. For example, describe a context in on the number line. (DOK 2) student might demonstrate a total which a total number of objects can be expressed number of objects in n groups of n

    as 5 × 7. objects each.

    3.OA.2. 3.1.g. Both the CCSS and the MMFR Interpret whole-number quotients of whole Model division with successive or repeated represent whole number quotients by numbers, e.g., interpret 56 ? 8 as the number of subtraction, partitioning, and sharing. (DOK 2) partitioning.

    objects in each share when 56 objects are

    partitioned equally into 8 shares, or as a number of

    shares when 56 objects are partitioned into equal

    shares of 8 objects each. For example, describe a

    context in which a number of shares or a number of

    groups can be expressed as 56 ? 8.

    3.OA.3. 3.1.f. The MMFR does not specify that Use multiplication and division within 100 to solve Model multiplication using arrays, equal-sized students use multiplication and

    word problems in situations involving equal groups, groups, area models, and equal-sized moves division to solve word problems.

    arrays, and measurement quantities, e.g., by using on the number line. (DOK 2)

    drawings and equations with a symbol for the 3.1.g. 1unknown number to represent the problem. Model division with successive or repeated

    subtraction, partitioning, and sharing. (DOK 2) 1See Glossary, Table 2.

    SECC | Mathematics 6

    CCSS/MS Framework Alignment Analysis

Common Core State Standards for Mathematics Comments 2007 MS Mathematics Framework Revised

    3.OA.4. The MMFR does not specify that Determine the unknown whole number in a students determine the unknown multiplication or division equation relating three whole number in a multiplication or whole numbers. For example, determine the division equation until grade 4.2.b.

    unknown number that makes the equation true in

    each of the equations 8 × ? = 48, 5 = ? ? 3,

    6 × 6 = ?.

    3.OA.5. 3.2.c. The MMFR does not introduce the Apply properties of operations as strategies to Use real number properties to develop multiple distributive property until grade 4.2.d. 2multiply and divide. Examples: If 6 × 4 = 24 is algorithms and to solve problems. (DOK 2)

    known, then 4 × 6 = 24 is also known. - Associative property of addition

    (Commutative property of multiplication.) 3 × 5 × 2 - Commutative property of addition

    can be found by 3 × 5 = 15, then 15 × 2 = 30, or by - Identity property of addition

    5 × 2 = 10, then 3 × 10 = 30. (Associative property

    of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2

    = 16, one can ?nd 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8

    × 2) = 40 + 16 = 56. (Distributive property.)

    3.OA.6. 3.1.g. The MMFR does not introduce factors Understand division as an unknown-factor problem. Model division with successive or repeated and multiples until grade 4.1.l.

    For example, ?nd 32 ? 8 by ?nding the number that subtraction, partitioning, and sharing. (DOK 2)

    makes 32 when multiplied by 8.

    3.OA.7. 3.1.f. The MMFR does not specify that Fluently multiply and divide within 100, using Model multiplication using arrays, equal-sized students know from memory all strategies such as the relationship between groups, area models, and equal-sized moves products of two one-digit numbers by multiplication and division (e.g., knowing that 8 on the number line. (DOK 2) the end of grade 3; however grade × 5 = 40, one knows 40 ? 5 = 8) or properties of 4.1.i., ―recall multiplication and division operations. By the end of grade 3, know from 3.1.g. facts,‖ insinuates that students will be memory all products of two one-digit numbers. Model division with successive or repeated fluent by grade 4.

    subtraction, partitioning, and sharing. (DOK 2)

    2 Students need not use formal terms for these properties.

    SECC | Mathematics 7

    CCSS/MS Framework Alignment Analysis

Common Core State Standards for Mathematics Comments 2007 MS Mathematics Framework Revised

    3.OA.8. 3.2.b. Grade 3.2.b objective does not specify Solve two-step word problems using the four Determine the value of missing quantities or that students solve two-step word operations. Represent these problems using variables within equations or number problems. The MMFR does not specify equations with a letter standing for the unknown sentences, and justify the process used. (DOK Order of Operations until grade 7.1.a. 3quantity. Assess the reasonableness of answers ). 2) (see footnote

    using mental computation and estimation strategies 3including rounding.

    3.OA.9. 3.2.a. The MMFR does not specify that Identify arithmetic patterns (including patterns in the Create, describe, and extend growing and students explain patterns using addition table or multiplication table), and explain repeating patterns with physical materials and properties of operations.

    them using properties of operations. For example, symbols including numbers. (DOK 2)

    observe that 4 times a number is always even, and

    explain why 4 times a number can be decomposed 3.1.a.

    into two equal addends. Compose and decompose four-digit whole

    numbers with representations in words,

    physical models, and expanded and standard

    forms. (DOK 1)

    3.NBT.1. 3.1.c. Inherent in being able to round Use place value understanding to round whole Estimate sums and differences of whole numbers is the use of place value 4 numbers to the nearest 10 or 100.numbers to include strategies such as understanding.

    rounding. (DOK 2)

    3.NBT.2. 3.1.e.

    Fluently add and subtract within 1,000 using Add (up to three addends) and subtract four-

    strategies and algorithms based on place value, digit whole numbers with and without

    properties of operations, and/or the relationship regrouping. 4between addition and subtraction. (DOK 1)

    3.2.d.

    Model and identify the inverse relationships of

    addition/subtraction. (DOK 2)

    3.NBT.3. 3.1.f. The MMFR does not specify that Multiply one-digit whole numbers by multiples of 10 Model multiplication using arrays, equal-sized students multiply by multiples of 10. in the range 1090 (e.g., 9 × 80, 5 × 60) using groups, area models, and equal-sized moves

    strategies based on place value and properties of on the number line. (DOK 2) 4 operations.

    3This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order

    when there are no parentheses to specify a particular order (Order of Operations). 4A range of algorithms may be used.

    SECC | Mathematics 8

    CCSS/MS Framework Alignment Analysis

Common Core State Standards for Mathematics Comments 2007 MS Mathematics Framework Revised

    3.NF.1. 3.1.d. The MMFR does not specify that Understand a fraction 1/b as the quantity formed by Identify and model representations of fractions students understand a fraction as a 1 part when a whole is partitioned into b equal (halves, thirds, fourths, fifths, sixths, and whole partitioned. However, in parts; understand a fraction a/b as the quantity eighths). (DOK 1) modeling representations of fractions, 5formed by a parts of size 1/b. students are portioning the whole into

    parts.

    3.NF.2. The MMFR does not specify Understand a fraction as a number on the number representing fractions on the number 5line; represent fractions on a number line diagram. line. Representing a fraction by a. Represent a fraction 1/b on a number line defining the interval from 0 to 1 or the diagram by de?ning the interval from 0 to 1 as the use of benchmark numbers does not whole and partitioning it into b equal parts. appear in the MMFR until grade 5.1.k. Recognize that each part has size 1/b and that the

    endpoint of the part based at 0 locates the number

    1/b on the number line.

    b. Represent a fraction a/b on a number line

    diagram by marking off a lengths 1/b from 0.

    Recognize that the resulting interval has size a/b

    and that its endpoint locates the number a/b on the

    number line.

     3.NF.3. The MMFR does not specify that Explain equivalence of fractions in special cases, students understand or explain and compare fractions by reasoning about their fraction equivalence until grade 5.1.e. 5 size.The framework does not compare like a. Understand two fractions as equivalent (equal) if and unlike fractions until grade 5.1.a. they are the same size, or the same point on a

    number line.

    b. Recognize and generate simple equivalent

    fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the

    fractions are equivalent, e.g., by using a visual

    fraction model.

    c. Express whole numbers as fractions, and

    recognize fractions that are equivalent to whole

    numbers. Examples: Express 3 in the form

    3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at

    the same point of a number line diagram.

    d. Compare two fractions with the same numerator

    or the same denominator by reasoning about their

    SECC | Mathematics 9

    CCSS/MS Framework Alignment Analysis

Common Core State Standards for Mathematics Comments 2007 MS Mathematics Framework Revised

    size. Recognize that comparisons are valid only

    when the two fractions refer to the same whole.

    Record the results of comparisons with the symbols

    >, =, or <, and justify the conclusions, e.g., by using

    a visual fraction model.

    3.MD.1. The MMFR specifies that students tell Tell and write time to the nearest minute, and time to the hour, half-hour, quarter-

    measure time intervals in minutes. Solve word hour, and five-minute interval at grade problems involving addition and subtraction of time 2.4.b. The framework does not specify intervals in minutes, e.g., by representing the that students solve word problems problem on a number line diagram. involving the addition and subtraction

    of time intervals by representing the

    problem on a number line.

    3.MD.2. 3.4.c. The MMFR does not specify that Measure and estimate liquid volumes and masses Measure capacity, weight/mass, and length in students solve word problems using of objects using standard units of grams (g), both English and metric systems of the four operations involving masses 6kilograms (kg), and liters (l). Add, subtract, measurement. (DOK 1) or volumes.

    multiply, or divide to solve one-step word problems

    involving masses or volumes that are given in the

    same units, e.g., by using drawings (such as a

    beaker with a measurement scale) to represent the 7 problem.

    3.MD.3. 3.5.a

    Draw a scaled picture graph and a scaled bar graph Compare data and interpret quantities

    to represent a data set with several categories. represented on tables and different types of Solve one- and two-step ―how many more‖ and graphs (line plots, pictographs, and bar ―how many less‖ problems using information graphs), make predictions, and solve problems presented in scaled bar graphs. For example, draw based on the information. (DOK 3)

    a bar graph in which each square in the bar graph

    might represent 5 pets.

    5 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8. 6 Excludes compound units such as cm3 and finding geometric volume of a container. 7 Excludes multiplicative comparison problems (problems involving notions of ―times as much,‖ see Glossary, Table 2).

    SECC | Mathematics 10

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