1: Fourth Grade Math
- Page ID
- 217667
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- 1.1: Place Value and Names for Whole Numbers
- Much like learning a language, learning algebra begins with getting to know the basic vocabulary. As you continue to learn, you add to your vocabulary and practice it often so that it because easy. In algebra, numbers and symbols are used like words and ideas in a language. The most basic numbers used in algebra are those we use to count objects.
- 1.2: Adding and Subtracting Whole Numbers
- This page covers fundamental properties of addition and subtraction for whole numbers, emphasizing the Commutative and Associative Properties, the Additive Identity, and the order of operations. It includes exercises for hands-on practice with arithmetic operations, such as finding sums, differences, and perimeters of shapes, along with applications in real-world contexts.
- 1.3: Multiplying Whole-Digit Numbers
- This page provides an overview of fundamental properties of addition and subtraction, highlighting the order of operations, commutative and associative properties, and the additive identity. It applies these concepts to calculating perimeters of polygons and introduces real-world applications, including alternative fuels. Additionally, it features various exercises focusing on basic operations and visualization of data trends, such as Jason's examination score improvements.
- 1.4: Introduction to Division
- This page covers the concept of division, detailing its representation through symbols, long division, and fractions. Key terms like dividend, divisor, and quotient are defined. It explores visual models, long division methods for larger numbers, and the pattern of dividing by powers of 10. It emphasizes the inverse relationship of division to multiplication and provides real-life examples to illustrate division's practical applications.
- 1.5: More on Division of Whole Numbers
- This page introduces the concept of division, covering key terms, properties, and notation, emphasizing the relationship between division and repeated subtraction. It explains long division for multi-digit numbers, detailing the steps involved and the importance of checking answers through multiplication. Techniques for estimating and translating word problems into mathematical notation are discussed, with practical examples showcasing the application of division in real-world scenarios.
- 1.6: Extra Division Practice and Word Problems
- This page details homework assignments aimed at enhancing students' comprehension of division through word problems and visuals. It encourages exploration of various division interpretations, independent work, and peer collaboration. Students must illustrate their problem-solving methods and reflect on the commutative and associative properties of division, providing examples or counterexamples for deeper understanding.
- 1.7: Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms
- This page covers equivalent fractions and methods for reducing them to lowest terms using common factors. It explains testing for equivalence through cross products and provides examples. The content includes exercises to determine the equivalence of fractions, reduce fractions, and apply arithmetic with fractions. Additionally, it addresses raising fractions to higher terms and highlights common mistakes in simplification and calculations.
- 1.8: Equivalent Fractions
- This page covers the concepts of fractions, including their definition, equivalent fractions, and methods for simplification. It explains the Cancellation Rule, emphasizes prime factorization, and demonstrates creating equivalent fractions by manipulating numerators and denominators. The treatment of negative fractions is also discussed, alongside exercises focused on finding the greatest common divisor (GCD) and applying fraction simplification in real-world scenarios.
- 1.9: Comparing Fractions
- This page covers comparing and simplifying fractions and mixed numbers. It details methods for identifying equivalent fractions by finding a common denominator and comparing numerators. The content includes examples of using the least common denominator (LCD) to facilitate comparisons of fractions, as well as ordering them using inequality symbols (greater than and less than).
- 1.10: Decimals
- This page covers the fundamentals of decimals, including their naming, writing, conversion to fractions, and rounding techniques. It emphasizes the importance of place value and provides examples to illustrate how to interpret and manipulate decimal representations. Key processes include converting decimals into different forms, rounding based on digit evaluation, and recognizing equivalent decimals.
- 1.11: Points, Lines, and Planes
- This page introduces fundamental geometric concepts from Euclid, including points, lines, and planes, detailing definitions and distinguishing between line segments, rays, and lines. It explores parallel and perpendicular lines with grid lines as references and incorporates basic set theory principles like union and intersection. The importance of geometry is highlighted through historical references to Plato, alongside practical applications in daily life.
- 1.12: Basic Geometric Concepts and Figures
- This page provides an overview of fundamental geometric concepts, including points, lines, angles, and planes, as well as classifications of triangles and polygons. It details characteristics of parallel and perpendicular lines, supplementary and complementary angles, and the properties of triangles and polygons. Key classifications include triangles by angles and sides, with examples illustrating the sum of interior angles for triangles (180°) and quadrilaterals (360°).
- 1.13: Classifying Polygons
- This page introduces polygons as closed, two-dimensional shapes formed by straight lines, categorizing them into convex and concave. It explains the properties of convex polygons, including their diagonals, and explores the correlation between the number of sides and diagonals. The page offers examples and exercises for identifying and classifying polygons, reinforcing key vocabulary and understanding of polygon properties.
- 1.14: Finding Area by Decomposing and Rearranging
- This page details the concept of area in two-dimensional shapes, defining it as the total number of square units that fit within a shape. It includes exercises on composing and decomposing shapes to demonstrate that area remains constant when rearranged. Key principles stated are that two shapes have the same area if they can be matched exactly and that decomposing shapes helps in calculating area. Important terms like 'compose,' 'decompose,' and 'region' are also clarified to aid understanding.
- 1.16: Finding Multiples and Factors
- A number is a multiple of n if it is the product of a counting number and n. If a number m is a multiple of n, then we say that m is divisible by n. If a • b = m, then a and b are factors of m, and m is the product of a and b. To find all the factors of a counting number, divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor. Then, list all the factor pairs and write all the factors in order from smallest to largest.