GRADE 3: MODULE 4 - Multiplication and Area
3.MDA.5 Understand the concept of area measurement.
a. Recognize area as an attribute of plane figures;
b. Measure area by building arrays and counting standard unit squares;
c. Determine the area of a rectilinear polygon and relate to multiplication and addition.
GRADE 4: MODULE 5 - Fraction Equivalence, Ordering, and Operations
4.NSF.1 Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), a/b, is equivalent to a fraction, n×a/nxb, by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.
4.NSF.2 Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 and represent the comparison using the symbols >, =, or <.
4.ATO.5 Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence.
4.NSF.3 Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.
a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation;
b. Add and subtract mixed numbers with like denominators;
c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
4.NSF.4 Apply and extend an understanding of multiplication by multiplying a whole number and a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100).
a. Understand a fraction 𝑎/𝑏 as a multiple of 1/𝑏 ;
b. Understand a multiple of 𝑎/𝑏 as a multiple of 1/𝑏 , and use this understanding to multiply a fraction by a whole number;
c. Solve real-world problems involving multiplication of a fraction by a whole number (i.e., use visual fraction models and equations to represent the problem).
4.MDA.4 Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot.
GRADE 5: MODULE 4 - Multiplication and Division of Fractions and Decimal Fractions
5.NSF.3 Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., 𝑎/𝑏 = 𝑎 ÷ 𝑏).
5.NSF.4 Extend the concept of multiplication to multiply a fraction or whole number by a fraction.
a. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths;
b. Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product;
c. Interpret multiplication in which both factors are fractions less than one and compute the product.
5.NSF.5 Justify the reasonableness of a product when multiplying with fractions.
a. Estimate the size of the product based on the size of the two factors;
b. Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number;
c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number;
d. Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1.
5.NSF.6 Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number.
5.NSF.7 Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.
a. Interpret division of a unit fraction by a non-zero whole number and compute the quotient;
b. Interpret division of a whole number by a unit fraction and compute the quotient.
5.NSF.8 Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations.
5.MDA.2 Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot.
5.NSBT.7 Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings.
5.ATO.1 Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).
5.ATO.2 Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases.