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Grade 3 Mathematics CCRS Standards and Alabama COS CCRS Standard Standard ID 1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. Example: Describe a context in which a total number of objects can be expressed as 5 × 7. Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. 3.OA.1 Evidence of Student Attainment Students: Given any multiplication problem in the form a x b = c, Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (i.e., given 3 x 5 = 15, students make 3 piles of buttons with 5 buttons in each pile. They explain that 15 represents the total number of buttons, 3 is the number of piles and 5 is the number of buttons in each pile) , Teacher Vocabulary Knowledge Students know: Skills Students are able to: Understanding Resources Students understand that: Characteristics of Represent quantities Putting together multiplication and operations contexts. (multiplication) equal sized groups may physically, pictorially, or be represented by symbolically, multiplication equations and totals found Use mathematical through multiplication. language to communicate the connections between multiplication equations and related representations, Click below to access all ALEX resources aligned to this standard. ALEX Resources Write word problems containing multiplication contexts. Write a corresponding word problems containing a multiplication context. 2. Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. 3.OA.2 Franklin County Schools Students: Given any division problem in the form a ÷ b = c, Represent the problem physically or pictorially and describe the relationship between the dividend, divisor, and quotient in the equation and the attributes of the representation (e.g., given 15 ÷ 3 = 5, students make 3 piles of Students know: Students are able to: Students understand that: Characteristics of Represent quantities Both partitioning division contexts. and operations (division) physically, into equal-sized shares pictorially, or and partitioning equally symbolically, among a given number of groups may be Use mathematical modeled by division equations and the language to desired results found communicate the through division. connections between division equations and Click below to access all ALEX resources aligned to this standard. ALEX Resources Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Example: Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Evidence of Student Attainment Teacher Vocabulary Knowledge buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons, 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile), Skills Understanding Resources related representations, Write word problems containing division contexts. Write a corresponding word problem containing a division context. 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. 3.OA.3 (1See Appendix A, Table 2.) See glossary Students: Given a variety of for problem types multiplication and division (Table 2). word problems within 100, Explain and justify solutions and solution paths using connections among a variety of representations (e.g., place value blocks, drawings, open arrays, and equations with a symbol for the unknown). Students know: Students are able to: Characteristics of Represent quantities Multiplication is multiplication and and operations division contexts, (multiplication and putting together equal division) physically, sized groups and pictorially, or division is sharing into Multiplication and symbolically, equal-sized shares or is division strategies. sharing equally among a Strategically use a given number of Click below to groups, variety of access all ALEX representations to solve resources Mathematical multiplication and aligned to this division word problems, problems can be solved standard. using a variety of strategies, models, Use informal and ALEX mathematical language representations, Resources to communicate the Variables represent connections among multiplication and unknown quantities division contexts and when representing related physical, mathematical situations pictorial, or symbolic algebraically. representations, Accurately compute products and quotients, Franklin County Schools Students understand that: Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources Use symbols to represent unknown quantities in equations. 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Example: Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?. Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. 3.OA.4 5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × Operations and Algebraic Thinking Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5 Franklin County Schools Students: Students know: Students are able to: Solve single operation multiplication/division equations containing a single unknown (e.g. 8x? = 48, 5= __ ÷3, 6x6 = ___). Strategies for solving simple equations with one unknown. Efficiently apply strategies for solving simple equations with one unknown, Students: Given multiplication and division problems within 100, Students understand that: Equalities contain phrases that name the same amount on each side of the equal sign. Justify solutions for single unknown equations. Commutative Property of Multiplication Associative Use the properties of Property of operations and descriptive Multiplication language for the property to justify their products Distributive and quotients (e.g., If I Property know that 8 x 5 is 40, and two more groups of 8 would be 16, then 8 x 7 must be 40 + 16 or 56). Students know: Students are able to: Commutative, Associative, Identity and Zero Properties of Multiplication and the Distributive Property, Strategically and efficiently apply properties of multiplication and division in order to find products and quotients. Strategies for finding products and quotients. Click below to access all ALEX resources aligned to this standard. ALEX Resources Students understand that: The order in which factors are multiplied does not change the Click below to product. access all ALEX resources aligned to this standard. ALEX Resources Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property) (2Students need not use formal terms for these properties.) 6. Understand division as an unknown-factor problem. Example: Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Operations and Algebraic Thinking Understand properties of multiplication and the relationship between multiplication and division. 3.OA.6 Students: Given a division problem with an unknown quotient, Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation. Factor Students know: Students are able to: Students understand that: Strategies for Use symbols to The relationship finding quotients and represent unknown products. quantities in equations, between multiplication and division (that one Use mathematical "undoes" the other) can be used to solve language to problems, communicate the connections between an unknown quotient problem and the related unknown factor problem, Efficient application of computation strategies are based on the numbers in the problems. Click below to access all ALEX resources aligned to this standard. ALEX Resources Use the inverse relationship between multiplication and division to find quotients. 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or Operations and Algebraic Thinking Multiply and divide within 100. 3.OA.7 Franklin County Schools Students: Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient, Use an efficient strategy (e.g., recall, inverse operations, Students know: Students are able to: Students understand that: Click below to access all ALEX Strategies for Use multiplication resources finding products and and division strategies Efficient application aligned to this quotients. efficiently based on the of computation standard. numbers in the strategies are based on problems. the numbers in the ALEX problems. Resources Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources arrays, derived facts, properties of operations, etc.) to name the product or quotient. Operations and Algebraic Thinking Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.8 (3This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) Students: Given a variety of twostep word problems involving all four operations, Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities, Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus 50 is 125."). Students know: Students are able to: Characteristics of addition, subtraction, multiplication, and division situations, Strategically use a Multiplication is variety of representations to solve putting together equal two-step word problems sized groups, involving all four operations, Division is sharing Addition, subtraction, multiplication, and division strategies, into equal-sized shares or as sharing equally among a given number of groups, Click below to Strategies for access all ALEX Mathematical mentally computing resources and estimating sums, problems can be solved aligned to this Use mathematical using a variety of differences, standard. products, and language and strategies, models, and quotients. contextual situations to representations, ALEX communicate the Resources connections among the Solutions can be four operations and evaluated by using related physical, reasoning to compare pictorial, or symbolic the actual solution with representations and estimated solutions. justify solutions/solution paths, Use symbols to represent unknown quanities in equations that relate to word problem contexts, Accurately compute sums, differences, products and quotients, Use logical Franklin County Schools Students understand that: Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources reasoning, mental computation strategies, and estimation strategies to justify the reasonableness of solutions. 9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Example: Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Operations and Algebraic Thinking Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.9 Students: Students know: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends). Characteristics of Identify arithmetic numbers and patterns in number properties of sequences, in the operations (e.g., addition table or odd, even), multiplication table, Properties from Table 3, etc. Use logical reasoning and properties of numbers and operations to explain arithmetic patterns. 10. Use place value understanding to round whole numbers to the nearest 10 or 100. Number & Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 4 Students: Given any number less than 1,000, Students know: Students are able to: Place value (ones, tens, hundreds), Count by 10s and 100s, (4 A range of algorithms may be used.) 3.NBT.1 Franklin County Schools Round it to the nearest 10 or 100 and justify the answer using place value vocabulary, (e.g., "Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150). Rounding. Students are able to: Determine what is halfway between two multiples of 10 or 100, Round to the nearest 10 or 100, Use place value vocabulary and logical reasoning to justify solutions to rounding problems. Students understand that: Characteristics of Click below to numbers and properties access all ALEX of operations justify resources patterns which can be aligned to this used to reason about standard. mathematical situations, form conjectures, and ALEX solve problems. Resources Students understand that: Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10. Click below to access all ALEX resources aligned to this standard. ALEX Resources Grade 3 CCRS Standard 11. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Mathematics CCRS Standards and Alabama COS Standard ID Number & Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 4 (4 A range of algorithms may be used.) 3.NBT.2 12. Multiply onedigit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. Number & Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 4 (4 A range of algorithms may be used.) 3.NBT.3 Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Students: Students know: Students are able to: Fluently add and subtract within 1000, using strategies based on place values, properties of operations, and/or the relationship between addition and subtraction, Tools for modeling addition and subtraction, Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems. Model addition and Relationships subtraction problems using appropriate tools, between models of addition and subtraction problems and symbolic Record strategies for solving addition and recordings of those subtraction problems, models can be used to justify solutions and solution strategies. Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems. Students: Students know: Students are able to: Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 1090) and justify their answers. Place value models for multiplying numbers (e.g., open arrays, place value blocks), Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning. Strategies for solving addition and subtraction problems, Use mental strategies based on an understanding of place value, properties of operations, and knowledge of one-digit multiplication to find Strategies for multiplying one-digit products, numbers, Use a variety of place value models of Strategies for mentally multiplying multiplication problems one-digit numbers by to justify strategies and multiples of powers solutions. Resources Students understand that: Click below to access all ALEX resources aligned to this standard. ALEX Resources Students understand that: Patterns in the place Click below to value system and properties of operations access all ALEX resources can be used to aligned to this efficiently compute standard. products. ALEX Resources of 10. 13. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b Number & Operations— Fractions Develop understanding of Franklin County Schools Students: Given any fraction in the form a/b, Students know: Fractions, Students are able to: Students understand that: Click below to access all ALEX resources Write fractions that correspond to pictorial Fractional parts are aligned to this standard. Grade 3 CCRS Standard equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Mathematics CCRS Standards and Alabama COS Standard ID fractions as numbers.5 (5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.) 3.NF.1 Evidence of Student Attainment Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1). (e.g., 3/5 = 1/5 + 1/5 + 1/5). Teacher Vocabulary Knowledge Strategies for creating models of fractional quantities (e.g., folding, repeatedly dividing the whole in half, etc.). Write the corresponding fraction and explain the relationship of the numerator and denominator to the model. Number & Operations— Fractions Develop understanding of fractions as numbers.5 a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part (5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.) 3.NF.2 Franklin County Schools Students: Given any common fraction a/b between 0 and 1 (denominators of 2, 3, 4, 6, 8), Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction. or physical models, Understanding created when a whole is partitioned into equal sized pieces (using up the whole), Create models of fractions that correspond to fractions written in the form a/b, The unit fraction (1/b) names the size of the unit with respect to Communicate the the referenced whole, relationship between Resources ALEX Resources models of fractions and The numerator the corresponding written fraction. counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned. Given a model of a fraction, 14. Understand a fraction as a number on the number line; represent fractions on a number line diagram. Skills Students know: Students are able to: Students understand that: Represent fractions A fractional quantity in the form a/b on a number line including can be modeled using a Strategies for Click below to creating number line correctly partitioning the variety of interval from 0 to 1 into representations (e.g., access all ALEX models of fractions "b" equal parts and part of a whole, part of resources less than 1 (e.g., counting "a" parts to a group, a distance on a aligned to this marking off equal place the fraction, numberline) each of standard. lengths by which may reveal estimation, recursive Explain and justify important features of halving). ALEX given contexts. the creation and Resources Fractions, placement of a fraction less than 1 on a number line. Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 15. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Number & Operations— Fractions Develop understanding of fractions as numbers.5 a. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. (5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.) 3.NF.3 b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/ ). Explain why 3 the fractions are equivalent, e.g., by Franklin County Schools Students: Students know: Students are able to: Use visual models (e.g., fraction manipulatives, number lines, or pictures) to generate simple equivalent fractions including fractions equivalent to whole numbers, Strategies for comparing fractions (e.g., comparing numerators of like fractions, comparing denominators of fractions with like numerators, comparing to landmark fractions such as 1/2), Generate simple equivalent fractions using visual models, Given two fractions, use logical reasoning and a variety of models to represent and order the fractions (using <, =, >) and justify their answers, Communicate the reason why it is not valid to make a comparison Students understand that: Two fractions are equivalent if they are the same portion of the Express the same same whole or are the Click below to same point on the whole number in access all ALEX number line, multiple ways as resources fractions (4 = 4/1 = 8/2 aligned to this Comparisons of = 16/4) and explain standard. their answers, fractions are valid only when the two fractions ALEX Strategically choose refer to the same Resources Strategies for and apply a variety of whole, generating representations or use equivalent fractions logical reasoning to Any fraction can be using visual models justify the comparison named in many ways (e.g., fraction circles, of two fractions, (equivalent fractions) fraction bars, and different names are diagrams, pictures, useful for different Represent the etc.). comparison of fractions problem situations. Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID using a visual fraction model. Evidence of Student Attainment Teacher Vocabulary Knowledge between fractions that refer to different wholes (e.g., why it may not be valid to say 1/2 >1/4 if the 1/2 refers to a small pizza and the 1/4 refers to an extra-large pizza or "Susie said her 1/6 pizza was bigger than my 1/2 pizza, is she correct?"). c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/ ; recognize that 1 6/ = 6; locate 4/ 1 4 and 1 at the same point of a number line diagram. Skills Understanding Resources using <, =, and > notation. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 16. Tell and write time to the nearest minute, and measure time intervals in minutes. Measurement & Data Solve problems involving measurement and Franklin County Schools Students: Students know: Students are able to: Students understand that: Tell and write time to the nearest minute using Conventions for time notation, Accurately read and Analog and digital write time to the nearest minute from clocks represent the Click below to access all ALEX resources aligned to this standard. Grade 3 Mathematics CCRS Standards and Alabama COS CCRS Standard Standard ID Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.1 Evidence of Student Attainment Teacher Vocabulary Time sequence patterns, analog and digital clocks, Use strategies (e.g., watch the movement of a second or minute hand, count the changing of digits) to estimate and measure time intervals in minutes, Measurement & Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.2 (6Excludes compound units such as cm3 and Franklin County Schools Students: Liquid volume Accurately measure Mass the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales, graduated cylinders, beakers, and measuring cups to determine measures to the nearest whole unit. Given a variety of onestep word problems involving same unit volume or mass measurements, Explain and justify solutions using a variety Skills analog and digital clocks, Understanding time at any particular moment, Measure time Clocks show the Strategies for determining elapsed intervals in minutes, passage of time with time (e.g., using the movement of the number lines). Strategically select hands or the changing and apply methods for of digits, showing elapsed time to Representations for solve word problems. use in solving problems are selected based on the context and numbers in the problem. Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines. 17. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 Knowledge Students know: Students are able to: Personal benchmarks for metric standard units of mass (gram & kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units, Measure liquid volume and mass in metric standard units, Resources ALEX Resources Students understand that: The liquid volume of the object is expressed as the number of unit Choose appropriate volumes needed to fill Click below to measurement tools and the same space, access all ALEX units of measure, resources The mass of an aligned to this Represent quantities object is expressed as standard. the number of standard and operations physically, pictorially, or units needed to balance ALEX Characteristics of symbolically, the object, Resources addition, subtraction, multiplication, and Mathematical Strategically use a division contexts that problems can be solved variety of involve representations to solve using a variety of measurements. one-step word problems strategies, models, and representations. that involve measurement. Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID finding the geometric volume of a container.) (7Excludes multiplicative comparison problems (problems involving notions of “times as much”).) (See Appendix A, Table 2.) Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources of representations. 18. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. Example: Draw a bar graph in which each square in the bar graph might represent 5 pets. Measurement & Data Represent and interpret data. 3.MD.3 19. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is Measurement & Data Represent and interpret data. 3.MD.4 Students: Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1, Scaled pictograph Scaled bar graph Reason quantitatively to answer one- and twostep "how many more?" and "how many less?" problems using information presented in the scaled pictographs and bar graph. Franklin County Schools Students: Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch, half inch, or quarter inch) of several objects (e.g., measure Students know: Students are able to: Strategies for collecting, organizing, and recording data (including scaled pictographs and scaled bar graphs), Choose and apply appropriate strategies for organizing and recording data, Strategies for counting and comparing quantities, Strategies for solving addition and subtraction one and two-step problems. Line plots Students know: Line plots, Students understand that: Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs, Read and interpret graphical representations (pictographs and bar graphs with scales other Understand that than 1) of data, logical reasoning and Communicate and connections between representations provide defend solutions and justifications for solutions paths. solutions. Students are able to: Students understand that: Use standard units and the related tools to Questions Standard units, measure length to the concerning nearest quarter inch, mathematical contexts can be answered by Related tools for collecting, organizing, Organize and measuring length. and analyzing data and represent length measurement data on a data displays. Click below to access all ALEX resources aligned to this standard. ALEX Resources Click below to access all ALEX resources aligned to this standard. ALEX Resources Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID marked off in appropriate units— whole numbers, halves, or quarters. Evidence of Student Attainment Teacher Vocabulary Knowledge the length of all class members' fingers) or by making repeated measurements (e.g., measuring how far a marble rolls under certain conditions), Skills Understanding Resources line plot, Form conjectures based on the display of the data. Communicate questions and descriptions related to the data display. 20. Recognize area as an attribute of plane figures, and understand concepts of area measurement. a. A square with side length 1 unit called “a unit square,” is said to have “one square unit” of area and can be used to measure area. Measurement & Data Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.5 Students: Area Explain the result of Plane figure measuring the area of a plane figure as a number Unit square of "unit squares" needed to cover the object without gaps or overlaps. Students know: Students are able to: Students understand that: Measureable Measure area using The area of a plane attributes of objects, manipulative square specifically area, units to cover a plane figure is measured by figure, the number of samesize squares that exactly Units of measure Click below to Explain and justify cover the interior space access all ALEX for area (unit of the figure. squares). procedures for resources determining the area of aligned to this a plane figure. standard. ALEX Resources b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 21. Measure areas by counting unit squares (square cm, square m, square in, square ft, and Measurement & Data Geometric measurement: understand Franklin County Schools Students: Given a variety of plane figures, Accurately measure area by counting standard Students know: Students are able to: Students understand that: Click below to access all ALEX resources Measurable Accurately measure attributes of objects, area using standard and The area of a plane aligned to this non-standard square figure is measured by standard. Grade 3 CCRS Standard improvised units). Mathematics CCRS Standards and Alabama COS Standard ID concepts of area and relate area to multiplication and to addition. 3.MD.6 22. Relate area to the operations of multiplication and addition. Measurement & Data Geometric measurement: understand a. Find the area of a concepts of area and relate area to rectangle with whole-number side multiplication and to lengths by tiling it, addition. 3.MD.7 and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with Franklin County Schools Evidence of Student Attainment Teacher Vocabulary Knowledge (square centimeter, square meter, square inch, and square foot) and non-standard unit squares (e.g., orange pattern blocks, floor tiles, etc.). specifically area, Distributive Students: Given a polygon that may Property be decomposed into 2 or more rectangles, Rectilinear figures Find the total area by decomposing the figure into non-overlapping rectangles, finding the area of each, and find the sum of the areas. Given a rectangle with whole number length sides, Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width). Using array cards or tiles, Create and explain rectangular models to show that the area of a Skills Understanding units (to the nearest whole unit). counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure. Students know: Students are able to: Students understand that: Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width), Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property, Strategies for measuring area. Strategies for finding sums and products of whole numbers. Resources ALEX Resources The area of a plane figure is measured by the number of samesize squares that exactly cover the interior space of the figure, Multiplication is Model the area of putting together equal rectangles using sized groups, Click below to manipulatives or graph access all ALEX paper, Rectangular arrays resources represent groups (rows) aligned to this Strategically and of equal size (number of standard. fluently choose columns), strategies for finding ALEX sums and products, Resources Multiplication is distributive over the Accurately compute addition of whole sums and products. numbers. Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. Evidence of Student Attainment Teacher Vocabulary Knowledge Skills Understanding Resources rectangle with wholenumber side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c. (the Distributive Property). d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real-world problems. 23. Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Measurement & Data Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Franklin County Schools Students: Perimeter Find and justify Area solutions to real world and mathematical Polygons problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas, or with the same area and different perimeters. Students know: Students are able to: Measureable attributes of objects, specifically perimeter and area, Strategically use a variety of models and representations to solve measurement problems involving area and perimeter, Strategies for modeling measurement problems involving perimeter and area, Students understand that: Perimeter is measured in length Click below to units and is the distance access all ALEX around a 2-D figure, resources aligned to this The area of a plane standard. Accurately compute figure is measured by using whole numbers, the number of same ALEX size squares that exactly Resources cover the interior space Use logical of the figure. Strategies for reasoning to justify representing and solutions and solution computing perimeter paths by connecting and area. models to equations and computations. Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment 24. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Geometry Students: Reason with shapes and their attributes. Justify their 3.G.1 identification/sorting of shapes (triangles, quadrilaterals, pentagons, hexagons, squares, rectangles, rhombuses) by referring to their shared attributes, 25. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example: Partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Geometry Students: Reason with shapes Given squares, and their attributes. rectangles, or circles, 3.G.2 Teacher Vocabulary Franklin County Schools Express the area of each part as a unit fraction of the whole (e.g., partition a shape into 4 parts with equal area, and describe the Skills Understanding Resources Rhombus Students know: Students are able to: Rectangle Names for 2-D shapes, (e.g.triangle, quadrilateral, pentagon, hexagon, square, rectangle, rhombus), Identify attributes of Shapes may be 2-D shapes, (e.g., number of sides, equal assigned to different sides, right angles, categories of shapes parallel sides), based on different Click below to selections of shared access all ALEX attributes and that the Classify 2-D shapes resources shared attributes can based on their aligned to this define a larger category. attributes, standard. Square Quadrilateral Students understand that: Defining attributes for 2-D shapes, (e.g., right angles, equal length Draw shapes based sides, parallel sides, on specified attributes. straight sides, closed figure). Draw corresponding shapes when given a list of attributes. Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about equal area, Knowledge Students are able to: Area Students know: Partition Strategies for Decompose circles, decomposing shapes squares, and rectangles The same fractional into equal shares, into equal shares, parts of same- size 2-D shapes have equal area but do not have to be Fraction Communicate the vocabulary; halves, size of shares using the congruent (e.g., When two same-size thirds, fourths, appropriate fraction rectangles are cut in quarters, fifths, terminology, half vertically, eighths, and tenths. horizontally, or Justify equal area of diagonally, the pieces congruent and nonare all one half of the congruent shares as original rectangle, have equal shares of the equal area but are not same size whole. all congruent). ALEX Resources Students understand that: Click below to access all ALEX resources aligned to this standard. ALEX Resources Grade 3 CCRS Standard Mathematics CCRS Standards and Alabama COS Standard ID Evidence of Student Attainment area of each part as 1/4 of the area of the shape). Franklin County Schools Teacher Vocabulary Knowledge Skills Understanding Resources