DOCUMENT RESUME

ED 469 099 SE 066 845

TITLE Sample Curriculum Model, Grade 2, Based on the 1998 ArkansasState Mathematics Framework.

INSTITUTION Arkansas State Dept. of Education, Little Rock.

PUB DATE 1998-00-00NOTE 33p.; For Sample Curriculum Models, Grades K-8, see SE 066

843-851.

AVAILABLE FROM For full text: http://arkedu.state.ar.us/curriculum/benchmarks.html.

PUB TYPE Guides Non-Classroom (055) Legal/Legislative/RegulatoryMaterials (090)

EDRS PRICE EDRS Price MF01/PCO2 Plus Postage.

DESCRIPTORS *Academic Standards; Algebra; Geometry; *Grade 2; MathematicsCurriculum; *Mathematics Instruction; Measurement; NumberConcepts; Numeracy; Patterns in Mathematics; PrimaryEducation; Probability; *State Curriculum Guides; Statistics

IDENTIFIERS *Arkansas

ABSTRACT

This document consists of a sample curriculum model for grade2 mathematics based on the 1998 Arkansas State Mathematics Framework. Thedocument is divided into five sections: (1) Number Sense, Properties, andOperations;'(2) Geometry and Spatial Sense; (3) Measurement; (4) DataAnalysis, Statistics, and Probability; and (5) Patterns, Algebra, andFunction. Within each section the standards are exemplified and articulatedby benchmarks, suggested assessments, and possible strategies and activitiesfor teaching the standard. A blackline master checklist is included as anappendix. (MM)

Reproductions supplied by EDRS are the best that can be madefrom the original document.

SAMPLE CURRICULUM MODEL

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HAS

BEEN GRANTED BY

TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

GRADE 2

U.S. DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement

EDUCATIONAL RESOURCES INFORMATION

his

CENTER (ERIC)his document has been reproduced as

r eived from the person or organizationoriginating it.

Minor changes have been made toimprove reproduction quality.

Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy.

based on the 1998 Arkansas State Mathematics FrameworkArkansas Department of Education, 1998

2

I COPY AVAI BLE

.s6

Grade Level_2_NUMBER SENSE, PROPERTIES, AND OPERATIONS

StandardNPO.1.0

Benchmarks Assessments Strategies/Activities

5LE NP0.1.1 Students will write . Teacher observation . Students drawnumerical symbols . Peer and self pictures of

Demonstrate related to sets evaluation manipulatives andnumber sense which are . Teacher-made tests write the numerical(concepts of represented by . Checklist symbol for thecounting, grouping,and place value)using

pictures ofmanipulatives.

. Statewide tests

. Performancepictures.. Students are givenpictures of

manipulatives. Students will countforward to 1000and will countforward and backby twos, threes,fives, and tensfrom any givennumber.

manipulatives or real-world objects andthey write thenumerical symbol foreach picture.. The class collect1000 pop tops andcashes them in at arecycling center.

Students willdemonstrate thepatterning of placevalue.

. Count the pop topstaking two, three,five, and ten at atime.. Whole class, as achorus, count to 1000by fives and tens.. Participate incounting songs andrhymes.. Read: Dancing inthe Moon: CountingRhymes byEichenberg, Fritz;Hippos Go Beserk byBoynton, Sandra; OneWatermelon Seed byLottridge, Celia; TheButton Box by Reid,Margarette.

5LE NP0.1.2 Students will . Teacher observation . Students provediscuss and model . Peer and self their paper-pencil and

Develop meaningfor the operations

(concretely,pictorially, and

evaluation. Teacher-made test

mental math answersby using manipulatives.

by modeling and symbolically) . Checklist . Students model

3

discussing a problem situations . Appro- the concept ofvariety of problem involving 2-digit priate response to multiplication usingsituations. addition with and teacher direct questions manipulatives. (Ex.

without carrying . Improved vocabulary Form four groups withand 2-digit . Verbal explanation three objects in asubtraction with . Demon- group and discuss theand without stration ways of finding howregrouping. . Writing many objects there

are in all.). Students discuss,in small groups,problem situationsusing 2-digit addition,2-digit subtraction,and simplemultiplication.. Read: Willy andHis Wheel Wagon byGibbons, Gail

Grade Level_2_NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NP0.1.0 Benchmarks Assessments Strategies/Activities

SLE NP0.1.3 Students will apply and . Teacher . See NPO.1.1master counting forward to observation . Students are given

Apply and master 1000 and will apply and . Peer and counting sticks and arecounting, grouping,place value, and

estimation.

master counting forwardand back by twos, threes,fives, and tens.

selfevaluation. Checklist. Teacher-

told to display about 10sticks. They are guidedto develop the roundingstrategies. The

Students will apply and made test students repeat themaster the patterning of . State- activity using bundles ofplace value. wide test

. Perform-ten and round to thenearest hundred using

Students will estimate tothe nearest tens andhundreds using roundingstrategies.

once the strategies developedin the previous exercise.

5LE NP0.1.4 Students will relate . Appro- . See NP0.1.2mathematical terminology priate . Students will make

Solve problems using and symbols of operations response to flash cards containingterminology and involving addition and teacher the symbols ofsymbols of operations(e.g., add, subtract,multiply, and divide).

subtraction (add, subtract,+, -, =, sum, addend,subtrahend, minuend,difference, and equal) to

directquestions. Verbalexplanation

operations andmathematicalterminology. They willuse the flash cards at

problem situations. . Teacherobservation

home and with a partnerat school.

. Peer andselfevaluation. Anecdo-tal record

. Students will takeproblem solvingsituations and representthem symbolically andnumerically.

. State-wide tests. Teacher-made test. Writing

5

Grade Level 2NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NP0.1.0 Benchmarks Assessments Strategies/Activities

SLE NP0.1.5 Students will demonstrate . Teacher . Students will checkcompetency with addition observation paper-pencil and mental

bemonstrate and subtraction facts using . Peer and calculations to basiccompetency of mental math and self addition and subtractionoperations (e.g. add,subtract, multiply, and

technology. evaluation. Appro-

using calculators.. Set up a computer

divide) using mental priate center with appropriatemath and technology. response to

teacherdirectquestions

software for studentuse. (Ex. Subtractwith Balancing Bear bySunburst or Troll Math

. State-wide tests

Class Level 2: I CanCarry and Borrow)

. Teacher-made test. Perform-once

. Play games thatenhance mental math,such as "Around TheWorld"

SLE NPO 1.6 Students will concretely,pictorially, and symbolically

. Appro-priate

. Students will writefractions for fraction

Use manipulatives to demonstrate the concept response to bars.demonstrate and of fractions as part of a teacher . Students are given

compare rational whole using the fractions direct color tiles or colornumbers/fractions(e.g., find simple

1/2, 1/3, 1/4, 1/5, 1/6,1/8, and 1/10.

questions. Verbal

cubes or interlink cubesand are told to

parts of a whole). explanation. Teacherobservation. Peer andselfevaluation. Teacher-made test. State-wide tests. Demon-stration

represent a specifiedfraction. (Ex. Thestudent chooses tencubes and holds up oneand says that the onecube is 1/10 of the tencubes.). Students are givenpictures of pies andthey write thecorresponding fraction.They determine whichpie would offer themthe largest/smallestpiece, thus determiningthe largest and smallestfraction.

6

Grade Level 2

NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NP0.1.0 Benchmarks Assessments Strategies/Activities

5LE NP0.1.7

Communicate numbersense, properties, and

Students will communicateunderstanding of numbersense, properties,addition, and subtraction

. Teacherobservation. Peer andself

. See NP0.1.1,NP0.1.2, NP0.1.3,NP0.1.4, NP0.1.5,NP0.1.6

operations throughjournal writing,creating problems,constructing

through journal writing,creating problems,constructing mathematicalsentences, etc.

evaluation. Anecdo-tal records. Verbal

. Students compose amath story usingcorrect number sense,properties, and basic

mathematical explanation addition andsentences, etc. . Journal

. Appro-priateresponse toteacherdirectedquestions. Improvedvocabulary. State-wide tests. Teacher-made test. Writing

subtraction. The storyis recorded in theirjournals.. Students are givenan addition orsubtraction problem andare told to write howthey would find theanswer. They thenorally share with theclass their method forsolving the problem.This is placed in theirjournals.

7

Grade Level_2_NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NP0.2.0 Benchmarks Assessments Strategies/Activities

5LE NPO.2.1 Students will represent . Teacher . See NP0.1.0numbers and 2-digit observation . Students represent

Represent numbers addition with and without . Peer and the number of studentsand operations carrying and 2-digit self in the teacher's class in(addition, subtraction,multiplication, and

subtraction with andwithout regrouping in a

evaluation. Appro-

the past years using aline graph. They

division) in a variety of variety of forms using priate analyze and compareforms using manipulatives, symbols, and response to the data using additionmanipulatives, symbols,and graphs(pictographs, etc.)

graphs. teacherdirectedquestions

and subtraction.

. State-wide test. Teacher-made test. Demon-stration

5LE NPO.2.2 Students will apply . Appro- . See NPO.1.1 andelementary number theory priate NP0.1.3

Apply elementarynumber theory (skip

(skip counting, patterns,number series, odd and

response toteacher

. Students will countby fives and tens to

counting, patterns,number series, odd and

even numbers, ordinalnumbers, etc.).

directquestions

determine the value ofa hand full of dimes and

even numbers,multiples, fractions,etc.).

. Verbalexplanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. Teacher-made test. State-wide test. Perform-once

nickels.. Students willcontinue the pattern forcounting quarters todetermine the amountof money representedby a handful of playquarters.. Students willidentify odd and evennumbers on a hundredchart by circling theodd numbers and puttinga square around theeven numbers.. Students identifytheir place in line bysaying first, second,third, etc.. Read: Bicycle Raceby Crews, Donald;Harriet Goes to theCircus by Maestro,Betsy; I Can Count the

Petals of a Flower byWahl, John, and StacyWahl

Grade Level 2

NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NP0.2.0 Benchmarks Assessments Strategies/ Activities

SLE NPO.2.3 Students will apply . Teacher . See NPO.1.2addition, subtraction observation . Students estimate

Apply computation (variety of meanings), and . Peer and how many people would(add, subtract,multiply, and divide)

estimation to real-worldproblems.

selfevaluation

be in a room if two orthree specific

and estimation to real- . Anecdo- classrooms areworld problems. tal records

. State-wide test

combined. They checktheir answer byaddition.

. Teacher-made test. Writing

. Students guess thenumber of items in aguessing jar. Thewinner gets the items inthe jar.

5LE NPO.2.4 Students will use mentalmath, manipulatives, and

. Teacherobservation

. See NP0.1.2,NP0.1.5, NP0.2.1

Use mental math,manipulatives, and

technology to solve 2-digitaddition problems (with and

. Peer andself

. Students are askedto solve a number of 2-

technology to solve without carrying) and 2- evaluation digit addition and 2-problems. digit subtraction (with a . Teacher- digit subtraction

variety of meanings) made test problems either mentallyproblems (with and without . State- or with manipulatives.regrouping). wide test

. ProjectThey check theiranswers using acalculator.

1 0

Grade Level 2NUMBER SENSE, PROPERTIES, AND OPERATIONS

Standard NPO.2.0 Benchmarks Assessments Strategies/Activities

5LE NP0.2.5 Students will describe andcompare quantities by using

. Teacherobservation

. See NPO.1.6,

Describe and compare concrete and real-world . Peer andquantities by using models of the fractions selfconcrete and real-world models offractions.

1/2, 1/3, 1/4, 1/5, 1/6,1/8, and 1/10.

evaluation. Anecdo-tal records. Verbalexplanation. Journal. Appro-priateresponse toteacherdirectedquestions. Improvedvocabulary. State-wide tests. Demon-stration. Exhibi-tion

11

2rade Level 2GEOMETRY AND SPATIAL SENSE

Standard 65.1.0 Benchmarks Assessments Strategies/Activities

5LE 65.1.1 Students will classify and . Teacher . Read: Shapesconstruct geometric observation by Reiss, John, Jr.;

Sort, classify, and shapes/figures using a . Peer and Circles. Triangles, andconstruct geometricshapes/figures using a

variety of manipulatives. selfevaluation

Squares by Hoban,Tana.

variety of . Project . Students willmanipulatives. . State-

wide test. Demon-stration. Teacher-made test

construct squares,triangles, circles,rectangles, and ovalsusing straws andforming a mobile.

5LE GS.1.2 Students will describe,draw, compare, and

. Teacherobservation

. See 65.1.1

. Students willDescribe, model, draw,construct, compareand classify shapes in

classify shapes twodimensions.

. Peer andselfevaluation

construct models ofhorizontal, vertical,perpendicular (form

one, two, and three Students will identify lines . Portfolio right angles), anddimensions. as horizontal, vertical,

perpendicular, parallel and. State-wide test

parallel lines withstraws or string. If

name lines and line . Demon- string is used, thensegments using two points. stration

. Teacher-made test

students will glue thestring to paper andplace in their portfolio.. Given a line and aline segment, thestudent will write thename using two points onthe line or line segment.

12

2rade Level 2GEOMETRY AND SPATIAL SENSE

Standard 65.1.0 Benchmarks Assessments Strategies/Activities

SLE 65.1.3 Students will determine . Teacher . Students are givenand draw similar and observation pictures of similar and

Determine the congruent figures. . Peer and congruent figures.relationship between self They differentiate andshapes/figures using Students will trace and evaluation label the figures.congruence and construct slides, flips, and . Teacher . Students constructsimilarity, and using turns. made test pictures by tracing two-transformations (flips,slides, and rotations).

. Portfolio

. State-wide test

dimensional objects thathave been slid, flipped,or turned. These areplace in their portfolio.

5LE 65.1.4 Students will predict the . Teacher . Students are askedresults of combining and observation what shapes/figures

Predict and determine dividing shapes/figures. . Peer and would be formed bythe results of self combining two rectanglescombining, dividing,and subdividing

evaluation. Portfolio

or dividing onerectangle. They are

shapes/figures. . State-wide test

given two rectangles andassess their answers.

. Project Students trace theshapes/figures formedwith the rectangles andplace these in theirportfolio. The activityis repeated using othershapes/figures, thistime having acompetition to see whocould form the mostshapes/figures.. Students take scrapmaterial and cut theminto shapes and gluethem on paper to forma quilt square.

13

Grade Level 2GEOMETRY AND SPATIAL SENSE

Standard 65.1.0 Benchmarks Assessments Strategies/Activities

5LE 65.1.5 Students will demonstratespatial awareness

. Appro-priate

. Read: Over, Under,and Through: and Other

Demonstrate spatialawareness (positionalrelationship, size,direction, area,volume, etc.).

(positional relationship,size, direction, area,etc.).

response toteacherdirectquestions. Teacherobservation

Spatial Concepts byHoban, Tana.. Students are eachgiven a sheet of blankpaper. With a partnerthey turn back to back.

. Peer andselfevaluation. State-wide test. Demon-stration

One partner tells theother partner what todraw (one step at atime). The descriptioncan only be orally andthe picture is not lookedat by the describeruntil the describer isfinished.

5LE 65.1.6 Students will use . State- . Extend 65.1.5 tomanipulatives to wide test have the describer tell

Use manipulatives and demonstrate geometric . Teacher- his/her partner wheretechnology to concepts (positional made test to place attribute blocksdemonstrategeometric concepts

relationship, size,direction, area, etc.).

. Demon-stration

to form a picture.. Use appropriate

(positional . Teacher computer software suchrelationship, size,direction, area,volume, etc.).

observation. Peer andselfevaluation

as Shape Upl bySunburst.

14

Grade Level 2GEOMETRY AND SPATIAL SENSE

Standard 65.1.0 Benchmarks Assessments Strategies/Activities

5LE GS .1.7

Demonstrate

Students will demonstrategeometric and spatialsense of two- and three-

. Appro-printresponse to

. See 65.1.3,65.1.4, 65.1.5,65.1.6. Have students

geometric and spatial dimensional objects teacher verbalize or writesense through written through oral and written direct responses to teacher'sand oral communication. questions questions.communication (e.g.,draw and describe a

. Verbalexplanation

. A display of threeor four objects is set

color cube model using . Teacher up in the class. Theisometric dot paper). observation

. Peer andselfevaluation. Improvedvocabulary. Portfolio

students are to write,in complete sentences, adescription of thelocation of each objectin the display. This isthen place in theirportfolio.

. State-wide test. Teacher-made test. Writing

15

Grade Level 2GEOMETRY AND SPATIAL SENSE

Standard GS. 2.0 Benchmarks Assessments Strategies/Activities

5LE GS.2.1 Students will estimate and . Teacher . Identify various

Estimate and measuremeasure the size (length,width, perimeter) of

observation. Peer and

objects in the classroomthat represent

the size of geometric geometric figures/shapes self geometric shapes andfigures/shapes in the in the real world using evaluation determine their sizereal world (length,width, perimeter, area,volume, etc.).

non-standard units andstandard units (inches,feet, centimeters, and 1/2

. Anecdo-tal records. Teacher-

(length and width) usingnon-standard andstandard units of

inch). made test. State-wide test. Perform-once

. Log orjournal

measure. (Ex. Abottom of a box oftissue represents arectangle or square.The students measurethe width and lengthusing a plastic chain todetermine how manylinks long or wide thebottom of the box isand determines theperimeter. The activityis repeated using a rulerto measure to thenearest 1/2 inch orcentimeter.)

5LE &S.2.2 Students will replicate and . Appro- . Students areexplain geometric patterns priate presented a pattern

Construct and explain using concrete and pictorial response to using attribute blocksgeometric patterns models, with two teacher and are asked tousing concrete and attributes. direct continue the pattern andpictorial models, with questions transfer it pictorially toone or more attributes . Verbal paper.(color, shape, size,etc.).

explanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. State-wide test

. Students constructtheir own geometricpattern using attributeblocks. They transferthe pattern to paper.The pattern is left intact and anotherstudent transfers it topaper and extends thepattern.

. Demon-stration. Project

16

Grade Level 2GEOMETRY AND SPATIAL SENSE

Standard GS.2.0 Benchmarks Assessments Strategies/Activities

5LE GS.2.3 Students will use . Teacher . See G5.1.6manipulatives and observation . The students are

Use manipulatives and technology to solve . Peer and assigned the task oftechnology to solve problems involving self covering a floor using 1problems involving perimeter and area. evaluation foot square tiles. Theyperimeter, area,volume, etc.

. Anecdo-tal records

. State-wide test. Perform-ance

. Teacher-made test

are to determine howmany tiles would beneeded to go around theroom along the wall onetime (perimeter) andhow many would it taketo cover the floor(area).. Students useappropriate software toreenforce the conceptsof perimeter and area.

SLE GS.2.4 Students will demonstrategeometric and spatial

. Appro-priate

. See GS.2.1,GS. 2.2, and GS.2.3.

Illustrate geometric sense of two- and three- response to Students will verbalizeconcepts through dimensional objects teacher and/or write theirwritten and oral through written and oral direct answers to thecommunication. (For communication as questions teacher's questions.example, "I am a represented in real life. . Verbal The written answers willrectangular house. My explanation be placed in theirwindows are squares.My door is a rectangle.

. Teacherobservation

portfolios.

My roof is a triangle.") . Peer andselfevaluation. Improvedvocabulary. Portfolio. State-wide test. Teacher-made test. Writing

17

Grade Level 2

MEASUREMENT

Standard M.1.0 Benchmarks Assessments Strategies/Activities

5LE M.1.1 Students will demonstrate . Teacher . Students are given aand apply the concept of observation chart of recorded

Demonstrate and apply comparison in time (which . Peer and temperatures for athe concept of takes longer), money self specific month over acomparison (large,small, long, short, etc.)

(which is more),temperature (what is the

evaluation. Anecdo-

period of five years.The students make

according to a given hottest), and weight tal records comparisons of theattribute (color,shape, size, etc.).

(which is heavier)according to four or five

. Appro-priate

temperatures.. Students are given a

attributes (shape, size,purpose, textures, etc.).

response toteacherdirectquestions. Verbalexplanation. Improvedvocabulary. State-wide test. Teacher-made test

choice of toy catalogs.They are to choose

and cut out three ofthe toys and theirprices they desire themost. They comparethe prices of the toys.. Students are given awide variety of fruitsand are to weigh eachin order to comparetheir weights.. Students are taughtto use a stopwatch.They time each other incompleting a certaintask and compare thetimes.

5LE M.1.2 Students will select and . Teacher . See GS. 2 . 1

use the appropriate units observation . Extend M.1.1 toSelect, demonstrate,and defend the use ofappropriate units ofmeasure.

of measure fortemperature (degrees),money (bills and coins),length (inches, feet,centimeters, V2 inch),capacity (cups, pints,quarts, gallons), and time

. Peer andselfevaluation. Verbalexplanation. Appro-priate

have the studentsidentify the unit ofmeasure used for eachactivity.. Students will use aclock to determine theproper time for

(15-minute intervals, a.m.,p.m., noon, midnight).

response toteacherdirectquestions. Improvedvocabulary

scheduled activities.. Students will make atreat that requires nocooking such as puddingor gelatin.

. Anecdo-tal records. Checklist

. State-wide test. Teacher-made test. Writing

.19

Grade Level_2_MEASUREMENT

Standard M.1.0 Benchmarks Assessments Strategies/Activities

5LE M.1.3 Students will convert from . Teacher . See M.1.2one unit of measurement observation . Read: The Twelve

Convert from one to another in length (1 . Peer and Days of Christmas bymeasurement to foot = 12 inches), money self Wildsmith, Brian.another within the (all coins and one-dollar evaluation . Purchase items fromsame system (feet toyards, centimeters to

bill and five-dollar bill),and time (average month =

. Appro-priate

the sales paper in thenewspaper.

meters, etc.). 30 days; 365 days = 1 response to . Students determineyear, 24 hours = 1 day). teacher

directquestion. Verbalexplanation

how many days ofschool they attend in aschool year and convertthe total days tomonths.

. Improvedvocabulary. State-wide test

. Students calculatehow many days old theyare.

. Demon-stration. Teacher-made test

0

Grade Level_2_MEASUREMENT

Standard M.2.0 Benchmarks Assessments Strategies/Activities

5LE M.2.1 Students will useappropriate standard and

. Teacherobservation

. See M.1.1, M.1.2,and M.1.3

Select and use non-standard measuring . Peer andappropriate standard instruments (rulers for self(inches, feet), non- length; scales for weight; evaluationstandard (paper clip,thumbnail), and metric

clock for time;thermometer for

. State-wide test

(centimeter, meter) temperature; measuring . Demon-measuring instruments cups or beakers for stration(e.g., rulers, scales,measuring tape, yardstick, meter stick,thermometer, etc.).

capacity). . Teacher-made test. Checklist. Anecdo-tal records

21.

Grade Level_2_MEASUREMENT

Standard M.3.0 Benchmarks Assessments Strategies/Activities

5LE M.3.1 Students will estimate and . Teacher . Extend M.2.1 bymeasure quantities in non- observation having the students

Estimate and measure standard and standard . Peer and estimate the answersquantities such asweight, length, area,volume, money, time,and temperature.

units (inches, pounds,degrees, hours, feet,centimeters, cups, pints,quarts, gallons).

selfevaluation. State-wide test

before the actualmeasurement isdetermined.

. Demon-stration. Teacher-made test. Checklist. Anecdo-tal records. Appro-priateresponse toteacherdirectquestions. Log orjournal

SLE M.3.2 Students will solveproblems using standard

. Appro-priate

. See M.2.1

Solve problems using and non-standard response tomeasuring instruments measuring instruments teacherand technology. (ruler, scale, clock, etc.). direct

questions. Verbalexplanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. State-wide test. Teacher-made test. Writing

4,2°

Grade Level_2_MEASUREMENT

Standard M.3.0 Benchmarks Assessments Strategies/Activities

5LE M.3.3 Students will orally and in . Teacher . Extend M.3.1 bywritten form pose observation having the students

Pose problems using problems using non- . Peer and dictate then write acustomary (inches,feet, etc.), non-

standard and standardmeasurements in real-

selfevaluation

problem in a real-world situation that

standard (paper clip,thumbnail, etc.), and

world situations. . State-wide test

could be solved usingnon-standard and

metric measurements . Teacher- standard units of(centimeters, meters,etc.) in real-world

made test. Appro-

measure. (Ex. Josegoes to an

situations. priateresponse toteacherdirectquestions. Portfolio. Verbalexplanation. Improvedvocabulary

amusement park andrealizes he needs toknow how tall he is inorder to determine ifhe can ride some ofthe rides that haveheight limitations.How can Josedetermine hisheight?)

. Project

. Writing

Grade Level_2_DATA ANALYSIS, STATISTICS AND PROBABILITY

Standard DSP.1.0 Benchmarks Assessments Strategies/Activities

5LE DSP.1.1 Students will identify the . Teacher . Students identifypurpose (problem observation the purpose for data

Utilize the scientificmethod for dataanalysis.

statement) for datacollection (organization,etc.).

. Peer andselfevaluation

collection (e.g.,What the favoredflavor of ice cream

A. Identify the pur- . State- of the students inpose (problemstatement) for

Students will make,record, and analyze

wide test. Appro-

the class; Comparisonof the parents that

data collection. predictions about the final priate went to college andB. Make a prediction results of data collection response to those who did not to

about the finalresults of data

(occurred sooner, later,etc.).

teacherdirect

the number ofgrandparents that

collected. questions went to college orC. Collect and

organize dataStudents will collect,organize and display (line

. Perform-ance

not). They predictthe final results of

(tables, graphs,etc.).

plots, bar graphs, etc.)data in a variety of

. Verbalexplanation

the data collection(e.g., more students

D. Analyze andinterpret data

formats (physically,pictorially, and with

. Improvedvocabulary

will like chocolate;more parents went to

(prediction,inference, con-

clusion, etc.).E. Display data

using appropriatebar graphs, linegraphs, tables,pie graphs, etc.,with and withouttechnology.

written symbols). . Project. Writing

college thangrandparents). Theycollect data (e.g.,poll students,interview parents andgrandparents, etc.)and organize it(e.g., tally marks,checklist, etc.).They display thedata in a variety offormats (e.g. glue acotton ball of acorresponding colorof a flavor to aposter board to makeCI bar graph;transfer theinformation to thecorrect format of aline plot or stem andleaf plot; make acircle graph depictingthe number offathers, mothers,grandmothers, andgrandfathers, thatwent to college.)

24

SLE DSP.1.2 Students will orally,pictorially, and in written

. Teacherobservation

. Extend DSP.1.1 tohave students orally

Explain the results of format explain the results . State- and in writing explaindata collection usingoral and writtencommunication.

of data collection, wide test. Perform-once

the results of thedata collected.

. Peer andselfevaluation. Appro-priateresponse toteacherdirectquestions. Verbalexplanation. Improvedvocabulary. Writing. Project

25

G.rade Level_2_DATA ANALYSIS, STATISTICS AND PROBABILITY

Standard OSP.2.0 Benchmarks Assessments Strategies/Activities

5LE DSP.2.1 Students will make . Teacher . See DSP.1.1predictions and observation . Students

Predict the results of demonstrate the concept . Peer and determine thedata collection and of chance through the use self likelihood of flippingdemonstrate the of manipulatives. evaluation heads or tails with aconcept of chance . State- coin.through the use of wide test . Studentsmanipulatives. (For . Appro- discriminate againstexample: What is the priate fair and unfairprobability of drawingone red marble from abag of multicoloredmarbles?)

response toteacherdirectquestions

spinner activities.

. Verbalexplanation. Improvedvocabulary. Demon-stration. Log orjournal

SLE DSP.2.2 Students will record the . Teacher . Extend DSP.1.2results of data collection observation and DSP.2.1

Record the results of with a variety of symbolic . State-data collection with a formats including line wide testvariety of formatsthat could include

plots, stem and leaf plots,and circle graphs using oral

. Peer andself

charts, graphs, tables,and technology, usingoral and/or writtencommunication.

and written communication. evaluation. Appro-priateresponse toteacherdirectquestions. Verbalexplanation. Improvedvocabulary. Project. Log orjournal

26

Grade Level_2_DATA ANALYSIS, STATISTICS AND PROBABILITY

Standard DSP.3.0 Benchmarks Assessments Strategies/Activities

5LE DSP.3.1 Students will predict . Teacher . See DSP.1.1 andresults and analyze data to observation DSP.2.1

Predict results,analyze data, and findout why some resultsare more likely, lesslikely, or equally likely.

be more likely, less likely,or equally likely.

. Peer andselfevaluation. State-wide test. Appro-priateresponse toteacherdirectquestions. Verbalexplanation. Improvedvocabulary. Perform-ance

. Log orjournal

5LE DSP.3.2 Students will, in written . Teacher . Students areform, make a true observation presented with a

Make a true statement statement based on the . State- series of numbersbased on a simpleconcept of average(median, mean, mode,and range) for a small

simple concepts of mode,median, and range.

wide test. Peer andselfevaluation

and are told todetermine the mode,the median, and therange. They write

sample size. . Appro-priateresponse toteacherdirectquestions. Verbalexplanation. Improvedvocabulary. Exhibi-tion

the answers usingcomplete sentences.. Students take theages of theindividuals in theirfamily and calculatethe mode, median,and range of theages, then write andexplain the results incomplete sentences.

. Teacher-made test

27

Grade Level_2_DATA ANALYSIS, STATISTICS AND PROBABILITY

Standard DSP.3.0 Benchmarks Assessments Strategies/Activities

5LE DSP.3.3 Students will use the tools . Teacher . Students will useof technology to assist in observation appropriate computer

Use the tools of presenting information. . Peer and software to presenttechnology to assist in self information such asgathering, organizing,and presentinginformation.

evaluation. Appro-priateresponse toteacherdirectquestions

Math Keys byHoughton Mifflin.

. Verbalexplanation. Improvedvocabulary. Exhibi-tion. Project. Writing

28

Grade Level_2_PATTERNS, ALGEBRA AND FUNCTION

Standard PAF.1.0 Benchmarks Assessments Strategies/Activities

5LE PAF.1.1 Students will sort a wide . Teacher . See GS.1.1variety of materials using observation . Students sort and

Sort and classify awide variety of

two attributes (color, size,shape, etc.).

. Peer andself

classify play groundequipment.

materials. evaluation. Anecdo-tal records. State-wide test. Exhibi-tion

. Students sort andclassify the numbers1 through 20 (e.g.,numbers with onedigit are separatedfrom numbers withtwo digits, etc.)

. Demon-stration. Checklist

5LE PAF.1.2 Students will describe and . Appro- . See GS.2.2extend a wide variety of priate . See NP0.1.1 have

Describe, extend, and patterns to symbols using a response to students determinecreate a wide variety wide variety of materials teacher the pattern for skipof patterns using (transfer from concrete to direct counting.concrete models. symbols). questions

. Verbalexplanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. State-wide test. Perform-ance

. Checklist

Grade Level_2_PATTERNS, ALGEBRA AND FUNCTION

Standard PAF.1.0 Benchmarks Assessments Strategies/Activities

5LE PAF.1.3 Students will connect . Teacher . Students aremanipulative, pictorial, and observation given a sheet of

Demonstrate equality symbolic representation (in . Peer and numerical comparisons(=) and inequality (<, >) any order) of number self presented pictoriallyusing manipulatives and

symbols.

sentences using <, >, =, evaluation. Appro-priateresponse toteacherdirectquestions

and symbolically tocomplete with orwithout manipulatives.

. Verbalexplanation. Improvedvocabulary. State-wide test. Demon-stration. Teacher-made test

5LE PAF.1.4 Students will write an . Appro- . Extend PAF.1.3 toanswer for an unknown priate include mathematical

Demonstrate the that will form a true response to sentences presentedbeginning concept of a mathematical statement. teacher with variables.variable. (Use boxes,letters, or othersymbols to stand forany number or objectin simple situations,with or withoutconcrete material,such as 6 + = 8 or 3+ B = 4, etc.).

(e.g., - 9 = 7; 7 += 16; 4 x = 8)

directquestions. Verbalexplanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. State-wide test. Teacher-made test. Demon-stration

30

Grade Level_2_PATTERNS, ALGEBRA AND FUNCTION

Standard PAF.1.0 Benchmarks Assessments Strategies/Activities

5LE PAF.1.5 Students will express . Teacher . Students will bemathematical relationships observation assigned

Express mathematical on one- and two- . Peer and mathematical termsrelationships in one- dimensions (e.g., 1 foot = self and theirand two-dimensions. 12 inches, 1 ft. = 12 in.; evaluation abbreviations as an(Length x Width = 24 hours = 1 day, 24 hrs. . State- extension to weeklyArea, L x W = A, etc.) .= 1 day; etc.). wide test spelling tests.

. Teacher-made test. Journal. Perform-once

. Extend M.1.2 tohave students writethe units of measureboth one- and two)dimensionally.

5LE PAF.1.6 Students will pictorially,orally, and in writing

. A ppro-priate

. See PAF.1.2

Use oral and/or communicate to interpret a response towritten communication wide variety of created teacherto interpret createdpatterns.

patterns. directquestions. Verbalexplanation. Teacherobservation. Peer andselfevaluation. Improvedvocabulary. State-wide test. Teacher-made test. Perform-ance

. Writing

31

Mathematics Checklist for Second GradeStudent Name:

COMPETENCIES

Number Sense, Properties, and Operations

Introduced Progressing Proficient

Count and keep track of large quantities (100-999)Use objects to show hundreds, tens, and ones place valueCompare and order numbers to 100Use a variety of strategies to estimate a quantityDevelop and use strategies for adding and subtracting; use bothhorizontal and vertical notationsModel addition and subtraction situations; know when to add orsubtractUse the Hundreds Chart to add and subtract; find the distancebetween two numbersJudge the reasonableness of the answer to a computation problemIllustrate and explain the relationship between addition andsubtractionCreate a story problem for a given equationAdd a string of numbers by grouping numbers that go togetherRecord and explain solution strategies using appropriate vocabularyRepresent a number in a variety of numerical forms (ex: 28; 10+10+8;2 tens and 8 ones; almost 30; <30; etc.)Show relationships between counting, grouping, and place value using

manipulativesShow relationship between skip counting and grouping (usingmanipulatives)Group objects into same size setsConstruct an array to represent a number and show halves, thirds,and fourthsModel fractions using manipulatives and real-world objectsUse the calculator as a problem-solving tool

Geometry and Spatial SenseDraw a given shapeVisualize, construct, and draw rectangular arraysIllustrate and describe the characteristics of a triangle and arectangleBuild and take apart 2- and 3-dimensional shapesIdentify a 3-dimensional object by the outlines of its facesIdentify objects with mirror symmetry; show line of symmetryCreate 2-dimensional symmetrical designsShow the rotations (turns) of a given object

32

Mathematics Checklist- Second Grade Page 2Introduced Progressing Proficient

MeasurementExplain need for measuring with standard units (compare results ofmeasuring with different non-standard units)Measure lengths of objects using inchesShow how many inch squares will fit in a space; show how many inchcubes will fit in a containerEstimate length, area, volumeCount by 5 and 10 using money

Tell time to five-minute intervalsCompare lengths of time in familiar settings (Which is longer: lunch orrecess?)

Data, Probability, and StatisticsCreate a Venn Diagram to show relationships between and amongitemsCollect, record, and represent categorical dataCollect, record (tally), and represent numerical dataRecognize and explain the range of data; identify outliersInterpret and make hypotheses based on dataUse more than one representation to view dataUse a chart or table to solve problemsUse experiences to tell whether an event is likely or unlikely to occur

Patterns, Algebra, and FunctionsShow and describe patterns in the world (nature)Match symbols to objects, numbers, quantities, and wordsForm a number sentence for a real-world problemUse manipulatives to model balancing a number sentence (2+3=1+4)

Find the missing addendDemonstrate an understanding of the commutative property ofadditionWrite numerical expressions to equal a given answerWrite equations to solve problemsSkip count by 2, 3, 4, 5, and 10

Comments:

33

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