Math: Volume and Whole Number Multiplication and Division

Multiply and Divide Whole Numbers (Represent Problems and Solve Them)

• 5.4B represent and solve multi-step problems involving the four operations with whole numbers using equations [and strip diagrams] with a letter standing for the unknown quantity; – R RC2
  • 5.3A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division; – S RC2
  • 5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm; – S RC2
  • 5.3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm; – S RC2

Measuring and Calculating Volume

• 5.4H represent and solve problems related to perimeter and/or area and related to volume. – R RC3
  • 5.4G use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh); and – NT
  • 5.6A recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; – S RC3
  • 5.6B determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. – S RC3

Add and Subtract Rational Numbers (Whole Numbers and Decimals) (Suggested: 12 days)

• 5.3K add and subtract positive rational numbers fluently; – R RC2 [whole numbers and decimals]

Order of Operations (Suggested: 3 days)

• 5.4F simplify numerical expressions that do not involve exponents, including up to two levels of grouping; [whole numbers: all four operations; decimals: addition and subtraction only] – R RC1
  • 5.4E describe the meaning of parentheses and brackets in a numeric expression; – S RC1

Prime and Composite Numbers (Suggested: 3 days)

• 5.4A identify prime and composite numbers; – S RC1

Grade 3 Fraction Concepts (Suggested: 12 days)

• Represent Fractions and Use Fraction Notation
  • 3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines; – S RC1
    • 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line; S RC1
    • 3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line; – S RC1
    • 2.9D determine the length of an object to the nearest [whole, half, or fourth inch] marked unit using rulers, yardsticks, meter sticks, or measuring tapes
• Unit Fractions
  • 3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b; – S RC1
    • 3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number; – S RC1
    • 3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape. – S RC3
• Fraction Equivalence
  • 3.3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines; – R RC1
    • 3.3G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model; – S RC1
• Compare Fractions
  • 3.3H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. – R RC1
• Problem Solving
  • 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8; – S RC1