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Download this informative guide to learn how to best support your fifth grader as they learn and master important fifth grade math concepts.

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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.

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

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:

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, 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.

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.

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.

**• 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.

**• 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.

**• 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.

**• 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.

**• 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).

**• 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:

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.

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.

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.

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.

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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