GRADE 2 MATHEMATICS CURRICULUM GUIDE

LCPS MATH Unit Summary Grade 2I can collect and organize data to construct picture graphs, pictographs, and bargraphs. I can read the information presented on these data graphs(representations).The student will identify the place value and value of each digit in a three digitnumber, round two-digit numbers to tens, and compare whole numbers (0-999)using symbols.I can count forward by twos, fives, and tens to 100 starting at various multiples of2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens. I cancount backwards by tens from 100 starting at different numbers, includingI can use objects to determine whether a number is odd or even. I can explainwhy the number is odd or even.I can recall and write addition facts, with sums to 20 or less, and thecorresponding subtraction facts (written either horizontally or vertically).I can estimate and find sums of addends (99 or less) using a variety ofstrategies and tools.I can estimate and find differences of two numbers (99 or less) using a variety ofstrategies and tools.Big IdeasEssential Questions 2014-15Classroom routines (about 10 minutes each day)can be used to introduce, support, and extendtopics throughout the yearly curriculum in order toprovide students with regular practice in importantmathematical ideas. What strategy would you use to determine time tothe nearest five minutes, using analog and digitalclocks?How can you demonstrate an understanding ofcounting by fives to predict five minute intervalswhen telling time to the nearest five minutes?How does a calendar measure time?How does a calendar represent yesterday, today, andtomorrow?How can you determine the date of the third Tuesdayin any given month?What is data?How is data collected?How is data represented?What is the relationship of ones, tens, andhundreds?How are numbers written to show how manyhundreds, tens, and ones are in the number?Why would you round a number? (Rounding gives aclose, easy-to-use number to use when an exactnumber is not needed for the situation at hand.)What is a pattern?What are different ways numbers can be grouped forskip counting?How can the same quantity be represented in words,numerals, and objects?Why would you use estimation skills in situations?What is the structure of an addition problem? Asubtraction problem?

LCPS MATH Unit SummaryGrade 22014-15Prerequisite SkillsVocabularyVDOE Vertical Alignment document K-31.8 The student will tell time to half‐hour1.11 The student will use calendar language appropriately1.1 The student willa) count/write numbers to 100;b) group up to 100 objects into tens/ones and writenumeral – place value1.2 The student will count by 1/2/5/10 to 100 and backby 1 from 301.14 The student will investigate/ID/describe forms ofdata collection using tables/picturegraphs/object graphs1.5 The students will recall add/sub facts w/ sums to 18or lessVDOE Vocabulary Word Wall Cards2.13--yesterday, today, tomorrow, names of months,names of days2.14--thermometer, Fahrenheit, Celsius, temperature2.17--data, picture graph, tally mark, table, picture graph,bar graph, columns, rows2.1--digit, place value, ones, tens, hundreds, equal,greater than, less than2.4--digit, sequence, skip count, pair, even, odd2.5--add, subtract, sum, difference2.6—addition, add, addend, sum, estimate, plus2.7--subtraction, difference, subtract, estimate, minus,subtrahend, minuendAchievement CriteriaHow to Assess Achievement“The content of the mathematics standards is intended tosupport the following five process goals for students: becoming mathematical problem solvers communicating mathematically reasoning mathematically making mathematical connections and using mathematical representations to model andinterpret practical situations.”-2009 Mathematics Standards of LearningClick here for a brief audio powerpoint slidewith more information about the Process GoalsSample Math Tasks are available in VISION:Search: LCPS-Math: K-12 Math TasksEnrollment key: mathisfunhttp://loudounvision.net/NCSM Great Tasks(available in all LCPS Elementary Schools—click link)Classroom Routines1st quarter: The First 20 Days Classroom RoutinesNUMBER TALKS:Example: l/Classroom NumberTalk Gr3.swfNumber Talks sample flipcharts available on the Elementary Math Resources VISION siteINVESTIGATIONS:Mathematical Thinking in Grade 2Investigation 2, Session 1: How Many Days Have We Been in School?Today’s Number p. 124How Many Pockets? P. 127Time and Time Again p. 131Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary MathResources VISION site: http://loudounvision.net/Search: Math—Elementary ResourcesEnrollment key: MATH (all caps)

LCPS MATH Unit SummaryUnit: 2Quarter 1VDOE Standards of Learning:VDOE Process Goals:Grade 22014-15Extending Place Value2.2 The student will a) identify ordinal positions first through twentieth, using anordered set of objects; and b) write the ordinal numbers.2.1 a, b, c The student will a) read, write, and identify the place value of each digit in a3-digit numeral, using numeration models; b) round two-digit numbers to the nearestten, and c) compare two whole numbers between 0 and 999, using symbols ( , , or )and words (less than, greater than, or equal to).2.4 The student will a) count forward by 2, 5s, 10s to 100, starting at various multiplesof 2, 5, 10. b)count backward by 10s from 100; and c) recognize even and oddnumbers.2.20 The student will identify, create, and extend a wide variety of patterns.Problem Solving, Communication, Connections, Reasoning, Representations Learning Targets: I can communicate (verbally and in writing) the ordinal positions for eachobject in a set of 20 objects that are in order (i.e. left-to-right, right-to-left, topto-bottom, and bottom-to-top).I can identify the place value and value of each digit in a three digit number,round two-digit numbers to tens, and compare whole numbers (0-999) usingsymbols.I can count forward by twos, fives, and tens to 100 starting at various multiplesof 2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens.I can count backwards by tens from 100 starting at different numbers,including 1.I can use objects to determine whether a number is odd or even. I can explainwhy the number is odd or even.Big IdeasEssential Questions Understand ordinal position identification. Place value is constructed around the Base 10system. Using a variety of models (base ten, Digiblocks,pictorial representations) helps studentsunderstand the magnitude of numbers. A variety of strategies to compare and round twoor three digit numbers should be investigated,including number lines. Demonstrate understanding of skip countingpatterns, forwards and backwards. Identify and model even and odd numbers (evennumbers are modeled by pairs and odd numbershave one left over when grouped by pairs).What are the ordinal number words for the 20objects pictured?What is the value of each digit in a three digitnumber?What strategies can you use to round to thenearest ten?Which symbol, ( , , or ), would you use tocompare two given numbers?What are the missing numbers in the pattern?How can you tell the difference between an oddand even number?How can you model odd and even numbers?Are there an odd or even number of objects?How do you know?

LCPS MATH Unit SummaryGrade 22014-15Prerequisite SkillsVocabularyVDOE Vertical Alignment document K-3VDOE Vocabulary Word Wall Cards1.1The student willa) count/write numbers to 100;b) group up to 100 objects into tens/ones andwrite numeral ‐ place value1.2The student will count by 1/2/5/10 to 100 andback by 1 from 30Achievement Criteria“The content of the mathematics standards is intended tosupport the following five process goals for students: becoming mathematical problem solvers communicating mathematically reasoning mathematically making mathematical connections and using mathematical representations to model andinterpret practical situations.”-2009 Mathematics Standards of LearningClick here for a brief audio powerpoint slidewith more information about the Process GoalsDifferentiation Have students use large grid paper with large squares onwhich to draw their objects in ordinal positions. Allow students who have difficulty with drawing to usestamps or stickers. If students are struggling with going all the way to thetwentieth position, break the ordinal positions up intosmaller groups, like first through tenth and then elevenththrough twentieth. Tape ordinal position cards to the floor. Assign ordinalpositions to the students as their line position for the day,and have them stand on the appropriate cards. Use grid paper to help students compare place valuesvertically rather than horizontally. Have students use a blank number line and makedecisions about where to place numbers on it. By placingthe numbers being compared to each other on the numberline, students are able to see instantly which number islarger and which is smaller by looking at their position onthe line. Students may choose to add as many othernumbers to the line as needed to make a goodcomparison. Use green and red highlighters to color the first number2.22.12.4ordinal numberdigitsequencehorizontalplace valueskip countverticalonesevenordinal position termstensodd(first through twentieth) hundredsgreater thanless thanequal toHow to Assess AchievementSample Math Tasks are available in VISION:Search: LCPS-Math: K-12 Math TasksEnrollment key: mathisfunhttp://loudounvision.net/NCSM Great Tasks(available in all LCPS Elementary Schools—click link)ResourcesInvestigations:Coins, Coupons, and Combinations:Investigation 1: “10’s and Doubles”: Sessions 4, 5, 6,Investigation 2: Grouping by 2’s, 5’s, and 10’sInvestigation 4: One HundredPutting Together and Taking ApartInvestigation 2: Working with 100ESS Lessons:2.2--Ordinals2.1--Race to 1002.1--Rounding On the 100 Chart2.1--Three-Digit Place Value2.4--Guess My Pattern2.4--Even or Odd?Brain Pop Jr:2.1--One Hundred2.1--Place Value2.1--Rounding2.1--Comparing Numbers , 2.4--Even and Odd

LCPS MATH Unit SummaryGrade 2in the comparison green and the second number red. Thisvisual suggests to students that green is where you startand red is where you stop or finish. Create a card with the expression “is greater than”written on one side and the expression “is less than” onthe other. Have students flip the card as needed tocomplete the comparison. Have them take turns saying thecomparison. Allow students to use calculators to help them confirmtheir calculations. Use a poster-sized hundred chart and largermanipulatives for students with fine motor challenges. Have students explore adding numbers together todiscover the results: odd odd even, even even even,odd even odd, even odd odd. Have student explore subtracting numbers to discoverthe results: odd – odd even, even – even even, odd –even odd, even – odd odd.Intervention Ideas(available in all LCPS Elementary Schools—click link)ELL Model Performance Indicators(click to link)2014-15Safari Montage:2.2, 2.1, 2.4--Number Sense2.1--Cyberbase: Number Sense: And They CountedHappily Ever After2.4--Numbertime Numbers to 100, Patterns of 52.4--Numbertime Numbers to 100, Patterns of 102.4--Number and Numbers to 100, Counting by 102.4--Emily’s First 100 Days of SchoolMath Literature Connections (click link)Additional resources (including FLIPCHARTS based onVDOE ESS lessons) may be found on the Elementary MathResources VISION site: http://loudounvision.net/Search: Math—Elementary ResourcesEnrollment key: MATH (all caps)

LCPS MATH Unit SummaryUnit: 3Quarter 1VDOE Standards of Learning:VDOE Process Goals:Grade 22014-15Computational Fluency2.5 The student will recall addition facts with sums to 20 or less and thecorresponding subtraction facts.2.9 The student will recognize and describe the related facts that represent anddescribe the inverse relationship between addition and subtraction.2.20 The student will identify, create, and extend a wide variety of patterns.(Geometric and growing patterns are addressed in quarter 2).*2.20 is to be connected to 2.5 and 2.9 (see Big Ideas)Problem Solving, Communication, Connections, Reasoning, Representations Learning Targets: I can recall and write addition facts, with sums to 20 or less, and thecorresponding subtraction facts (written either horizontally or vertically). (2.5)I can demonstrate how addition and subtraction facts are related usingmodels/structures and describe their relationship. (2.9)I can identify, create, and apply a wide variety of patterns. (2.20)Big Ideas Relating addition to subtraction by exploringpatterns in fact families:5 6 11, 6 5 1111 – 5 6, 11 – 6 5Activities such as Today’s Number helps studentsto explore number patterns in sums anddifferencesFor example: If Today’s Number is 12, studentsmay observe patterns in sums:0 12 121 11 122 10 123 9 12, etc.Gaining facility in manipulating whole numbers toadd and subtract and in understanding the effectsof the operations on whole numbersRecognizing whether numerical solutions arereasonableDeveloping proficiency with basic addition andsubtraction and related factsPrerequisite SkillsVDOE Vertical Alignment document K-31.5 recall add/sub facts w/ sums to 18 orless1.17 recognize/describe/extend/creategrowing/repeating patternsEssential Questions What are the addition facts of sums up totwenty? What is the corresponding subtraction fact toeach addition fact? What are the related facts for a given addition orsubtraction fact? (e.g., given 3 4 7, write 7 – 4 3 and 7 – 3 4). What is the relationship between an additionand subtraction problem of a related fact? What patterns can you identify in related facts?VocabularyVDOE Vocabulary Word Wall Cards2.52.92.20addrelated factpatternsadditionfact familycore/unitplusinverse operationsumsubtractsubtractionminusdifference

LCPS MATH Unit SummaryGrade 2Achievement Criteria“The content of the mathematics standards is intended tosupport the following five process goals for students: becoming mathematical problem solvers communicating mathematically reasoning mathematically making mathematical connections and using mathematical representations to model andinterpret practical situations.”-2009 Mathematics Standards of LearningClick here for a brief audio powerpoint slidewith more information about the Process GoalsDifferentiation Allow students to use a calculator to check their sums. To generate two-digit numbers, have students use 10sided number cubes instead of digit cards. For an extra challenge, pose the following problem: Youhave a bag with five cubes in it. Some of the cubes are red,and some are blue. Show three of the possiblecombinations of red and blue cubes that could be in thebag, and list all the related facts for each combination. Have students use linking cubes on an interactivewhiteboard to model operations. Provide a template for students to use to fill in therelated facts (e.g., ). Lines of the templatemay be color-coded like the examples in the activity.Intervention Ideas(available in all LCPS Elementary Schools—click link)ELL Model Performance Indicators(click to link)2014-15How to Assess AchievementSample Math Tasks are available in VISION:Search: LCPS-Math: K-12 Math TasksEnrollment key: mathisfunhttp://loudounvision.net/NCSM Great Tasks(available in all LCPS Elementary Schools—click link)ResourcesInvestigations:Coins, Coupons, and CombinationsInvestigation 3: Introducing Addition and SubtractionSituationsPutting Together and Taking ApartInvestigation 1: Combining and SeparatingESS Lessons:2.5 Four In A Row Addition2.9 Related Facts2.20 Exercising PatternsBrainPop Jr.:2.5 Basic Adding2.5 Counting On2.5 Basic Subtraction2.5 DoublesSafari Montage:2.5 Numbertime Addition and Subtraction: Patterns ofAddition2.5 Numbertime Addition and Subtraction: Plus andMinus2.5 Numbertime Addition and Subtraction: Difference2.5 Numbertime Numbers to 100: Counting On and Back2.5 Subtraction2.20 Cyberchase: Patterns in Music: Out of SyncMath Literature Connections (click link)Additional resources (including FLIPCHARTS based onVDOE ESS lessons) may be found on the Elementary MathResources VISION site: http://loudounvision.net/Search: Math—Elementary ResourcesEnrollment key: MATH (all caps)

LCPS MATH Unit SummaryUnit: 4Quarter 2VDOE Standards of Learning:Grade 22014-15Applying Place Value to Computation/Problem Solving2.5 The student will recall addition facts with sums to 20 or less and thecorresponding subtraction facts.2.6 The student given two whole numbers whose sum is 99 or less, will a) estimatethe sum; and b) find the sum, using various methods of calculation.2.7 The student, given two whole numbers, each of which is 99 or less, willa) estimate the difference; and b) find the difference using various methods ofcalculation.2.21 The student will solve problems by completing numerical sentences involvingthe basic facts for addition and subtraction. The student will create story problems,using the numerical sentences.2.22 The student will demonstrate an understanding of equality by recognizing thatthe symbol in an equation indicates equivalent quantities and the symbol indicatesthat quantities are not equivalent.VDOE Process Goals:Problem Solving, Communication, Connections, Reasoning, Representations Learning Targets: I can estimate and find sums of addends (99 or less) using a variety ofstrategies and tools.I can estimate and find differences of two numbers (99 or less) using a varietyof strategies and tools.I can use mathematical models to represent basic addition and subtractionnumber sentences and create story problems for those sentences.I can demonstrate that some number sentences are balanced ( ) and some arenot balanced ( ).Big Ideas A variety of contexts are necessary for children todevelop an understanding of the meanings of theoperations such as addition and subtraction. Thesecontexts often arise from real-life experiences inwhich they are simply joining sets, taking away orseparating from a set, or comparing sets.Although young children first compute usingobjects and manipulatives, they gradually shift toperforming computations mentally or using paperand pencil to record their thinking. Therefore,computation and estimation instruction in theearly grades revolves around modeling, discussing,and recording a variety of problem situations. Thishelps students transition from the concrete to therepresentation to the symbolic in order to developmeaning for the operations.Developing and using strategies and algorithms tosolve problems and choosing an appropriatemethod for the situation (strategies focusing onthe place value of the numbers should bereinforced, for ex: 23 38 20 3 30 8 50 11 61)Essential Questions What is the sum of the two whole numbers?How can estimating the sum be helpful in findingthe sum of the problem?How is regrouping in subtraction similar toregrouping in addition?Why do you subtract the smaller number fromthe larger number instead of the other wayaround?How can an unknown number be represented ina number sentence?How are addition and subtraction related?Can you explain how you know whether

This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work. NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by