5th grade Math Teacher Companion Document

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1 5th grade Math Teacher Companion Document Standard Beginning (1) Progressing (2) Proficient (3) Exceptional (4) Essential Idea Unable to perform the skill is even with able to perform the skill. Operations and Algebraic Thinking Evaluates numerical expressions 5.OA.1 Unable to evaluate numerical expressions even with with support is able to perform the skill. with support uses parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. uses parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Independently uses complex thinking that extends an in-depth application of the skill. and application of evaluating expressions using parentheses, brackets, or braces in numerical expressions. Writes and interprets numerical expressions 5.OA.2 Unable to write and interpret numerical expressions even with with support writes and interprets parentheses, brackets, or braces in numerical expressions with these symbols. writes and interprets parentheses, brackets, or braces in numerical expressions with these symbols. and application of writing and interpreting parenthesis, brackets, or braces in numerical expressions with these symbols. Analyzes patterns and relationships 5.OA.3 Unable to generate, analyze patterns and identify relationships even with with support can generate two numerical patterns using two given rules, identify relationships and form ordered pairs from the patterns and graph the ordered pairs on a coordinate plane. generates two numerical patterns using two given rules. Identify relationships and form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane. and application of generating two numerical patterns using two given rules. Identify relationships and form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane.

2 Numbers and Operations in Base Ten Identifies place value relationships 5.NBT.1 Identifies and explains patterns in powers of ten. 5.NBT.2 Unable to recognize patterns between place value even with Unable to recognize patterns in place value when multiplying by powers of ten even with with support recognizes 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. with support explains patterns in the number of zeros 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. Can use whole-number exponents to denote powers of 10. recognizes 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. explains patterns in the number of zeros 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. Can use whole-number exponents to denote powers of 10. Independently uses complex thinking that extends an in-depth application to 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. Independently uses complex thinking that extends an in-depth application to explain patterns in the number of zeros 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. Can use whole-number exponents to denote power of 10. July th grade Math Companion Document Page 2 of 10

3 Numbers and Operations in Base Ten (Continued) Reads, writes, and compares decimals 5.NBT.3 Unable to read, write and compare decimals to thousandths even with with support reads, writes, and compares decimals to thousandths using baseten numerals, number names, expanded form, and symbols >, =, and <. reads, writes, and compares decimals to thousandths using base-ten numerals, number names, expanded form, and symbols >, =, and <. (e.g., = (1/10) + 9 (1/100) + 2 (1/1000).) and application to read, write, and compare decimals to thousandths using base-ten numerals, number names, expanded form, and symbols >, =, and <. Rounds decimals 5.NBT.4 Unable to use place value understanding to round decimals to any place even with with support uses place value understanding to round decimals to any place. uses place value understanding to round decimals to any place. and application to round decimals to any place. Multiplies whole numbers 5.NBT.5 Unable to fluently multiply multi-digit whole numbers using the standard algorithm even with with support fluently multiplies multi-digit whole numbers using the standard algorithm. Independently, consistently and fluently multiplies multi-digit whole numbers using the standard algorithm. Independently uses complex thinking that extends an in-depth application to fluently multiply multi-digit whole numbers using the standard algorithm. Divides whole numbers 5.NBT.6 Unable to find wholenumber quotients of whole numbers even with Unable to illustrate and explain the calculations even with with support finds wholenumber quotients of whole numbers. with support illustrates and explains the calculation by using equations, rectangular arrays, and/or area models. finds 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. Explains these calculation by using equations, rectangular arrays, and/or area models. application to 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 and explains using equations, rectangular arrays, and/or area models. July th grade Math Companion Document Page 3 of 10

4 Numbers and Operations in Base Ten (Continued) Performs operations with decimals 5.NBT.7 Unable to perform operations with decimals to hundredths even with with support adds, subtracts, multiplies, and divides decimals to hundredths using a strategy and explain the reasoning used. adds, subtracts, multiplies, and divides decimals to hundredths using a strategy and explain the reasoning used. -Strategies: concrete model, drawing, strategies based on place value, properties of operations, relationship between addition and subtraction. Independently uses complex thinking that extends an in-depth application to add, subtract, multiply, and divide decimals to hundredths using strategies and explain the reasoning used. July th grade Math Companion Document Page 4 of 10

5 Numbers and Operations- Fractions Adds and subtracts fractions using equivalent fractions 5.NF.1 Solves word problems by adding and subtracting fractions 5.NF.2 Interprets division of whole numbers as fractions 5.NF.3 Unable to add and subtract fractions even with Unable to solve word problems by adding and subtracting fractions even with Unable to interpret the division of whole numbers as fractions even with with support adds and subtracts fractions with unlike denominators. with support solves word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. with support interprets a fraction as division of the numerator by the denominator (a/b = a b) and solves word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. adds and subtracts fractions with unlike denominators (including mixed numbers) by finding common denominators. solves word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators: -using visual fraction models or equations to represent the problem -using benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. interprets a fraction as division of the numerator by the denominator (a/b = a b) and solves word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. application of adding and subtracting fractions with unlike denominators (including mixed numbers) by finding common denominators. application of solving word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators using strategies. and application of interpreting a fraction as division of the numerator by the denominator (a/b = a b) and solving word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. July th grade Math Companion Document Page 5 of 10

6 Numbers and Operations- Fractions (Continued) Multiplies fractions by whole numbers or fractions 5.NF.4 Interprets multiplication as scaling 5.NF.5 Unable to multiply fractions by whole numbers or fractions even with Unable to interpret multiplication as scaling event with with support applies and extends previous understandings of multiplication to multiply a fraction or whole number by a fraction. with support interprets multiplication as scaling by comparing and explaining. applies and extends previous understandings of multiplication to multiply a fraction or whole number by a fraction. -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. -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. interprets multiplication as scaling by -Comparing the size of a product to the size of one factor on the basis of the size of the other factor. -Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. application of applying and extending previous understandings of multiplication to multiply a fraction or whole number by a fraction. -Interprets 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. -Finds the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and 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 as rectangular areas. application of applying multiplication as scaling by comparing the size of a product to the size of one factor on the basis of the size of the other factor and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a number by a fraction less than 1 results in a product smaller than the given number. July th grade Math Companion Document Page 6 of 10

7 Numbers and Operations- Fractions (Continued) Solves word problems by multiplying fractions and mixed numbers 5.NF.6 Unable to solve word problems by multiplying fractions and mixed numbers even with with support multiplies fractions and mixed numbers. solves word problems involving multiplication of fractions and mixed numbers using visual fraction models or equations to represent the problem. and application of solving word problems involving multiplication of fractions and mixed numbers using visual fraction models or equations to represent the problem. Divides whole numbers and fractions 5.NF.7 Unable to divide whole numbers and fractions even with with support can divide whole numbers and fractions. divides unit fractions by whole numbers and whole numbers by unit fractions. -Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. and application of applying division of unit fractions by whole numbers and whole numbers by unit fractions. -Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. July th grade Math Companion Document Page 7 of 10

8 Measurement and Data Converts within a measurement system 5.MD.1 Creates and analyzes line plots 5.MD.2 Understands concepts of volume 5.MD.3 Measures volume 5.MD.4 Unable to convert within a measurement system even with Unable to create and analyze line plots even with Unable to understand concepts of volume even with Unable to measure volume even with with support converts within a measurement system, and use these conversions in solving multi-step, real world problems. with support makes a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) and solves problems involving information presented in line plots. with support recognizes volume as an attribute of solid figures and understands concepts of volume measurement. with support measures volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems. makes a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) and solves problems involving information presented in line plots. recognizes volume as an attribute of solid figures and understands concepts of volume measurement. -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. -A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. measures volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. application of applying conversions among differentsized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems. application of making a line plot to display a data set of measurements in fractions of a unit and solves problems involving information presented in line plots. application of applying the recognition of volume as an attribute of solid figures and understanding concepts of volume measurement. application of applying measures volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. July th grade Math Companion Document Page 8 of 10

9 Measurement and Data (Continued) Solves word problems involving volume 5.MD.5 Unable to solve word problems involving volume even with with support relates volume to the operations of multiplication and addition and solves word problems involving volume. relates volume to the operations of multiplication and addition and solves word problems involving volume. -Find the volume of a 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. -Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of rectangular prisms with whole-number edge lengths. -Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. application of relating volume to the operations of multiplication and addition and solves word problems involving volume. -Find the volume of a 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. -Applies formulas and recognizes volume as additive and uses this technique to solve real-world problems. July th grade Math Companion Document Page 9 of 10

10 Geometry Interprets points on a coordinate plane 5.G.1 Graphs points on a coordinate plane 5.G.2 Understands categories of 2D figures 5.G.3 Classifies 2D figures 5.G.4 Unable to interpret points on a coordinate plane even with Unable to graph points on a coordinate plane even with Unable to understand categories of 2D figures even with Unable to classify 2D figures even with with support uses a pair of perpendicular number lines to define a coordinate system and to define a given point by using an ordered pair of numbers. Understands the meaning of each number in the ordered pair. with support graphs points in the first quadrant of the coordinate plane, and interprets coordinate values of points in the context of the situation. with support understands that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. with support classifies two-dimensional figures in a hierarchy based on properties. uses a pair of perpendicular number lines to define a coordinate system and to define a given point by using an ordered pair of numbers. Understand that the first number indicates how far to travel from the origin along the X-axis, and the second number indicates how far to travel along the y-axis. graphs points in the first quadrant of the coordinate plane, and interprets coordinate values of points in the context of the situation. understands that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. classifies two-dimensional figures in a hierarchy based on properties. and application of applying the use of a pair of perpendicular number lines to define a coordinate system and to define a given point by using an ordered pair of numbers. and application of applying graphed points in the first quadrant of the coordinate plane, and interprets coordinate values of points in the context of the situation. and application of understanding that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. application of classifying twodimensional figures in a hierarchy based on properties. July th grade Math Companion Document Page 10 of 10

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