2: Fifth Grade Math
- Page ID
- 218251
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\ket}[1]{\left| #1 \right>}\)
\(\newcommand{\bra}[1]{\left< #1 \right|}\)
\(\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}\)
\(\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}\)
\(\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}\)
\(\newcommand{\op}[1]{\hat{\mathbf{#1}}}\)
\(\newcommand{\expect}[1]{\langle #1 \rangle}\)
\(\newcommand{\dfn}[1]{\emph{\textbf{#1}}}\)
- 2.1: Ordering and Rounding Decimals
- This page discusses comparing and rounding decimal numbers, focusing on using number lines and digit comparison. It details strategies such as comparing corresponding digits and the significance of placeholder zeros. Rounding rules are clarified with examples, showcasing the adjustment of digits and dropping trailing zeros without altering values. Exercises reinforce these concepts, highlighting the proper technique for rounding decimals, as shown with the example of rounding 10.473 to 10.5.
- 2.2: Exponents and Powers of 10
- This page covers exponentiation, focusing on powers of 10 and introduces the rule for multiplying exponents with a common base, supported by examples and practice problems. It also explains square and cube roots with definitions and examples, illustrating the foundational principles of these concepts, and extending to higher roots. Emphasis is placed on the efficiency of exponential notation for expressing repeated multiplication.
- 2.3: Comparing, Expanded and Written Form, and Rounding of Decimals
- This page covers decimal fractions in the decimal number system, emphasizing the role of digits after the decimal point in representing fractional values and explaining how to read and write them accurately. It also discusses rounding decimal numbers, detailing the process of identifying and adjusting the round-off digit. Practical examples and exercises for both interpreting decimal fractions and rounding decimals are included to reinforce understanding and skill development.
- 2.4: Basic Multi-Digit Multiplication and Division
- This textbook provides comprehensive coverage of multiplication and division of whole numbers, emphasizing their properties and operations. It covers multiplication as repeated addition, the commutative and associative properties, and the effects of identity and zero. Division is introduced as repeated subtraction, with attention to remainders, non-commutativity, and checking answers.
- 2.5: Adding and Subtracting Fractions
- This page covers the addition and subtraction of fractions, emphasizing the need for a least common denominator (LCD) when dealing with different denominators. It includes definitions and methods for finding the least common multiple (LCM) through prime factorization. Step-by-step examples illustrate these processes, along with exercises that progress in complexity, including negative fractions.
- 2.6: Multiplying and Dividing Fractions
- This page covers the multiplication of fractions and mixed numbers, detailing techniques such as converting mixed numbers to improper fractions and simplifying by canceling common factors. It provides a variety of practice problems that reinforce these concepts, utilizing visual aids and reasoning skills to deepen understanding. Exercises include finding parts of fractions, performing calculations, and applying knowledge to word problems.
- 2.7: Adding, Subtracting and Multiplying Decimals
- This page covers key concepts in decimal operations, including addition, subtraction, multiplication, and division. It emphasizes aligning decimal points for accurate calculations and provides methods for rounding and converting between decimals and fractions. Examples and exercises reinforce these skills, including converting decimals to percentages. The importance of managing decimal placement is highlighted throughout, ensuring proficiency in handling decimal numbers effectively.
- 2.8: Rounding Decimals
- This page covers rounding decimal numbers, elaborating on methods previously applied to integers. It details how to identify the round-off digit and adjust it based on the neighboring digit's value. Procedures for digits on either side of the decimal are explained, illustrated with examples, and underscores the importance of consistency in rounded representations. The page concludes with exercises for practice.
- 2.9: Multiplication of Whole Numbers
- This page provides a comprehensive overview of multiplication, introducing fundamental concepts like multiplicands and multipliers, and methods including simplifying with zeros and using calculators. It includes practice problems that range from basic to complex calculations, emphasizing techniques for mental math and aligning non-zero digits. Exercises feature practical applications and unit conversions, reinforcing arithmetic skills.
- 2.10: Division of Whole Numbers
- This page provides a comprehensive overview of division, detailing methods for dividing whole numbers by both single and multiple-digit divisors. It covers step-by-step techniques, including long division and estimation, along with practical examples and exercises for practice. The content stresses the importance of understanding quotients and remainders while also discussing the use of calculators in division.
- 2.11: Unit Conversion - American System
- In this section we will develop a technique for converting units used in the American system. We begin with a discussion of common measurements of length in the United States.
- 2.12: Area and Volume of Geometric Figures and Objects
- This page covers the definitions, formulas, and calculations for area and volume in geometry. It details how to compute area for shapes like triangles and circles, and volume for three-dimensional figures such as cones, spheres, and cylinders, providing key formulas and examples. The page emphasizes the importance of practicing these calculations through exercises for both area and volume to enhance understanding and application of the concepts.
- 2.13: Order of Operations
- This page explains the order of operations in mathematics, crucial for consistent simplification of expressions. It details steps using the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) and provides examples to illustrate these rules. Additionally, it covers absolute values and emphasizes the necessity of a standard procedure to avoid ambiguous results. Exercises are included to strengthen comprehension of these concepts.
- 2.14: Cartesian Plane
- In this section, we will learn how to locate and label points on a coordinate plane using ordered pairs. We'll practice identifying quadrants, understanding axes, and interpreting visual information that’s foundational for graphing equations.

