Mathematics Scope & Sequence Grade 5 Revised: May 10, 2016

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1 Mathematics Scope & Sequence Grade 5 Revised: May 10, 2016 First Nine Weeks (39 ) 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or = 5.3K add and subtract positive rational numbers fluently Represent the value of the digit in decimals to the thousandths place using expanded notation. (5.2A) Represent the value of the digit in decimals up to the thousandths place using numerals. (5.2A) Recognize the comparison symbols, what they mean, and how to read them. (5.2B) Place Value and Decimals 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals 5.2C round decimals to tenths or hundredths Write a comparison of two decimals to the thousandths place using the symbols >,<, or =. (5.2B) Compare decimals to the thousandths using comparison symbols and number lines. (5.2B) Locate decimals on a number line to conceptually understand where the numbers are located. (5.2C) Compare decimals (using benchmark decimals) to the thousandths place using a number line. (5.2B) Order decimals to the thousandths place using a number line. (5.2B) Create a number smaller, in-between, or larger than given numbers. (5.2B) Round decimals to the tenths. (5.2C) Round decimals to the hundredths. (5.2C) 8-10 Estimate to determine the solutions to mathematical problems involving addition and subtraction of decimals. (5.3A) Estimate to solve real-world problems involving addition and subtraction of decimals. (5.3A) Add and subtract decimals through thousandths (including money). (5.3K) Textbook Sections: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8 First nine weeks continued on the next page.

2 Multiply, with fluency, three-digit numbers by two digit numbers using the standard algorithm. (5.3B) Multiply and Divide Whole Numbers 5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm 5.3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm Multiply three digit numbers by two digit numbers using area models and arrays with base ten blocks to demonstrate the standard algorithm (builds on mental math and partial products). (5.3B) Solve multi-step problems involving multiplication of whole numbers. (5.3B) Represent division problems using expanded notation, base ten models, and area models. (5.3C) Solve problems where the divisor is the number of groups and also where the divisor is the size of the groups. (5.3C) Solve division problems with up to four digit dividends and up to a two digit divisor using the standard algorithm and strategies such as drawing diagrams. (5.3C) Interpret the remainder dependent upon the context of the problem (quotient would be rounded up when finding the number of buses to transport students, but rounded down when sharing baseballs among a group of students). (5.3C) Estimate to determine the solutions to mathematical problems involving multiplication and division of whole numbers using strategies such as front-end estimation, rounding, and compatible numbers. (5.3A) 6-8 Textbook Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 Multiply Decimals 5.3E solve for products of decimals to the hundredths, including situations involving money, using strategies based on placevalue understandings, properties of operations, and the relationship to the multiplication of whole numbers 5.3D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models Solve for products of decimals to the hundredths using strategies based on place-value understanding, including patterns and expanded form. (5.3E) Represent multiplication of decimals with products up to the hundredths using objects, pictorial models (drawing a diagram), and area models. (5.3D) Solve for products of decimals to the hundredths using strategies based on properties of operations. (5.3E) Solve for products of decimals to the hundredths in situations involving money. (5.3E) Solve for products of decimals to the hundredths using strategies based on the relationship to the multiplication of whole numbers. (5.3E) 7-9 Textbook Sections: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 Divide Decimals 5.3G solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm 5.3F represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using strategies such as patterns. (5.3G) Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using objects such as base ten blocks. (5.3F) Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using pictorial models, including area models. (5.3F) Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using algorithms including the standard algorithm. (5.3G) Estimate to solve involving division using strategies such as compatible numbers. (5.3A) 5-7 Textbook Sections: 4.1, 4.2, 4.3, 4.4, 4.5 First nine weeks continued on the next page.

3 Add and Subtract Fractions 5.3K add and subtract positive rational numbers fluently 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations Represent addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Estimate to determine solutions to real-world problems involving addition and subtraction of fractions using models such as number lines, and strategies such as rounding. (5.3A) Add and subtract fractions and mixed numbers fluently using strategies such as common denominators, simplest form, and renaming. (5.3K) Add and subtract a combination of positive rational numbers, such as ½ (5.3K) 4 Textbook Sections: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8

4 Second Nine Weeks (39 ) Add and Subtract Fractions (Continued) 5.3K add and subtract positive rational numbers fluently 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations Represent addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Estimate to determine solutions to real-world problems involving addition and subtraction of fractions using models such as number lines, and strategies such as rounding. (5.3A) Add and subtract fractions and mixed numbers fluently using strategies such as common denominators, simplest form, and renaming. (5.3K) Add and subtract a combination of positive rational numbers, such as ½ (5.3K) 4 Textbook Sections: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 Multiply and Divide Unit Fractions and Whole Numbers 5.3L divide whole numbers by unit fractions and unit fractions by whole numbers. 5.3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models; 5.3J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 7 and 7 1/3 using objects and pictorial models, including area models; Textbook Sections: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 Second nine weeks curriculum continued on next page. Represent multiplication of a whole number and a fraction that refers to the same whole using objects such as fraction bars and circles, and pictorial models, including area models. (5.3I) Represent multiplication of a whole number and a fraction that refers to the same whole as repeated addition of a unit fraction. (5.3I) Represent the product of a whole number and a fraction that refers to the same whole as a mixed number or an improper fraction. (5.3I) Solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. (5.3I) Define unit fractions as a fraction where the numerator is one and the denominator is a positive integer (ex: 1/2, 1/3, 1/4, 1/5). (5.3L) Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 7 and 7 1/3 using objects, such as fraction bars, pictorial models, including area models, number lines, and strategies including drawing a diagram. (5.3J) Divide whole numbers by unit fractions and unit fractions by whole numbers. (5.3L) 6-8

5 Expressions 5.4F simplify numerical expressions that do not involve exponents, including up to two levels of grouping 5.4A identify prime and composite numbers 5.4E describe the meaning of parentheses and brackets in a numeric expression Define a composite number as a whole number greater than one that has more than two factors. (5.4A) Define a prime number as a whole number greater than 1 that has exactly two factors, 1 and itself. (Recognize that 1 is not prime; recognize that 2 is the only even prime number and that not all odd numbers are prime). (5.4A) Identify and classify prime and composite numbers in a given set using a variety of strategies including concrete models, pictorial models, divisibility rules, and factor pairs. (5.4A) Describe the meaning of parentheses and brackets in a numeric expression. (5.4E) Describe how the use of parentheses and brackets will affect the evaluation of expressions based on the order of operations. For example, 4(14 + 5) is 4 times as large as (14 + 5). (5.4E) 4-6 Simplify numerical expressions without exponents using the order of operations. (5.4F) Simplify numerical expressions with up to two levels of grouping. Example: [5 +2 (3 1)] 10. (5.4F) Simplify numerical expressions that may contain fractional values (when adding and subtracting). (5.4F) Algebraic Expressions and Equations Textbook Sections: 7.1, 7.2, 7.3, 7.4, B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity Textbook Sections: 8.1, 8.2, 8.3, 8.4 : Represent and solve an equation with an unknown quantity using a pan balance. (5.4B) Read algebraic expressions (example: r + 21 as some number plus 21 as well as r plus 21 ). (5.4B) Represent and solve multi-step addition, subtraction, multiplication, and division equations with an unknown quantity using strip diagrams, with a letter standing for the unknown quantity. (5.4B) Write algebraic expressions from verbal descriptions using letters and numbers. (5.4B) Evaluate an expression when given a possible value for the unknown. (5.4B) C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph Generate a numerical pattern when given a multiplicative rule in the form y = ax or an additive rule in the form y= x + a, and use the values to complete input / output tables and graph the values. (5.4C) Patterns 5.4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph 5.8B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. (5.4D) Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. (5.8B) Determine the ordered pair that represents a point on a coordinate plane in Quadrant I. (5.8B) Name all specific points given on a line graph and organize the related number pairs in a table with appropriate labels in Quadrant I. (5.8B) 4-6 Textbook Sections: 10.1, 10.2, 10.3, 10.4 Second nine weeks curriculum continued on next page.

6 Formulas 5.4B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity 5.4H read and solve problems related to perimeter and/or area and related to volume 5.4G use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh) Use concrete objects such as centimeter cubes to develop formulas for the volume of a rectangular prism (V = l x w x h, and V = Bh) and the special form for a cube (V=s x s x s). (5.4G) Use pictorial models to develop the formulas for the volume of a rectangular prism (V = l x w x h and V = Bh) and of a cube (V= s x s x s). (5.4G) Represent with models, problems related to perimeter of polygons, area of rectangles and composite figures formed by rectangles, and volume of rectangular prisms. (5.4H) Connect mathematical concepts and real world problems, such as fencing for perimeter and painting a wall for area. (5.4H) Solve perimeter problems with known/unknown dimensions that may contain decimal and fractional quantities, and problems where dimensions must be measured. (5.4H) Solve area and volume problems with known/unknown dimensions. (5.4H) Solve area problems involving a whole with missing parts or sum of parts.(5.4h) 4-6 Represent and solve multi-step problems using addition, subtraction, multiplication, and division equations, with whole numbers, using a letter standing for the unknown quantity. (5.4B) Textbook Sections: 9.1, 9.2, 9.3, Dimensionanl Figures 5.5A classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Identify essential attributes of two-dimensional figures. (5.5A) Identify properties of two-dimensional figures. (5.5A) Classify two dimensional figures based on their attributes and properties using graphic organizers such as tables, Venn diagrams, and thinking maps. Example: All rectangles have the property that opposite sides are parallel; therefore every rectangle is a parallelogram. (5.5A) Identify and classify regular polygons and those that are not regular. (5.5A) 3-5 Textbook Sections: 11.1, 11.2, 11.3, 11.4

7 Third Nine Weeks (47 ) Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume. (5.6A) Volume 5.6A recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a threedimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; 5.6B determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. Recognize that the volume of a three-dimensional figure is the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible. (5.6A) Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. (5.6B) Recognize that in the formula V=Bh the B is area of the base. (5.6B) 4-6 Textbook Sections: 12.1, 12.2, 12.3, 12.4, 12.5 Convert Units of Measure 5.7A solve problems by calculating conversions within a measurement system, customary or metric Describe tools that would be used to measure length, capacity, weight, and mass. (5.7A) Solve problems by calculating conversions (which could include fractional values) with customary units of length, capacity, and weight. (5.7A) Solve problems by calculating conversions (which could include decimal values) with metric units of length, capacity, and mass. (5.7A) Solve problems, including multi-step problems, involving measurement conversions using strategies such as drawing strip diagrams, making tables and graphs, identifying patterns, and writing equations. (5.7A) Estimate relative sizes of measurement units within one system including: Km/m lb/oz kg/g hr/min/sec. (5.7A) 3-4 Textbook Sections: 13.1, 13.2, 13.3, 13.4, 13.5, 13.6, 13.7 Graphing 5.8C graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an inputoutput table. 5.8A describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin Demonstrate an understanding of the Quadrant 1 coordinate grid by describing its key attributes, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0). (5.8A) Explain how the value of the x and y in an ordered pair determines the movement along the x-axis and y-axis. (5.8A) Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane, including the importance of the increments or scale. (5.8B) Graph, in the first quadrant of the coordinate plane, ordered pairs of whole numbers, fractions, and decimals (possibly between grid lines) arising from mathematical and real-world problem; including those generated by number patterns or found in an input-output table. (5.8C) B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane Textbook Sections: 14.1, 14.2, 14.3, 14.4 Third nine weeks curriculum continued on next page.

8 Categorical Data 5.9C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot. 5.9A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots Represent categorical data in the form of whole numbers, decimals, and/or fractions with frequency tables and bar graphs. (5.9A) Solve one-step and two-step problems using data in the form of whole numbers, decimals, and/or fractions from a frequency table, and bar graph. (5.9C) 3-5 Textbook Sections: 15.1, 15.2, 15.3, 15.4 Numerical Data 5.9C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot 5.9A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots Represent numerical data, including data sets of measurements in fractions or decimals, with dot plots and stem-and-leaf plots. (5.9A) Represent discrete paired data on a scatter plot. (5.9B) Recognize that data tables are represented as an ordered pair. (5.9B) Solve one-step and two-step problems using data from a dot plot, stem-and-leaf plot, or scatterplot. (5.9C) B represent discrete paired data on a scatterplot Textbook Sections: 16.2, 16.2, 16.3, 16.4, 16.5, 16.6 Explain taxes, why we pay taxes, and how taxes are used. (5.10A) Personal Financial Literacy 5.10A define income tax, payroll tax, sales tax, and property tax 5.10B explain the difference between gross income and net income 5.10C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments 5.10D develop a system for keeping and using financial records 5.10E describe actions that might be taken to balance a budget when expenses exceed income Define income tax, payroll tax, sales tax, and property tax. (5.10A) Explain differences between gross and net income. (5.10B) Identify advantages and disadvantages to using different methods of payment including check, credit card, debit card, and electronic payments. (5.10C) Develop a system for keeping financial records. (5.10D) Develop a system for using financial records. (5.10D) Balance a simple budget (5.10F) F balance a simple budget Textbook Sections: 17.1, 17.2, 17.3, 17.4, 17.5, 17.6, 17.7 STAAR Review 8

9 Fourth Nine Weeks (52 ) STAAR Review 5 STAAR TEST Math- Tuesday, March 28, 2017 Science Wednesday, May 10, 2017 Continue to work on the TEKS below to achieve mastery. Mastery of addition and subtraction of positive rational numbers fluently is the goal. Work for Mastery 5.3K add and subtract positive rational numbers fluently 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations Represent addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as fraction bars, pictorial models, number lines, and the commutative and associative properties of addition. (5.3H) Estimate to determine solutions to real-world problems involving addition and subtraction of fractions using models such as number lines, and strategies such as rounding. (5.3A) Add and subtract fractions and mixed numbers fluently using strategies such as common denominators, simplest form, and renaming. (5.3K) Add and subtract a combination of positive rational numbers, such as ½ (5.3K) Only students who have reached mastery should proceed to the enrichment units below.

10 Multiplying and Dividing Positive Rational Numbers 5.3E solve for products of decimals to the hundredths, including situations involving money, using strategies based on placevalue understandings, properties of operations and the relationship to the multiplication of whole numbers. 5.3G solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm 5.3L divide whole numbers by unit fractions and unit fractions by whole numbers 6.3E multiply and divide positive rational numbers 5.3D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. 5.3F represent quotients of decimals to the hundredths, up to four-digit dividends and twp-digit whole number divisors, using objects and pictorial models, including area models 5.3I represent and solve multiplication of a whole number and fraction that refers to the same whole using objects and pictorial models, including are models 5.3J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 7 7 using objects and pictorial models, including area models. 6.3B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one Represent multiplication of decimals with products up to the hundredths using objects, pictorial models (drawing a diagram), and area models. (5.3D) Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. (5.3E) Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using objects such as base ten blocks, and pictorial models (including area models). (5.3F) Divide decimals to the hundredths, up to four-digit dividends and two digit whole number divisors using strategies (such as patterns) and the standard algorithm. (5.3G)) Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects such as fraction bars and circles, and pictorial models, including area models. (5.3I) Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 7 and 7 1/3 using objects, such as fraction bars, pictorial models, including area models, number lines, and strategies including drawing a diagram. (5.3J) Divide whole numbers by unit fractions and unit fractions by whole numbers. (5.3L) Determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one. (6.3B) Model multiplication and division of positive rational numbers using manipulatives. (6.3E) Connect operations with models to standard algorithms. (6.3E) Multiply and divide positive rational numbers flexibly, accurately and efficiently. (6.3E) Estimate to evaluate reasonableness of a solution. (6.3E)

11 Fractions, Decimals, and Percent 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or = 6.4G generate equivalent forms of fractions, decimals, and percent using real-world problems, including problems that involve money 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations 6.4E represent ratios and percent with concrete models, fractions, and decimals. 6.4F represent benchmark fractions and percent such as 1%, 10%, 25%, 33 %, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers Compare two decimals to thousandths and represent comparisons using the symbols >,<, =. (5.2B) Order two decimals to thousandths. (5.2B) Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects such as clock faces and rectangular regions. (5.3H) Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using number lines. (5.3H) Represent ratios and percent with concrete models such as 10 by 10 grids, fractions, and decimals. (6.4E) Represent benchmark fractions and percent such as 1%, 10%, 25%, 33 1/3 % and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers. (6.4F) Generate equivalent forms of fractions, decimals, and percent using real-world problems, including problems that involve money. (6.4G) Interpret everyday uses of fractions, decimals, and percent. (6.4G) 6.5C use equivalent fractions, decimals, and percent to show equal parts of the same whole Use equivalent fractions, decimals, and percent to show equal parts of the same whole. (6.5C)