RI Math K-8 GLEs revised 4.4.07

8/14/2019 RI Math K-8 GLEs revised 4.4.07

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http://www.ed.state.nh.us/Education/doe/organization/curriculum/NECAP/GLEs.htm


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Rhode Island K 8 Mathematics Grade-Level E

2 Final VersionJune, 2006Edited August 2, 2007

Reading the Mathematics GLEs

Grade 6 Grade 7

M(N&O)74 Accurately solves problems involving thaddition or subtraction of integers, raising numbers to whnumber powers, and determining square roots of perfect numbers and non-perfect square numbers.

M(N&O)74 Accurately solves problems involvinproportional reasoning; percents involving discounts,tax, or tips; and rates.

(IMPORTANT: Applies the conventions of order ofoperations including parentheses, brackets, or

exponents.)

M(N&O)64 Accurately solves problems involvingsingle or multiple operations on fractions (proper,improper, and mixed

), or decimals; and addition or

subtraction of integers; percent of a whole; or problemsinvolving greatest common factor or least commonmultiple.

(IMPORTANT: Applies the conventions of order ofoperations with and without parentheses.)

CONTENT AREA Mstands for mathematics.

STEM Bolded statementcommunicating main

curricular focus and is thesame or similar acrossgrades (K-12).

STRAND In thiscase, N&O

stands for Numberand Operations.

UNDERLINING Indicatesconcepts and skills that are new to agrade level.

BOLD BOX Indicates thestandards to be assessed on theNECAP state assessment; allother standards are guidance folocal curriculum andassessment.

GRADE LEVEgrade 8. Noticein a bold box- in

guide local currcolumn to the lestandard in the assessed in the


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Number and Operations ContinuedGrade 3 Grade 4

M(N&O)35 No GLE at this grade M(N&O)45 No GLE at this grade

M(N&O)33 Demonstrates conceptualunderstanding of mathematical operationsby

describing or illustrating the inverse relationshipbetween addition and subtraction of whole numbers;and the relationship between repeated addition andmultiplication using models, number lines, orexplanations. (State)

M(N&O)43 Demonstrates conceptualunderstanding of mathematical operationsby

describing or illustrating the relationship betweenrepeated subtraction and division (no remainders); theinverse relationshipbetween multiplication and divisiof whole numbers; or the addition or subtraction ofpositive fractional numbers with like denominators usmodels, number lines, or explanations. (State)

M(N&O)34 Accurately solves problems involvingaddition and subtraction with regrouping; the concept

of multiplication; and addition or subtraction ofdecimals (in the context of money). (State)

M(N&O)44 Accurately solves problems involvinmultiple operations on whole numbers or the use of thproperties of factors and multiples;and addition or

subtraction of decimals and positive proper fractionswith like denominators. (Multiplication limited to 2digits by 2 digits, and division limited to 1 digitdivisors.) (State)

(IMPORTANT: Applies the conventions of order ofoperations where the left to right computations are

modified only by the use of parentheses.)


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Geometry and Measurement continuedGrade K Grade 1

M(G&M)K7 Demonstrates conceptual understanding ofmeasurable attributes using comparative language to describeand compare attributes of objects (length [longer, shorter],

height [taller, shorter], weight [heavier, lighter], temperature[warmer, cooler], and capacity [more, less]); and comparesobjects visually and with direct comparison. (Local)

M(G&M)17 Demonstrates conceptual understandimeasurable attributes using comparative language to dand compare attributes of objects (length [longer, shorter

height [taller, shorter], weight [heavier, lighter], tempera[warmer, cooler], and capacity [more, less]); compares ovisually, with direct comparison, and using non-standard(Local)

M(G&M)K8 Determines elapsed and accrued time as itrelates to calendar patterns (days of the week, yesterday, today,and tomorrow), the sequence of events in a day; and identifiesa clock and calendar as measurement tools (days of week,months of the year). (Local)

M(G&M)18 Determines elapsed and accrued time arelates to calendar patterns (days of the week, months of year

), the sequence of events in a day; and recognizes anand on the hour. (Local)

M(G&M)K9 Demonstrates understanding of spatialrelationships using location and positionby using positionalwords to locate and describe where an object is found in the

environment. (Local)

M(G&M)19 Demonstrates understanding of spatialrelationships using location and positionbyusingposiwords (e.g., close by, on the right, underneath, above, be

to describe one location in reference to another on a mapdiagram, and in the environment. (Local)


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Geometry and Measurement continuedGrade 6 Grade 7

M(G&M)62 No GLE at this grade


M(G&M)64 Demonstrates conceptual understanding ofcongruencybypredicting and describing the transformationalsteps (reflections, translations, and rotations) needed to showcongruence (including the degree of rotation) and as the resultof composing and decomposing two- and three-dimensional

objects using models or explanations; and using line androtational symmetry to demonstrate congruent parts within ashape. (Local)

M(G&M)61 Uses properties or attributes of angles(right, acute, or obtuse) or sides (number of congruent

sides, parallelism, or perpendicularity) to identify,describe, classify, or distinguish among different typesof triangles (right, acute, obtuse, equiangular, scalene,isosceles, or equilateral) or quadrilaterals (rectangles,squares, rhombi, trapezoids, or parallelograms). (State)

M(G&M)71 Uses properties of angle relationshipresulting from two or three intersecting lines (adjacen

angles, vertical angles, straight angles, or anglerelationships formed by two non-parallel lines cut by transversal), or two parallel lines cut by a transversal solve problems. (State)

M(G&M)72 Applies theorems or relationships(triangle inequality or sum of the measures of interiorangles of regular polygons) to solve problems. (State)

M(G&M)63 Uses properties or attributes (shape ofbases, number of lateral faces, number of bases, number ofedges, or number of vertices

) to identify, compare, ordescribe three-dimensional shapes (rectangular prisms,triangular prisms, cylinders, spheres, pyramids, or cones).(State)

M(G&M)74 Applies the concepts of congruencybsolving problems on a coordinate plane involvingreflections, translations, or rotations. (State)


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M(G&M)65 Demonstrates conceptual

understanding of similarity by describing theproportional effect on the linear dimensions of polygonsor circles when scaling up or down while preserving theangles of polygons, or by solving related problems(including applying scales on maps). Describes effectsusing models orsc explanations. (State)

M(G&M)75 Applies concepts of similarity bysolving problems involving scaling up or down and

their impact on angle measures, linear dimensions andareas of polygons, and circles when the lineardimensions are multiplied by a constant factor.Describes effects using models orsc explanations.(State)

M(G&M)66 Demonstrates conceptualunderstanding of perimeter ofpolygons, the area ofquadrilaterals or triangles, and the volume ofrectangularprisms by using models, formulas, or by solving

problems; and demonstrates understanding of therelationships of circle measures (radius to diameter anddiameter to circumference) by solving related problems.Expresses all measures using appropriate units. (State)

M(G&M)76 Demonstrates conceptualunderstanding of the area of circles or the area orperimeter of composite figures (quadrilaterals, trianglor parts of circles), and the surface area ofrectangu

prisms, or volume ofrectangular prisms, triangularprisms, or cylinders using models, formulas, or bysolving related problems.Expresses all measures usinappropriate units. (State)

M(G&M)67 Measures and uses units of measuresappropriately and consistently, and makes

conversions within systems when solving problems

across the content strands. (State)

See Benchmarks in Appendix B.


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M(G&M)68 No GLE at this grade M(G&M)78 No GLE at this grade

M(G&M)69 No GLE at this grade M(G&M)79 No GLE at this grade

M(G&M)610 No GLE at this grade M(G&M)710 Demonstrates conceptual understandspatial reasoning and visualizationby sketching three-dimensional solids; and draws nets of rectangular andtriangular prisms, cylinders, and pyramids and uses the na technique for finding surface area. (Local)


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Data, Statistics, and Probability continueGrade K Grade 1

M(DSP)K5 No GLE at this grade M(DSP)15 For a probability event in which the samspace may or may not contain equally likely outcome

groups use experiments to describes the likelihood or c

of an event (using more likely, less likely, or equalllikely). (Local)

M(DSP)K6 No GLE at this grade M(DSP)16 No GLE at this grade


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Problem Solving, Reasoning, and Proof contK 2 3 5

M(PRP)22 Students will use mathematical reasoning andproofand be able to:

Use models, known facts, properties, and relationshipsto explain their thinking.

Justify solution processes and answers (e.g., "I chosethis method to solve the problem because...").

Draw conclusions using inductive reasoning. Identify the missing information needed to find a

solution to a given story problem.

Use patterns and relationships to analyze mathematicalsituations (e.g., count by fives).

M(PRP)52 Students will use mathematical reasoninproofand be able to:

Draw conclusions and solve problems usingelementary deductive reasoning and reasoning byanalogy.

Make and defend conjectures and generalization Use models, known facts, properties, and relation

to explain thinking and to justify answers and soprocesses.

Recognize the pervasive use and power of reasona part of mathematics.


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Communication, Connections, and RepresentationK 2 3 5

M(CCR)22 Students will create and use representationsto communicate mathematical ideas and to solve problems

and be able to:

Create and use age level appropriate representations toorganize, record, and communicate mathematical ideas(e.g., students should recognize the relationship amongseven counters, seven tally marks, and the symbol 7).

Select, apply, and translate among mathematicalrepresentations to solve problems (e.g., representingfractions with circles, with geoboards, and with patternblocks).

Link different representations. Use representations to model and interpret physical,

social, and mathematical phenomena.

Use conventional and self-generated (invented)representations and connect them.

Realize that any representation is subject to multipleinterpretations (e.g., drawings and graphs can be readin a different way).

M(CCR)52 Students will create and use representatto communicate mathematical ideas and to solve prob

and be able to:

Use physical models and diagrams to representimportant mathematical ideas (e.g., multiplicatio

Use appropriate representations to solve problemportray, clarify, or extend a mathematical idea.

Recognize equivalent representations of conceptprocedures and translate among them as appropr(for example, understand how the addition of whnumbers, fractions, and decimals are related).


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Communication, Connections, and RepresentationK 2 3 5

M(CCR)23 Students will recognize, explore, and developmathematical connections and be able to:

Link conceptual and procedural knowledge (e.g., theywill know that when they regroup, they are simplychanging the representation of the minuend, but not itsvalue).

Recognize and use mathematics in other curriculumareas (e.g., science, social studies).

Recognize and use mathematics in their daily lives(e.g., graphs, tables, or maps).

Identify mathematical situations occurring in literaturefor children.

Identify examples of geometry in nature, art, andarchitecture.

M(CCR)53 Students will recognize, explore, and demathematical connections and be able to:

See mathematics as an integrated whole. Recognize relationships among different topics i

mathematics.

Recognize and use mathematics in other curriculareas and in their daily lives.

Link concepts and procedures. Use mathematical skills, concepts, and applicatio

other disciplines (e.g., graphs in social studies, pin art, or music and geometry in technology educ


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Rhode Island K 8 Mathematics Grade-Level Expectations


Appendix A: M(N&O)23

M(N&O)23Demonstrates conceptual understanding of mathematical operations involving addition and subtraction of whole

numbers by solving problems involving joining actions, separating actions, part-part whole relationships, and comparison situations.(See Appendix A.)

Classification of word problems: Researchers have identified four basic categories of addition andsubtraction problems: problems with joining actions, separating actions, part-part whole relationships, andcomparison situations. Table 1 contains some examples to illustrate the distinctions in the categoriesidentified by the researchers, but there may be additional ways to express the same actions, relationships, orsituations. For example, the following are additional ways to ask questions related to the Join StartUnknown category.

Example 1: I am thinking of a number that when you add 5 to it, the answer is 13. What number am Ithinking of?Example 2: John puts a five-pound toy inside an empty wooden box. The box and toy together weigh 7pounds. How much does the empty box weigh?

In summary, students should have experiences with problem solving in addition and subtraction across avariety of problem types.It is important to remember that any problem situation that fits the equations givenand the category can be asked, not just problems as stated in Table 1.

Teaching students to add and subtract involves providing students with an opportunity to explore a rich setof problems with different semantic structures and to develop a variety of strategies to quantify, represent,calculate, express, and justify results. (Gutstein, E., Romberg, 1995)

Table 1: Classification of Word Problems1

Join

(Result Unknown)Connie had 5 marbles. Juangave her 8 more marbles. How

many marbles does Conniehave altogether?

5 + 8 =

(Change unknown)Connie has 5 marbles. How many moremarbles does she need to have 13

marbles altogether?

5 + = 13

(Start Unknown)Connie has some marbles. Juan gave her5 more marbles. Now she has 13

marbles. How many marbles did Conniehave to start with?

+ 5 = 13

Separate (Result Unknown)Connie had 13 marbles. Shegave 5 marbles to Juan. Howmany marbles does she haveleft?

13 5 =

(Change unknown)Connie has 13 marbles. She gave someto Juan. Now she has 5 marbles left.How many marbles did Connie giveJuan?

13 = 5

(Start Unknown)Connie has some marbles. She gave 5 toJuan. Now she has 8 marbles left. Howmany marbles did Connie have to startwith?

5 = 8

Part-

Part-

Whole

(Whole Unknown)Connie has 5 red marbles and 8 blue marbles. Howmany marbles does Connie have?

5 + 8 =

(Part Unknown)Connie has 13 marbles. All the marbles are either blue or red.Connie has 5 red marbles. How many blue marbles does Conniehave?

13 5 =

Compare (Difference Unknown)Connie has 13 marbles. Juanhas 5 marbles. How manymore marbles does Conniehave than Juan?

13 5 =

(Compare Quantity Unknown)Juan has 5 marbles. Connie has 8 moremarbles than Juan. How many marblesdoes Connie have?

5 + 8 =

(Referent Unknown)Connie has 13 marbles. She has 5 moremarbles than Juan. How many marblesdoes Juan have?

13 5 =

1Carpenter, Fennema, Peterson, Chiang, and Loef (1989) cited in Gutstein, E., Romberg, T.,Teaching Children to Add and Subtract, Journal of Mathematical Behavior, 14, 283-324 (1995).


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Appendix B: Measurement Benchmarks

The following is a list of the measurement benchmarks and equivalences that can be usedinproblems across the content strands at each grade level to address the expectations in M(G&M)X7for the Tri-State New England Assessment2.

M(G&M)X7Uses units of measures appropriately and consistently, and makes conversionswithin systems when solving problems across the content strands.

The type of measure (e.g., length, time, etc.), the unit (e.g., inches, feet, etc.), the degree of accuracywhere appropriate (e.g., inch); and equivalences (e.g., 12 inches in a foot) are identified forgrades 2 8. In addition to measurement benchmarks identified below students will be expected touse the appropriate units when solving problems involving area, volume, surface area, conversions,and rates (e.g., miles per hour, price per pound, pounds per square inch) on the TSNE Assessment1.

Measures

Grade 2 Grade 3 Grade 4

Length

Unit (accuracy):

Inch (to whole inch); Foot (towhole inch); Centimeter (towhole centimeter); Meter (towhole centimeter)Equivalencies:

12 inches in 1 foot; 100centimeters in 1 meter

Unit (accuracy):

Inch (to 1/2 inch); Foot (towhole inch); Centimeter (towhole centimeter);Meter (towhole centimeter)Equivalencies:

12 inches in 1 foot; 100centimeters in 1 meter

Unit (accuracy):

Inch (to 1/4 inch); Foot;Centimeter (to 0.5 centimeter);Meter (to 0.5 centimeter);Yard; Mile (use in scalequestions); Kilometer (use inscale questions)

Equivalencies:

12 inches in 1 foot; 100centimeters in 1 meter; 3 feetin 1 yard; 36 inches in 1 yard

Time Unit (accuracy):

Hour (to 15 minute interval)Equivalencies:

60 minutes in 1 hour

Unit (accuracy):

Hour (to 5 minute interval);Day; YearEquivalencies:

24 hours in 1 day; 7 days in 1week; 365 days in 1 year

Unit (accuracy):

Hour (to 5 minute interval);Day; YearEquivalencies:

24 hours in 1 day; 7 days in 1week; 365 days in 1 year;60seconds in 1 minute; 60minutes in 1 hour

Temperature Unit (accuracy):

Degree (to 1 degree)Unit (accuracy):

C and F (to 1 degree)Unit (accuracy):

C and F (to 1 degree)

Capacity Units (accuracy):

Quart (to whole quart)Unit (accuracy):

Quart (to whole quart)

Mass Unit (accuracy):

Kilogram (to whole kilogram);Gram (to whole gram)

Unit (accuracy):

Kilogram (to whole kilogram);Gram (to whole gram)

Weight Unit (accuracy):Pound (to whole pound)

Unit (accuracy):Pound (to whole pound)

2

Contractors will be asked to devise a system to measure the degree to which students use units of measures and makeconversions consistently and appropriately when applicable to problems across content strands.


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References

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Abedi, J., Hofstetter, C., Baker, E., and Lord, C. (2001a). NAEP math performance and test accommodations: Interactions withstudent language background. CSE Technical Report 536. National Center for Research on Evaluation, Standards, and Student

Testing.

Abedi, J. and Lord, C. (2001b). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219-234.

DeLange, J. (1987).Mathematics Insights and Meaning. University of Utrecht, Netherlands.

Fuson, K.. (2002).Developing Mathematical Power in Whole Number Operations. A Research Companion to Principles andStandards for School Mathematics.

Hanson, M.R., Hayes, J.R., Schriver, K., LeMahieu, and Brown, P.J. (1998). A Plain language approach to the revision of test items.AERA. San Diego, CA.

Kopriva, R. (2000). Ensuring accuracy in testing for English language learners: A Practical guide for assessment. Council ofChief State School Officers, SCASS-LEP Consortium. Washington, DC.

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Mid-continental Educational Laboratory (McREL). (2000). K 12 Mathematics Standards.Mid-continent Research for Educationand Learning.

National Assessment Governing Board. (2005). 2005 NAEP Mathematics Assessment and Item Specifications. National AssessmentGoverning Board, U.S. Department of Education.

National Council of the Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. National Council of theTeacher of Mathematics.

National Council of the Teachers of Mathematics. (1993).Research Ideas for the Classroom: Early Childhood Mathematics.Macmillan Publishing Company.

National Council of the Teachers of Mathematics. (1993).Research Ideas for the Classroom: Middle Grades Mathematics.Macmillan Publishing Company.

National Research Council. (2001).Adding it Up: Helping Children Learn Mathematics. National Academy Press.

New Hampshire Department of Education. (2000).Draft K 12 Mathematics Curriculum Framework. New Hampshire Departmentof Education.

New Hampshire Department of Education. (1995). K 12 Mathematics Curriculum Framework. New Hampshire Department ofEducation.

New Hampshire, Rhode Island, and Vermont Department of Education. (2003).New England Common Assessment Program DraftGrade-Level Expectations. New Hampshire, Rhode Island, and Vermont Department of Education.

New Standards Project. (1998). Performance Standards: Volume 1: Elementary School. National Center on Education and the

Economy and the University of Pittsburgh.

New Standards Project. (1997). Performance Standards: Volume 2: Middle School. National Center on Education and the Economyand the University of Pittsburgh.

Petit, M. (2003). ForcedChoices. Center for Assessment for the New England Compact.

Rhode Island Department of Education.Rhode Island Mathematics Framework. Rhode Island Department of Education.

Vermont Department of Education. (2000). Vermonts Framework of Standards and Learning Opportunities. Vermont Department ofEducation.

Vermont Department of Education. (2003). Vermont Draft Grade-Level Expectations. Vermont Department of Education.

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Webb, Norman. (2002).Depth of Knowledge Levels for Four Content Areas.http://facstaff.wcer.wisc.edu/normw/All%20content%20areas%20%20DOK%20levels%2032802.doc

Webb, Norman. (1997). Research Monograph Number 8, Criteria for Alignment of Expectations and Assessments on Mathematicsand Science Education. Council of Chief State School Officers.
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RI Math K-8 GLEs revised 4.4.07