# 5 th Grade: Trimester 1 Report Card Mathematics Florida Standards (MAFS) End of Trimester Targets Unit #

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1 5 th Grade Mathematics Report Card Correlations with End of Trimester Targets of Proficiency (20-209) This document contains the Mathematics Florida Standards (MAFS) assessed for each trimester. 5 th Grade: Trimester Report Card Mathematics Florida Standards (MAFS) End of Trimester Targets Unit # Operations and Algebraic Thinking (OA) Write and interpret numerical expressions. MAFS.5.OA..: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (Whole Numbers Only) MAFS.5.OA..2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. (Whole Numbers Only) Use parentheses, brackets, or braces in numerical expressions. Evaluate expressions with grouping symbols. Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them. Recognize that in a whole number, a digit in one place represents 0 times as much as it represents in the place to its right. Number and Operations in Base Ten (NBT) Understand the place value system. MAFS.5.NBT..: Recognize that in a multi-digit number, a digit in one place represents 0 times as much as it represents in the place to its right and /0 of what it represents in the place to its left. MAFS.5.NBT..2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 0, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 0. Use whole-number exponents to denote powers of 0. MAFS.5.NBT..a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. Recognize that in a whole number, a digit in one place represents /0 of what it represents in the place to its left. Recognize that in a decimal, a digit in one place represents 0 times as much as it represents in the place to its right. Recognize that in a decimal, a digit in one place represents /0 of what it represents in the place to its left. Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 0. Use whole-number exponents to denote powers of 0., 4 Explain patterns in the placement of the decimal point when a decimal is multiplied by a power of 0. Read and write decimal numbers to the thousandths. Read and write decimals to the thousandths using number names. 2 4 MAFS.5.NBT..b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. MAFS.NBT..4: Use place value understanding to round decimals to any place. Read and write decimals to the thousandths in expanded form. Compare two decimals to thousandths using >, =, and < symbols. Round decimals to any place. Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

2 Number and Operations in Base Ten (NBT) Perform operations with multi-digit whole numbers and with decimals to hundredths. 5 th Grade: Trimester (continued) MAFS.5.NBT.2.5: Fluently multiply multi-digit whole numbers using the standard algorithm. MAFS.5.NBT.2.6: 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. Fluently multiply up to five-digit by two-digit whole numbers using the standard algorithm.* *This is the only unit in which the standard is taught; however, there are fluency checks in Trimester 2 and to assess mastery. You may decide to chunk the targets by trimester. For example, mastery in Trimester could be: Fluently multiply up to -digits by 2-digits using the algorithm. Fluently multiply up to 5-digits by 2-digits using any strategy. Multiply up to 5-digits by 2-digits using the algorithm. Find whole-number quotients of whole numbers with up to fourdigit dividends and two-digit divisors using strategies based on place value. Find whole-number quotients of whole numbers with up to fourdigit dividends and two-digit divisors using strategies based on the properties of operations. Find whole-number quotients of whole numbers with up to fourdigit dividends and two-digit divisors using strategies based on the relationship between multiplication and division. Illustrate and explain the calculation by using equations. Illustrate and explain the calculation by using rectangular arrays. Illustrate and explain the calculation by using area models. 2 MAFS.5.NBT.2.: 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 addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to the hundredths using models, drawings, or other strategies. Subtract decimals to the hundredths using models, drawings, or other strategies. Relate whichever strategy used to a written method and explain the reasoning used. Multiply decimals to the hundredths using models, drawings, or other strategies., 4 4 Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

3 Operations and Algebraic Thinking (OA) 5 th Grade: Trimester 2 Report Card Mathematics Florida Standards (MAFS) End of Trimester Targets Unit # MAFS.5.OA..: Use parentheses, brackets, or braces in numerical Evaluate expressions with grouping symbols and operations on Write and interpret expressions, and evaluate expressions with these symbols. fractions. numerical expressions. Analyze patterns and relationships. MAFS.5.OA..2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. MAFS.5.OA.2.: 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. Interpret numerical expressions with fractions without evaluating them. 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. Graph the ordered pairs on a coordinate plane. 9 Number and Operations in Base Ten (NBT) Number and Operations Fractions (NF) Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. Use equivalent fractions as a strategy to add and subtract fractions. MAFS.5.NBT..2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 0, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 0. Use whole-number exponents to denote powers of 0. MAFS.5.NBT.2.: 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 addition and subtraction; relate the strategy to a written method and explain the reasoning used. MAFS.5.NF..: 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. MAFS.5.NF..2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., 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. Use whole-number exponents to denote powers of 0. 5 Explain patterns in the placement of the decimal point when a decimal is divided by a power of 0. Divide decimals to the hundredths using models, drawings, or other strategies. Relate whichever strategy used to a written method and explain the reasoning used. Add fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum of fractions with like denominators. Subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent difference of fractions with like denominators. Add mixed numbers with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum of fractions with like denominators. Subtract mixed numbers with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent difference of fractions with like denominators. Solve word problems involving addition of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Solve word problems involving subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., 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. Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

4 Number and Operations Fractions (NF) Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5 th Grade: Trimester 2 (continued) MAFS.5.NF.2.: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of the whole numbers leading to answers in the form of fractions or mixed numbers. MAFS.5.NF.2.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. MAFS.5.NF.2.4a: 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. MAFS.5.NF.2.4b: 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. MAFS.5.NF.2.5a: Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. MAFS.5.NF.2.5b: Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than results in a product greater than the given number (recognizing multiplication by whole numbers greater than as a familiar case); explaining why multiplying a given number by a fraction less than results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by. MAFS.5.NF.2.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. MAFS.5.NF.2.a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. MAFS.5.NF.2.b: Interpret division of a whole number by a unit fraction, and compute such quotients. MAFS.5.NF.2.c: 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. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of the whole numbers leading to answers in the form of fractions or mixed numbers. Multiply a whole number by a fraction. Multiply a fraction 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. 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. Represent fraction products as rectangular areas. Interpret multiplication as scaling (resizing) by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing) by explaining why multiplying a given number by a fraction greater than results in a product greater than the given number. Interpret multiplication as scaling (resizing) by explaining why multiplying a given number by a fraction less than results in a product smaller than the given number. Interpret multiplication as scaling (resizing) by relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by. Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers using equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number. Compute division of a unit fraction by a non-zero whole number. Interpret division of a whole number by a unit fraction. Compute division of a whole number by a unit fraction. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using equations to represent the problem. Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

5 5 th Grade: Trimester 2 (continued) Measurement and Data (MD) Represent and interpret data. MAFS.5.MD.2.2: Make a line plot to display a data set of measurements in fractions of a unit (/2, /4, /). Use operations on fractions for this grade to solve problems involving information presented in line plots. Use addition and subtraction on fractions to solve problems involving information presented in line plots. Make and read a line plot that displays a data set of measurements in fractions of a unit (/2, /4, /). Every increment will be labeled with a fraction or whole number. Use operations on fractions (from Grade 5) to solve problems involving information presented in line plots. Make and read a line plot to display a data set of measurements in fractions of a unit. Not all increments are labeled with values. 6 Geometry (G) Graph points on the coordinate plane to solve real-world and mathematical problems. MAFS.5.G..: 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). 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. Understand that the second number indicates how far to travel in the direction of the second axis. Understand that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 9 MAFS.5.G..2: Represent real world and 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. Interpret coordinate values of points in the context of the situation. 9 Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

6 5 th Grade: Trimester Report Card Mathematics Florida Standards (MAFS) End of Trimester Targets Unit # Convert like measurement units within a given measurement system. MAFS.5.MD..: Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec).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. Convert among different-sized standard measurement units within a given measurement system. Use these conversions in solving multi-step, real world problems. 0 MAFS.5.MD..: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Recognize volume as an attribute of solid figures. MAFS.5.MD..a: A cube with side length unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. Understand that a cube with side length unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. Measurement and Data (MD) Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MAFS.5.MD..b: 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. MAFS.5.MD..4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft., and improvised units. MAFS.5.MD..5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Understand that 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. Measure volume by counting cube units. Measure volume by using cubic cm, in, and ft. Measure volume using improvised units. Relate volume to the operations of multiplication and addition. Solve real world and mathematical problems involving volume. 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 multiplying the edge lengths. MAFS.MD..5a: 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 base. Represent threefold whole-number products as volumes. Show that multiplying the edge lengths is the same as multiplying the height by the area of the base. Use the Associative Property of Multiplication to show that the order in which multiplying edge lengths does that matter. Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

7 5 th Grade: Trimester (continued) Measurement and Data (MD) Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MAFS.5.MD..5b: 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. MAFS.5.MD..5c: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Apply the formula V = l w 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. Apply the formula 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. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts in the context of real world problems. Geometry (G) Classify two-dimensional figures into categories based on their properties. MAFS.5.G.2.: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. MAFS.5.G.2.4: Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Finalize Mastery of 5 th Grade Mathematics Florida Standards (MAFS) during the rd Trimester. Copyright 20 by School Board of Palm Beach County, Department of K-2 Curriculum July 20

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