# ELEMENTARY MATH GRADE 5. The Level 2 student is approaching proficient in

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1 ELEMENTARY MATH GRADE 5 PLD Standard Below Proficient Approaching Proficient Proficient Highly Proficient The Level 1 student is below The Level 2 student is approaching proficient in The Level 3 student is The Level 4 student is highly mathematics knowledge/skills applying mathematics mathematics knowledge/skills mathematics knowledge/skills performs significantly below knowledge/skills as specified in the Utah Core State Standards. performs at the standard for performs significantly above Policy the standard for the gradelevel/course, is likely able to standard for the grade to access grade-level content, level/course, is able to access performs slightly below the the grade level/course, is able the standard for the grade partially access grade level content and engages with higher order thinking skills with extensive support. level/course, is able to access grade-level content and engages in higher order thinking skills with some independence and support. and engages in higher order thinking skills with some independence and minimal support. above grade-level content, and engages in higher order thinking skills independently. Range 5.OA.1 Range 5.OA.2 Range 5.OA.3 Range 5.NBT.1 Operations and Algebraic Thinking Evaluates a simple numerical Evaluates a numerical Uses parentheses, brackets, or Inserts parentheses, brackets, expression using parentheses, expression using parentheses, braces in numerical or braces (without nesting), in brackets, or braces (without brackets, or braces (without expressions (without nesting), numerical expressions to make nesting). nesting). and evaluates expressions a statement true. with these symbols. Writes a numerical expression, using one operation, from a written statement (e.g., divide 144 by 12). Continues two numerical patterns (when given a table), using two given rules. Writes simple numerical expressions and interprets numerical expressions, without evaluating them. Continues two numerical patterns using two given rules. Writes numerical expressions (limited to two operations; e.g., "divide 144 by 12, and then subtract 9") and interprets numerical expressions, without evaluating them. Generates two numerical patterns using two given rules. Identifies apparent relationships between corresponding terms. Writes numerical expressions using multiple operations, involving real-world and mathematical contexts. Generates two numerical patterns using two multi-step given rules, in mathematical contexts. Explains the relationship between corresponding terms. Number and Operations in Base Ten Uses visual models or Uses visual models or Recognizes (in any multi-digit Recognizes (in any multi-digit calculation (in any multi-digit calculation (in any multi-digit number, including decimals to number, including decimals to whole number) to demonstrate whole number) to recognize thousandths) that a digit in thousandths) that a digit in a digit in one place represents that a digit in one place one place represents 10 times one place represents 10 times 10 times as much as it represents 10 times as much as as much as it represents in the as much as it represents in the represents in the place to its it represents in the place to its place to its right and 1/10 of place to its right and 1/10 of right, or 1/10 of what it right and 1/10 of what it what it represents in the place what it represents in the place represents in the place to its represents in the place to its to its left. to its left, in real-world or left. left. mathematical context problems.

2 Range 5.NBT.2 Range 5.NBT.3a Range 5.NBT.3b Range 5.NBT.4 Range 5.NBT.5 Range 5.NBT.6 Continues a given pattern that Recognizes patterns in the shows the number of zeroes of the product when multiplying a number by powers of 10. Reads decimals to the thousandths place. number of zeroes of products when multiplying a number by powers of 10. Can use whole number exponents greater than zero to denote powers of 10. Reads and writes decimals to the thousandths place, using base-ten numerals and number names. Explains patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explains patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Uses whole number exponents to denote powers of 10, including 10 to the power of zero. Reads and writes decimals to the thousandths place, using base-ten numerals, number names, and expanded form (e.g., = 3 X X X X (1/10) + 9 X (1/100) + 2 X (1/1000). Compares two decimals to the Compares two decimals to the Compares two decimals to the tenths place, using >, =, and hundredths place, using >, =, thousandths place (with < symbols to record the results of comparisons. and < symbols to record the results of comparisons. varying place values), using >, =, and < symbols to record the results of comparisons. understanding to round multidigit understanding to round multi- understanding to round multi- numbers to the tenths digit whole numbers to the digit numbers up to any place place. hundredths place. (within content limits). Multiplies two two-digit numbers using a standard algorithm. Multiplies three-digit by twodigit whole numbers, using a standard algorithm. Fluently multiplies multi-digit whole numbers using a standard algorithm. Interprets a multiplication problem to identify the factor of 10 by which one number is greater or lesser than another. Writes numbers in expanded form in a variety of formats (e.g., = 7 X X X (1/10) + 2 X (1/1000) + (1/100) X 9). Compares and orders decimals to the thousandths place (with varying place values), from least to greatest or vice-versa. Uses rounding strategies in real-world situations. Fluently multiplies multi-digit whole numbers, in real-world and mathematical contexts, using a standard algorithm. Finds whole-number quotients Finds whole-number quotients Finds whole-number quotients Finds whole-number quotients two digit dividends and twodigit three digit dividends and two- four digit dividends and two- four digit dividends and two- divisors), using digit divisors), using strategies digit divisors), using strategies digit divisors) in context. rectangular arrays or area based on place value and the properties of operations. based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrates and explains the calculation by using equations, rectangular arrays, and/or area

4 Range 5.NF.4a 5.NF.4b Range 5.NF.5.a 5.NF.5b Range 5.NF.6 Range 5.NF.7 Range 5.MD.1 Interprets multiplication scaling by comparing the size of a product to the size of one factor on the basis of the size of the second factor, without performing the indicated multiplication (where both factors are whole numbers). Solves real-world problems involving multiplication of fractions by using visual fraction models or equations to represent the problem (limited to fractions with single-digit numerators or denominators). Interprets multiplication scaling by comparing the size of a product to the size of one factor on the basis of the size of the second factor, without performing the indicated multiplication (where one factor is a fraction less than one). q g of a rectangle with fractional fractions in both an additive side lengths by tiling it with and multiplicative sense with unit squares of the appropriate different wholes, and displays unit fraction side lengths, and the quantities with visual shows that the area is the same as would be found by multiplying the side lengths. Multiplies fractional side lengths to find areas of rectangles, and represents fraction products as rectangular areas. Interprets multiplication Interprets multiplication scaling by comparing the size scaling by comparing the size of a product to the size of one of a product to the size of one factor on the basis of the size factor on the basis of the size of the second factor, without of the second factor by performing the indicated performing the indicated multiplication, focusing on multiplication with 2 one factor being a fraction fractions. greater than or lesser than one. Solves real-world problems Solves real-world problems involving multiplication of involving multiplication of fractions by using visual fractions and mixed numbers. fraction models or equations to represent the problem. Uses several mixed numbers, often with multi-digit numerators or denominators, to solve real-world problems. Solves real-world problems Solves real-world problems Solves real-world problems Creates real-world problems involving division of unit involving division of unit involving division of unit numbers by unit fractions, fractions by non-zero whole fractions by non-zero whole fractions by non-zero whole using visual fraction models numbers and division of whole numbers and division of numbers and division of and equations to represent the numbers by unit fractions, whole numbers by unit whole numbers by unit problem. using visual fraction models fractions, using visual fraction fractions, using visual fraction and equations to represent the models and equations to models and equations to problem (limited to single digit represent the problem. represent the problem. whole numbers and denominators). Measurement and Data & Geometry Converts among differentsized Converts among different- Converts among different- Creates real-world multi-step standard measurement sized standard measurement sized standard measurement problems. Chooses the units within a given units within a given units within a given appropriate measurement unit measurement system. measurement system; uses measurement system; uses based on the given context. these conversions to solve these conversions in solving single-step problems, using multi-step, real-world manipulatives or visual problems. Plots data on a given line plot with a data set of measurements in fractions of a unit (1/2, 1/4, 1/8), where the given data set is limited to a fractions of a unit (1/2, 1/4, or 1/8), where the given data set is limited to a common fractions of a unit (1/2, 1/4, 1/8). Uses operations on fractions to solve problems fractions of a unit (1/2, 1/4, 1/8). Solves multi-step word problems using the four

5 Range 5.MD.2 Range 5.MD.3 5.MD.4 Range 5.MD.5 Range 5.G.1 5.G.2 Range 5.G.3 5.G.4 g common denominator. Solves addition and subtraction comparison problems using the data. Uses unit cubes to find the volume of rectangular prisms with whole number edges (limited to single digit dimensions). Solves volume problems of a right rectangular prism by using unit cubes. denominator. Solves problems using all four operations. Uses unit cubes (number of unit cubes, edge length, height) to find the volume of rectangular prisms. Uses the information that the number of unit cubes is related to the edge length; uses visual Solves volume problems by relating the number of unit cubes in a prism to the multiplication of the edge lengths. Identifies the key components Interprets coordinate values of of the coordinate plane (x - points in the first quadrant axis, x -coordinate, y -axis, y - (e.g., reading line graphs), in coordinate and origin). context. Locates given points in the first quadrant of the coordinate plane. Identifies two-dimensional Classifies some twodimensional (fifth grade) (fifth grade) figures based on properties limited to sides and figures into categories based angles. on their properties (sides and angles). p involving information presented in line plots (division is limited to a whole number divided by a fraction or a fraction divided by a whole number). Uses unit cubes (number of unit cubes, edge length, height) to find the volume of rectangular prisms. Represents the volume of a solid figure as n cubic units (including cubic cm, cubic, in., cubic ft., and improvised units). Solves real-world and mathematical problems by applying the formulas for volume. Finds the volume of two non-overlapping right rectangular prisms by adding the volumes of the two nonoverlapping parts. Represents real-world and mathematical problems by locating and graphing points in the first quadrant of the coordinate plane. p g operations and interprets the solution to the data. Compares the volumes of different prisms by using unit cubes. Creates real-world mathematical problems that would be solved by finding volume. Using real-world data, creates a representation and draws conclusions based on the data presented. Understands that attributes Draws or constructs belonging to a category of twodimensional (fifth grade) figures according to the specific two-dimensional figures also belong to all definitions provided, subcategories of that category attributes described, or and classifies twodimensional (fifth grade) categories given. figures in the hierarchy based on these properties.

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