Grade 3Grade 3OverviewOverview

This overview provides only the highlights of the new learning that should take place at the third-grade level. The specific skills and subject matter that third graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-three students are: symbolically comparing number quantities, applying an algorithm to add and subtract whole numbers fluently, applying the concept of fractions, recalling basic multiplication and division facts, generating strategies to multiply one single-digit whole-number factor and one

double-digit whole-number factor, using symbols to represent an unknown quantity in a simple addition, subtraction, or

multiplication equation, understanding the attributes of circles, classifying polygons, classifying lines, line segments, and angles, predicting the results of one transformation, generating strategies to determine perimeters of polygons, telling time to the nearest minute, applying a procedure to find the range of a data set, comparing the benefits of multiple representations of a given data set; and

understanding when the probability of an event is 0 or 1.Grade 3

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Mathematical Processes

Big Ideas: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation

Standard 3-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators:3-1.1 Analyze information to solve increasingly more sophisticated problems. 3-1.2 Construct arguments that lead to conclusions about general mathematical

properties and relationships.3-1.3 Explain and justify answers on the basis of mathematical properties, structures,

and relationships.3-1.4 Generate descriptions and mathematical statements about relationships between

and among classes of objects. 3-1.5 Use correct, complete, and clearly written and oral mathematical language to

pose questions, communicate ideas, and extend problem situations. 3-1.6 Generalize connections between new mathematical ideas and related concepts

and subjects that have been previously considered.3-1.7 Use flexibility in mathematical representations. 3-1.8 Recognize the limitations of various forms of mathematical representations.

Essential Questions: What types of organizers can you use to record problem solving clues? (3-1.1) How can you use a number line to solve problems? (3-1.1) How can the strategy Predict and Test help you solve problems? (3-1.1) How can context clues be used to solve the problem? (3-1.1) How are the strategies “making a model” and “drawing a picture” alike and

different? (3-1.1, 3-1.8) How is addition related to multiplication? (3-1.2) How can you use multiplication arrays to find quotients? (3-1.2) How can arrays show multiplication and the commutative property of

multiplication? (3-1.3, 3-1.7) How can drawing a picture help you solve problems? (3-1.1, 3-1.7) How can models help you understand division? (3-1.7)

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Grade 3 Number and Operations

Big Ideas: Place Value, Operations with Whole Numbers, and Fractions

Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

Indicators:3-2.1 Compare whole-number quantities through 999,999 by using the terms is less

than, is greater than, and is equal to and the symbols <, >, and =.3-2.2 Represent in word form whole numbers through nine hundred ninety-nine

thousand. 3-2.3 Apply an algorithm to add and subtract whole numbers fluently. 3-2.4 Apply procedures to round any whole number to the nearest 10, 100, or 1,000. 3-2.5 Understand fractions as parts of a whole. 3-2.6 Represent fractions that are greater than or equal to 1. 3-2.7 Recall basic multiplication facts through 12 x 12 and the corresponding division

facts. 3-2.8 Compare the inverse relationship between multiplication and division. 3-2.9 Analyze the effect that adding, subtracting, or multiplying odd and/or even

numbers has on the outcome.3-2.10 Generate strategies to multiply whole numbers by using one single-digit factor

and one multi-digit factor. 3-2.11 Use basic number combinations to compute related multiplication problems that

involve multiples of 10.3-2.12 Analyze the magnitude of digits through 999,999 on the basis of their place

value.

Essential Questions: How does the place of a digit affect its value? (3-2.2, 3-2.12) How can you use place value to find the value of a digit? (3-2.2) How can you use place value to compare two numbers? (3-2.1) How can you use place value to order a set of whole numbers? (3-2.1) How does using a number line differ from using rules to round? (3-2.4) How can you estimate sums? (3-2.4) How is mental addition different from using paper and pencil? (3-2.3) How can you use base ten blocks to model 3-digit addition? (3-2.3)

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How can you use regrouping when adding? (3-2.3) When would you use each method, (Paper and Pencil or Mental Math)? (3-2.3) How will rounding differences affect everyone’s answers? (3-2.4) How do the two ways to subtract differ? (3-2.3) How can you use models to show subtraction? (3-2.3) How can the subtraction algorithm be extended for large numbers? (3-2.3) When would you use an estimate rather than an exact answer? (3-2.4) How do you subtract across zeros? (3-2.3) How can you show a fraction as part of a whole? a group? (3-2.5) How can you model a mixed number? (3-2.6) How can you multiply by a factor of (0-12)? (3-2.7) How is multiplying by ___ like and different than multiplying by ___? (3-2.7) What rules can you make when multiplying by 1 or 0? (3-2.7) How can you multiply with the factors of 5 and 10? (3-2.7) How can you use patterns or related facts to multiply by 9? (3-2.7) When would one strategy be more appropriate than the other? (3-2.7) How can you use the associative property to multiply 3 numbers? (3-2.7) How can you predict if the product, sum, or difference will be odd or even? (3-2.9) How can you use basic facts to multiply larger numbers? (3-2.11) How can you use arrays to show multiplication? (3-2.10, 3-2.11) What strategy can you use to solve a multiplication problem? (3-2.10, 3-2.11) How are multiplication and division related? (3-2.8) How can you write division and multiplication fact families? (3-2.8) What strategies can you use to divide? (3-2.7, 3-2.8) How can you work backward to solve problems? (3-2.7)

Help Page for Standard 3-2

Notes:Assessments

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Assessment examples can be accessed at http://www.s2martsc.org/.  Module 1-1 (3-2.1, 3-2.2, 3-2.12)Module 1-2 (3-2.3, 3-2.4, 3-2.9) Module 2-1 (3-2.7, 3-2.8, 3-2.9)Module 3-2 (3-2.5, 3-2.6)Module 4.3 (3-2.10, 3-2.11)  Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed. Assessment Examples:   Chapter Review and Test PrepChapter Tests MAP Testing OdysseyExit tickets Questioning Strategies Journaling/Written AssessmentsProjectsPair Share

Textbook Correlations

3-2.1 Lessons 2.1-2.33-2.2 Lessons 1.2-1.43-2.3 Lessons 3.3-3.5, 4.3-4.5, 4.7, 4.83-2.4 Lessons 2.4, 2.53-2.5 Lessons 16.1-16.33-2.6 Lessons 16.1, 16.43-2.7 Lessons 8.3-8.7, 9.1-9.8, 10.1-10.5, 11.1-11.5, 12.1- 12.5, 13.1-13.5 3-2.8 Lessons 11.4, 11.5, 12.4, 13.1,13.5 3-2.9 Lesson 10.33-2.10 Lessons 10.6, 10.7, 10.83-2.11 Lessons 10.5-10.83-2.12 Lessons 1.2-1.4

Key Concepts (Vocabulary)

evenodd

Identity Property of Multiplication

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digitsexpanded formstandard formword formplace value patterncompareis equal to =is less than <is greater than >orderroundestimate compatible numbersaddendregroupfact familyinverse operationsdifferencefactorsproduct

Zero Property of MultiplicationmultipleAssociative Property of Multiplicationdividegroupdividenddivisorquotientfractionnumeratordenominatorten thousandshundred thousandsvaluesumtradesymbolequationexpressionrule

Literature

Shark Swimathon by Stuart J. Murphy Even Steven and Odd Todd by Kathryn Cristaldi Math for All Seasons by Greg Tang Stay In Line by Teddy Slater The Best of Times: Math Strategies that Multiply

by Greg Tang Bats on Parade by Kathi Appelt The Doorbell Rang by Pat Hutchins A Remainder of One by Elinor J. Pinczes One Hundred Hungry Ants by Elinor J. Pinczes Go, Fractions! by Judith Bauer Stamper Jump, Kangaroo, Jump! by Stuart J. Murphy Apple Fractions by Jerry Pallotta 12 Ways to Get to 11 (Addition) by Eve Merriam Animals on Board (Addition) by Stuart J. Murphy Elevator Magic (Subtraction) by Stuart J. Murphy

Literature (continued)

Monster Musical Chairs (Subtraction) by Stuart J Murphy

Anno's Mysterious Multiplying Jar by Mitsumasa

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Anno Divide and Ride by Stuart J. Murphy

Check out this site for literature on different topics: http://www.thereadingnook.com/math/ Technology

Supporting Content Web Sites District website

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

http://www.newberry.k12.sc.us/InstructionalLinks/ math/Math_TOC_Page.html

Base 10 Blocks Virtually http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=category_g_2_t_1.html

Place Value Game to Hundred Thousands http://www.toonuniversity.com/flash.asp?err=503&engine=15

Place Value Tutorial, Practice, and Games http://www.aaamath.com/plc31e-placevalue-w2n.html

Place Value Puzzler http://www.funbrain.com/tens/index.html

Place Value Playoff! (http://www.quia.com/mc/279741.html

Place Value Play off Concentration http://www.quia.com/cc/279741.html

Space Chase Place Value http://teacher.scholastic.com/lessonrepro/reproducibles/profbooks/m970818c.htm

SMART Notebook Lessons/Activities http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Technology (continued) Cookie Dough

http://www.funbrain.com/cgibin/shtml.cgi?A1=../numwords/index.html

Place Value Games http://www.mathwire.com/games/pvgames.html

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What’s Your Name? (Students practice numbers in standard, word, and expanded forms.) http://www.beaconlearningcenter.com/WebLessons/WhatsYourName/default.htm

Genius Boxing http://www.mrnussbaum.com/geniusboxing.htm

Base 10 Blocks Virtually http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=category_g_2_t_1.html

Compare Two Numbers http://www.quia.com/pop/7512.html

Comparing Number Values http://www.toonuniversity.com/flash.asp?err=509&engine=9

Compare Numbers: Three Levels http://www.crickweb.co.uk/assets/resources/flash.php?&file=ncmenu

Number Sense http://pbskids.org/cyberchase/games/numbersense/index.html

Greatest to Least http://www.starrmatica.com/standalone/starrMaticaComparingNumbersCometoOrder.swf

For Place Value overall: Promethean Planet http://www.prometheanplanet.com/server.php?ResourceSearch%5Bsearch_text%5D=place+value&ResourceSearch%5Bsubject%5D=00200n009002002002&ResourceSearch%5Bgrade%5D=00200n009002003002&display=006007001&ResourceSearch%5Baction%5D=advanced&change=ResourceSearchResults&catMatchType=includeChildren&searchType=basic&x=31&y=11

Round Numbers to Nearest Thousand http://www.aaamath.com/est41c-round1000.html

Rounding for 3rd Graders http://www.prometheanplanet.com/server.php?show=ConResource.10258

Rounding Memory Game http://www.numbernut.com/advanced/activities/estimate_mem20_round1000.shtml

Technology (continued) Rounding to Nearest Hundred Memory Game

http://www.numbernut.com/advanced/activities/estimate

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_mem20_round100.shtml Seashell Rounding Activity Page

http://www.janbrett.com/piggybacks/rounding.htm Glowla’s Estimation Contraption

http://pbskids.org/cyberchase/games/ballparkestimation/index.html

Estimation Valley Golf http://www.mrnussbaum.com/estimationvalley.htm

Estimator Four http://www.shodor.org/interactivate/activities/EstimatorFour/?version=1.6.0_02&browser=MSIE&vendor=Sun_Microsystems_Inc.

Front End Estimation http://www.321know.com/est73ax2.htm

Space Shuttle Launch http://www.playkidsgames.com/games/shuttleLaunch/shuttleLaunch.htm

Save the Apples http://www.playkidsgames.com/games/apples/savetheApples.htm

Math Baseball http://www.funbrain.com/math/index.htl UFO Addition and Subtraction Mystery Game

http://www.dositey.com/addsub/mystery2AS.htm Addition and Subtraction Practice

http://www.ixl.com/math/grade/third/ All About Multiplication

http://illuminations.nctm.org/LessonDetail.aspx?id=U109

Arithmetic Four http://www.shodor.org/interactivate/activities/ArithmeticFour/

Multiplication Facts Practice from zero to 12 http://www.aaastudy.com/mul39ex2.htm

Camel Times Tables http://www.bbc.co.uk/schools/ks1bitesize/numeracy/multiplication/index.shtml

Division Mine http://www.bbc.co.uk/schools/ks1bitesize/numeracy/division/index.shtml

Math Baseball http://www.funbrain.com/math/index.html

Technology (continued) Soccer Shootout

http://www.funbrain.com/fractop/index.html

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Tic Tac Toe Squares http://www.funbrain.com/tictactoe/index.html

Meteor Multiplication http://www.arcademicskillbuilders.com/games/meteor/meteor.html

Drag Race Division http://arcademicskillbuilders.com/games/drag_race/drag_race.html

Demolition Division http://www.arcademicskillbuilders.com/games/demolition/demolition.html

Lemonade Larry http://www.prongo.com/lemon/game.html

Inverse Operations http://www.ixl.com/math/practice/grade-3-relate-multiplication-and-division

Interactive Multiplication Table http://www.mathcats.com/explore/multiplicationtable.html

Fun 4 The Brain Multiplication! http://www.fun4thebrain.com/mult.html

Fun 4 The Brain Division! http://www.fun4thebrain.com/division.html

Fly a Kite http://www.harcourtschool.com/activity/fly_a_kite/

SMART Notebook Lessons/Activities, and SMART Ideas Software activities. http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Fractions: Parts of a Whole http://nlvm.usu.edu/en/nav/frames_asid_102_g_1_t_1.html?from=category_g_1_t_1.html

Naming Fractions http://nlvm.usu.edu/en/nav/frames_asid_104_g_1_t_1.html?from=category_g_1_t_1.html

Visualizing Fractions http://nlvm.usu.edu/en/nav/frames_asid_103_g_1_t_1.html?from=category_g_1_t_1.html

Technology (continued) Eggsactly with a Dozen Eggs

http://illuminations.nctm.org/LessonDetail.aspx?ID=L336

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Eggsactly with Eighteen Eggs http://illuminations.nctm.org/LessonDetail.aspx?ID=L337

Investigating Fractions with Pattern Blocks http://illuminations.nctm.org/LessonDetail.aspx?ID=L343

Fun with Fractions http://illuminations.nctm.org/LessonDetail.aspx?ID=L344

Fraction Fun http://www.vectorkids.com/vkfractions.htm

Melvin’s Make a Match http://pbskids.org/cyberchase/games/equivalentfractions/index.html

Pizza Party http://www.primarygames.com/fractions/question1.htm

Crossing the River http://www.harcourtschool.com/activity/cross_the_river/

Understand Fractions http://www.harcourtschool.com/activity/con_math/g03c21.html

Fraction Race http://www.harcourtschool.com/activity/fraction_race_b/

Kids and Cookies http://www.teacherlink.org/content/math/interactive/flash/kidsandcookies/kidcookie.php

Identify the Fraction (Enter site as guest.) http://www.ixl.com/math/practice/grade-2-identify-the-fraction

Which shape matches the fraction? (Enter site as guest.) http://www.ixl.com/math/practice/grade-2-which-shape-illustrates-the-fraction

Parts of a group (Enter site as guest.) http://www.ixl.com/math/practice/grade-2-fractions-parts-of-a-group

Word Problems with Fractions (Enter site as guest.) http://www.ixl.com/math/practice/grade-2-fractions-word-problems

Technology (continued) Thirteen Ways of Looking at a Half

http://pbskids.org/cyberchase/games/fractions/index.html Batter’s Up Baseball

http://www.prongo.com/math/multiplication.html

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Base 10 Blocks Online http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=category_g_2_t_1.html

Multiplication Activity (Have manipulatives available for students to use to help them solve the problems. Use as practice.) http://www.numbernut.com/basic/activities/mult_quiz_2x1nocarry-v.shtml

Ghost Blasters http://resources.oswego.org/games/Ghostblasters1/gbcd.html

Suggested Streamline Videohttp://www.scetv.org/education/StreamLineSC/ http://search.discoveryeducation.com/CurriculumStandardLookup.cfm

Cross Curricular Opportunities:

Social StudiesCenturies & Decades (TE p. 1C)

WritingMath Journals, Word Problems, Write to Explain

ReadingClassify & Categorize Math Problems

ScienceRound Numbers (TE p. 1C)Understanding Multiplication (TE p. 172C), Understanding Division (TE p. 252C)

PEUse connecting cubes to create a model of Multiplication (TE p. 172C)Use connecting cubes to create a model of division (TE p. 252 C)

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Third Grade---Support DocumentNumber and Operations

Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

The indicators for this standard are grouped by the following major concepts: Number Structure and Relationships – Whole Numbers Number Structure and Relationships – Fractions Operations – Addition and Subtraction Operations – Multiplication and Division

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follow.

Number Structure and Relationships - Whole NumbersIndicators3-2.1 Compare whole-number quantities through 999,999 by using the terms is less

than, is greater than, and is equal to and the symbols <, >, and =.3-2.2 Represent in word form whole numbers through nine hundred ninety-nine

thousand. 3-2.12 Analyze the magnitude of digits through 999,999 on the basis of their place value.

Second grade students had experiences comparing whole-number quantities through 999 by using the terms is less than, is greater than, and is equal to and symbols <, >, and =. Third grade builds on this by comparing whole-number quantities through 999,999 (terms and symbols).

In second grade, students were expected to represent quantities in word form through twenty and multiples of ten through ninety while third grade students are expected to represent whole numbers in word form through nine hundred ninety-nine thousand. Third grade students should be able to correctly read number representations through the hundred thousands. An example is 123,456 which is read as “one hundred twenty-three thousand, four hundred fifty-six.”

Second grade focused on the conceptual development of place value which was strengthened by a hands-on approach using manipulatives. Even at this level, it is important that third grade students continue to use manipulatives that are proportional in nature. It is most common for 64,432 to be shown as 6 ten-thousands, 4 thousands, 4 hundreds, 3 tens, 2 ones, or as 64,432 ones; however, partial grouping is a prerequisite skill as it is the basis for trades, so students should be able to represent numbers in different equivalent forms (e.g., expanded notation). It is important that they also see the

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number as 64 thousands, 3 hundreds, 13 tens, 2 ones, as well as 644 hundreds, 2 tens and 12 ones.

Second grade focused on understanding composing and decomposing 3 digit numbers. Students can apply their understanding of place value to numerals up to 6 digits in third grade. This will help build their facility with mental computation, estimation skills, and performing paper-and-pencil computations for all operations in mathematics as they progress through to middle school.

Teacher Note: Place value is the value given to a digit by virtue of the place it occupies in the number relative to the units place. When speaking of the base ten system each place to the left of the units place represents ten times the value of the place to the immediate right. The position of the digits in a number will determine the value of the digit.

When writing large numbers, it is important to note that a common student misconception is that two thousand five is written as 20005. This can be avoided by writing numbers within a labeled grid. The student will immediately observe that there is not the physical space to record the number when beginning with the thousands place. Another common mistake is to say “and” where commas occur in a number. A special effort should be made to avoid that mistake. For example, one thousand five hundred sounds very close to one thousand and 5 hundredths. Correcting that error immediately will avoid later confusion for the student.

In second grade students analyzed the magnitude of digits through 9,999 on the basis of their place values. Third grade students expand that to hundred thousands.

Number Structure and Relationships - FractionsIndicators3-2.5 Understand fractions as parts of a whole. 3-2.6 Represent fractions that are greater than or equal to 1.

Third grade is the first time students are expected to develop an understanding of the meanings and uses of fractions to represent parts of a whole as well as to represent fractions that are greater than or equal to 1. Therefore, students should be given sufficient experiences with concrete and pictorial models to fully grasp the concept.

Third grade students will begin to associate fraction names with parts. They should work with a single item (concrete and pictorial) that can be cut/divided into smaller, equal parts. This includes drawing, coloring, using tiles, number lines, etc. to show the part/whole relationship. The emphasis is on the relationship of the part to the whole. Therefore, identifying the whole before cutting/dividing and then having an identical whole for comparison once discussion begins is critical. The notion of fractional parts being equal size portions/pieces needs to be stressed.

Emphasis should be placed on helping children understand that the bottom number (denominator) of the fraction tells into how many pieces the item has been cut/divided and the top number (numerator) tells how many of those pieces you have.

Third grade is the first time students are introduced to representing fractions equal to or greater than one. The emphasis is on representing fractions that are equal to or greater than one. That is, using models or pictures students should be able to represent

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fractions. Third grade students should NOT change those fractions to improper fractions. That will be dealt with in fourth grade.

Teacher Notes: It is important that students understand the distinction between fraction of a set, fraction of a region (area model) and fractions on a number line (linear model). For example, when equally dividing a candy bar, the portions should be equal – equal area in each piece. However, when dividing a set of objects like toys or pattern blocks, equal division depends on the number of items in the set, not the area of each item. When working with linear models, equal division depends on the distance from one point to another. Students need experiences with all three forms.

Connections To:

Other Third Grade Indicators3-4.7 Analyze the results of combining and subdividing circles, triangles, quadrilaterals,

pentagons, hexagons, and octagons.

This indicator can be related to fractions through a discussion of the fractional relationships that result from combining and subdividing the shapes.

Operations - Addition and Subtraction

Indicators3-2.3 Apply an algorithm to add and subtract whole numbers fluently. 3-2.4 Apply procedures to round any whole number to the nearest 10, 100, or 1,000. 3-2.9 Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers has on the outcome. (This is also repeated under “Operations – Multiplication” below.)

In second grade, students generated strategies to add and subtract two-digit numbers with and without grouping. As a result of sharing those generated strategies students developed an understanding of the concepts of addition and subtraction, even though their work was limited to concrete and pictorial models with two digits. In third grade the emphasis is on applying an algorithm. Students should take the strategies developed using concrete/pictorial models in second grade and connect them to algorithms in 3rd grade. As a result, by the end of third grade students should exhibit fluency when solving a wide range of addition and subtraction problems involving whole numbers.

When adding and subtracting, students should be given, and should also create, a wide range of problems that show real world situations. Before computing, students should estimate the outcome. “Rounding is the most familiar form of estimation. Estimation based on rounding is a way of changing the problem to one that is easier to work with mentally.” (Van de Walle, Pg. 234) In second grade students generated strategies to round numbers through 90 to the nearest 10. Students should build on those previously generated strategies and apply them to round whole numbers to the nearest 10, 100, or 1,000. Since students use their knowledge of place value to add and subtract, that

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should be connected to rounding as a means of determining the reasonableness of answers. Rounding should include both front end estimation (rounding before completing an operation) and end estimation (performing an operation and then rounding). Students should compare the results of both techniques to determine which technique would be more appropriate for the situation.

Students should be given opportunities to come to the conclusion that the sum of two odd or two even numbers will be even; while the sum of one odd and one even will be odd. The same is true for subtraction. So, for example, if they are adding two even numbers and get an odd number answer, they may conclude that the answer is incorrect.

Connections To:

Other Third Grade Indicators3-3.1 Create numeric patterns that involve whole-number operations3-3.2 Apply procedures to find missing numbers in numeric patterns that involve

whole-number operations.3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction,

or multiplication equation.

Since these connections are obvious, no further explanation will be given here. For information about the indicators see the indicators under the Algebra standard 3-3.

Operations – Multiplication and DivisionIndicators3-2.7 Recall basic multiplication facts through 12 x 12 and the corresponding division facts.3-2.8 Compare the inverse relationship between multiplication and division.3-2.9 Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers has on the outcome. (This is also repeated under “Operations - Addition and Subtraction” above.)3-2.10 Generate strategies to multiply whole numbers by using one single -digit factor and one multi-digit factor.3-2.11 Use basic number combinations to compute related multiplication problems that involve multiples of 10.

In second grade, students interpreted models of equal grouping (multiplication) as repeated addition and arrays as well as interpreting models of equal sharing (division) as repeated subtraction and arrays.

Third grade students should be able to explain the meaning of multiplication and division, and begin to recall multiplication facts through 12 x 12 and the corresponding division facts. Students should be given experiences that foster conceptual understanding and connect to the symbolic. Third grade students should begin with concrete and pictorial representations, such as rectangular arrays and repeated addition using one and two-digit numbers.

As the verb “generate” implies in indicator 3-2.10, students should be given opportunities to share their strategies as they develop an understanding of multiplying

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one single-digit factor and one multi-digit factor. Students should be able to rely on their knowledge of place value and decomposing and composing numbers from second grade to help them generate strategies. For example, a generated strategy could be decomposing a 2 digit number and multiplying each digit by the other 1 digit factor. In other words, a strategy for multiplying 27 X 9 could be to decompose 27 to 20 + 7 and multiplying 20 x 9 = 180 and 7 x 9 = 63 and then adding the products 180 + 63 = 243. Therefore, students will need multiple experiences. The emphasis is on student understanding, not memorizing a process. The entire third grade experience with regard to multiplying one single-digit factor and one multi-digit factor should be limited to work with concrete and pictorial models. Students should NOT progress to symbolic operation until fourth grade. Heavy emphasis with concrete and pictorial models ensures conceptual understanding and serves as the foundation for fourth grade symbolic work.

Continuing to use models and pictorial representations in third grade will help students connect to the symbolic representation of the concept of multiplying and dividing as well as comparing the inverse relationship between the two. Students should be able to explain the relationship between the two operations.

Students should use their knowledge of the effect that adding and subtracting odd and/or even numbers has on the outcome to predict answers. They should be given time to test their strategies for accuracy. Third grade students should be given opportunities to come to the conclusion that the product of two odd numbers is odd, the product of two even numbers is even, and that the product of an odd and even number is even.

Connections To:

Other Third Grade Indicators3-3.1 Create numeric patterns that involve whole-number operations. 3-3.2 Apply procedures to find missing numbers in numeric patterns that involve

whole-number operations. 3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction,

or multiplication equation.

Since these connections are obvious no further explanation will be given here. For information about the indicators see the indicators under the Algebra standard 3-3.

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Grade 3 Algebra

Big Ideas: Numeric Patterns, Unknown Quantities, and Increases over Time

Standard 3-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time.

Indicators:3-3.1 Create numeric patterns that involve whole-number operations. 3-3.2 Apply procedures to find missing numbers in numeric patterns that involve

whole-number operations.3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction,

or multiplication equation. 3-3.4 Illustrate situations that show change over time as increasing.

Essential Questions: How can you find the missing addend? (3-3.3) How do fact families relate addition and subtraction? (3-3.3) How can you use arrays or multiplication tables to find missing factors? (3-3.3) What information can be found on a line graph? (3-3.4) How would you create a numeric pattern by adding, subtracting, or multiplying?

(3-3.1) How would you find a missing number in a numeric pattern? (3-3.2)

Help Page for Standard 3-3

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Notes:Assessments:

Assessment examples can be accessed at http://www.s2martsc.org/.  Module 1-3 (3-3.1, 3-3.2, 3-3.3)Module 2-2 (3-3.1, 3-3.2, 3-3.3)

Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed. Assessment Examples:   Chapter Review and Test PrepChapter Tests MAP Testing OdysseyExit tickets Questioning Strategies Journaling/Written AssessmentsProjectsPair Share

Textbook Correlations

3-3.1 Lessons 15.3, 15.43-3.2 Lessons1.1, 15.2-15.4 3-3.3 Lessons 3.1, 4.13-3.4 Lesson 6.7

Key Concepts (Vocabulary)

evenoddpatternaddend

fact familyinverse operationsline graphtrendsvariable

Literature

180 Think-Aloud Math Word Problems by Denise Nessel

Anno's Magic Seeds by Mitsumasa AnnoLiterature (continued)

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The Grapes of Math by Greg Tang Math for All Seasons by Greg Tang Math Potatoes: Mind-Stretching Brain Food by Greg

Tang One Grain of Rice by Demi Read It! Draw It! Solve It! Grade 3 by Elizabeth D.

Miller The Best Vacation Ever by Stuart J. Murphy The King's Chessboard by David Birch

Check out this site for literature on different topics: http://www.thereadingnook.com/math/ Technology

Supporting Content Web Sites District website

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

http://www.newberry.k12.sc.us/InstructionalLinks/ math/Math_TOC_Page.html

What Comes Nex_? Teaching Children Mathematics http://illuminations.nctm.org/LessonDetail.aspx?id=L286

Patterns That Grow http://illuminations.nctm.org/LessonDetail.aspx?id=U103

Petals Around the Rose http://illuminations.nctm.org/LessonDetail.aspx?id=L576

Number Patterns and Rules http://www.harcourtschool.com/activity/rubber_number_patterns_and_rules/

Patterns Video http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/5_Patterns/index.html

Crack Hacker’s Safe http://pbskids.org/cyberchase/webisode_1/web_1game.html

Patterns to the Rescue http://pbskids.org/cyberchase/parentsteachers/lessons/lessonplans/lesson4.html

Technology (continued) SMART Notebook Lessons/Activities

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http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Number Cracker http://www.funbrain.com/cracker/index.html

Missing Numbers in a Sequence http://www.beaconlearningcenter.com/WebLessons/MissingNumbers/default.htm

Find Missing Numbers http://www.321know.com/g1fm_by5.htm

Pattern Lessons http://www.aaamath.com/pat.htm Chairs Around the Table

http://illuminations.nctm.org/LessonDetail.aspx?id=L627 Function Machine

http://teams.lacoe.edu/documentation/classrooms/amy/algebra/3-4/activities/functionmachine/functionmachine3_4.html

Function Machine from National Library of Virtual Manipulatives http://nlvm.usu.edu/en/NAV/frames_asid_191_g_3_t_1.html

Stop that Creature! http://pbskids.org/cyberchase/games/functions/functions.html

Missing Addend http://www.harcourtschool.com/activity/show_me/e453.htm

Finding a Missing Number in a Sequence http://www.aaastudy.com/pat_by4.htm

Suggested Streamline Videohttp://www.scetv.org/education/StreamLineSC/ http://search.discoveryeducation.com/CurriculumStandardLookup.cfm

Cross Curricular Opportunities

Visual ArtsFind and design geometric patterns in Art p. TE 320C

ReadingSummarize (TE p. 360A)

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ScienceUnderstand congruence (TE p. 320C)

Third Grade---Support Document

Algebra

3-22

Standard 3-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time.

The indicators for this standard are grouped by the following major concepts: Patterns, Relationships, and Functions Representations, Properties, and Proportional Reasoning Change in Various Contexts

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follow.

Patterns, Relationships, and FunctionsIndicators3-3.1 Create numeric patterns that involve whole-number operations. 3-3.2 Apply procedures to find missing numbers in numeric patterns that involve

whole-number operations.

In second grade, students analyzed numeric patterns and examined relationships to complete and extend growing and repeating patterns with numbers, symbols and objects. While first grade students examined patterns in addition and subtraction to acquire basic facts, there was no emphasis on patterns involving operations. Third grade is the first time students are formally introduced to patterns involving operations.Third grade students are expected to create patterns that involve the whole-number operations of addition and subtraction and basic multiplication. This should include situations where elements of the pattern are missing either within the sequence or at the end of the sequence.

Representations, Properties, and Proportional ReasoningIndicators3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction,

or multiplication equation.

In second grade, students had experiences generating strategies for addition and subtraction pairs of two-digit whole numbers with regrouping. Third graders build on these skills, using symbols to represent unknown quantities in addition, subtraction, and multiplication equations. Students use symbols to represent specific unknown quantities such as 3 x __ = 12. Students need to understand that the symbol is a placeholder for an unknown quantity and that for each equation or problem solving situation, the symbol represents a different number. Students should start with simple number sentences to ensure understanding.

In fourth grade, they will begin to use variables to represent missing quantities in simple expressions and equations. “To help students develop skills of solving equations with one variable, it is advisable to maintain the image of the balance pans. The balance makes it reasonably clear to students that if you add or subtract value from one side, you

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must add or subtract like values from the other side to keep the scales balanced.” (Teaching Student-Centered Mathematics 3-5, Van de Walle p. 312.) Teacher Note: Students often have a common misunderstanding with regard to the concept of equivalence. Prior to the third grade, students may have simply written an answer after the equal sign. Now, students must clearly understand that the equal sign does not mean “perform an operation”. It means that there is a relationship of equivalence between the two expressions on either side of that equal sign.

Connections to:

Other 3rd Grade Indicators:3-2.2 Apply an algorithm to add and subtract whole numbers fluently. 3-2.7 Recall basic multiplication facts through 12 x 12 and the corresponding division

facts.

Literature:

Safari Park by Stuart MurphyThe story is about children who share tickets at an amusement park. The children

have to decide if they have enough tickets to do all of the things they want to do there and still share with one child who lost his tickets. Students can use 20 manipulatives as tickets and act out each scenario. The teacher can show equations that use symbols for unknowns as students represent them with manipulatives. After this is modeled, students can use the later scenarios in the story to create equations using symbols.

Change in Various ContextsIndicators3-3.4 Illustrate situations that show change over time as increasing.

First grade students classified change over time as qualitative or quantitative. In other words they understood, in simple form, that attribute change is qualitative and numeric change is quantitative. Second grade students illustrated and analyzed qualitative and quantitative change over time. In other words they were able to distinguish between the time and quantitative or time and qualitative elements. Third grade students should build on those prior learning experiences by specifically finding examples of situations that show change over time as increasing. The emphasis here is on understanding that the change is increasing over the time period. For example, students may record the temperature when they arrive at school and again at two-hour intervals during the day. The next day students could examine the data in light of the increase of temperature (change) over time. Students will deal with the decreasing aspect in 4th grade and pull both increasing and decreasing together in later grades.

Connections to:

Other 3rd Grade Indicators:

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Students should also be able to interpret data in tables and graphs to describe the change that has occurred.

3-6.1 Interpret data in tables, bar graphs, pictographs, and dot plots. 3-6.4 Analyze dot plots and bar graphs to make predictions about populations.

Literature:

The 512 Ants on Sullivan Street by Carol A. LosiThis story illustrates a growing pattern (doubling) and thus increasing change

over time. After each page students can describe the change and make predictions about how many ants will show up next. Afterwards, students can relate the story to change over time as increasing – as time passed, the number of ants that showed up increased.

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Grade 3 Geometry

Big Ideas: Identification and Classification of Two-Dimensional Shapes

Standard 3-4: The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes.

Indicators:3-4.1 Identify the specific attributes of circles: center, radius, circumference, and

diameter. 3-4.2 Classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or

octagons according to the number of their sides. 3-4.3 Classify lines and line segments as either parallel, perpendicular, or intersecting.3-4.4 Classify angles as either right, acute, or obtuse.3-4.5 Classify triangles by the length of their sides as either scalene, isosceles, or

equilateral and by the size of their angles as either acute, obtuse, or right. 3-4.6 Exemplify points, lines, line segments, rays, and angles. 3-4.7 Analyze the results of combining and subdividing circles, triangles,

quadrilaterals, pentagons, hexagons, and octagons. 3-4.8 Predict the results of one transformation—either slide, flip, or turn—of a

geometric shape.

Essential Questions: How are points, lines, line segments, and angles related? (3-4.6) How are acute, right, and obtuse angles alike? How are they different? (3-4.4, 3-

1.3, 3-1.4, 3-1.5) How do you classify lines? (3-4.3, 3-1.4) How are two-dimensional shapes classified? (3-4.2, 3-1.4) What ways can you classify triangles? (3-4.5, 3-1.4) What are the different parts of a circle? (3-4.1) How can you use Venn diagrams to solve problems? (3-4.2, 3-1.1, 3-1.4) What shapes can you make by combining and taking apart two-dimensional

shapes? (3-4.7, 3-1.4) How can you tell if two shapes are congruent? (3-1.4) How does a slide, flip, or turn affect a shape? (3-4.8) In what ways can you classify triangles? (3-4.5)

Help Page for Standard 3-4

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Notes:Assessments

Assessment examples can be accessed at http://www.s2martsc.org/.  Module 3-3 (3-4.3, 3-4.4, 3-4.6, 3-4.7)Module 3-4 (3-4.1, 3-4.2, 3-4.5)Module 4-1 (3-4.8)  Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed. Assessment Examples:   Chapter Review and Test PrepChapter Tests MAP Testing OdysseyExit tickets Questioning Strategies Journaling/Written AssessmentsProjectsPair Share

Textbook Correlations

3-4.1 Lesson 14.63-4.2 Lessons 14.4, 14.73-4.3 Lesson 14.33-4.4 Lesson 14.23-4.5 Lesson 14.53-4.6 Lesson 14.13-4.7 Lesson 14.83-4.8 Lesson 14.10

Key Concepts (Vocabulary)

pointlineline segmentrayanglevertexKey Concepts (Vocabulary)

polygonquadrilateralpentagonhexagonoctagonequilateral triangle

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continued

acuteobtuseright angleacute angleobtuse angleintersecting lines perpendicular linesparallel linestwo-dimensional shapecongruent flipturn

isosceles trianglescalene triangleright triangleobtuse triangleacute trianglecirclecenterradiusdiametercircumferenceslide

Literature

Captain Invincible and the Space Shapes by Stuart J. Murphy

The Greedy Triangle by Marilyn Burns When a Line Bends… a Shape Begins by Rhonda

Gowler Greene Circus Shapes by Stuart J. Murphy Cubes, Cones, Cylinders, and Spheres by Tana Hoban

Check out this site for literature on different topics: http://www.thereadingnook.com/math/

Technology

Supporting Content Web Sites District website

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

http://www.newberry.k12.sc.us/InstructionalLinks/ math/Math_TOC_Page.html

Polygons http://www.prometheanplanet.com/server.php?show=ConResource.9366

Polygons and Quadrilaterals http://www.prometheanplanet.com/server.php?show=ConResource.8261

Classifying Shapes http://www.prometheanplanet.com/server.php?show=ConResource.514

Sorting Polygons

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http://illuminations.nctm.org/LessonDetail.aspx?ID=L277

Name the Polygon http://www.aaamath.com/geo318-polygons- numbers.html Baseball Geometry

http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50646

Online Geoboard http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm

Polygon Capture http://illuminations.nctm.org/LessonDetail.aspx?ID=L270

Polygon Game http://www.math-play.com/Polygon-Game.html SMART Notebook Lessons/Activities

http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Parallel, Perpendicular, and Intersecting Lines http://www.ixl.com/math/practice/grade-4-parallel-perpendicular-intersecting

SMART Notebook Lessons/Activities http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Icy Slides, Flips, Turns http://www.harcourtschool.com/activity/icy_slides_flips_turns/

Slides, Flips, and Turns Lesson Plan http://www.uen.org/Lessonplan/preview.cgi?LPid=16273

Slide, Flip, and Turn Activity http://illuminations.nctm.org/lessons/developgeometric/tangramactivitysheet.pdf

Technology (continued)

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SMART Board http://technology.usd259.org/resources/whiteboards/smart-lessons/notebook_lessons/2nd-3rdGradeFlipsSlidesRotationsWithSenteoQuiz.notebook

Slides, Flips, and Turns for Two-Dimensional Figures http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Senteo/Canada/Elementary/K-3/Math/Slides+Flips+and+Turns+for+Two+Dimensional+Figures+Question+set.htm

Transformation Games http://www.ntc-school.com/sec/math/t_resources/gamezone/pdfs/mac3_04/class_ch06.pdf

Shape Cutter http://illuminations.nctm.org/ActivityDetail.aspx?ID=72

Tangram Puzzles http://illuminations.nctm.org/LessonDetail.aspx?id=L168

Suggested Streamline Videohttp://www.scetv.org/education/StreamLineSC/ http://search.discoveryeducation.com/CurriculumStandardLookup.cfm

Cross Curricular Opportunities

Social StudiesCenturies & decades (TE p. 1C)

WritingMath Journals, Word Problems, Write to Explain

ArtFind and Design Patterns (TE p. 320C)

Third Grade---Support Document

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Geometry

Standard 3-4: The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes.

The indicators for this standard are grouped by the following major concepts: Dimensional Plane/Spatial Relationships Transformation

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follow.

DimensionalIndicators3-4.1 Identify the specific attributes of circles: center, radius, circumference, and

diameter. 3-4.2 Classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or

octagons according to the number of their sides. 3-4.5 Classify triangles by the length of their sides as scalene, isosceles, or equilateral

according to and by the sizes of their angles as acute, obtuse, or right.

Previously, students have identified a circle, but this is the first time students have encountered the attributes of a circle - center, radius, circumference, and diameter. This indicator only asks students to identify these attributes. For example, students are not required to calculate the circumference of a circle but are expected to understand that circumference is the distance around a circle. Ample opportunities for students to explore each attribute should be provided as well as definitions/explanations.

In 1st grade, students classified shapes as polygons/non-polygons and identified objects as circles, squares, triangles, or rectangles. Now, students classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or octagons according to the number of their sides. Students need many examples/models to see that polygons with the same number of sides may look quite different, but are still classified the same way. For example, all four sided polygons are quadrilaterals regardless of their side lengths. Activities in which students classify a set of objects by the number of sides would be good practice for this indicator.

Once the students have an understanding that all three-sided polygons are classified as triangles, they can begin classifying triangles by their side lengths and angle measures. Again, the students will need many different visual examples/models for this indicator. The vocabulary is new for 3rd grade students, so ample practice and review will be needed for mastery of these terms. Activities that require students to sort a set of triangles by the length of the sides (scalene, isosceles, equilateral) or by sizes of the angles (acute, obtuse, right) will help students master this indicator.

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Connections To:

Other Third Grade Indicators:Classifying angles as right, acute, or obtuse is also a 3rd grade standard addressed in the Plane/Spatial Relationships section of Geometry.3-4.4 Classify angles as either right, acute, or obtuse.

Technology:

Shape Tool - http://illuminations.nctm.org/ActivityDetail.aspx?ID=35Shape Sorter - http://illuminations.nctm.org/ActivityDetail.aspx?ID=34Investigating Shapes (Triangles) (Will need to adapt for 3rd grade) http://illuminations.nctm.org/LessonDetail.aspx?id=U52

Plane/Spatial RelationshipsIndicators3-4.3 Classify lines and line segments as either parallel, perpendicular, or intersecting.3-4.4 Classify angles as either right, acute, or obtuse.3-4.6 Exemplify points, lines, line segments, rays, and angles. 3-4.7 Analyze the results of combining and subdividing circles, triangles,

quadrilaterals, pentagons, hexagons, and octagons.

Third grade is the first time students encounter the difference between a point, line, line segment, ray, and angle. Students are asked to classify lines and line segments as parallel, perpendicular, or intersecting. They are also asked to classify angles as right, acute, or obtuse. An in-depth understanding will require many examples/models of each type of line/line segment and angle, along with emphasis placed on explanations and vocabulary. It is important to show lines, line segments, and angles in a variety of ways so the students do not memorize one type of example.

In order for students to exemplify points, lines, line segments, rays, and angles, they should be able to give an example or illustration that shows their understanding of each. Again, many examples/models must be provided for the students to gain this knowledge. Guiding the students to explain the differences between this terminology such as a line segment and a ray will help solidify their understanding. Students are not expected to use symbolic notation at this level.

In 2nd grade, students predicted the results of combining and subdividing polygons and circles. Now, in 3rd grade, students will analyze the results of combining and subdividing circles, triangles, quadrilaterals, pentagons, hexagons, and octagons. In order to analyze the results, the students will need experiences in combining and subdividing these shapes. Using manipulatives, such as geoboards, can help students see these results. The emphasis in third grade is on students seeing the relationship between various two-dimensional shapes. The indicator at this grade level does not require that students use the two-dimensional shapes to build three-dimensional shapes. That transition will be made in fourth grade. By analyzing the results of combining and subdividing the specified shapes in third grade, students will have the foundational knowledge for fourth

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grade when they analyze the relationship between three-dimensional shapes and two-dimensional nets. Connections to:

Other Third Grade Indicators3-5.4 Generate strategies to determine the perimeters of polygons.

As a part of their work with determining the perimeters of polygons, students should examine how combining and subdividing shapes affects the perimeter. This should be accomplished informally with shapes that have easily determined perimeters. For example, it would be difficult and not appropriate at this grade for students to compare the perimeter of a rectangle to the perimeter of the two triangles that would result from subdividing the rectangle (because at this grade students would not have sufficient knowledge to determine the length of the diagonal that was cut to form the two triangles). On the other hand, if subdividing a rectangle results in two squares, it would be appropriate at third grade to discuss that relationship.

Technology:

Shape Cutter - http://illuminations.nctm.org/ActivityDetail.aspx?ID=72

TransformationalIndicator3-4.8 Predict the results of one transformation—either slide, flip, or turn—of a geometric shape.

In third grade, students will have their first encounter with transformations (slide, flip, or turn) of shapes. Using geometric shaped manipulatives for the students to perform a transformation such as a slide, flip, or turn will help them conceptually understand the results. After many opportunities, the students should visualize the changes and be able to predict the result of one transformation.

Teacher Note: Prior knowledge from first grade of positional and directional terms north, south, east, and west can be linked to transformations when describing the location and movement of the geometric shape. The use of grid paper to apply transformations using the positional and directional terms would be appropriate.

Connection to:

Technology:

Shape Cutter http://illuminations.nctm.org/ActivityDetail.aspx?ID=72 Tangram Puzzles (students use a flip, slide, or turn to place pieces)

http://illuminations.nctm.org/LessonDetail.aspx?id=L168

Grade 3

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Measurement

Big Ideas: Length, Time, Weight, and Volume, Systems of Measure, Perimeter, and Money

Standard 3-5: The student will demonstrate through the mathematical processes an understanding of length, time, weight, and liquid volume measurements; the relationships between systems of measure; accurate, efficient, and generalizable methods of determining the perimeters of polygons; and the values and combinations of coins required to make change.

Indicators:3-5.1 Use the fewest possible number of coins when making change. 3-5.2 Use appropriate tools to measure objects to the nearest unit: measuring length in

meters and half inches; measuring liquid volume in fluid ounces, pints, and liters; and measuring mass in grams.

3-5.3 Recognize the relationship between meters and yards, kilometers and miles, liters and quarts, and kilograms and pounds.

3-5.4 Use common referents to make comparisons and estimates associated with length, liquid volume, and mass and weight: meters compared to yards, kilometers to miles, liters to quarts, and kilograms to pounds.

3-5.5 Generate strategies to determine the perimeters of polygons. 3-5.6 Use analog and digital clocks to tell time to the nearest minute. 3-5.7 Recall equivalencies associated with time and length: 60 seconds = 1 minute and

36 inches = 1 yard.

Essential Questions: How can you count forward to make change? (3-5.1) How do digital and analog clocks differ? (3-5.6) When would you use each customary unit of length? (3-5.7, 3-5.2) When would an estimate be better than an actual measurement? (3-5.2, 3-5.7) How are fluid ounces, cups, pints, quarts, and gallons related? (3-5.2) How are ounces and pounds related? (3-5.2) How are metric units of length related? (3-5.2) When would you use each unit of measure? (3-5.2) How can you compare liters and milliliters? (3-5.2) How can knowing how customary and metric units relate help you solve measurement problems? (3-5.3) How does knowing a benchmark for a measurement unit help you estimate

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measurements? (3-5.4) How do you know which measuring tool you should use to measure an object? (3-5.2) What strategies can you use to find perimeter? (3-5.5, 3-4.7) How can you find the perimeter of a shape? (3-5.5)

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Help Page for Standard 3-5

Notes:Assessments

Assessment examples can be accessed at http://www.s2martsc.org/.  Module 2-3 (3-5.6, 3-5.1)Module 3-1 (3-5.2, 3-5.3, 3-5.4)Module 4-2 (3-5.5)  Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed. Assessment Examples:   Chapter Review and Test PrepChapter Tests MAP Testing OdysseyExit tickets Questioning Strategies Journaling/Written AssessmentsProjectsPair Share

Textbook Correlations

3-5.1 Lesson 5.33-5.2 Lessons 17.1 – 17.4, 18.1 - 18.4, 18.7 3-5.3 Lesson 18.53-5.4 Lesson 18.63-5.5 Lessons 18.8, 18.93-5.6 Lessons 5.4, 5.53-5.7 Lessons 5.4, 17.1, 17.2

3-36

Key Concepts (Vocabulary)

changehalf hourquarter hourhourminuteanalog clockdigital clockseconddollardecimal pointequivalentlengthfoot (ft)yard (yd)mile (mi)inch (in)cup (c)capacity

pint (pt)quart (qt)gallon (gal)weightounce (oz)pound (lb)centimeter (cm)meter (m)kilometer (km)milliliter (mL)liter (L)massgram (g)kilogram (kg)perimetervolume fluid ounce (fl)

Literature

Get Up and Go! by Stuart J. Murphy Bunny Money by Rosemary Wells Nine O’Clock Lullaby by Marilyn Singer A House for Birdie (Volume or Capacity) by Stuart J.

Murphy Cook-A-Doodle-Doo! (Capacity) by Susan Stevens

Crummel How Big is a Foot? (Length) Rolf Myller How Tall, How Short, How Far Away? (Length) by

David A. Adler

Check out this site for literature on different topics: http://www.thereadingnook.com/math/

Technology

Supporting Content Web Sites District website

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

http://www.newberry.k12.sc.us/InstructionalLinks/ math/Math_TOC_Page.html

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Technology (continued) Time Concentration

http://www.harcourtschool.com/activity/con_math/g03c05.dcr

Telling Time with the Grouchy Ladybug http://askeric.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Measurement/MEA0200.html

Telling Time Game http://www.harcourtschool.com/activity/telling_time_gr3/

Time to the Minute http://www.harcourtschool.com/activity/elab2004/gr3/17.html

SMART Notebook Lessons/Activities http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Clockworks http://www.mrnussbaum.com/clockworks/index.html

Module on Time http://eisenhowermathematics.truman.edu/pdfs/Northeast%20Module%20Completed.pdf

Clockwork: The Time Telling Game (http://www.kidsnumbers.com/clock-work.php

Sid the Science Kid – Exploring Measurement video http://www2.totlol.com/watch/3hlkRcTmFxY/Sid-The-Science-Kid---Exploring-Measurement---Pbs-Kids/0/

Measure It! http://www.funbrain.com/measure/ Virtual Ruler http://www.quizville.com/measuring.php Artie Ounces Soda Jerk

http://www.mrnussbaum.com/soda.htm All About Measurement from Kids Konnect

http://www.kidskonnect.com/content/view/293/27/ Kid’s Corner

http://www.cdfa.ca.gov/dms/kidspage/KidsIndex.htm Pour and Score

http://pbskids.org/cyberchase/games/hardproblems/ The Ruler Game

http://www.rickyspears.com/rulergame/

Technology (continued) Measures

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http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/measures/index.htm

Estimation of Length Video http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/2_Estimation_of_Length/index.html

Weight and Capacity Video http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/6_Weight_and_Capacity/index.html

Measurement Lessons from AAA Math http://www.aaamath.com/mea.htm

Virtual Measurement Manipulatives http://nlvm.usu.edu/en/nav/category_g_2_t_4.html

Math Flash Measurement 1 www.hcbe.net/itc/powerpoints/files/7BF37756C3DB4D0D9CB8695216170416.ppt

Body Measurements Lessons from Illuminations http://illuminations.nctm.org/LessonDetail.aspx?id=L659

Which customary unit is appropriate? http://www.ixl.com/math/practice/grade-3-which-customary-unit-is-appropriate

Compare Customary Units http://www.ixl.com/math/practice/grade-3-compare-customary-units-by-multiplyingWhich metric unit is appropriate? http://www.ixl.com/math/practice/grade-3-which-metric-unit-is-appropriate

Length Strength http://www.harcourtschool.com/activity/length_strength3/

Estimate Customary Length using Inch Ruler http://www.harcourtschool.com/activity/elab2004/gr3/22.html

Length Strength http://www.harcourtschool.com/menus/math2004/math2004_gr2.html

Measure and Measure Song http://www.harcourtschool.com/jingles/jingles_all/1measure.html

Ounce or Pound http://www.harcourtschool.com/activity/ounces_pounds/

Technology (continued) Length Strength

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http://www.harcourtschool.com/activity/length_strength2_centi/

Perimeter Explorer http://www.shodor.org/interactivate/lessons/PerimeterElem/

Adam Ant http://www.beaconlearningcenter.com/WebLessons/AdamAnt/page1.htm

Geoboard http://nlvm.usu.edu/en/nav/frames_asid_281_g_2_t_4.html?open=activities&from=category_g_2_t_4.html

Suggested Streamline Videohttp://www.scetv.org/education/StreamLineSC/ http://search.discoveryeducation.com/CurriculumStandardLookup.cfm

Cross Curricular Opportunities

Science Tell time to the nearest quarter hour (TE p. 100C)Change units of capacity (TE p. 372C)

Social StudiesMeasure distance on a map (TE p. 372C)

Third Grade---Support Document

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Measurement

Standard 3-5: The student will demonstrate through the mathematical process an understanding of length, time, weight, and liquid volume measurements; the relationships between systems of measure; accurate, efficient, and generalizable methods of determining the perimeters of polygons; and the values and combinations of coins required to make change.

The indicators for this standard are grouped by the following major concepts: Money Length, Liquid Volume, and Mass and Weight Time Perimeter Equivalencies

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follows.

MoneyIndicators3-5.1 Use the fewest possible number of coins when making change.

In second grade students used a variety of counting procedures to determine the value of a collection of coins and bills. Also, second grade students used various combinations of coins to make change up to one dollar. Students have previously used cent and dollar notations

The focus in third grade is to make change using the fewest number of coins possible. Students should be provided experiences with realistic-looking models of coins and bills as well as real coins. Making change and then keeping track of the coins used can be used as a tool to challenge students to determine whether or not there are other combinations that require fewer coins to achieve the same results. This should be related to real world situations where clerks need to give a customer the fewest number of coins when making change – both from the clerk’s efficiency perspective and for the customer’s convenience.

Length, Liquid Volume, and Mass and WeightIndicators3-5.2 Use appropriate tools to measure objects to the nearest unit:

measuring length in meters and half inches; measuring liquid volumein fluid ounces, pints, and liters; and measuring mass in grams.

3-5.3 Recognize the relationship between meters and yards, kilometers andmiles, liters and quarts, and kilograms and pounds.

3-5.4 Use common referents to make comparisons and estimatesassociated with length, liquid volume, and mass and weight: meterscompared to yards, kilometers to miles, liters to quarts, and

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kilograms to pounds.

In previous grades the emphasis was on length and weight. Students used nonstandard and standard units to compare and order objects. Appropriate tools were used to measure objects to whole-inch units. Students have previously generated and used common measurement referents for inches, feet, yards and centimeters.

In third grade students should select and use the appropriate tool to measure length to the nearest meter and half inch; to measure liquid volume in fluid ounces, pints, and liters; and to measure mass in grams. In addition to measuring to the units just specified, third grade students should recognize that a meter is slightly more than a yard, that a kilometer is about one-half as much again as a mile, that a liter is slightly more than a quart and that a kilogram is slightly more than two pounds. It is not necessary that third grade students know the exact equivalencies. Rather it is more important that they understand the relationship between the specified measurements. This should be accomplished through experiences not through memorization of facts.

First grade students generated common referents for whole inches and in second grade they generated common referents for feet, yards, and centimeters. In third grade student should use their understanding of the relationship between meters/yards, kilometers/miles, liters/quarts, and kilograms/pounds to generate common referents. For example, if experiences lead students to the referent that a yard is about the distance from the elbow to the tip of the middle finger, then they should know that a meter is slightly more than that benchmark. Having benchmarks for the specific units mentioned gives students a basis on which to make estimates for those measures. Again, however, these benchmarks should be derived from a variety of meaningful experiences for students. Strict memorization of meaningless facts will soon be forgotten. A variety of experiences in context will be meaningful and lasting.

Other than the introduction of centimeters in second grade, this is the first time students will have experience with the metric system. Therefore, sufficient learning experiences need to be provided for students. While students have worked with liquid volume and weight in second grade, the concepts of metric liquid volume and mass are new for third grade students. Skill with both U.S. Customary and metric units and tools is important for students. As children learn about the units and tools in both systems of measurement, they see that the same process of measurement is used for both systems, but the units are different.

Within each area of measurement, students need to learn to use standard units and tools of measuring and to develop the ability to estimate. Students deepen and expand their understanding and use of measurement.

In addition, third grade students should focus on the relationship of measurement to fractions, specifically, since fractional parts of a unit are introduced in third grade. Since third grade students should measure length to the nearest one-half inch, it is only natural that a link be made between fractions and measurement.

Connections To:

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Other Third Grade Indicators3-2.5 Understand fractions as part of a whole.3-2.6 Represent fractions that are greater than or equal to 1.

Since this connection was addressed in the last paragraph above, no further explanation will be provided. For details regarding the elements of essential learning for 3-2.5 and 3-2.6 see the Number and Operations standard.

TimeIndicator3-5.5 Use analog and digital clocks to tell time to the nearest minute.

In previous grades students used analog and digital clocks to tell time to the hour, half hour, quarter hour, and five-minute interval. Third graders are expected to tell time to the nearest minute using analog and digital clocks.

Digital and analog timepieces are part of the children’s world, and they should learn to read time with both. For both digital and analog devices, the underlying concept is the constant passing of seconds, minutes, and hours. The digital clock shows the current time only. It permits students to read times easily but does not relate times very well. To know that a digital reading of 7:58 is nearly 8 o’clock, the child must know that there are 60 minutes in an hour, that 58 is close to 60, and that 2 minutes is not a very long time. An analog clock shows current time but also does more. The 12 numerals and moving hands enable children to note the beginning and ending times for an event. When a parent says “It is 2:00; we have 16 minutes before the movie begins at 2:16,” a clock face makes it easy to see 2:00 and the distance the minute hand must move to reach 2:16. It shows “close to” times without the need for understanding big numbers or even how many minutes are in an hour.

Students benefit when asked to predict the reading on a digital clock when shown an analog clock, and vice versa; set an analog clock when shown a digital clock. This can be done with both one-handed and two-handed clocks.

Use two real clocks, one with only an hour hand and one with two hands. (Break off the minute hand from an old clock.) Cover the two-handed clock. Throughout the day, direct attention to the one-handed clock. Discuss the time in approximate language. Have students predict where the minute hand should be. Uncover the other clock and check.

PerimeterIndicator3-5.6 Generate strategies to determine the perimeters of polygons.

Third grade is the first time students are formally introduced to the concept of perimeter. As a result students should generate strategies to determine the perimeters of polygons. Perimeter is the measure of the distance around a closed figure and is an extension of length measurement. Problems dealing with realistic situations give children practical experiences that help them to determine perimeters and to distinguish perimeter from the measures of area with which they will deal in later grades.

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Teachers should use Cuisenaire rods, trains of Unifix cubes, color tiles, or centimeter rulers to find perimeters of such things as picture and window frames, greeting card borders, and other objects that have trims. They can also use tape measures or trundle wheels to determine perimeters of classrooms, area rugs, playground areas, and larger regions. Real-life connections are made to mathematics as children engage in projects in which they determine the perimeter of a picture in order to put a border around it and investigate the cost of the chain-link fence that encloses a play area at school.

As the term “generate strategies” indicates, students should “figure out” how to find the perimeter of areas/objects. It is not appropriate for students to simply memorize that perimeter is the distance around an area/object. While they may start with the definition/information, it is important to provide students with learning experiences that enable them to determine how to find the perimeter of a specified area/object. Geoboards are tools students may use to determine the perimeter of various polygons and how those perimeters differ based on the size of the polygon. In fourth grade students will apply formulas to determine the perimeter of polygons. Therefore, in third grade it is extremely important that students have multiple opportunities to develop a conceptual understanding that they can transfer to symbolic manipulation in fourth grade.

Connections To:

Other Third Grade Indicators3-4.7 Analyze the results of combining and subdividing circles, triangles,

quadrilaterals, pentagons, hexagons, and octagons.

A connection between this indicator and the indicator that requires students to generate strategies to determine the perimeter of polygons (3-5.6 above) expands students’ understanding and lays the foundation for later understanding that perimeter of combined or subdivided shapes will change while area remains constant.

EquivalenciesIndicators3-5.7 Recall equivalencies associated with time and length: 60 seconds = 1

minute and 36 inches = 1 yard.

In second grade students were asked to recall equivalencies associated with length and time: 12 inches = 1 foot, 3 feet = 1 yard, 60 minutes = 1 hour, and 24 hours = 1 day. This skill is maintained in third. Students are now expected to recall that 36 inches = 1 yard and that 60 seconds = 1 minute. Repeated experiences will help students not only recall the equivalencies but be able to visualize the connection between the related units.

Grade 3Data Analysis and Probability

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Big Ideas: Organizing, Interpreting, Analyzing, and Making Predictions about Data, Multiple

Representations of a Data Set, and Probability

Standard 3-6: The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability.

Indicators:3-6.1 Apply a procedure to find the range of a data set. 3-6.2 Organize data in tables, bar graphs, and dot plots.3-6.3 Interpret data in tables, bar graphs, pictographs, and dot plots. 3-6.4 Analyze dot plots and bar graphs to make predictions about populations. 3-6.5 Compare the benefits of using tables, bar graphs, and dot plots as representations

of a given data set.3-6.6 Predict on the basis of data whether events are likely, unlikely, certain, or

impossible to occur. 3-6.7 Understand when the probability of an event is 0 or 1.

Essential Questions: How are tally tables and frequency tables alike? (3-6.2, 3-6.3) What information can be found on a pictograph? (3-6.3) What information can be found on a bar graph? (3-6.3) How can making a bar graph help solve problems? (3-6.2, 3-6.3) How can you find the range of a set of data on a dot plot? (3-6.1, 3-6.2, 3-6.3) How can you use the results from part of a group to predict the results for the

whole group? (3-6.4) How can you decide whether to display data in a table, a bar graph, or a dot plot?

(3-6.5) How can you describe the likelihood of an event occurring? (3-6.6) How can you predict and record the possible outcomes? (3-6.6) What steps do you use to test, record, and display outcomes of experiments? (3-

6.7, 3-6.6)

Help Page for Standard 3-6

Notes:Assessments

Assessment examples can be accessed at

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http://www.s2martsc.org/.  Module 4-4 (3-6.1, 3-6.2, 3-6.3 3-6.4, 3-6.5)Module 4-5 (3-6.6, 3-6.7)  Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed. Assessment Examples:   Chapter Review and Test PrepChapter Tests MAP Testing OdysseyExit tickets Questioning Strategies Journaling/Written AssessmentsProjectsPair Share

Textbook Correlations

3-6.1 Lessons 6.5, 6.63-6.2 Lessons 6.1, 6.4, 6.53-6.3 Lessons 6.1 – 6.6, 6.83-6.4 Lessons 6.6 – 6.8 3-6.5 Lesson 6.83-6.6 Lessons 7.1 – 7.33-6.7 Lesson 7.3

Key Concepts (Vocabulary)

datatally tablefrequency tablepictographkeybar graphscalehorizontal bar graphKey Concepts (Vocabulary) continued

vertical bar graphdot plotrange

modepredictline graphtrendseventprobabilitylikelyunlikely

impossibleuncertainoutcome

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experiment equally likely

Literature

Do You Wanna Bet? by Jean Cushman Jumanji by Chris Van Allsburg Math by All Means: Probability, Grades 3-4 by

Marilyn Burns Probably Pistachio by Stuart J. Murphy

Check out this site for literature on different topics: http://www.thereadingnook.com/math/

Technology

Supporting Content Web Sites District website

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

http://www.newberry.k12.sc.us/InstructionalLinks/ math/Math_TOC_Page.html

Every Breath You Take http://illuminations.nctm.org/LessonDetail.aspx?ID=L243

Sticks and Stones http://illuminations.nctm.org/LessonDetail.aspx?id=L585

As People Get Older, They Get Taller http://illuminations.nctm.org/LessonDetail.aspx?id=U171

Introduction to Bar Graphs http://www.shodor.org/interactivate/lessons/IntroBarGraphs/

Online Bar Graph http://nlvm.usu.edu/en/nav/frames_asid_323_g_2_t_5.html?from=category_g_2_t_5.html

Create a Graph http://nces.ed.gov/nceskids/createagraph/default.aspx

Technology (continued) Bar Grapher

http://www.amblesideprimary.com/ambleweb/mentalmaths/grapher.html

Bar Graphs and Dot Plots lesson (Only use 1st lesson to cover 3rd grade indicators.)

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http://www.keymath.com/documents/da1/CondensedLessonPlans/DA_CLP_01.pdf

SMART Notebook Lessons/Activities http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+Activities/Correlated+Search+us.htm

SMART Board Interactive Whiteboard Lessons and Resources http://www.scholastic.com/interactivewhiteboards/

Interactivate Bar graph http://www.shodor.org/interactivate/activities/bargraph/

Data Analysis and Probability Games http://www.mathwire.com/games/datagames.html

Understanding Graphs http://www.bbc.co.uk/schools/ks2bitesize/maths/activities/interpretingdata.shtml

Slug Ball http://pbskids.org/cyberchase/parentsteachers/show/episodes/609.html

Exploring the Range of Data http://www.harcourtschool.com/activity/elab2004/gr4/25_b.html

Predicting Outcomes http://www.harcourtschool.com/activity/elab2004/gr4/28.html

Data Analysis and Probability Promethean Board activities http://www.prometheanplanet.com/server.php?ResourceSearch%5Bsearch_text%5D=data+and+probability&ResourceSearch%5Bsubject%5D=00200n009002002002&ResourceSearch%5Bgrade%5D=00200n009002003002&display=006007001&ResourceSearch%5Baction%5D=advanced&change=ResourceSearchResults&catMatchType=includeChildren&searchType=basic&x=40&y=9

Sticks and Stones http://illuminations.nctm.org/LessonDetail.aspx?id=L585

Spinner http://nlvm.usu.edu/en/nav/frames_asid_186_g_2_t_5.html?open=activities&from=category_g_2_t_5.html

Technology (continued) Certain, Probable, Unlikely, Impossible

http://www.ixl.com/math/practice/grade-3-certain-probable-

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unlikely-impossible Is It Likely or Is It Unlikely

http://www.genevaschools.org/standards/m11.pdf Likely or Unlikely

http://www.uen.org/Lessonplan/preview.cgi?LPid=6180 Probability Games

http://www.betweenwaters.com/probab/probab.html Data Analysis and Probability Games

http://www.mathwire.com/games/datagames.html Four Great Math Games

http://teacher.scholastic.com/lessonrepro/lessonplans/grmagam.htm

Suggested Streamline Videohttp://www.scetv.org/education/StreamLineSC/ http://search.discoveryeducation.com/CurriculumStandardLookup.cfm

Cross Curricular Opportunities

WritingJournal writing

Social StudiesRead and interpret data in a table (TE p. 100C)

Third Grade---Support Document

Data Analysis and Probability

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Standard 3-6: The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability.

The indicators for this standard are grouped by the following major concepts: Data Collection and Representation Data Analysis Probability

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follow.

Collection and Representation

Indicators3-6.2 Organize data in tables, bar graphs, and dot plots.3-6.5 Compare the benefits of using tables, bar graphs, and dot plots as representations

of a given data set.

Second grade experiences required students to collect data through surveys and organize data into charts, pictographs and tables. Third grade students expand upon this knowledge by constructing more sophisticated graphs and tables to display data. Specifically, third grade students should organize data in tables, bar graphs, and dot plots. Also, third grade students should compare the benefits of using those different forms of representation. When comparing, students should recognize that the various forms of representation give different levels of depth of information about the data set. Therefore, students should not only deal with tables, bar graphs and dot plots they create but should examine those forms of representation in newspapers, magazine, etc. in order to experience how representation impacts interpretation and can thus be misleading.

Teacher Notes: A dot plot is made by making a horizontal line and placing an “x” or “dot” above the corresponding value on the line for every data element (ex. color of eyes, favorite food items, etc). Every piece of data is thus shown on a dot plot.

When organizing data in tables, bar graphs, and dot plots, the scale should be limited to one. Students will progress to scales greater than one in fourth grade.

Connections To:

Literature

Lemonade for Sale by Stuart MurphyStudents can create a bar graph to match the data while the teacher reads the story.

The students can describe what is happening with the data (more Tuesday than Monday, etc.), why it is important to increase the vertical axis by tens instead of ones, and how the bar graph informed the kids about their goal. This allows students to understand the benefits of organizing data.

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Technology:

For information re dot plots go to: http://www.amstat.org/education/gaise/ www.amstat.org/Education/stn/pdfs/STN68.pdf

Data Analysis

Indicators3-6.3 Interpret data in tables, bar graphs, pictographs, and dot plots. 3-6.4 Analyze dot plots and bar graphs to make predictions about populations. 3-6.1 Apply a procedure to find the range of a data set.

Second grade students created survey questions, collected data, and organized the data in charts, pictographs and tables. As indicated under the major concept of “Collection and Representation” above, third grade students should organize data in tables, bar graphs, and dot plots. With regard to analysis of that data, third grade students should not only be able to interpret those data in those forms of representation but should also include pictographs. Also, third grade students should analyze dot plots and bar graphs to make predictions about populations. Analyzing data from a representative sample of a population allows students to make predictions about that population.

Third grade is the first time students are introduced to the concept of range of a data set. Therefore, students will need many learning experiences on that topic. Determining range (distance between the highest and lowest data values) helps students recognize how spread out the data are. Students can use this information to make conjectures about the data.

Connections To:

Other Third Grade Indicators3-3.5 Illustrate situations that show change over time as increasing.

Probability

Indicators3-6.6 Predict on the basis of data whether events are likely, unlikely, certain, or

impossible to occur. 3-6.7 Understand when the probability of an event is 0 or 1.

Prior to third grade, students’ experiences with probability consisted of describing events as more or less likely to occur. In the third grade, students will be responsible for describing common events at a deeper level. In third grade students should use data to predict whether events are certain, likely, unlikely, and impossible with regard to probability.

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Third grade students generally grasp the concept of certain and impossible quickly, but have trouble understanding the difference between likely and unlikely. Therefore, when introducing the four terms, begin with outcomes that are certain (the sun will rise everyday, I will pull a piece of gum out of a package of bubble gum) or impossible (Pigs will fly, I will pull a piece of candy out of a package of bubble gum). Afterwards, the focus should move toward outcomes that are likely (I will eat sometime today, I will pull a green marble out of my pocket filled with nine green and two yellow marbles) and unlikely (It will snow in July in South Carolina, I will pull a yellow marble out of my pocket filled with nine green and two yellow marbles).

Students need to understand when the probability of an event is 1 or 0. The requirements of this indicator mean more than simply reciting that “1 means certain” and “0 means impossible”. As the verb “Understand” implies, students should be able to explain and give examples of events that fit each probability.

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