2nd Grade Math Worksheet - A Parent's Guide

Many educators, politicians, and parents believe the instruction of mathematics in the United States is in crisis mode, and has been for some time. Indeed, recent test results show that American 15-year-olds were outperformed by 29 other countries on math testing scores. To help counter this crisis, educational, civic, and business leaders worked together to develop the Common Core State Standards (CCSS).

Girl solving math worksheet problems

The goal of Common Core is to establish consistent, nationwide guidelines of what children should be learning each school year, from kindergarten all the way through high school, in English and math. Though CCSS sets forth these criteria, states and school districts are tasked with developing curricula to meet the standards.

The 2014-15 school year will be important for Common Core as the standards are fully implemented in many remaining states of the 43 (and the District of Columbia) that have embraced their adoption. CCSS has its advocates as well as its critics, and the debate on its merits has become more pronounced in recent months. Irrespective of the political differences with Common Core, its concepts are critical for students because the standards help with understanding the foundational principles of how math works. This guide steers clear of most of the controversy surrounding CCSS and primarily focuses upon the math your secondgrader will encounter.

Common Core Standards

A stated objective of Common Core is to standardize academic guidelines nationwide. In other words, what second-graders are learning in math in one state should be the same as what students of the same age are learning in another state. The curricula may vary between these two states, but the general concepts behind them are similar. This approach is intended to replace wildly differing guidelines among different states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level, including second grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by so-called “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards, which mandate a “mile-wide, inch-deep” curriculum in which children are being taught so much in a relatively short span of time that they aren’t effectively becoming proficient in the concepts they truly need to succeed at the next level. Hence, CCSS works to establish an incredibly thorough foundation not only for the math concepts in future grades, but also toward practical application for a lifetime.

For second grade, Common Core’s focus places a great emphasis in strengthening fluency in addition and subtraction. The idea that numbers are based on tens is expanded and reinforced, and units of measurement receive more attention. Ultimately, this focus will enable children to develop rigor in real-life situations by developing a base of conceptual understanding and procedural fluency.

Critical Areas of Focus

For many parents, second grade feels like the first year that school is really serious for their children. Many of the “cute” approaches to teaching math that might have been prevalent in kindergarten and first grade give way to an increased focus on critical concepts students will require in the next few years. Base 10 notation will give kids a better understanding of numbers up to 1,000—and they will need that understanding once operations eventually start using three-digit numbers. The simple addition and subtraction introduced in first grade not only will be re-emphasized, but also will be expanded to include two-digit numbers. And once addition becomes easier, students will be ready for the multiplication skills that will be taught in third grade. Here are the four critical areas that Common Core brings to second-grade math:

Base 10 Notation

Base 10 is the idea that our number system is based on tens. Count to 10 and start again, only with the number in the tens spot increased by one. When the tens spot turns over from nine, you add a hundreds place, and so on. For second grade, students build upon this idea concept by learning about numbers up to 1,000, as well as understanding the concept of place value—that a number such as 629 is the same as 6 hundreds, 2 tens, and 9 ones.

Addition and Subtraction

All the flash cards and other drilling to get addition and subtraction facts down in first grade pay off in second grade, as those concepts are applied to adding and subtracting numbers up to 100 and, eventually, 1,000. Students will learn multiple strategies to add and subtract bigger numbers, including the traditional place value method their parents were likely taught, and breaking apart addends on two twodigit numbers (i.e., for 29+34, splitting the equation into 20+30=50 and 9+4=13, then adding 50+13 for the correct answer of 63).

Standard Units of Measure

Centimeters and inches become the stars of the measuring world as students use rulers to gauge distance. Also taught is the concept that the smaller unit of measurement used, the more of that unit will be necessary to cover the length of something measured. Addition and subtraction of measurements are introduced, too.

Happy/Smiling kids in School

Shapes

The big push into geometry won’t come until later grades, but understanding and drawing twodimensional and three-dimensional shapes are still emphasized with an eye toward the future.

Overview of Topics

From the four critical areas of focus discussed in the previous section, Common Core also further clarifies the skills second-graders should know by the end of the school year. For example, the fluency requirement at this level is singledigit sums and differences (i.e., basic addition and subtraction, committed to memory by the end of the year) and adding and subtracting within 100. The four topics presented here, taken directly from CCSS itself, include some specifics on what kids will be taught at in Grade 2.

Operations and Algebraic Thinking

  • Represent and solve problems using addition and subtraction. Students will add and subtract numbers up to 100 to solve word problems.
  • Add and subtract within 20 The basic math facts introduced in first grade will reach a fluency level in second—kids can answer from memory addition and subtraction problems with an answer of 20 or less.
  • Work with equal groups of objects to gain foundations for multiplication. As already mentioned, the addition learned in second grade will form a base for multiplication in third. Second-graders will learn:
    • To determine whether a group of objects (up to 20) is odd or even (for example, by pairing them by 2s)
    • To write an equation that expresses a number as the sum of two equal addends (e.g., 12 is the same as 6+6)
    • To use an array to determine the total number of objects with up to five rows and five columns, and to write an equation to express that number as a sum of equal addends (for example, an array of 3 rows and 3 columns equals 3+3+3)

Number Operations in Base 10

  • Understand place value. Students will be taught that a three-digit number can be broken down into a hundreds place, a tens place, and a ones place, and that a hundred is essentially a “bundle” of tens. Second-graders will also learn to skip count by fives, tens, and hundreds to 1,000.
  • Use place value understanding and properties of operations to add and subtract. The emphasis on base 10 will be applied to addition and subtraction with numbers up to 100. What parents might understand as “carrying” and “borrowing” will be introduced. Students will also learn how to mentally add or subtract by 10 and by 100.

Measurement and Data

  • Measure and estimate lengths in standard units. Students will measure objects using standard tools such as rulers, yard and meter sticks, and tape measurers. They will use two different methods of measurement (e.g., centimeters and inches) to measure the same object and estimate and compare the differences
  • Relate addition and subtraction to length. Word problems will combine measurement with addition and subtraction concepts—in other words, a student might be asked how much shorter one object is than another.
  • Work with time and money. Students will learn to tell time from analog and digital clock down to five-minute increments (e.g., 1:35 a.m., 2:20 p.m., and so on) and learn the concept of a.m. and p.m. Word problems will incorporate money, especially specific denominations (pennies, nickels, dimes, and quarters, and dollars).
  • Represent and interpret data. Line plots, bar graphs, and picture graphs will be used to represent measurement data, and students will perform comparisons or simple arithmetic using information from a graph.

Geometry

  • Reason with shapes and their attributes. Students will recognize shapes, including quadrilaterals, cubes, hexagons, pentagons, and triangles, based on the number of faces, angles, and sides. In another move toward learning multiplication, second-graders will be taught how to partition a rectangle into same-size squares and count the results, as well as divide rectangles and circles into even shares and identify the shares as halves, thirds, and quarters.

The Truth About CCSS and Performance

Common Core aims to improve educational performance and standardize what students should learn at every grade in preparation for a lifetime of application, but it does not set curricula, nor does it direct how teachers should teach. As with any educational reform, some teachers, schools, and school districts will struggle with CCSS, some will seamlessly adapt, and some will thrive. As a parent, your responsibility is to monitor what your secondgrader is learning, discover what is working or isn’t working for your child, and to communicate with his or her teacher—and to accept that your children’s math instruction does differ from what you learned when you were younger, or even what they might have learned last year. The transition can be a little daunting for parent and student alike, but that’s not a product of the standard itself. Common Core simply takes a new, more pointed approach to improving the quality of math instruction in this country.

The Benefits

As previously mentioned, CCSS decreases the number of topics students learn at each grade. However, the remaining topics are covered so extensively that the chances a child will master the corresponding skills increase. An analogy to this approach is comparing two restaurants. One restaurant has a varied menu with dozens of items; the other only serves hamburgers, fries, and milk shakes. The quality of the food at the first restaurant may vary upon the cooks’ experience, the multitude of ingredients required for so many offerings, and the efficiency (or lack thereof) of the staff. Because the second restaurant only serves three items, mastering those three items efficiently should result in an excellent customer experience. That’s not to say the first restaurant won’t succeed (because many do), but there’s always a chance that something on the menu won’t live up to the business’s own expectations. By reducing the number of math topics taught, Common Core helps ensure students are truly ready for what comes next. Given the attention given to the included concepts, more practical applications and alternate operations of the math can be explored.

Coinciding with the reduction of topics is an emphasis on vigor—achieving a “deep command” of the math being taught. Students will be challenged to understand the concepts behind mathematical operations rather than just resorting to rote memorization and processes to get a right answer. Speed and accuracy are still important; kids won’t be getting away that easily from flash cards and quizzes that increase fluency. Moreover, Common Core places even additional emphasis on practical application—after all, the math kids learn now will be important when they become adults, even if they never have to think about prime numbers or symmetrical lines in their day-to-day lives.

Finally, CCSS links standards from grade to grade so that the skills learned at one level translate into the tools they need to learn at the next level. This coherence would seem an obvious educational approach, but often, there is no link—students are taught a skill in second grade that might not be used (and might have to be re-taught) until fourth. Each new concept in Common Core is an extension of a previous, already learned concept.By reducing the number of math topics taught, Common Core helps ensure students are truly ready for what comes next. Given the attention given to the included concepts, more practical applications and alternate operations of the math can be explored.

Math Practices to Help Improve Performance

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice” that teachers at all levels are encouraged to develop in their students. These eight practices, designed to improve student performance, are described here, with added information on how they apply to second-graders.

  • Make sense of problems and persevere in solving them Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until it’s solved. Secondgraders, for example, are still developing their reading skills and might struggle simply comprehending a word problem. This CCSS math practice encourages them to take their time to read and try understanding the problem, emphasizing that the process is ultimately important even if it doesn’t result in a correct answer. Second-graders will also be encouraged to use pictures or objects to better visualize the problem and solution.
  • Reason abstractly and quantitatively Students decontextualize and contextualize problems. By decontextualizing, they break down the problem into anything other than the standard operation. By contextualizing, they apply math into problems that seemingly have none. For example, if a second-grade word problem talks about cats and dogs, students who are decontextualizing might draw pictures of puppies and kittens to help them get to a solution. Students this age who are contextualizing may count on their fingers when asked how many minutes are left before recess.
  • Construct viable arguments and critique the reasoning of others Students use their acquired math knowledge and previous results to explain or critique their work or the work of others. Most secondgraders will jump at the chance to work a problem on the board for the class. Besides boosting their confidence, the ability to explain the math will increase their ability to excel at it.
    Girl solvig geometry problems
  • Model with mathematics This is just like it sounds: Students use math to solve real-world problems. Second-graders can be challenged to take the math skills they have learned into their own lives. For example, a student who is handing out Valentines at school can use addition to determine if two packs of 15 cards will be enough for her class of 28 students, and then subtraction to see if she will have any extras to give to her favorite teachers.
  • Use appropriate tools strategically Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. With Common Core’s secondgrade focus on units of measurement, this initiative is strongly emphasized as students learn what type of measuring instrument is most suited to determine a certain distance.
  • Attend to precision Students strive to be exact and meticulous—period. Second-graders will be expected to become fluid in the simpler addition and subtraction facts, because not knowing what 7+8 is will affect trying to answer 28+17. Furthermore, if a student can’t come up with the right answer on a more complex problem, he should be taking steps to figure out how or should ask for help (especially at this age).
  • Look for and make use of structure Students will look for patterns and structures within math and apply these discoveries to subsequent problems. For example, second-graders might be asked to solve 37+20. With the zero on the end of 20, they might determine that all they need to do is add 3+2 to get 5 for the tens place and an overall, quickly realized answer of 57.
  • Look for and express regularity in repeated reasoning Students come to realizations—“a-ha” moments is a good term for these realizations—about the math operations that they are performing and use this knowledge in subsequent problems. For example, a secondgrader may realize that adding or subtracting even numbers will always result in an even number, which is something he or she can look for in future operations.
    Reasoning in 2nd Grade Math Worksheet

How to Help Your Children Succeed Beyond CCSS

Some of parents’ trepidation with Common Core isn’t so much with the guidelines themselves, but with the testing now aligned with CCSS via local math curricula. Standardized testing was stressful for students and parents before; with the ongoing Common Core implementation, many families simply don’t know what to expect.

Fortunately, CCSS does not have to be that stressful, for you or your secondgrader. Here are some tips to help your children succeed with Common Core math:

Be informed; be involved

If Common Core concerns you, intrigues you, or confuses you, don’t hesitate to learn as much about it—in your child’s classroom, at your kids’ school, and on a national level. Talk with teachers, principals, and other parents. Seek advice on how you can help your kids, and yourself, navigate CCSS math. If you want to take further action, become involved with PTA or other organizations and committees that deal with your school’s curriculum. The more you know, the more, ultimately, you can help your child.

Give them some real-world math

A basic tenet of Common Core is to apply math principles to real-world situations. Why not start now? Give your child math problems when you are out and about—the store, in traffic, the park, and so on. For example, if you are at the grocery store and want to use the express lane, ask your student to figure out how many more items you can add to your cart and still stay under 20.

Take time to learn what they are learning

You might look at a worksheet your child brings home and think, “This isn’t the math I’m used to.” Because Common Core emphasizes understanding the process of arriving at an answer, your child may be taught additional ways to fry a mathematical egg, so to speak. Instead of shunning these approaches, learn them for yourself. Once you comprehend these additional methods, you will be better able to help your child comprehend them as well

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer, especially within Common Core. Second, ask your children to show you their homework, particularly the challenging stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident in explaining their work to you, they will carry that confidence into the classroom when the teacher asks for those same explanations.

Seek more help if necessary

If your second-grader is struggling with the new math standards, talk with his or her teacher first. You then might want to seek outside resources to help your child. Several online resources provide math help, including worksheets and sample tests that conform to Common Core standards. Tutoring might be an option you consider as well. Innovative iPad-based math programs have emerged that combine the personalized approach of a tutor with today’s technology. This revolutionary approach also may feature a curriculum based on Common Core, thus ensuring your child’s learning at home is aligned with what he or she is learning at school.

Math Practice Worksheets

Operations and Algebraic Thinking

  • 13 + 16 = ___

  • Find the missing number. 15 + 27 + 14 = 29 + ____

  • Select the correct equation to find the total number of stars.

    2nd Grade Math Worksheet - stars
    • 5 + 5 = 20
    • 5 + 5 + 5 + 5 = 20
    • 5 + 5 + 5 + 5 = 25
    • 5 + 5 + 5 + 5 + 5 = 25
  • Arthur stacked cans of milk in different shelve. If there are 5 shelve and 8 cans of milk per shelf, how many cans of milk has he stacked?

    • 8 + 8 + 8 + 8 + 8 = 40
    • 8 + 8 + 8 + 8 = 40
    • 5 + 5 + 5 + 5 + 5 = 40
  • 52 students in the school cafeteria bought hamburgers, 63 bought pizza and 42 bought salad. How many total students bought lunch at the cafeteria?

  • Select the equivalent equation for the given statement Andy scores a total of 109 points in 2 games of Subway Surfers. If he scores 41 points in the 1st game, how many points did he score in the 2nd game?

    • 41 + __ = 109
    • 109 + __ = 41
    • 41 × __ = 109
    • 109 ÷ __ = 41
  • There are 141 oil paintings, 161 sculptures and 68 charcoal paintings in a museum. What is the total number of paintings in this museum?

  • 19 + 13 = ?

    • 10+3+10+3
    • 19+9+10+3
    • 0+9+10+3
    • 10+9+10+3
  • Pick the odd number.

    • 96
    • 58
    • 37
    • 56
  • Compare the numbers using the given operation. 18 - 8 _____ 4 + 6

    • <
    • >
    • =

Number Operations in Base 10

  • Select the expanded form of the given numeral. 223

    • 30 + 2 + 200
    • 3 + 200 + 20
    • 300 + 2 + 20
    • 300 + 2 + 20
  • Find the number that has the given expanded form. 30 + 6 + 400

  • 873 - what digit is in the tens place?

  • Count the number of unit squares in the given image

    2nd Grade Math Worksheet - blocks
  • 853 - what place is the 5 in?

    • Ones
    • Tens
    • Hundreds
    • Thousands
    • Ten Thousands
  • 8 tens 1 ones - 5 tens 2 ones = ___ tens ___ ones

  • Fill in the missing number 80 tens = _ hundreds

    2nd Grade Math Worksheet - blocks vertical
  • Select the numbers represented by the image

    2nd Grade Math Worksheet - blocks
    • 4 tens
    • 40 tens
    • 4 hundreds
  • If you have 3 hundreds, 12 tens and 4 ones, how much do you have?

  • Find the missing numbers by counting the tens and ones
    33 + 39 = 30 + 3 + 30 + 9

    • Adding the tens: 30 + 30 = _
    • Adding the ones: 3 + 9 = _
    • So, 33 + 39 = 60 + 12 = _

Measurement and Data

  • What is the length of the cloud?

    2nd Grade Math Worksheet - length of the cloud
  • Select the correct option

    Faith has to finish a test in one hour. If she starts the test at 10:00 am, she will finish the test at 11:00___

    • AM
    • PM
  • Which time comes latest in the day?

    • 8:12 pm
    • 10:12 pm
    • 12:30 pm
    • 10:48 am
  • What is quarter past 8:00?

  • How much money is this? 5*Dimes, 1*Nickels, 4*Pennies

    2nd Grade Math Worksheet - Dimes/Nickels/Pennies
  • How much longer is the banana compared to the raspberry?

    2nd Grade Math Worksheet - Banana/Rashberry
  • Sarah has 1 quarter and 2 dimes. Sonia has 1 quarter and 2 nickels. How much money do they have put together?

  • Given below is the number of cars sold by a car dealer this week.
    How many lesser green cars were sold by the car dealer than red cars this week?

    2nd Grade Math Worksheet - Cars/Dealers
  • Anne’s pencil is 23 cm long. Jane’s pencil is 8 cm shorter than Anne’s. Peter’s pencil is 4 cm longer than Jane’s. Whose pencil is the longest?

    • Anne
    • Jane
    • Peter
    • Can’t say
  • Given below is the number of cakes sold by a baker on different days
    How many fewer cakes were sold on Saturday than on Sunday?

    2nd Grade Math Worksheet - cakes

Geometry

  • Identify the shape

    2nd Grade Math Worksheet - Geometric Shapes
    • Sphere
    • Cube
    • Cuboid
    • Cone
    • Kite
  • Identify the number of lines of symmetry

    2nd Grade Math Worksheet - symmetrical lines
  • How many angles does a triangle have?

    2nd Grade Math Worksheet - triangle
  • Select all images that have exactly 4 angles

    • 2nd Grade Math Worksheet - Trapezuim
    • 2nd Grade Math Worksheet - Square
    • 2nd Grade Math Worksheet - Rectangle
  • How many vertices and angles does the trapezoid have?

    2nd Grade Math Worksheet - Trapezium
    • 4 vertices and 4 angles
    • 4 vertices and 5 angles
    • 5 vertices and 5 angles
  • Select all images that have at least 4 faces

    • 2nd Grade Math Worksheet - Cuboid
    • 2nd Grade Math Worksheet - Cone
    • 2nd Grade Math Worksheet - Cylindrical
    • 2nd Grade Math Worksheet - Rectangular
  • Select all images that have at least 3 angles and at most 4 vertices

    • 2nd Grade Math Worksheet - Triangle
    • 2nd Grade Math Worksheet - Polygon
    • 2nd Grade Math Worksheet - Cuboid
    • 2nd Grade Math Worksheet - Rectangular
  • Count the number of unit squares in the given image

    2nd Grade Math Worksheet - blocks
  • Anne cut a rectangular cake into 3 rows and 4 columns. How many pieces of cake did she get?

  • What fraction of the image is blue in color?

    2nd Grade Math Worksheet - blocks
    • Half
    • One-third
    • Two-thirds
    • One-quarter

Answer Key

Operations and Algebraic Thinking

  • (1) 29
  • (2) 27
  • (3) D
  • (4) A
  • (5) 157
  • (6) 1
  • (7) 209
  • (8) 4
  • (9) C
  • (10) C

Number Operations in Base 10

  • (1) B
  • (2) 436
  • (3) 7
  • (4) 48, 6
  • (5) B
  • (6) 2, 9
  • (7) 8
  • (8) B, C
  • (9) 424
  • (10) 60, 12, 72

Measurement and Data

  • (1) 14
  • (2) 2
  • (3) 2
  • (4) 8:15
  • (5) 59
  • (6) 3
  • (7) 80
  • (8) 13
  • (9) 1
  • (10) 15

Geometry

  • (1) B
  • (2) 5
  • (3) 3
  • (4) A, B, C
  • (5) A
  • (6) A, D
  • (7) A
  • (8) 9
  • (9) 12
  • (10) D

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