Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics Second Grade 2012-2013 Common Core Georgia Performance Standards Curriculum Map Unit 1 Extending Base Ten Understanding MCC2.NBT.1 MCC2.NBT.2 MCC2.NBT.3 MCC2.NBT.4 MCC2.MD.10

Unit 2 Becoming Fluent with Addition and Subtraction MCC2.OA.1 MCC2.OA.2 MCC2.NBT.5 MCC2.MD.10

8/13 - 9/21

9/24 - 10/31

Unit 3 Understanding Measurement, Length, and Time MCC2.MD.1 MCC2.MD.2 MCC2.MD.3 MCC2.MD.4 MCC2.MD.5 MCC2.MD.6 MCC2.MD.7 MCC2.MD.9 MCC2.MD.10 11/1 - 12/13

Unit 4 Applying Base Ten Understanding MCC2.NBT.6 MCC2.NBT.7 MCC2.NBT.8 MCC2.NBT.9 MCC2.MD.8 MCC2.MD.10

12/14 -2/1

Unit 5 Understanding Plane and Solid Figures MCC2.G.1 MCC2.G.2 MCC2.G.3 MCC2.MD.10

2/4

- 3/15

Unit 6 Developing Multiplication

Unit 7 Show What We Know

MCC2.OA.3 MCC2.OA.4 MCC2.MD.10

ALL

3/18 - 4/25

4/29 - 5/24

Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics 8 Look for and express regularity in repeated reasoning. Unit 1: Extending Base Ten Understanding MCC2.NBT.1 Understand that the three digits of a three-digit number MCC2.NBT.3 Read and write numbers to 1000 using base-ten numerals, represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 number names, and expanded form. hundreds, 0 tens, and 6 ones. Understand the following as special cases: MCC2.NBT.4 Compare two three-digit numbers based on meanings of a. 100 can be thought of as a bundle of ten tens — called a ―hundred.‖ the hundreds, tens, and ones digits, using >, =, and < symbols to record b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, the results of comparisons two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit ones). scale) to represent a data set with up to four categories. Solve simple putMCC2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s. together, take-apart, and compare problems10 using information presented in a bar graph.

Unit 2: Becoming Fluent with Addition and Subtraction MCC2.OA.1 Use addition and subtraction within 100 to solve one- and MCC2.NBT.5 Fluently add and subtract within 100 using strategies two-step word problems involving situations of adding to, taking from, based on place value, properties of operations, and/or the relationship putting together, taking apart, and comparing, with unknowns in all between addition and subtraction. positions, e.g., by using drawings and equations with a symbol for the MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit unknown number to represent the problem. scale) to represent a data set with up to four categories. Solve simple putMCC2.OA.2 Fluently add and subtract within 20 using mental strategies. together, take-apart, and compare problems 10 using information By end of Grade 2, know from memory all sums of two one-digit presented in a bar graph. numbers. Unit 3:Understanding Measurement, Length, and Time MCC2.MD.1 Measure the length of an object by selecting and using MCC2.MD.7 Tell and write time from analog and digital clocks to the appropriate tools such as rulers, yardsticks, meter sticks, and measuring nearest five minutes, using a.m. and p.m. tapes. MCC2.MD.8 Solve word problems involving dollar bills, quarters, MCC2.MD.2 Measure the length of an object twice, using length units of dimes, nickels, and pennies, using $ and ¢ symbols appropriately. different lengths for the twomeasurements; describe how the two Example: If you have 2 dimes and 3 pennies, how many cents do you measurements relate to the size of the unit chosen. have? MCC2.MD.3 Estimate lengths using units of inches, feet, centimeters, MCC2.MD.9 Generate measurement data by measuring lengths of and meters. several objects to the nearest whole unit, or by making repeated MCC2.MD.4 Measure to determine how much longer one object is than measurements of the same object. Show the measurements by another, expressing the length difference in terms of a standard length making a line plot, where the horizontal scale is marked off in wholeunit. number units. MCC2.MD.5 Use addition and subtraction within 100 to solve word MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit problems involving lengths that are given in the same units, e.g., by using scale) to represent a data set with up to four categories. Solve simple putdrawings (such as drawings of rulers) and equations with a symbol for together, take-apart, and compare problems10 using information the unknown number to represent the problem. presented in a bar graph. MCC2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. Unit 4:Applying Base Ten Understanding MCC2.NBT.6 Add up to four two-digit numbers using strategies based MCC2.NBT.9 Explain why addition and subtraction strategies work, on place value and properties of operations. using place value and the properties of operations. MCC2.NBT.7 Add and subtract within 1000, using concrete models or MCC2.MD.8 Solve word problems involving dollar bills, quarters, drawings and strategies based on place value, properties of operations, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. and/or the relationship between addition and subtraction; relate the Example: If you have 2 dimes and 3 pennies, how many cents do you strategy to a written method. Understand that in adding or subtracting have? three-digit numbers, one adds or subtracts hundreds and hundreds, tens MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit and tens, ones and ones; and sometimes it is necessary to compose or scale) to represent a data set with up to four categories. Solve simple put-

decompose tens or hundreds. together, take-apart, and compare problems10 using information MCC2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and presented in a bar graph. mentally subtract 10 or 100 from a given number 100–900. Unit 5: Understanding Plane and Solid Figures MCC2.G.1 Recognize and draw shapes having specified attributes, such MCC2.G.3 Partition circles and rectangles into two, three, or four equal as a given number of angles or a given number of equal faces. Identify shares, describe the shares using the words halves, thirds, half of, a third triangles, quadrilaterals, pentagons, hexagons, and cubes. of, etc., and describe the whole as two halves, three thirds, four fourths. MCC2.G.2 Partition a rectangle into rows and columns of same-size Recognize that equal shares of identical wholes need not have the same squares and count to find the total number of them. shape MCC2.G.3 Partition circles and rectangles into two, three, or four equal MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit shares, describe the shares using the words halves, thirds, half of, a third scale) to represent a data set with up to four categories. Solve simple putof, etc., and describe the whole as two halves, three thirds, four fourths. together, take-apart, and compare problems 10 using information Recognize that equal shares of identical wholes need not have the same presented in a bar graph. shape Unit 6: Developing Multiplication MCC2.OA.3 Determine whether a group of objects (up to 20) has an odd MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit or even number of members, e.g., by pairing objects or counting them by scale) to represent a data set with up to four categories. Solve simple put2s; write an equation to express an even number as a sum of two equal together, take-apart, and compare problems10 using information addends. presented in a bar graph. MCC2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics. Grades K-2 Key: CC = Counting and Cardinality, G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, OA = Operations and Algebraic Thinking.

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2 nd  Understanding Plane and Solid Figures  6 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.G.3  Partition circles and rectangles into two, three, or four equal shares, describe the shares  using the words halves, thirds, half of, a third of , etc., and describe the whole as two halves, three  thirds, four fourths.  Recognize that equal shares of identical wholes need not have the same shape. 

Skills (what students must be able to do) 

Concepts (what students need to know) 

DOK Level /  Bloom’s 

partition  describe  use  recognize 

circles  rectangles  equal shares  halves  thirds  fourths  wholes  shape 

3  2  3  2 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  Circles and rectangles can be divided into halves,  thirds, fourths, etc. 

How can I divide circles and rectangles into equal  parts? 

Equal shares can be different shapes within the  same whole 

How do I name the equal parts?  How do I compare equal parts of different shapes? 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Explanations and Examples  This standard introduces fractions in an area model. Students need experiences with different sizes, circles,  and rectangles. For example, students should recognize that when they cut a circle into three equal pieces,  each piece will equal one third of its original whole. In this case, students should describe the whole as three  thirds. If a circle is cut into four equal pieces, each piece will equal one fourth of its original whole and the  whole is described as four fourths. 

Students should see circles and rectangles partitioned in multiple ways so they learn to recognize that equal  shares can be different shapes within the same whole. An interactive whiteboard may be used to show  partitions of shapes. 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math:  MCC2.MD.7  2 nd  Understanding Measurement, Length, and Time  5 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.MD.7  Tell and Write time from analog and digital clocks to the nearest five minutes using a.m.  and p.m. 

Skills (what students must be able to do)  Tell  Write  Use 

Concepts (what students need to know)  Analog time  Digital time  5 minutes  a.m.  p.m. 

DOK Level /  Bloom’s  1  2  2 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions) 

Time can be determined to the nearest  5 minutes using  How can I tell the time on a clock?  analog and digital clocks.  Time can be described as a.m. or p.m. 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Explanations and Examples  In first grade, students learned to tell time to the nearest hour and half­hour. Students build on this  understanding in second grade by skip­counting by 5 to recognize 5­minute intervals on the clock. They need  exposure to both digital and analog clocks. It is important that they can recognize time in both formats and  communicate their understanding of time using both numbers and language. Common time phrases include  the following: quarter till ___, quarter after ___, ten till ___, ten after ___, and half past ___.  Students should understand that there are 2 cycles of 12 hours in a day ­ a.m. and p.m. Recording their daily  actions in a journal would be helpful for making real­world connections and understanding the difference  between these two cycles. An interactive whiteboard or document camera may be used to help students  demonstrate their thinking. 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2 nd  Applying Base Ten Understanding  5 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.MD8  Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $  and ¢ symbols appropriately.  Example: If you have 2 dimes and 3 pennies, how many cents do you  have? ·  Relate to whole number, place value and base‐ten understandings  ·  Understand the relationship between quantity and value  ·  Limit problems to the use of just dollar and cent symbols.  Skills (what students must be able to do) 

Concepts (what students need to know) 

DOK Level /  Bloom’s 

Solve 

word problems 

3 

Relate 

money (dollar bills, quarters, dimes, nickels,  pennies, symbols $ and  ¢) 

whole numbers  Understand 

place value 

4 

base‐ten  quantity and value 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  Appropriate symbols ($ and ¢) should be used when  describing amounts of money 

What symbols do I use when writing different amounts of  money? 

There is a relationship between quantity and value of  coins and bills. 

What is each coin/bill worth?  How do I solve money word problems? 

Different combinations of coins can be equal in value. 

How do I represent an amount of money using a variety  of coin/bill combinations?

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Next step, create assessments and engaging learning experiences  Explanations and Examples  Since money is not specifically addressed in kindergarten, first grade, or third grade, students  should have multiple opportunities to identify, count, recognize, and use coins and bills in and out  of context. They should also experience making equivalent amounts using both coins and bills.  “Dollar bills” should include denominations up to one hundred ($1.00, $5.00, $10.00, $20.00,  $100.00).  Students should solve story problems connecting the different representations. These  representations may include objects, pictures, charts, tables, words, and/or numbers. Students  should communicate their mathematical thinking and justify their answers. An interactive  whiteboard or document camera may be used to help students demonstrate and justify their  thinking.  Example: Sandra went to the store and received $ 0.76 in change. What are three different sets of  coins she could have received?  Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2  Extending Base Ten Understanding  6 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.NBT.2 Count within 1000, skip count by 5’s, 10’s, and 100’s. Skip counting forward and backwards  within 1000. Avoid sing song memorization. Skip counting is a useful strategy for multiplication, but only  if students understand what is happening when they skip count. Develop  understanding by using a  number line  or number chart when counting. 

Skills (what students must be able to do) 

Concepts (what students need to know) 

DOK Level /  Bloom’s 

Count within 1000  Skip counting by 5’s, 10’s, and 100’s both  forward and backwards 

Skip counting using number line or chart 

1 

Relationship between skip counting and  multiplication 

2 

Develop an understanding of both a number  line and a number chart 

3 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  Skip counting by 5’s, 10’s, and 100’s provides a useful  strategy for 

Skip counting helps me to multiply 

How do I skip count by 5’s, 10’s, and 100’s? 

How does skip counting help me to understand  multiplication? 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Explanations and Examples  Students need many opportunities counting, up to 1000, from different starting points. They should  also have many experiences skip counting by 5s, 10s, and 100s to develop the concept of place  value.  Examples: · · ·

The use of the 100s chart may be helpful for students to identify the counting patterns. The use of money (nickels, dimes, dollars) or base ten blocks may be helpful visual cues. The use of an interactive whiteboard may also be used to develop counting skills. 

The ultimate goal for second graders is to be able to count in multiple ways with no visual support. 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2  Extending Base Ten Understanding  6 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.NBT.3 Read and write numbers to 1000 using base‐ten numerals, number names, and expanded  form. 

Skills (what students must be able to do) 

Read  Write  Using 

Concepts (what students need to know) 

Base‐ten numerals  Number names  Expanded form 

DOK Level /  Bloom’s  1  2 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  A 4 digit number is made up of ones, tens, hundreds,  and thousands and can be expressed in different forms 

What are the different ways I can write 4 digit numbers?  How can I use what I know about place and value to  determine the worth of a given number? 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Explanations and Examples  Students need many opportunities reading and writing numerals in multiple ways.  Examples: · · ·

Base­ten numerals  Number names  Expanded form 

637  six hundred thirty seven  600 + 30 + 7 

(standard form) (written form) (expanded notation) 

When students say the expanded form, it may sound like this: “6 hundreds plus 3 tens plus 7 ones” OR 600  plus 30 plus 7.” 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2 nd  Applying Base Ten Understanding  5 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.NBT.7  Add and subtract within 1,000, using concrete models or drawings and strategies based on  place value, properties of operations, and /or the relationship between addition or subtraction , relate  strategy to written method, understand that in adding or subtracting 3 digit numbers, one adds or  subtract hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to  compose or decompose tens or hundreds.  Skills (what students must be able to do) 

Concepts (what students need to know) 

DOK Level /  Bloom’s 

Use models/drawings  Relate strategies  Understand  Compose numbers  Decompose numbers 

Addition within 1000  Subtraction within 1000  Strategies  Place value  Relationships  Methods  3digit numbers  Hundreds  Tens  one 

3 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  Using money and base ten blocks and expanded  notation 

How can 1000 be expressed? 

Ones can be grouped to make 10 and 10 to make 100  and 100 to make 1000. 

What strategies can we utilize in order to add/subtract 3  digit numbers? 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Explanations and Examples  There is a strong connection between this standard and place value understanding with addition and  subtraction of smaller numbers. Students may use concrete models or drawings to support their addition or  subtraction of larger numbers. Strategies are similar to those stated in 2.NBT.5, as students extend their  learning to include greater place values moving from tens to hundreds to thousands. Interactive whiteboards  and document cameras may also be used to model and justify student thinking. 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard  Content Area  Grade/Course  Unit of Study  Duration of Unit 

Forsyth County Schools 

Math  2nd  Becoming Fluent with Addition and Subtraction  5 weeks 

Insert a CCGPS standard below (include code). CIRCLE the SKILLS that students need to be able to do and  UNDERLINE the CONCEPTS that students need to know.  MCC2.O.A.1  Use addition and subtraction within 100 to solve one and two step word problems  involving situations of adding to take from, putting together, taking apart, and comparing with  unknowns in all positions. eg. Using drawings and equations with symbols for unknown number to  represent the problem. 

Skills (what students must be able to do) 

Concepts (what students need to know) 

DOK Level /  Bloom’s 

Use  Solve  Adding to  Taking from  Putting together  Taking apart  Comparing  Representing 

Addition  Subtraction  1 and 2 step word problems  Drawings  Equations  Symbols  Unknown number 

1  3 

2  3  2/3 

Step 5:  Determine BIG Ideas  (enduring understandings  Step 6:  Write Essential Questions (these guide  students will remember long after the unit of study)  instruction and assessment for all tasks.  The big ideas are  answers to the essential questions)  Equations and/or drawings can be used to manipulate  known numbers to solve for the unknown. 

How can you solve one and two step word problems  using various strategies? 

Next step, create assessments and engaging learning experiences

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011 

CCGPS Unwrapped Standard 

Forsyth County Schools 

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011

CCGPS Unwrapped Standard 

Forsyth County Schools 

Word problems that are connected to students’ lives can be used to develop fluency with addition and  subtraction. Table 1 describes the four different addition and subtraction situations and their relationship to the  position of the unknown. 

Examples: · · ·

·

Take From example: David had 63 stickers. He gave 37 to Susan. How many stickers does David have  now?  63 – 37 = Add To example: David had $37. His grandpa gave him some money for his birthday. Now he has $63.  How much money did David’s grandpa give him?  $37 +        = $63 Compare example: David has 63 stickers. Susan has 37 stickers. How many more stickers does David  have than Susan?  63 – 37 =  o  Even though the modeling of the two problems above is different, the equation, 63 ­ 37 = ?, can  represent both situations (How many more do I  need to make 63?) Take From (Start Unknown) David had some stickers. He gave 37 to Susan.  Now he has 26 stickers.  How many stickers did David have before?  ­ 37 = 26 

It is important to attend to the difficulty level of the problem situations in relation to the position of the unknown. · · ·

Result Unknown, Total Unknown, and Both Addends Unknown problems are the least complex for  students. The next level of difficulty includes Change Unknown, Addend Unknown, and Difference Unknown The most difficult are Start Unknown and versions of Bigger and Smaller Unknown (compare  problems). 

Second graders should work on ALL problem types regardless of the level of difficulty. Mastery is expected in  second grade. Students can use interactive whiteboard or document camera to demonstrate and justify their  thinking.

Adapted for Forsyth County Schools from The Leadership and Learning Center, 2011