Kindergarten

## Fifth Grade Math Common Core State Standards and Curriculum

Fifth grade math standards aim to prepare your student for higher mathematical concepts. During what is commonly the last year of elementary school, they will need all the practice and preparation available to them. Fifth grade finalizes and ensures competence in skills required for future math topics. Understanding fifth grade math Common Core State standards helps educators and parents further prepare students for academic shifts that occur during middle school.

### CCSS 5th Grade Math: What Your Student Should Already Know

In order to achieve success in 5th grade math standards, students will need to be confident with the math taught before. This grade deepens and expands upon the math concepts students learned in fourth grade, third grade, as well as first and second. By the start of fifth grade, your student should have the ability to:
• Comfortably ➗ and ✖ numbers with more than one digit.
• Peers should be familiar with place value and the base ten system up. With this knowledge, they should use systematic strategies to multiply and divide in equations involving numbers with more than one digit. Students should create efficiency in their multiplication processes and be comfortable with the methods they practice.They should also perceive the inherent correlation between division according to fifth grade Common Core math standards and multiplication. Students will utilize this knowledge to create further efficiency in equation procedures.

• Understand what makes fractions equal (equivalent) and perform basic fraction operations.
• Students should be able to perform operations with various fractions (add/subtract) as long as the denominators are alike. Furthermore, they should incorporate their grasp of how fraction problems include various factors and how these factors can be used to pinpoint parts that are equivalent. Students should also understand the meaning of multiplication in fractions and be familiar with multiplying fractions by whole numbers.
• Analyze, classify, and identify various shape properties.
• By the end of fourth grade, students should have knowledge of properties of two-dimensional shapes and be comfortable with identifying them on sight. These include parallels, right angles, obtuse angles, and acute angles. They should also be familiar with drawing and identifying different lines. These include line segments, lines, points, and rays.They should have practice evaluating angles by using a protractor, estimating angles, and classifying them as obtuse, acute, and right. Further geometrical concepts cannot be understood without this core knowledge. The concepts shown above are crucial to your student’s success with 5th grade Common Core standards. Math learned in fifth grade will carry over to the next level. It will also determine their ease of transition and prosperity in future math. It is natural, even typical, for students to learn at varying paces. However, if you feel that your student is dangerously behind in certain subjects, it may be necessary to seek extra help. Make sure that your student stays up to scratch in math during summer vacation. ArgoPrep has many different material sets, online and print, that are perfect for summer studies. These include workbooks, worksheets, and high-quality online educational content.

### Common Core Math Standards: Grade 5 Focus Areas Overview

Not unlike fourth grade, 5th grade Common Core math standards do not introduce a great many new mathematical concepts. Rather, it draws on what was learned in fourth grade and other levels with the intention of expanding, creating finishing touches, and firming the general grasp of the ideas. This is why the section above as well as mathematical review is so important to overall understanding of math concepts. According to CCSS math, 5th grade students will hone in on three main areas of study. These are:
• Area 1: Developing operations with fractions
• Area 2: Furthering of strategies for solving problems with more than one digit
• Area 3: Define and solve for volume in real-world example problems

### 5th Grade Math Common Core Standards: Focus Area Specifics and Study Suggestions

#### Area 1: Developing operations with fractions

Fifth grade peers aim to expand precursory applications of fractions. Methods will not be limited to like-denominator addition as of this year. Fifth grade curriculum covers addition and subtraction of fraction equations involving different denominators. Unlike denominator operations require extra solving steps, making fractional concepts seem more difficult than they did in the previous grade. For example, students may be asked to solve ½ plus ⅙. Additionally, students will work with mixed numbers, which involve non-fractions and fractions. An example of this includes multiplying ¼ times 1 and ⅕. Peers will multiply and divide fractions within certain limits. Students will learn multiplication and division processes for fractions. Fraction multiplication will not be limited to whole numbers or unit fractions. However, in the area of dividing fractions, students will focus on unit fractions and whole numbers represented in fraction form. Students will realize the correlation between fractions and division. Students will also come to recognize the interrelation of fractions and decimals. They will discern that decimals can be represented as fractions by way of correlating place value and denominator.

#### Study Suggestion for Area 1

Upping fluency with factors will aid in their fraction operation skills, especially in terms of simplifying and determining if one fraction is equivalent to another. Ensure plenty of practice here first. For fraction equivalence, try using physical models or illustrations. This will help them visualize the fractions they are working with. Visuals can also aid in fraction multiplication, addition, and subtraction. The ones provided by ArgoPrep are not only colorful and engaging, but aligned with 5th grade Common Core standards. Math practice with ArgoPrep means quality exercises and the highest engagement possible.

#### Area 2: Furthering of multi-digit operations strategies

Using what they know of both place value and the base-ten system, students create final touches on their strategies in operations. These include math problems involving dividing as well as multiplying. These problems can include up to four places (thousands.) The same is true for equations that involve adding numbers or subtracting them. Students will practice using the distributive property to solve multi-step equations involving more than one operation at a time.

#### Study Suggestion for Area 2

The distributive property is an important aspect of solving problems with more than one step. when it comes to 5th grade math standards. Creating an acronym for PEMDAS can make for a fun math-related activity. Practice writing out different equations and solving them together, referring to the acronym will make the process feel easier. Be sure that your student has plenty of practice with their basic times tables, as mastery in this area will reinforce their skills with higher numbers.

#### Area 3: Define and solve for volume in real-world example problems

Students have already had some practice with area. Using this, alongside using three-dimensional examples in their surroundings, students will calculate the volume of rectangular objects. Additionally, students will develop familiarity with plotting points on graphs. They will create fluency with x and y axes. Furthermore, they will draw from their previous understanding of line segments, rays, etc.

#### Study Suggestion for Area 3

Finding area is a skill that many students struggle with. Using physical objects from home can make the process more concrete. For example, you can use rectangular objects around your home to practice finding volume, such as tissue boxes, dressers, and more. Illustrations are also helpful. ArgoPrep provides thorough tutorials in geometry and calculating volume. Additionally, their helpful workbooks are stocked with activities and exercises that will ensure plenty of practice in this subject.

## Operations & Algebraic Thinking

### Write and interpret numerical expressions.

#### CCSS.MATH.CONTENT.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

#### CCSS.MATH.CONTENT.5.OA.A.2

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

### Analyze patterns and relationships.

#### CCSS.MATH.CONTENT.5.OA.B.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

## Number & Operations in Base Ten

### Understand the place value system.

#### CCSS.MATH.CONTENT.5.NBT.A.1

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

#### CCSS.MATH.CONTENT.5.NBT.A.2

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

#### CCSS.MATH.CONTENT.5.NBT.A.3

Read, write, and compare decimals to thousandths.
##### CCSS.MATH.CONTENT.5.NBT.A.3.A
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
##### CCSS.MATH.CONTENT.5.NBT.A.3.B
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

#### CCSS.MATH.CONTENT.5.NBT.A.4

Use place value understanding to round decimals to any place.

### Perform operations with multi-digit whole numbers and with decimals to hundredths.

#### CCSS.MATH.CONTENT.5.NBT.B.5

Fluently multiply multi-digit whole numbers using the standard algorithm.

#### CCSS.MATH.CONTENT.5.NBT.B.6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

#### CCSS.MATH.CONTENT.5.NBT.B.7

Add, subtract, multiply, and divide decimals to hundredths, 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 and explain the reasoning used.

## Number & Operations—Fractions

### Use equivalent fractions as a strategy to add and subtract fractions.

#### CCSS.MATH.CONTENT.5.NF.A.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

#### CCSS.MATH.CONTENT.5.NF.A.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

### Apply and extend previous understandings of multiplication and division.

#### CCSS.MATH.CONTENT.5.NF.B.3

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

#### CCSS.MATH.CONTENT.5.NF.B.4

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
##### CCSS.MATH.CONTENT.5.NF.B.4.A
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).
##### CCSS.MATH.CONTENT.5.NF.B.4.B
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

#### CCSS.MATH.CONTENT.5.NF.B.5

Interpret multiplication as scaling (resizing), by:
##### CCSS.MATH.CONTENT.5.NF.B.5.A
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
##### CCSS.MATH.CONTENT.5.NF.B.5.B
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

#### CCSS.MATH.CONTENT.5.NF.B.6

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

#### CCSS.MATH.CONTENT.5.NF.B.7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
##### CCSS.MATH.CONTENT.5.NF.B.7.A
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
##### CCSS.MATH.CONTENT.5.NF.B.7.B
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
##### CCSS.MATH.CONTENT.5.NF.B.7.C
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

## Measurement & Data

### Convert like measurement units within a given measurement system.

#### CCSS.MATH.CONTENT.5.MD.A.1

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

### Represent and interpret data.

#### CCSS.MATH.CONTENT.5.MD.B.2

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

### Geometric measurement: understand concepts of volume.

#### CCSS.MATH.CONTENT.5.MD.C.3

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
##### CCSS.MATH.CONTENT.5.MD.C.3.A
A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
##### CCSS.MATH.CONTENT.5.MD.C.3.B
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

#### CCSS.MATH.CONTENT.5.MD.C.4

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

#### CCSS.MATH.CONTENT.5.MD.C.5

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
##### CCSS.MATH.CONTENT.5.MD.C.5.A
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
##### CCSS.MATH.CONTENT.5.MD.C.5.B
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
##### CCSS.MATH.CONTENT.5.MD.C.5.C
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

## Geometry

### Graph points on the coordinate plane to solve real-world and mathematical problems.

#### CCSS.MATH.CONTENT.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

#### CCSS.MATH.CONTENT.5.G.A.2

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

### Classify two-dimensional figures into categories based on their properties.

#### CCSS.MATH.CONTENT.5.G.B.3

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

#### CCSS.MATH.CONTENT.5.G.B.4

Classify two-dimensional figures in a hierarchy based on properties.

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