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## A Parent’s Guide to Fifth Grade Math + Practice Worksheets

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## Why 5th Grade Math Worksheets Are Important

A stated objective of Common Core State Standards (CCSS) is to standardize academic guidelines nationwide. In other words, what fifth graders learn 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 fifth grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards. Many states mandate a “mile-wide, inch-deep” curriculum in which children are taught so much in a relatively short time span, that they aren’t effectively becoming proficient in the concepts they truly need to understand 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 fifth 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.

## How Our Fifth Grade Math Worksheets Reflect Common Core Standards

In fifth grade, our worksheets focus on developing three essential skills as recommended by CCSS:

• Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases
• Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
• Developing understanding of volume

## 5th Grade Math Worksheets: Critical Areas of Focus CCSS doesn’t overload fifth graders with too many new concepts, but it does greatly expand on some topics that were taught the previous year. However, this level’s focus does plant the seeds for the much more advanced math students will encounter in middle school. If anything, students, and parents, can consider fifth grade as a preview of what’s ahead—working hard this year will create a strong foundation and good habits for the future. Here are the three critical areas that Common Core brings to fifth grade math:

#### Fractions

Common Core covers fractions extensively in fifth grade, and it doesn’t let up for fifth. Students this year, will become fluent in adding and subtracting fractions and get their first chance to solve equations with two different denominators (e.g., 1/5 + 3/7). Fifth graders will also begin to multiply fractions and receive some limited instruction on dividing them (mostly a whole number divided by a fraction—15 ÷ 1/3, for example).

#### Division, Decimals

Division, with divisors of two or more digits, is the last of the four basic operations in which students will achieve multiple-digit fluency. Once fifth graders can add, subtract, multiply, and divide big numbers (as well as use estimation), the attention will turn toward decimals—how they work, are notated, and compared; how they relate to fractions; and how they are used in the four basic operations to the hundredths place.

#### Volume

Most of the Common Core geometry to this point has been two-dimensional— polygons, angles, lines, and so forth. Fifth grade introduces a third dimension, with an emphasis on volume, on 1x1x1 cubes as a unit of measurement, and on how addition and multiplication tie into these concepts.

## Overview of Fifth Grade Math Topics

From the three critical areas of focus discussed in the previous section, Common Core also further clarifies the skills fifth graders should know by the end of the school year. For example, the fluency requirement at this level is multi-digit multiplication—students should be proficient in multiplying big numbers before they move on to sixth grade. The five topics presented here, taken directly from CCSS itself, include some specifics on what kids will be taught in fifth grade.

#### Operations and Algebraic Thinking

• Write and interpret numerical expressions. Parentheses and brackets in mathematical expressions—for example, 2 x (5+7)—as well as the order of operations are introduced. Also, students will be taught to write simple expressions that record calculations, as well as to interpret numerical expressions without necessarily reaching an answer.

•Analyze patterns and relationships. Fifth graders will be challenged to generate two numerical patterns given two rules. In a hint of the algebra that will come in future grades, students will graph ordered pairs generated from these patterns onto a coordinate plane.

#### Number Operations in Base 10

• Understand the place value system. Place value has been taught before; here, it is reemphasized with an additional focus on understanding that a digit in a certain place is 10 times more of what it would be in the place to its right (e.g., 800÷10=80) and 1/10th of what it would be to its left (800x10=8,000). This is important because students will also be taught place values of decimals to thousandths, as well as place value operations with decimals (e.g., 0.63÷0.07=9, the same answer as if you multiplied the original equation by 100 to get 63÷7). Also, powers of 10 and exponents are introduced.

• Perform operations with multi-digit whole numbers and with decimals to hundredths. Multiplying multi-digit numbers is cemented in fifth grade. Furthermore, there’s the big jump in learning division, including four-digit dividends and two-digit divisors (e.g., 1,032÷16). Finally, operations using decimals are introduced.

#### Numbers and Operations: Fractions

• Use equivalent fractions as a strategy to add and subtract fractions. Before this year, fractional equations featured the same denominator for each part of the problem. In fifth grade, the denominators will differ, and students will need to determine equivalent fractions to solve problems. For example, 1/3 + 1/7 = 7/21 + 3/21 = 10/21.

• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers Essentially, this is learning how to add and subtract fractions with like denominators. Fractions multiplied by a whole number will also be taught at this level.

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Operations involving fractions really ramp up when students get to multiplication. They will learn that all division is essentially a fraction in which the numerator is divided by the denominator. Students won’t quite divide fractions by fractions yet, but they will divide whole numbers by unit fractions (fractions with 1 as the numerator). Word problems using all these areas of focus will be emphasized, and students will be encouraged to use a visual fraction model to help reach an answer (for example, with 2/3 x 4, imagine four pie charts split in three with two pieces in each shaded; simply count up the shaded parts to get 8/3). Finally, these fraction concepts will be tied into volume.

#### Measurement and Data

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. This includes measurements of length, weights, and time. Furthermore, word problems are emphasized—making change, figuring out elapsed time, computing perimeter, and so on.

• Represent and interpret data. Students will learn how to interpret and create their own line plots

• Geometric measurement: Understand concepts of angle and measure angles. Protractors will be employed to help provide an understanding of angles of different degrees.

#### Measurement and Data

• Convert like measurement units within a given measurement system. For example, 2 meters equals 20 decimeters, 200 centimeters, or 0.002 kilometers.

• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers Essentially, this is learning how to add and subtract fractions with like denominators. Fractions multiplied by a whole number will also be taught at this level.

• Represent and interpret data. Students will introduce fractions to line plots, which isn’t as simple as it might seem (after all, 2/8 would be plotted before 1/3 because the former is less).

• Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition. The concept of a cubic unit is introduced to offer a standard measurement for volume. Students will also learn how to compute and compare the volume of a rectangular prism (height x width x length).

#### Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems. This is another definite precursor to algebra, students will use graphs to plot points using X and Y axes on a coordinate system in the first quadrant of the plane

• Classify two-dimensional figures into categories based on their properties. Just because volume has been introduced doesn’t mean two-dimensional shapes have been forgotten. Students will learn how to understand the attributes that shapes can display and the relationships between those attributes. For example, a quadrilateral has four sides, a rhombus has four sides, and, therefore, a rhombus is a quadrilateral.

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 fifth grader. Here are some tips to help your children succeed with Common Core math:

#### 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 grocery store, in traffic, the park, and so on. For example, if you are putting gasoline into your car, before you start dispensing the fuel, ask your fifth grader how much money will be required to fill up your 15-gallon tank. Without a pencil and notebook to compute the answer, he or she might have to fall back on alternative math processes— processes that Common Core encourages—for a solution.

#### 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 (and beginning with fifth grade math, some answers can be self-checked to see if they are correct), 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 fifth 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.

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