3rd 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. 1 To help counter this crisis, educational, civic, and business leaders worked together to develop the Common Core State Standards (CCSS).

Girl solving math 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 thirdgrader will encounter.

1U.S. Students Slide in Global Ranking on Math, Reading, Science; NPR.org; Dec. 13, 2013

Common Core Standards

A stated objective of Common Core is to standardize academic guidelines nationwide. In other words, what third-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 third 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 third grade, Common Core’s focus places a tremendous emphasis on introductory multiplication. Fractions also make their first appearance, and two-dimensional shapes receive plenty of 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

Third grade is an absolutely essential year in terms of math education. Multiplication is a new concept to many students this age, but is one that must be mastered—the sooner, the better—because so much subsequent math, from fourth grade all the way through high school and beyond, will rely upon it. Of course, more complex addition and subtraction, introductory fractions, and geometry aren’t ignored, but multiplication (and, eventually, division) is the marquee attraction during this year. Here are the four critical areas that Common Core brings to third-grade math:

Multiplication

Students will develop fluency multiplying single-digit numbers. Strategies used include repeated addition (e.g., 4x3 is the same as 4+4+4), analyzing equal-sized groups, arrays, and area models, to arrive at a product. Students also will eventually learn the relationship between multiplication and division (though the really big Common Core push on division won’t occur until fourth grade).

Fractions

Fractions are another concept students will use for years to come. The idea of unit fractions (in which the numerator is 1, such as in ½) is introduced first. Visual models will be used to demonstrate that fractions are part of a whole. Adding and subtracting fractions won’t come until later grades, but students will be taught to visually compare fractions (for example, four friends dividing a pizza into four parts means each gets 1/4 of the pie; if they decided to divide into eight, each would get two slices; from this students see that 1/4 is greater than 1/8).

Area

Tied into multiplication is the concept of area— especially in the sense that the space covered by a square or rectangle is width times length. At first, students will compute area simply by counting unit squares. Eventually, Tthe rectangular arrays used to help with multiplication come into play (e.g., an array of 2 rows and 4 columns equals 8 units).

Happy kid solving math worksheet

Shapes

Students will continue to identify and define two-dimensional shapes by sides and angles. Furthermore, the fraction concepts introduced in third-grade will be tied into geometry—many of the visual models used will involve circles, triangles, and rectangles divided into equal parts.

Identify and Define Two-dimensional shapes in 3rd Grade Math Worksheet

Overview of Topics

From the four critical areas of focus discussed in the previous section, Common Core also further clarifies the skills third-graders should know by the end of the school year. For example, the fluency requirements at this level are single-digit products and quotients (i.e., basic multiplication and division, with times tables committed to memory by the end of the year) and adding and subtracting within 1,000. The five topics presented here, taken directly from CCSS itself, 2 include some specifics on what kids will be taught in Grade 3.

Operations and Algebraic Thinking

  • Represent and solve problems using multiplication and division. Students will learn to multiply single-digit numbers and divide numbers of less than 100 with whole quotients. They will also apply these strategies to solving word problems
  • Understand the properties of multiplication and the relationship between multiplication and division. The concept that 7 × 3 is the same as 3 × 7 will be emphasized. Also, the complementary relationship between multiplication and division will be introduced—for example, if 7 × 3=21, then 21 ÷ 3 =7 .
  • Multiply and divide numbers within 100. By the end of third grade, students will be expected to know by memory all single-digit multiplication operations (i.e., times tables), which in turn will provide fluency in division with these basic equations (in other words, easy division without remainders).
  • Solve problems involving the four operations, and identify and explain patterns in arithmetic. Students will solve two-step word problems using the four basic operations (addition, subtraction, multiplication, and division) as well as by estimation strategies such as rounding. They will also identify and apply patterns within the math (for example, an odd number times an odd number will always produce an odd number).

Number Operations in Base 10

  • Use place value understanding and properties of operations to perform multi-digit arithmetic. Students will strive toward fluently adding or subtracting numbers within a 1,000. They will master rounding numbers to the nearest 10 or 100, and they will also learn to multiply one-digit numbers by multiples of 10 but less than 100 (e.g., 6 × 40).

Number Operations—Fractions

  • Develop understanding of fractions as numbers. As third-graders get their first major exposure to fractions, many concepts will be introduced:
    • Students will understand the fraction 1/b as one part of a whole that is partitioned into b equal parts.
    • They will learn how to represent a fraction as part of a number line (between 0 and 1).
    • They will learn about equivalent fractions and be able to recognize simple equivalencies (e.g., 1/2 is the same a 2/4 and 5/10).
    • They will be able to compare fractions with the same numerator or denominator and determine which is larger or smaller.

Measurement and Data

  • Solve problems involving measurement and estimation. Students will learn to tell time to the minute, as well as solve basic addition and subtraction word problems involving time. Estimating The concept of volume and mass is introducedexplained, and third-graders will be taught to solve one-step word problems with volumes or mass involving the same unit (for example, one cup holds 8 ounces of juice and another holds 6 ounces; how much total juice is there?).
  • Represent and interpret data. Thirdgraders will draw scaled picture graphs to represent data (for example, a graph in which one square equals three of an object), and they will solve one- or twostep “how many more?” and “how many less?” word problems. Also, they will use rulers to gather measurement data to within a quarter-inch and represent the results on a line plot.
Student Solving Math Worksheet
  • Geometric measurement: Understand concepts of area and relate to multiplication and addition. The idea of a “square unit” is introduced to better explain and work with area. Students will learn how to measure area by counting the square units and by using addition and multiplying. The additive nature of area will be introduced—students will be taught how to compute area of rectilinear shapes by breaking them down into rectangles first.
  • Geometric measurement: Perimeter. As a continuation of their understanding of area, Sstudents are introduced to the concept of perimeter. They will learn how perimeter differs from area (for example, the perimeter of a fenced yard is how much fence is needed, while the area is how much grass is growing within) and will will solve equations and word problems involving the perimeter of polygons.
Mathematical Operations in 3rd Grade Math Worksheet

Geometry

  • Reason with shapes and their attributes. Different categories of shapes (e.g., quadrilaterals) will be explained, and students will classify shapes according to sides, angles, and so on. Coinciding with the introduction to fractions, thirdgraders will partition shapes into parts with equal areas.

2Grade 4: Introduction, Common Core State Standards Initiative

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 third-grader 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.

Happy Kid solving math worksheet in blackboard

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 third grade that might not be used (and might have to be retaught) until fifth. Each new concept in Common Core is an extension of a previous, already learned concept.

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.3 These eight practices, designed to improve student performance, are described here, with added information on how they apply to third-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. For example, multiplication is brand new to third-graders, so word problems involving the concept may be particularly challenging for students more conditioned to addition and subtraction problems. 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. Third-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 third-grade word problem involves bananas in bunches of 10, students who are decontextualizing may represent each bunch by drawing one banana. Kids this age who are contextualizing may organize bananas into bunches in a word problem that doesn’t otherwise use such terminology.
  • 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. With multiplication being so new, third-graders must become particularly adept at talking about how they arrived at an answer with their newly acquired skills. Besides boosting their confidence, the ability to explain the math will increase their ability to excel at it.
    Student solving geometry problems
  • Model with mathematics This is just like it sounds: Students use math to solve real-world problems. Third-graders can be challenged to take the math skills they have learned into their own lives. For example, student who eats three string cheeses a day can use multiplication to figure out how many he eats during a week or a month.
  • Use appropriate tools strategically Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. For third-graders, the introduction of multiplication offers a pertinent example of this practice: The new concept gives students another option when solving a problem. Take the equation 3 × 7—third-graders can either add 7 + 7 + 7 to get the answer, or they can use their new skills to multiply 3 by 7 and arrive at the same result.
  • Attend to precision Students strive to be exact and meticulous—period. The emphasis on committing times tables to memory demonstrates how precision is so essential to multiplication; not knowing the answer to 4 × 6 now will lead to trouble when trying to solve 14 × 36 in the future. 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.
  • 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, third-graders might understand that multiplying even numbers together will produce an even number, and then use that knowledge to help solve future equations.
  • Look for and express regularity in repeated reasoning Students come to realizations—“aha” 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 third-grader may realize that 2 multiplied by any number is simply that number added to itself, and then use addition strategies to get to the correct answer.
    Reasoning in 3rd 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 third-grader. 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 a basketball game and your child’s favorite player scores 6 points in the first quarter, ask her how many points the player might finish the game with based on that initial statistic.

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 third-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 iPadbased 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

  • The store ordered 4 boxes of styli. There were 8 styli in each box. Which image shows the total styli that the store ordered?

    • 3rd Grade Math Worksheet - 4 boxes of styli
    • 3rd Grade Math Worksheet - 4 boxes of styli
    • 3rd Grade Math Worksheet - 4 boxes of styli
  • Ken gets 8 points and 3 stars for every Mario game he wins. If he wins 8 Mario games, how many total points would he have?

  • Select the division statement for the array

    3rd Grade Math Worksheet   stars
    • 18 ÷ 3 = 6
    • 18 ÷ 2 = 9
    • 18 ÷ 6 = 2
    • 18 ÷ 3 = 8
  • Write the equivalent expression for the statement. How many sets of 5 are in 30?

    • 30 ÷ 5
    • 30 × 5
    • 5 × 30
  • Find the missing number:

    ___ × 7 = 28

  • Find the missing numbers in the sequence.

    9, 18, ___, 36, 45, ___

  • The table shows the relation between the meters of cloth used for stitching shirts. Which of the following describes the pattern between the meters of cloth and the shirts?

    3rd Grade Math Worksheet
    • Add 2
    • Multiply by 2
    • Multiply by 3
    • Add 3
  • Select the equivalent equation for the given statement. Amber got 16 gifts for Christmas. Her brother got b fewer gifts than her. They got a total of 30 gifts.

    • 16 + (16 − b) = 30
    • 16 + (16 + b) = 30
    • 16 − (16 + b) = 30
  • Computed value of 8 × 12 = _

    Estimate the same by rounding off both the numbers to the nearest tens.

    Estimated value of 8 × 12 = _ × _ = _

  • In a department store there are 83 glass bottles. 35 of those are damaged. The remaining glass bottles are divided equally into 4 cartons. Find the number of glass bottles in each carton.

Number Operations in Base 10

  • 266 + 675 = __

  • 160 − __ = 41

  • 173 domestic flights and 163 international flights land at airport A. 145 domestic flights and 133 international flights land at airport B. How many total international flights land at these two airports?

  • Estimate the product by rounding the first factor to the nearest tens.

    99 × 9 = __

  • 5 hundreds 8 tens 7 ones − 1 hundreds 2 tens 9 ones = __ hundreds __ tens __ ones

  • Round off 58 to the nearest tens

  • Two digit numbers less than 70 that can be rounded up to 70 are __, __, __, __, __

  • The estimated number of cookies sold by a baker in a month is 660. Select all numbers that could be the actual number of cookies sold.

    • 657
    • 651
    • 661
    • 668
  • The County Swimming program enrolled 297 kids of different ages last summer. This year, the program has 73 fewer kids. How many kids are enrolled in the program this year?

  • 6 × 3 = __

    60 × 3 = __

    6 × 30 = __

Numbers and Operations: Fractions

  • Enter the fraction that represents the shaded part.

    3rd Grade Math Worksheet
  • What fraction does the point ‘b’ correspond to on the number line?

    3rd Grade Math Worksheet
  • Mrs. Peterson cut a cake into 10 equal parts. 9 out of those were eaten and she put the remaining in a box. What fraction of the cake did she put in the box?

    3rd Grade Math Worksheet - Pastry cake
  • What fraction does the point ‘a’ correspond to on the number line?

  • What fraction of the given image is colored brown?

    3rd Grade Math Worksheet
  • The fraction 2/6 on the 2nd number line maps to which fraction on the 1st number line?

    3rd Grade Math Worksheet  lines
  • If the two fractions represented by the images are equivalent, what is the missing numerator?

    1/2 = __/4

    3rd Grade Math Worksheet  fractions
  • Justin divides a bottle of juice equally into 3 equal cups. How many bottles of juice would he need to get 9 such cups ready?

  • Alex served 3/6 of a pizza and Andrew served 5/6 of a similar pizza. Who served lesser quantity of pizza?

    3rd Grade Math Worksheet  Pizza
    • Alex
    • Andrew
    • Both served the same quantity
  • Who ran more around the park? Ric ran 8/4 rounds around a park. His brother Rob ran 2 rounds around the park.

    • Ric
    • Rob
    • Both ran the same number of rounds

Measurement and Data

  • 11 minutes = __ seconds

  • Enter the answer in hh:mm:ss format 2 hrs 15 mins 26 secs + 13 hrs 36 mins 8 secs

  • A string is 576 m long. 98 m was used for a project. How much string is left?

  • What is 30 minutes after 07:56 am?

  • Select the smallest, by weight.

    • 8 kg
    • 4 kg 800 g
    • 6 kg 700 g
    • 4 kg
  • Amber’s bookshelf is 6 ft. long and 3 ft. wide. The closet is 5 ft. long and 4 ft. wide. Which is bigger?

    • Book shelf
    • Closet
    • Both are of the same area
  • What is the area of this figure in sq cm?

    3rd Grade Math Worksheet  area
  • Roni’s room is 9 feet long and 8 feet wide. How many square feet of carpet does she need to cover the floor?

  • In a survey, kids were asked their favorite online game. The data collected is given below.
    How many total kids chose Angry Birds, Temple Run and Fruit Ninja as their favorite games?

    3rd Grade Math Worksheet  kids/online games
  • A car dealer sold different colored cars in December and the details are given below. How many total green, yellow and blue cars did he sell in December?

    3rd Grade Math Worksheet  car dealer/ color

Geometry

  • Select what is true about the shape given below.

    3rd Grade Math Worksheet  geometry shapes
    • It is a quadrilateral
    • It has 4 vertices
    • It has 5 angles
  • The lines are ______. (Select perpendicular if the lines are intersecting and perpendicular)

    3rd Grade Math Worksheet    lines intersecting
    • Intersecting
    • Parallel
    • Perpendicular
  • Enter the fraction that represents the yellow shaded part.

    3rd Grade Math Worksheet  geometry/shapes/fractions
  • Select all images that represent the fraction 1/3

    • 3rd Grade Math Worksheet  geometry/shapes/fractions
    • 3rd Grade Math Worksheet  geometry/shapes/fractions
    • 3rd Grade Math Worksheet  geometry/shapes/fractions
  • Select what is true about the angles of the triangle

    3rd Grade Math Worksheet  geometry angle
    • 1 angle is a right angle
    • 2 angles are greater than a right angle
    • none of these
  • How many pairs of parallel lines does the parallelogram have?

  • How many pairs of intersecting lines does the rhombus have?

    3rd Grade Math Worksheet  geometry lines
  • Calculate the perimeter.

    3rd Grade Math Worksheet  geometry perimeters
  • Carla built a fence for her dog’s play area. The fence is 10 feet long and 3 feet wide. How many feet of fencing did Carla use?

  • Sally’s garden is a perfect square. Each side measures 8 feet. What is the perimeter of her garden?

Answer Key

Operations and Algebraic Thinking

  • (1) C
  • (2) 64
  • (3) A
  • (4) A
  • (5) 4
  • (6) 27, 54
  • (7) C
  • (8) A
  • (9) 96, 10, 10, 100
  • (10) 12

Number Operations in Base 10

  • (1) 941
  • (2) 119
  • (3) 296
  • (4) 900
  • (5) 4, 5, 8
  • (6) 60
  • (7) 65, 66, 67, 68, 69
  • (8) A, C
  • (9) 224
  • (10) 18, 180, 180

Numbers and Operations: Fractions

  • (1) 6/8
  • (2) 1/9
  • (3) 1/10
  • (4) 3/7
  • (5) 5/8
  • (6) 1/3
  • (7) 2
  • (8) 3
  • (9) A
  • (10) C

Measurement and Data

  • (1) 660
  • (2) 15:51:34
  • (3) 478
  • (4) 8:26 am
  • (5) D
  • (6) B
  • (7) 52
  • (8) 72
  • (9) 750
  • (10) 98

Geometry

  • (1) A, B
  • (2) A
  • (3) 5/6
  • (4) B
  • (5) A
  • (6) 2
  • (7) 4
  • (8) 38
  • (9) 26
  • (10) 32

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