M.5: Grade 5

Grade 5

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Grade 5 completes the fraction work of the elementary years: students add and subtract fractions with unlike denominators, multiply fractions by fractions and by whole numbers, divide unit fractions by whole numbers and vice versa, and interpret fraction as division. Decimal operations extend to hundredths, and volume measurement introduces three-dimensional thinking. The coordinate plane, numerical expressions with grouping symbols, and numerical patterns connect arithmetic to algebra.

M.5.1Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols.M.5.10Add, 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.M.5.11Add 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).M.5.12Solve 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).M.5.13Interpret 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?)M.5.14Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.M.5.15Interpret multiplication as scaling (resizing), by:M.5.16Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.M.5.17Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.M.5.18Convert 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.M.5.19Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally).M.5.2Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.)M.5.20Recognize volume as an attribute of solid figures and understand concepts of volume measurement.M.5.21Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.M.5.22Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.M.5.23Use 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).M.5.24Represent 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.M.5.25Understand 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).M.5.26Classify two-dimensional figures in a hierarchy based on properties.M.5.3Generate 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.)M.5.4Recognize 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.M.5.5Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.M.5.6Read, write, and compare decimals to thousandths.M.5.7Use place value understanding to round decimals to any place.M.5.8Fluently multiply multi-digit whole numbers using the standard algorithm.M.5.9Find 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.M.5.GGeometryM.5.MDMeasurement and DataM.5.NBTNumber and Operations in Base TenM.5.NFNumber and Operations- FractionsM.5.OAOperations and Algebraic Thinking
Example Problems
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Goblins

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