### OA: Operations and Algebraic Thinking

#### (Framing Text): Write and Interpret numerical expressions.

OA.M.5.1: Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols.

#### (Framing Text): Analyze patterns and relationships.

OA.M.5.3: 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. (e.g., 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.)

### NBT: Number and Operations in Base Ten

#### (Framing Text): Understand the place value system.

NBT.M.5.4: 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.

NBT.M.5.6: Read, write, and compare decimals to thousandths.

NBT.M.5.6.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)).

NBT.M.5.6.b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

#### (Framing Text): Perform operations with multi-digit whole numbers and with decimals to hundredths.

NBT.M.5.9: 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.

NBT.M.5.10: 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 related operations, relate the strategy to a written method and explain the reasoning used.

### NF: Number and Operations - Fractions

#### (Framing Text): Use equivalent fractions as a strategy to add and subtract fractions.

NF.M.5.11: 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 (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

NF.M.5.12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators 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 (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2).

#### (Framing Text): Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

NF.M.5.13: 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 by using visual fraction models or equations to represent the problem. (e.g., 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?)

NF.M.5.14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

NF.M.5.14.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. (e.g., 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.)

NF.M.5.14.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.

NF.M.5.16: Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.

### MD: Measurement and Data

#### (Framing Text): Convert like measurement units within a given measurement system.

MD.M.5.18: 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.

#### (Framing Text): Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

MD.M.5.20: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

MD.M.5.20.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.

MD.M.5.20.b: A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units.

MD.M.5.21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

MD.M.5.22: Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.

MD.M.5.22.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).

MD.M.5.22.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.

### G: Geometry

#### (Framing Text): Graph points on the coordinate plane to solve real-world and mathematical problems.

G.M.5.23: 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).

G.M.5.24: Represent real-world 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.

#### (Framing Text): Classify two-dimensional figures into categories based on their properties.

G.M.5.25: Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles).

G.M.5.26: Classify two-dimensional figures in a hierarchy based on properties.

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.