Second Grade Overview
Overview
In 2nd Grade there are 4 critical learning areas:
Critical Learning Area 1
Students extend their understanding of the baseten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multidigit numbers (up to 1000) written in baseten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
Critical Learning Area 2
Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in baseten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.

Critical Learning Area 3
Critical Learning Area 4
Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two and threedimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.



Unit 1
Second Grade Mathematics
Unit 1
Operational Fluency of Addition and Subtraction
During Unit 1, your child will work on becoming fluent with adding and subtracting within 20. Basic facts for addition refer to all sums of two onedigit numbers. Over time, fluency with number relationships leads to memory of the addition facts and application to subtraction. Fluency is defined as solving facts quickly and accurately without halting, stumbling or reversing oneself. 

Students Need To
 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers.
 Use addition and subtraction within (20) to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
 Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph.
 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ...
Ways Parents Can Help
 Keep a set of flash cards in the car to practice as you run errands. Encourage your child to explain the strategy that they used to solve the problem.
 With a deck of cards, use the number cards to play Fact War. Each player flips 1 card and the player to say the sum first, gets both cards
 Have your child sort a set of flashcards based on the strategy that they would use to solve the problem. Have them select one strategy pile to solve.
 Students often overuse "counting on" for all math facts. Help your child to generate facts that are efficient for counting on and facts that are not efficient for counting on (you could create a list or use flashcards to make groups). Encourage your child to explain why counting on would not be efficient for a fact (such as 5+7).
Important Vocabulary
Add: to join two or more quantities to get one sum Addend: any number used to get a sum Data: collection of information Difference: difference between two numbers (subtraction) Equal: having the same amount or value Equality: state of being equal Equation: mathematical statement containing an equals sign to show that two expressions are equal Fluent: solving facts quickly and accurately without halting, stumbling or reversing oneself Fewer: less than Graph drawing or diagram used to record information Inverse Operation: opposite or reverse operations (e.g. addition and subtraction) 
Minuend: the quantity that you are subtracting from in a subtraction equation
Minus: to subtract More: greater than Number Line: line marked with numbers used to show operations Number Sentence: mathematical sentence written in numerals and mathematical symbols Plus: to add Related Fact: addition and/or subtraction sentences that are alike Scale: the increment used on a graph Strategy: a plan, a method or a way to solve a problem Subtract: to take one quantity away from another Subtrahend: the quantity subtracted from the minuend in a subtraction equation Sum: the total or whole amount; the result of adding 
Videos and Support Sites
Carroll County Public Schools Video Support

Some Support Sites: 
Unit 2
Second Grade Mathematics
Unit 2
Number and Operations in Base Ten
Place Value
Printable Parent Letter
During Unit 2, your child will use their understanding of addition and place value to develop fluency with addition and subtraction within 100. They will solve problems by applying their understanding of fact strategies and models for addition and subtraction. Your child will develop, discuss, and use efficient, accurate and generalizable methods to compute sums and differences of whole numbers to 1,000 using their understanding of place value and the properties of operations. They will select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds, leading them to understand why procedures work. 
Students Need To
 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
 Represent wholenumber sums and differences within 100 on a number line diagram
 Explain why addition and subtraction strategies work, using place value and the properties of operations
 Add up to four twodigit numbers using strategies based on place value and properties of operations
 Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem
 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?
 Count within 1000; skipcount by 5s, 10s…
 Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph
 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers
Ways Parents Can Help
 Help your child use addition or subtraction to solve real world problems (e.g. adding a bill, calculating change from a purchase…) and have them explain why the addition or subtraction strategy they used worked.
 Create and solve word problems involving money. For example, if you have 2 quarters and 3 dimes, how many cents do you have?
 Practice counting a group of all nickels (skip counting by 5) and then all dimes (skip counting by 10)
 Use the ace through nine cards from one or two decks of playing cards to help practice single digit addition facts. Your child can simply turn over or pick the two cards to add together. You can also play a game where each partner picks two cards from their face down pile and adds them together. The player whose cards made the largest sum gets all four cards. Repeat. The player with the most cards at the end wins.
Key Vocabulary
Video Support
Unit 3
Second Grade Mathematics
Unit 3
Number and Operations in Base Ten
Addition and Subtraction
Printable Parent Letter
During Unit 3, your child will build critical knowledge in the understanding of the baseten numeration system and placevalue concepts. This includes ideas of counting in units of fives, tens and multiples of hundreds, tens and ones as well as a grasp of number relationships, which they will demonstrate in a variety of ways, including comparing and ordering numbers. They will work to understand multidigit numbers in terms of placevalue recognizing that placevalue notation is shorthand for representing amounts of hundreds, tens and ones. 
Students Need To
 Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases
 100 can be thought of as a bundle of ten tens — called a “hundred."
 The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
 Read and write numbers to 1000 using baseten numerals, number names, and expanded form.
 Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
 Count within 1000; skipcount by 5s, 10s, and 100s.
 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?
 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
 Add and subtract within 1000, using concrete models or drawings
and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
 Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers.
Ways Parents Can Help
Help your child to make real world connections with money, addition and subtraction.
For example:
 provide opportunities for your child to count dollar bills and coins (for example, money in a wallet, money to pay for something at the store, change received from a purchase)
 help your child use addition or subtraction to solve real world problems (e.g. adding a bill, calculating change from a purchase… and have them explain why the addition or subtraction strategy they used worked
Key Vocabulary
Video Support
Unit 4
Second Grade Mathematics
Unit 4
Measurement
Printable Parent Letter
During Unit 4, your child will develop an understanding of the meaning and processes of measurement, including transitivity (e.g., if object A is longer than object B and object B is longer than object C, then object A is longer than object C). They will understand linear measure as an iteration of units and use rulers and other measurement tools with that understanding. They will understand the need for equallength units, the use of standards units of measure (centimeter and inch), and the inverse relationship between the size of a unit and the number of units used in a particular measurement. Your child will recognize that the smaller the unit, the more iterations that are needed to cover a given length. Time is a bit different from the other attributes that are commonly measured in school because it cannot be seen and because it is more difficult for students to comprehend units of time or how they are matched against a given time period or duration. 
Students Need To
 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
 Estimate lengths using units of inches, feet, centimeters, and meters.
 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
 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 wholenumber sums and differences within 100 on a number line diagram.
 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units.
 Given the dimensions of a polygon, determine the perimeter.
 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Ways Parents Can Help
 When measuring items, have your child help. If possible let them help with the selection of which measurement tool to use (ruler, yardstick, measuring tape…. Try to use measurement vocabulary.
 Give your child a ruler. Help them to measure the item twice, once in inches and once in centimeters. Talk about how the difference in the total number of units is different because centimeters are smaller than inches so it takes more of them to cover the given length.
 Help your child to find the difference in length between two objects by having them measure both and then finding the difference.
 Help your child to estimate various lengths. Have them measure the actual length to see how close they were with their estimate.
 Practice reading the time, to the nearest five minutes, on an analog clock.
Key Vocabulary
Video Support
Unit 5
Second Grade Mathematics
Unit 5
Measurement
Printable Parent Letter
During Unit 5, your child will describe and analyze shapes by examining their sides and angles. Students will investigate, describe, and reason about decomposing and combining shapes to make other shapes. Students will partition circles and rectangles into two, three or four equal shares, describing the shares using the words, halves, thirds, and half of. Students will recognize that equal shares of identical wholes need to have the same shape. Students will also work with equal groups of objects to gain foundations for multiplication. They will identify odd and even numbers based on equal groups of two. Students will begin to use number patterns to extend their knowledge of properties of numbers and operations. When skip counting to solve repeated addition problems students begin to build the foundations for understanding multiples and factors. 
Students Need To
 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
 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.
 Partition a rectangle into rows and columns of samesize squares and count to find the total number of them.
 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.
 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
Ways Parents Can Help
 Hunt for shapes in your world that are 2 dimensional. Try to identify them by name.
 Play a "Name My Shape" riddle game. Have the clues for the shape be the attributes of the shape. For example, "My shape has five sides and five angles. What is my shape?" pentagon.
 Have your child help you partition (cut) a rectangular (pan of brownies) or circular (cake) food item into two, three or four equal shares and then identify the share using the words halves, thirds or fourths.
 Rows vs. Columns: Look for opportunities to show your child arrays in the real world, i.e. seats in a theater, muffin baking tin, ice cube trays, arrangements of fruit in the grocery store, eggs in a carton, etc.
 Roll an Array! Use small candies or buttons to build the arrays. Roll two dice …the first roll will be the number of rows in the array and the second roll will be the number of columns. Use the small items to create an array. Count the total number of objects in the array. To make it even more fun, have a partner roll the dice, build an array, then count the total number of pieces in the array. The player with the greatest number of pieces in their array wins.
Key Vocabulary
Key Vocabulary to Know  
Array 2dimensional 3dimensional Angle Circle Column Congruent Corner Cube Equal Addends Equal Groups Equal Parts Equation Even Face Fourths Half/Halves 
Hexagon Odd Partition Plane figure Pentagon Quadrilateral Rectangle Repeated Addition Row Skip Count Solid figure Square Symmetry Thirds Triangle 