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CCRS StandardStandard IDEvidence of Student AttainmentTeacher VocabularyKnowledgeSkillsUnderstandingResources1. 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 ThinkingRepresent and solve problems involving multiplication and division.3.OA.1Students:Given any multiplication problem in the form a x b = c,
l 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) ,
l Write a corresponding word problems containing a multiplication context.Students know:
l Characteristics of multiplication contexts.Students are able to:
l Represent quantities and operations (multiplication) physically, pictorially, or symbolically,
l Use mathematical language to communicate the connections between multiplication equations and related representations,
l Write word problems containing multiplication contexts.Students understand that:
l Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53627" \t "_blank" ALEX Resources2. 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. Example: Describe a context in which a number of shares or a number of groups can be expressed as 56 8.Operations and Algebraic ThinkingRepresent and solve problems involving multiplication and division.3.OA.2Students:Given any division problem in the form a b = c,
l 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 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),
l Write a corresponding word problem containing a division context.Students know:
l Characteristics of division contexts.Students are able to:
l Represent quantities and operations (division) physically, pictorially, or symbolically,
l Use mathematical language to communicate the connections between division equations and related representations,
l Write word problems containing division contexts.Students understand that:
l Both partitioning into equalsized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53629" \t "_blank" ALEX Resources3. 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 (1See Appendix A, Table 2.)Operations and Algebraic ThinkingRepresent and solve problems involving multiplication and division.3.OA.3Students:Given a variety of multiplication and division word problems within 100,
l 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).l See glossary for problem types (Table 2).Students know:
l Characteristics of multiplication and division contexts,
l Multiplication and division strategies.Students are able to:
l Represent quantities and operations (multiplication and division) physically, pictorially, or symbolically,
l Strategically use a variety of representations to solve multiplication and division word problems,
l Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical, pictorial, or symbolic representations,
l Accurately compute products and quotients,
l Use symbols to represent unknown quantities in equations.
Students understand that:
l Multiplication is putting together equal sized groups and division is sharing into equalsized shares or is sharing equally among a given number of groups,
l Mathematical problems can be solved using a variety of strategies, models, representations,
l Variables represent unknown quantities when representing mathematical situations algebraically.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53631" \t "_blank" ALEX Resources4. 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 ThinkingRepresent and solve problems involving multiplication and division.3.OA.4Students:
l Solve single operation multiplication/division equations containing a single unknown (e.g. 8x? = 48, 5= __ 3, 6x6 = ___).Students know:
l Strategies for solving simple equations with one unknown.Students are able to:
l Efficiently apply strategies for solving simple equations with one unknown,
l Justify solutions for single unknown equations.Students understand that:
l Equalities contain phrases that name the same amount on each side of the equal sign.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53632" \t "_blank" ALEX Resources5. 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 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property) (2Students need not use formal terms for these properties.)Operations and Algebraic ThinkingUnderstand properties of multiplication and the relationship between multiplication and division.3.OA.5Students:Given multiplication and division problems within 100,
l Use the properties of operations and descriptive language for the property to justify their products and quotients (e.g., If I 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).l Commutative Property of Multiplication
l Associative Property of Multiplication
l Distributive Property Students know:
l Commutative, Associative, Identity and Zero Properties of Multiplication and the Distributive Property,
l Strategies for finding products and quotients. Students are able to:
l Strategically and efficiently apply properties of multiplication and division in order to find products and quotients.Students understand that:
l The order in which factors are multiplied does not change the product. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53635" \t "_blank" ALEX Resources6. Understand division as an unknownfactor problem. Example: Find 32 8 by finding the number that makes 32 when multiplied by 8.Operations and Algebraic ThinkingUnderstand properties of multiplication and the relationship between multiplication and division.3.OA.6Students:Given a division problem with an unknown quotient,
l Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation. l FactorStudents know:
l Strategies for finding quotients and products.Students are able to:
l Use symbols to represent unknown quantities in equations,
l Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem,
l Use the inverse relationship between multiplication and division to find quotients.Students understand that:
l The relationship between multiplication and division (that one "undoes" the other) can be used to solve problems,
l Efficient application of computation strategies are based on the numbers in the problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53639" \t "_blank" ALEX Resources7. 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 properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers.
Operations and Algebraic ThinkingMultiply and divide within 100.3.OA.7Students:Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient,
l Use an efficient strategy (e.g., recall, inverse operations, arrays, derived facts, properties of operations, etc.) to name the product or quotient.Students know:
l Strategies for finding products and quotients.Students are able to:
l Use multiplication and division strategies efficiently based on the numbers in the problems.Students understand that:
l Efficient application of computation strategies are based on the numbers in the problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53642" \t "_blank" ALEX Resources8. Solve twostep 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 (3This standard is limited to problems posed with whole numbers and having wholenumber 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).)Operations and Algebraic ThinkingSolve problems involving the four operations, and identify and explain patterns in arithmetic.3.OA.8Students:Given a variety of twostep word problems involving all four operations,
l 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,
l 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:
l Characteristics of addition, subtraction, multiplication, and division situations,
l Addition, subtraction, multiplication, and division strategies,
l Strategies for mentally computing and estimating sums, differences, products, and quotients. Students are able to:
l Strategically use a variety of representations to solve twostep word problems involving all four operations,
l Use symbols to represent unknown quanities in equations that relate to word problem contexts,
l Use mathematical language and contextual situations to communicate the connections among the four operations and related physical, pictorial, or symbolic representations and justify solutions/solution paths,
l Accurately compute sums, differences, products and quotients,
l Use logical reasoning, mental computation strategies, and estimation strategies to justify the reasonableness of solutions.Students understand that:
l Multiplication is putting together equal sized groups,
l Division is sharing into equalsized shares or as sharing equally among a given number of groups,
l Mathematical problems can be solved using a variety of strategies, models, and representations,
l Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53644" \t "_blank" ALEX Resources9. 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 ThinkingSolve problems involving the four operations, and identify and explain patterns in arithmetic.3.OA.9Students:
l 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).Students know:
l Characteristics of numbers and properties of operations (e.g., odd, even),
l Properties from Table 3, etc.Students are able to:
l Identify arithmetic patterns in number sequences, in the addition table or multiplication table,
l Use logical reasoning and properties of numbers and operations to explain arithmetic patterns.Students understand that:
l Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations, form conjectures, and solve problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53645" \t "_blank" ALEX Resources10. Use place value understanding to round whole numbers to the nearest 10 or 100.Number & Operations in Base TenUse place value understanding and properties of operations to perform multidigit arithmetic. 4(4 A range of algorithms may be used.)3.NBT.1Students:Given any number less than 1,000,
l 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).Students know:
l Place value (ones, tens, hundreds),
l Rounding.Students are able to:
l Count by 10s and 100s,
l Determine what is halfway between two multiples of 10 or 100,
l Round to the nearest 10 or 100,
l Use place value vocabulary and logical reasoning to justify solutions to rounding problems.Students understand that:
l 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.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53670" \t "_blank" ALEX Resources11. 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.Number & Operations in Base TenUse place value understanding and properties of operations to perform multidigit arithmetic. 4(4 A range of algorithms may be used.)3.NBT.2Students:
l Fluently add and subtract within 1000, using strategies based on place values, properties of operations, and/or the relationship between addition and subtraction,
l Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning.Students know:
l Tools for modeling addition and subtraction,
l Strategies for solving addition and subtraction problems,
l Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems.Students are able to:
l Model addition and subtraction problems using appropriate tools,
l Record strategies for solving addition and subtraction problems,
l Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems.Students understand that:
l Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53671" \t "_blank" ALEX Resources12. Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations.Number & Operations in Base TenUse place value understanding and properties of operations to perform multidigit arithmetic. 4(4 A range of algorithms may be used.)3.NBT.3Students:
l Efficiently use strategies based on place value and properties of operations to multiply onedigit numbers by multiples of 10 (from 1090) and justify their answers.Students know:
l Place value models for multiplying numbers (e.g., open arrays, place value blocks),
l Strategies for multiplying onedigit numbers,
l Strategies for mentally multiplying onedigit numbers by multiples of powers of 10.Students are able to:
l Use mental strategies based on an understanding of place value, properties of operations, and knowledge of onedigit multiplication to find products,
l Use a variety of place value models of multiplication problems to justify strategies and solutions.Students understand that:
l Patterns in the place value system and properties of operations can be used to efficiently compute products.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53672" \t "_blank" ALEX Resources13. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.Number & OperationsFractionsDevelop understanding of fractions as numbers.5(5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)3.NF.1Students:Given any fraction in the form a/b,
l 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).
Given a model of a fraction,
l Write the corresponding fraction and explain the relationship of the numerator and denominator to the model.Students know:
l Fractions,
l Strategies for creating models of fractional quantities (e.g., folding, repeatedly dividing the whole in half, etc.). Students are able to:
l Write fractions that correspond to pictorial or physical models,
l Create models of fractions that correspond to fractions written in the form a/b,
l Communicate the relationship between models of fractions and the corresponding written fraction.Students understand that:
l Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole),
l The unit fraction (1/b) names the size of the unit with respect to the referenced whole,
l The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53674" \t "_blank" ALEX Resources14. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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 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.
Number & OperationsFractionsDevelop understanding of fractions as numbers.5(5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)3.NF.2Students:Given any common fraction a/b between 0 and 1 (denominators of 2, 3, 4, 6, 8),
l 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.Students know:
l Fractions,
l Strategies for creating number line models of fractions less than 1 (e.g., marking off equal lengths by estimation, recursive halving). Students are able to:
l Represent fractions in the form a/b on a number line including correctly partitioning the interval from 0 to 1 into "b" equal parts and counting "a" parts to place the fraction,
l Explain and justify the creation and placement of a fraction less than 1 on a number line. Students understand that:
l A fractional quantity can be modeled using a variety of representations (e.g., part of a whole, part of a group, a distance on a numberline) each of which may reveal important features of given contexts. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53675" \t "_blank" ALEX Resources15. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
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.Number & OperationsFractionsDevelop understanding of fractions as numbers.5(5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)3.NF.3Students:
l Use visual models (e.g., fraction manipulatives, number lines, or pictures) to generate simple equivalent fractions including fractions equivalent to whole numbers,
l Given two fractions, use logical reasoning and a variety of models to represent and order the fractions (using <, =, >) and justify their answers,
l Communicate the reason why it is not valid to make a comparison 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 extralarge pizza or "Susie said her 1/6 pizza was bigger than my 1/2 pizza, is she correct?").Students know:
l 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),
l Strategies for generating equivalent fractions using visual models (e.g., fraction circles, fraction bars, diagrams, pictures, etc.).Students are able to:
l Generate simple equivalent fractions using visual models,
l Express the same whole number in multiple ways as fractions (4 = 4/1 = 8/2 = 16/4) and explain their answers,
l Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions,
l Represent the comparison of fractions using <, =, and > notation.Students understand that:
l Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line,
l Comparisons of fractions are valid only when the two fractions refer to the same whole,
l Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53678" \t "_blank" ALEX Resources16. Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.Measurement & DataSolve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.3.MD.1Students:
l Tell and write time to the nearest minute using analog and digital clocks,
l 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,
l Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines.Students know:
l Conventions for time notation,
l Time sequence patterns,
l Strategies for determining elapsed time (e.g., using number lines).Students are able to:
l Accurately read and write time to the nearest minute from analog and digital clocks,
l Measure time intervals in minutes,
l Strategically select and apply methods for showing elapsed time to solve word problems.StudewxO p
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l Analog and digital clocks represent the time at any particular moment,
l Clocks show the passage of time with the movement of the hands or the changing of digits,
l Representations for use in solving problems are selected based on the context and numbers in the problem.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53685" \t "_blank" ALEX Resources17. 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 onestep 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 (6Excludes compound units such as cm3 and finding the geometric volume of a container.)(7Excludes multiplicative comparison problems (problems involving notions of times as much ).) (See Appendix A, Table 2.)Measurement & DataSolve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.3.MD.2Students:
l Accurately measure 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,
l Explain and justify solutions using a variety of representations.l Liquid volume
l MassStudents know:
l 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,
l Characteristics of addition, subtraction, multiplication, and division contexts that involve measurements.Students are able to:
l Measure liquid volume and mass in metric standard units,
l Choose appropriate measurement tools and units of measure,
l Represent quantities and operations physically, pictorially, or symbolically,
l Strategically use a variety of representations to solve onestep word problems that involve measurement. Students understand that:
l The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space,
l The mass of an object is expressed as the number of standard units needed to balance the object,
l Mathematical problems can be solved using a variety of strategies, models, and representations.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53686" \t "_blank" ALEX Resources18. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep 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 & DataRepresent and interpret data.3.MD.3Students:
l Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1,
l 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.l Scaled pictograph
l Scaled bar graphStudents know:
l Strategies for collecting, organizing, and recording data (including scaled pictographs and scaled bar graphs),
l Strategies for counting and comparing quantities,
l Strategies for solving addition and subtraction one and twostep problems.Students are able to:
l Choose and apply appropriate strategies for organizing and recording data,
l Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data,
l Communicate and defend solutions and solutions paths.Students understand that:
l Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs,
l Understand that logical reasoning and connections between representations provide justifications for solutions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53688" \t "_blank" ALEX Resources19. 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 marked off in appropriate units whole numbers, halves, or quarters.Measurement & DataRepresent and interpret data.3.MD.4Students:
l 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 the length of all class members' fingers) or by making repeated measurements (e.g., measuring how far a marble rolls under certain conditions),
l Communicate questions and descriptions related to the data display.l Line plotsStudents know:
l Line plots,
l Standard units,
l Related tools for measuring length.Students are able to:
l Use standard units and the related tools to measure length to the nearest quarter inch,
l Organize and represent length measurement data on a line plot,
l Form conjectures based on the display of the data.Students understand that:
l Questions concerning mathematical contexts can be answered by collecting, organizing, and analyzing data and data displays.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53690" \t "_blank" ALEX Resources20. 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.
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.Measurement & DataGeometric measurement: understand concepts of area and relate area to multiplication and to addition.3.MD.5Students:
l Explain the result of measuring the area of a plane figure as a number of "unit squares" needed to cover the object without gaps or overlaps. l Area
l Plane figure
l Unit squareStudents know:
l Measureable attributes of objects, specifically area,
l Units of measure for area (unit squares).Students are able to:
l Measure area using manipulative square units to cover a plane figure,
l Explain and justify procedures for determining the area of a plane figure. Students understand that:
l The area of a plane figure is measured by the number of samesize squares that exactly cover the interior space of the figure.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53692" \t "_blank" ALEX Resources21. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).Measurement & DataGeometric measurement: understand concepts of area and relate area to multiplication and to addition.3.MD.6Students: Given a variety of plane figures,
l Accurately measure area by counting standard (square centimeter, square meter, square inch, and square foot) and nonstandard unit squares (e.g., orange pattern blocks, floor tiles, etc.).Students know:
l Measurable attributes of objects, specifically area,
l Strategies for measuring area. Students are able to:
l Accurately measure area using standard and nonstandard square units (to the nearest whole unit).Students understand that:
l The area of a plane figure is measured by counting the number of samesize squares (unit squares) that exactly cover the interior space of the figure.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53695" \t "_blank" ALEX Resources22. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with wholenumber side lengths by tiling it, 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 wholenumber 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 wholenumber 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.
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 realworld problems.Measurement & DataGeometric measurement: understand concepts of area and relate area to multiplication and to addition.3.MD.7Students:Given a polygon that may be decomposed into 2 or more rectangles,
l Find the total area by decomposing the figure into nonoverlapping rectangles, finding the area of each, and find the sum of the areas.
Given a rectangle with whole number length sides,
l 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,
l Create and explain rectangular models to show that the area of a 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).l Distributive Property
l Rectilinear figuresStudents know:
l Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width),
l Strategies for finding sums and products of whole numbers.Students are able to:
l Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property,
l Model the area of rectangles using manipulatives or graph paper,
l Strategically and fluently choose strategies for finding sums and products,
l Accurately compute sums and products.Students understand that:
l The area of a plane figure is measured by the number of samesize squares that exactly cover the interior space of the figure,
l Multiplication is putting together equal sized groups,
l Rectangular arrays represent groups (rows) of equal size (number of columns),
l Multiplication is distributive over the addition of whole numbers.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53696" \t "_blank" ALEX Resources23. Solve realworld 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 & DataGeometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.3.MD.8Students:
l Find and justify solutions to 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.l Perimeter
l Area
l PolygonsStudents know:
l Measureable attributes of objects, specifically perimeter and area,
l Strategies for modeling measurement problems involving perimeter and area,
l Strategies for representing and computing perimeter and area.Students are able to:
l Strategically use a variety of models and representations to solve measurement problems involving area and perimeter,
l Accurately compute using whole numbers,
l Use logical reasoning to justify solutions and solution paths by connecting models to equations and computations.Students understand that:
l Perimeter is measured in length units and is the distance around a 2D figure,
l The area of a plane figure is measured by the number of samesize squares that exactly cover the interior space of the figure.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53702" \t "_blank" ALEX Resources24. 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.GeometryReason with shapes and their attributes.3.G.1Students:
l Justify their identification/sorting of shapes (triangles, quadrilaterals, pentagons, hexagons, squares, rectangles, rhombuses) by referring to their shared attributes,
l Draw corresponding shapes when given a list of attributes.l Rhombus
l Rectangle
l Square
l QuadrilateralStudents know:
l Names for 2D shapes, (e.g.triangle, quadrilateral, pentagon, hexagon, square, rectangle, rhombus),
l Defining attributes for 2D shapes, (e.g., right angles, equal length sides, parallel sides, straight sides, closed figure). Students are able to:
l Identify attributes of 2D shapes, (e.g., number of sides, equal sides, right angles, parallel sides),
l Classify 2D shapes based on their attributes,
l Draw shapes based on specified attributes.Students understand that:
l Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53704" \t "_blank" ALEX Resources25. 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.GeometryReason with shapes and their attributes.3.G.2Students:Given squares, rectangles, or circles,
l Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about equal area,
l 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 area of each part as 1/4 of the area of the shape). l Area
l PartitionStudents know:
l Strategies for decomposing shapes into equal shares,
l Fraction vocabulary; halves, thirds, fourths, quarters, fifths, eighths, and tenths.Students are able to:
l Decompose circles, squares, and rectangles into equal shares,
l Communicate the size of shares using the appropriate fraction terminology,
l Justify equal area of congruent and noncongruent shares as equal shares of the same size whole.Students understand that:
l The same fractional parts of same size 2D shapes have equal area but do not have to be congruent (e.g., When two samesize rectangles are cut in half vertically, horizontally, or diagonally, the pieces are all one half of the original rectangle, have equal area but are not all congruent).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53705" \t "_blank" ALEX Resources
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
Grade 3 Mathematics CCRS Standards and Alabama COS
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var currentTallest = 0;
$(".print_row_content thead").each(function(){
if ($(this).height() > currentTallest) { currentTallest = $(this).height(); }
})
currentTallest = getHeightWithVariance(currentTallest);
$(".print_row_content th div").css("height", currentTallest);
});
function getHeightWithVariance(currentTallest) {
var threshold = 150,
defaultVariance = 15,
variancePct = 1.1;
if (currentTallest > threshold) {
currentTallest = Math.floor(currentTallest * variancePct);
} else {
currentTallest += defaultVariance;
}
return currentTallest;
}
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