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CCRS StandardStandard IDEvidence of Student AttainmentTeacher VocabularyKnowledgeSkillsUnderstandingResources1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Operations and Algebraic ThinkingWrite and interpret numerical expressions.5.OA.1Students:
l Write multistep numerical expressions involving all four operations using parentheses, brackets, and/or braces to convey the desired order of operations,
l Evaluate multistep numerical expressions involving all four operations and parentheses, brackets, and/or braces by applying conventions for order of operations.Students know:
l Strategies for rewriting numerical expressions that contain parentheses, brackets, and/or braces in equivalent forms that do not contain grouping symbols,
l Conventions for using parentheses, brackets and/or braces in writing numerical expressions.Students are able to:
l Efficiently apply strategies for rewriting and evaluating expressions that contain parentheses, brackets, and/or braces. Students understand that:
l There are conventions in mathematics such as, order of operations, that are arbitrary but have been agreed to for communication purposes,
l Mathematical symbols in expressions communicate the order of operations.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53768" \t "_blank" ALEX Resources2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Example: Express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.Operations and Algebraic ThinkingWrite and interpret numerical expressions.5.OA.2Students:Given verbal mathematical contexts involving multiple operations,
l Write and interpret the corresponding numerical expressions (e.g., express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7) ).
Given numerical expressions involving multiple operations,
l Explain the meaning of the expression without performing indicated calculations (e.g., recognize that 3 x (189 + 921) is three times as large as 189 + 921, without having to calculate the indicated sum or product).Students know:
l Meanings of operations (addition, subtraction, multiplication, and division) and conventions for grouping symbols.Students are able to:
l Use logical reasoning and mathematical vocabulary to interpret the meaning of mathematical expressions involving more than one operation.Students understand that:
l The operations of addition, subtraction, multiplication, and division all arise in multiple contexts (See Tables 1 and 2 for contexts),
l Mathematical symbols in equations communicate the order of operations.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53769" \t "_blank" ALEX Resources3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Example: Given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.Operations and Algebraic ThinkingAnalyze patterns and relationships.5.OA.3Students:Given two related rules,
l Accurately generate numbers in numerical patterns and form and graph ordered pairs consisting of corresponding terms,
l Use logical reasoning to identify and informally explain apparent relationships between corresponding terms (e.g., given the rule "add 3 starting at 0", and given the rule "add 6 starting at 0, observe that the terms in one sequence are twice the corresponding terms in the other sequence). l Coordinate plane
l Corresponding terms
l Ordered pairsStudents know:
l Strategies for generating and recording number patterns from rules,
l Techniques for graphing ordered pairs on a coordinate plane.Students are able to:
l Generate and record number patterns from rules,
l Graph ordered pairs on a coordinate plane,
l Use logical reasoning and informal language to explain relationships between corresponding terms in two sequences.Students understand that:
l Sequences of ordered pairs of corresponding numbers can be represented on a coordinate graph,
l Different representations of mathematical situations (verbal, number sentence, table, graph, etc.) reveal different features of the situation and aid in problem identification and solving,
l Noticing structure and regularities in mathematical statements and rules reveals connections that are useful in interpreting and utilizing the rules.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53772" \t "_blank" ALEX Resources4. Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.Number & Operations in Base TenUnderstand the place value system.5.NBT.1Students:When asked how two successive place values are related in a multidigit whole number or numbers with decimal places,
l Explain that the one to the right is 1/10 of the one to its left or that the one on the left is 10 times the one on the right.Students know:
l Place values,
l Place value models.Students are able to:
l Use logical reasoning and knowledge of place value to explain the relationship between two successive place values.Students understand that:
l Values of digits in any multidigit number (with or without decimal places) are based on patterns within a base10 place value system,
l Patterns created by the use of 10 digits in a place value system make a place value to the right 1/10 of the previous place value and a place value to the left 10 times the previous place value. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53775" \t "_blank" ALEX Resources5. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10.Number & Operations in Base TenUnderstand the place value system.5.NBT.2Students: Given multiplication problems involving a whole number times a power of 10,
l Choose strategies to find the products and describe the patterns relating the number of additional zeros in the products to the power of 10 in the problem.
Given multiplication and division problems involving a decimal and a power of 10,
l Choose strategies to find the products and quotients and describe the patterns relating the placement of the decimal in the answers to the power of 10 in the problem.
Given a power of 10 in standard form,
l Write the equivalent number using the appropriate wholenumber exponent.l Powers of 10
l ExponentStudents know:
l The meanings and structure of exponents,
l Strategies for finding products and quotients.Students are able to:
l Use logical reasoning to identify patterns,
l Convert powers of 10 from standard form to exponent form,
l Accurately compute products and quotients.Students understand that:
l Patterns and regularity in the number system can be used to solve problems,
l The same quantity can be represented in a number of forms including standard form and exponential form.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53776" \t "_blank" ALEX Resources6. Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000).
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Number & Operations in Base TenUnderstand the place value system.5.NBT.3Students:Given a number (including those with decimal parts from tenths to thousandths) orally or in written form,
l Represent that quantity in a variety of ways including words, baseten numerals, or expanded form and explain relationships among representations.
Given two decimal numbers (including those with decimal parts from tenths to thousandths),
l Use place value terminology and concepts to explain and justify the placement of <, =, > to compare the numbers and create true equalities and inequalities.l Expanded formStudents know:
l Place values including those to the right of the decimal point to thousandths,
l Meanings of mathematical symbols: <, =, >.Students are able to:
l Represent quantities in a number of forms including words, baseten numerals, and expanded form,
l Compare decimals to thousandths in equalities and inequalities and appropriately use symbols for equality and inequality. Students understand that:
l The same quantity can be represented with words, baseten numerals, and expanded form based on the place value of the digits,
l The value of a digit in a multidigit number depends on the place value spot it holds.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53777" \t "_blank" ALEX Resources7. Use place value understanding to round decimals to any place.Number & Operations in Base TenUnderstand the place value system.5.NBT.4Students:Given any decimal number,
l Justify the rounding of the number to a designated place value using models and place value vocabulary (e.g., 34.56 rounded to the nearest tenth is 34.6 because it is between the two tenths 34.5 and 34.6, but closer to 34.6).l RoundStudents know:
l Place value designations,
l Place value models (e.g., number lines and place value blocks). Students are able to:
l Count by 10s, 100s, 1000s, 10,000s, 0.1s, 0.01s, .001, etc.,
l Determine the number that is halfway between two consecutive multiples of powers of 10 (e.g., 350 & 360; 36,000 & 37,000; 0.01 & 0.02),
l Compare decimal numbers,
l Use place value vocabulary and models with logical reasoning to justify and communicate solutions to rounding problems.Students understand that:
l Rounding estimates quantities by changing the original number to the closest multiple of a power of 10,
l Rounding to place values is a useful rounding strategy to be chosen from a repetoire of estimation strategies when they consider it to be the most appropriate.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53780" \t "_blank" ALEX Resources8. Fluently multiply multidigit whole numbers using the standard algorithm.Number & Operations in Base TenPerform operations with multidigit whole numbers and with decimals to hundredths.5.NBT.5Students:Given a context which calls for the multiplication of two whole numbers,
l Choose the most appropriate strategy for computing the answer,
l Efficiently produce accurate results using the standard algorithm when appropriate. l Standard algorithm (multiplication)Students know:
l Strategies for computing answers to multiplication problems,
l Correct procedures for using the standard algorithm for multiplication.Students are able to:
l Strategically choose and apply appropriate strategies for multiplying accurately,
l Find products using the standard algorithm for multiplication.Students understand that:
l Efficient application of computation strategies is based on the numbers and operations in the problems,
l The steps used in the standard algorithm for multiplication can be justified by using properties of operations and understanding of place value,
l Among all techniques and algorithms that may be chosen for accurately performing multidigit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53782" \t "_blank" ALEX Resources9. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Number & Operations in Base TenPerform operations with multidigit whole numbers and with decimals to hundredths.5.NBT.6Students:Given division problems (up to 4digit dividends & 2digit divisors),
l Find wholenumber quotients and remainders using strategies that involve representations based on place value, properties of operations, and/or the relationship between multiplication and division,
l Justify solutions and solution paths through equations, rectangular arrays, and/or area models.l Rectangular arrays
l Area models
l Dividend
l Divisor
l Properties of operationsStudents know:
l Tools for modeling division problems,
l Strategies and methods for symbolically (numerically) recording strategies for solving division problems. Students are able to:
l Model division problems using appropriate tools,
l Record strategies for solving division problems,
l Use logical reasoning to communicate the relationship between models and symbolic (numeric) representations of solutions to division problems,
l Accurately compute quotients with remainders.Students understand that:
l Division problems can be solved using a variety of strategies, models, and representations,
l Efficient application of division computation strategies is based on the relationships between the numbers in the problem,
l Relationships between models of division problems and symbolic recordings of those models can be used to justify solutions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53783" \t "_blank" ALEX Resources10. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used.Number & Operations in Base TenPerform operations with multidigit whole numbers and with decimals to hundredths.5.NBT.7Students: Given addition, subtraction, multiplication, and division problems with decimals,
l Find sums, differences, products, and quotients using strategies that involve concrete models or drawings,
l Find sums, differences, products, and quotients using strategies based on place values, properties of operations, and/or the relationship between addition and subtraction, or between multiplication and division,
l Justify solutions and solution paths by relating the model/strategy to a written method. Students know:
l Tools for modeling decimal computation problems,
l Strategies and methods for symbolically (numerically) recording strategies for solving decimal computation problems.Students are able to:
l Model decimal computation problems using appropriate tools,
l Record strategies for solving decimal computation problems,
l Communicate the relationship between models and symbolic (numeric) representations of solutions to decimal computation problems,
l Accurately compute sums, differences, products and quotients in decimal problems.Students understand that:
l Decimal computation problems can be solved using a variety of strategies, models, and representations,
l Efficient application of decimal computation strategies is based on the numbers and operations in the problems,
l Relationships between models of decimal computation problems and symbolic recordings of those models can be used to justify solutions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53784" \t "_blank" ALEX Resources11. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)Number & OperationsFractionsUse equivalent fractions as a strategy to add and subtract fractions.5.NF.1Students:Given a variety of addition and subtraction problems involving fractions and mixed numbers with unlike denominators,
l Find the sums or differences by finding an equivalent sum or difference of fractions with like denominators.Students know:
l Strategies for generating equivalent fractions,
l Strategies for adding fractions with like denominators.Students are able to:
l Generate equivalent fractions using the generalization a/b = (n x a)/(n x b),
l Accurately add like fractions.Students understand that:
l Two fractions are equivalent if they are the same size share of the same whole or are the same point on a number line,
l Addition and subtraction of fractions are applied to fractions referring to the same whole,
l The unit fraction (1/b) names the size of the unit with respect to the referenced whole, and that the numerator counts the parts referenced and the denominator tells the number of parts into which the whole was partitioned,
l The operations of addition and subtraction are performed on counts with like names/labels/denominators and that the sum or difference retains the same name/label/denominator.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53786" \t "_blank" ALEX Resources12. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. Example: Recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.Number & OperationsFractionsUse equivalent fractions as a strategy to add and subtract fractions.5.NF.2Students:Given word problems involving the addition or subtraction of fractions referring to the same whole, including cases of unlike denominators,
l Explain and justify solutions and the reasonableness of solutions using connections among unit fractions, bench mark fractions, visual representations, and understanding of operations (e.g., addition and subtraction).Students know:
l Characteristics of addition and subtraction contexts for whole numbers and fractions (Table 1).
l Strategies for representing and solving addition and subtraction problems involving fractions,
l Strategies for generating equivalent fractions,
l Strategies for estimating sums and differences of fractions.Students are able to:
l Represent quantities (whole numbers and fractions) and operations (addition and subtraction) physically, pictorially, or symbolically,
l Strategically choose and apply a variety of representations to solve addition and subtraction word problems involving fractions,
l Use symbols to represent unknown quantities in addition and subtraction equations and solve such equations
l Accurately computes sums and differences of fractions,
l Use logical reasoning and connections among representations to justify solutions, the reasonableness of solutions, and solution paths.Students understand that:
l Addition and subtraction of fractions are applied to fractions referring to the same whole;
l The operation of addition with whole numbers and/or fractions represents both putting together and adding to contexts;
l The operation of subtraction with whole numbers and/or fractions represents taking apart, taking from, and additive comparison contexts;
l The operations of addition and subtraction are performed on counts with like names/labels/denominators and that the sum or difference retains the same name/label/denominator;Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53788" \t "_blank" ALEX Resources13. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Example: Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between which two whole numbers does your answer lie?Number & OperationsFractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.5.NF.3Students:Given a word problem involving division of whole numbers leading to answers in the form of fractions or mixed numbers,
l Apply their understanding of fractions as division problems to solve, explain, and justify their solutions, the reasonableness of their solutions, and their solution paths.Students know:
l Meaning for parts of a fraction (numerator, denominator),
l Interpretations of the operation of division of whole numbers,
l Strategies for partitioning.Students are able to:
l Use logical reasoning to justify the reasonableness of quotients that involve fractions and mixed numbers,
l Use patterns in the relationships between whole number division (when a is divided by b) and the meaning of the fraction (a/b) to explain a fraction as division,
l Apply understanding of fractions as division to solve word problems involving fraction and mixed number quotients.Students understand that:
l If objects are divided into b equal parts, then each part will contain a piece of size a/b.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53791" \t "_blank" ALEX Resources14. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. Example: Use a visual fraction model to show (2/3) 4 = 8/3, and create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.Number & Operations FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.5.NF.4Students:Given a story context involving multiplication of a fraction or whole number by a fraction,
l Use visual models and properties of operations to find and interpret the product and connect the steps with the visual models (manipulatives/pictures /diagrams including area models) to an equivalent sequence of operations in order to develop computational procedures [e.g., (a/b) (c/d) = ac/bd].
Given an equation involving multiplying a fraction or whole number by a fraction,
l Create a corresponding story context.Students know:
l Properties of operations,
l Contexts for multiplication of fractions and whole numbers,
l Strategies for using visual models (e.g., manipulatives, diagrams, pictures) to solve multiplication problems that involve fractions and whole numbers. Students are able to:
l Strategically choose and apply visual models to represent and solve problems involving the multiplication of fractions or whole numbers by fractions,
l Accurately compute products of fractions or whole numbers by fractions,
l Use logical reasoning to communicate connections between visual models and computational procedures for problems involving multiplication of fractions and whole numbers by fractions.Students understand that:
l Connections between representations and symbols provide justifications for solutions and solution paths,
l Properties of operations allow manipulation of mathematical expressions for sense making and easier computation.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53793" \t "_blank" ALEX Resources15. Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case), explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number, and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.Number & OperationsFractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.5.NF.5Students:Given a product and one factor,
l Create a pictorial or physical model and compare the size of the product to the size of the factor using multiplicative language (e.g., use a strip of paper 12 inches long and a strip 1/2 inch long to explain that it takes 24 of the 1/2 inch strips to make the 12 inch strip thus the 12 inch strip is 24 times as long as the 1/2 inch strip, or students could create a scale model of their desks showing the actual desk is 24 times larger than the model).
Given a multiplication problem involving a number times a fraction,
l Use logical reasoning (and possibly physical /pictorial models) and their understanding of the operation of multiplication to explain why the product will be greater than or less than the original number.
Given two equivalent fractions,
l Use logical reasoning and the properties of multiplication to relate the use of multiplying numerator and denominator of a fraction by the same number to generate equivalent fractions to the effect of multiplying the fraction by 1.l ScalingStudents know:
l Meanings of operations,
l Properties of multiplication,
l Strategies for modeling multiplicative comparisons with fractions and whole numbers.Students are able to:
l Use logical reasoning and mathematical models to communicate the connections between multiplication as scaling and the size of the product,
l Use logical reasoning and the properties of multiplication to communicate the relationship of the use of multiplying numerator and denominator of the fraction by the same number to generate equivalent fractions to the effect of multiplying a fraction by 1.Students understand that:
l Multiplication can be interpreted as putting together equal size groups and as comparison (Table 2),
l Comparisons can be interpreted as scaling (resizing),
l Properties of operations allow manipulation of mathematical expressions for sense making and easier computation.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53797" \t "_blank" ALEX Resources16. Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.Number & OperationsFractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.5.NF.6Students:Given a word problem involving the mulitplication of fractions and/or mixed numbers,
l Model and solve the problem,
l Explain and justify solutions and the reasonableness of solutions using connections among unit fractions, visual representations, and an understanding of multiplication.Students know:
l Properties of Multiplication,
l Characteristics of multiplication contexts for whole numbers and fractions,
l Strategies for representing and solving multiplication problems involving whole numbers and fractions.Students are able to:
l Strategically choose and apply a variety of representations to solve multiplication word problems involving fractions and mixed numbers,
l Apply knowledge of the properties of multiplication with knowledge of fractions to accurately compute products fractions, and mixed numbers,
l Use logical reasoning and connections among representations to justify solutions, reasonableness of solutions, and solution paths.Students unvw
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&Fdd$If[$\$gd963 $Ifgd963dd$If[$\$gd/ $Ifgdjderstand that:
l Multiplication may be viewed as putting together equal sized groups and as comparisons,
l Mathematical problems (multiplication of whole numbers and fractions) 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=53800" \t "_blank" ALEX Resources17. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
a. Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. Example: Create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.
b. Interpret division of a whole number by a unit fraction, and compute such quotients. Example: Create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.
c. Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Examples: How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?
(1 Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)Number & Operations FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.5.NF.7Students:Given a story context involving division of a unit fraction by a nonzero whole number, or division of a whole number by a unit fraction,
l Use visual models and properties of operations to explain and represent the division problem context, find the quotient, and explain the solution's relationship to the given multiplication problem.
Given a problem involving division of a unit fraction by a nonzero whole number, or division of a whole number by a unit fraction,
l Create a corresponding story context, a model to represent the division context, and accurately solve the problem.l Unit fractionStudents know:
l Properties of operations,
l Contexts for division of fractions and whole numbers,
l Strategies for using visual models (e.g., manipulatives, diagrams, pictures) to solve division problems that involve fractions and whole numbers.Students are able to:
l Strategically choose and apply visual models to represent and solve problems involving the division of unit fractions by nonzero whole numbers, or whole numbers by unit fractions,
l Accurately compute quotients of unit fractions and whole numbers using models,
l Use logical reasoning to communicate connections between visual models and computational procedures for problems involving division of unit fractions and whole numbers.Students understand that:
l Connections between representations and symbols provide justifications for solutions and solution paths,
l Properties of operations allow manipulation of mathematical expressions for sense making and easier computation,
l The operation of division represents; contexts of partitioning into equalsized shares, contexts of partitioning equally among a given number of groups, or contexts involving multiplicative comparisons.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53801" \t "_blank" ALEX Resources18. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems.Measurement & DataConvert like measurement units within a given measurement system.5.MD.1Students:Given a real world multistep problem involving measurements in different units (within the same measurement system),
l Strategically choose a unit useful in the solution of the problem, convert measures to this unit, solve the problem, and justify choices of units and strategies. Students know:
l Strategies for solving multistep problems involving measurement, measurement units, and the relationships among them,
l Strategies for converting measurements from one unit to another in the same measurement system.Students are able to:
l Strategically choose an appropriate common unit to use for computations when working with problems that contain measurements in different units,
l Strategically choose and apply representations and computation techniques for solving real life mathematical problems,
l Accurately compute solutions,
l Use logical reasoning to justifiy solution paths.Students understand that:
l The size of the unit of measurement and the number of units in the measurement are inversely related (The bigger the unit the fewer it takes for the measurement),
l When adding or subtracting measurements a common unit allows for meaningful computation.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53809" \t "_blank" ALEX Resources19. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Example: Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.Measurement & DataRepresent and interpret data.5.MD.2Students:
l Make and use line plots (scale to match unit of measure) to represent data generated by making measurements (to the nearest eighth unit) of several objects or by making repeated measurements,
l Use information from the constructed line plots to generate questions and solve problems including problems that involve all four operations with fractions.l Line plotStudents know:
l Techniques for constructing line plots,
l Standard units and the related tools for measuring,
l Strategies for adding, subtracting, multiplying, and dividing fractions.Students are able to:
l Use standard units and the related tools to make measurements to the nearest eighth unit,
l Organize and represent measurement data on a line plot,
l Choose and apply appropriate strategies to solve problems generated by conjectures from examining data displays,
l Communicate justification for strategy choice and solutions to problems involving measurements,
l Apply strategies for solving problems involving all four operations with fractions.Students understand that:
l Questions concerning mathematical contexts (in particular, measurement contexts) can be generated and 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=53811" \t "_blank" ALEX Resources20. Recognize volume as an attribute of solid figures, and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.Measurement & DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.5.MD.3Students:Given a solid figure,
l Describe the process for measuring volume including using samesized (unit) cubes and filling the figure completely with no gaps or overlaps.lVolume
l Unit cubeStudents know:
l Measurable attributes of objects, specifically volume,
l Units of measurement for volume, specifically unit cubes.Students are able to:
l Communicate the process of measuring volume in cubic units.Students understand that:
l The volume of a solid object is measured by the number of samesize cubes that exactly fill the interior space of the object.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53814" \t "_blank" ALEX Resources21. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.Measurement & DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.5.MD.4Students:Given a variety of rectangular solids with whole number length sides,
l Accurately measure volume by counting standard unit of measure (specifically cubic cm, cubic in., and cubic ft.) sized cubes and nonstandard (e.g., multilink cubes) unit sized cubes.Students know:
l Measurable attributes of objects, specifically volume,
l Strategies for measuring volume.Students are able to:
l Accurately measure volume using standard and nonstandard cubic units (to the nearest whole unit).Students understand that:
l The volume of a solid object is measured by the number of samesize cubes that exactly fill the interior space of the object.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53817" \t "_blank" ALEX Resources22. Relate volume to the operations of multiplication and addition, and solve real world and mathematical problems involving volume.
a. d the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.
b. Apply the formulas V = l w h and V = B h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving realworld and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve realworld problems.Measurement & DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.5.MD.5Students:Given a right rectangular prism with whole number length sides as a physical model and within a word problem context,
l Find and justify the volume of the prism as part or all of the problem's solution by relating a unit cube filled model to the corresponding multiplication problem(s).
Given unit cubes,
l Create and explain rectangular prism models to show that the volume of a right rectangular prism with wholenumber side lengths a, b, and c is represented by the multiplication problem a x b x c where the multiplication of the side lengths can be done in any order.
Given a solid figure composed of 2 or more right rectangular prisms in real world or mathematical contexts,
l Find the total volume by decomposing the figure into nonoverlapping rectangular prisms and find the sum of the volumes.l Associative Property
l Commutative Property
l Volume
l Right rectangular prism
l V = l x w x h
l V = b x hStudents know:
l Relationships between rectangular arrays and the corresponding multiplication problems,
l Strategies for measuring volume,
l Strategies for finding sums and products of whole numbers.Students are able to:
l Communicate the relationships between rectangular models of volume and multiplication and addition problems,
l Model the volume of rectangles using manipulatives,
l Strategically and fluently choose strategies for finding sums and products,
l Accurately compute sums and products.Students understand that:
l The volume of a rectangular prism is measured by the number of samesize cubes that exactly fill the interior space of the object,
l Multiplication is putting together equal sized groups and arrays.
l Rectangular arrays represent groups (rows) of equal size (number of columns),
l Layers of arrays can be used to determine volume.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53818" \t "_blank" ALEX Resources23. Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).GeometryGraph points on the coordinate plane to solve realworld and mathematical problems.5.G.1Students:Given a point on a coordinate plane,
l Explain how to identify its coordinates using appropriate vocabulary (xaxis, yaxis, x coordinate, ycoordinate, distance from the origin).
Given an ordered pair of numbers,
l Justify the placement of the corresponding point on a coordinate system.l Axes
l Xaxis
l Yaxis
l Coordinate system
l Origin
l Ordered pair
l CoordinatesStudents know:
l Coordinate system vocabulary: axes, xaxis, yaxis, origin, ordered pair, coordinates, xcoordinate, ycoordinate,
l Techniques for constructing a coordinate grid and plotting points on that grid.Students are able to:
l Construct a coordinate system,
l Explain how to identify the coordinates of a point on a coordinate system,
l Graph points corresponding to ordered pairs.Students understand that:
l Graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53823" \t "_blank" ALEX Resources24. Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.GeometryGraph points on the coordinate plane to solve realworld and mathematical problems.5.G.2Students:Given real world and mathematical problems involving a relationship between two variables,
l Create a first quadrant graph and explain its relationship to the context of the problem (e.g., Tickets cost $0.75 each. If 20 tickets are sold, the cost is $15, if 21 tickets are sold the cost is $15.75. Create a graph that shows the cost of any number of tickets.).
Given a graph of a real world or mathematical situation,
l Interpret the coordinate values of the points in the context of the situation.l Coordinate plane
l First quadrant
l Coordinate valuesStudents know:
l Coordinate system vocabulary; axes, xaxis, yaxis, origin, ordered pair, coordinates, xcoordinate, ycoordinate.Students are able to:
l Explain how to identify the coordinates of a point on a coordinate system,
l Graph points corresponding to ordered pairs,
l Represent real world and mathematical problems on a coordinate plane,
l Interpret coordinate values of points in the context of real world/mathematical situations.Students understand that:
l A variety of representation (e.g., diagrams, number lines, charts, and graphs) can be used to illustrate mathematical situations and relationships,
l These representations help in conceptualizing ideas and in solving problems,
l Graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53824" \t "_blank" ALEX Resources25. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. Example: All rectangles have four right angles and squares are rectangles, so all squares have four right angles.GeometryClassify twodimensional figures into categories based on their properties.5.G.3Students:Given a variety of 2D figures,
l Use logical reasoning and knowledge of relationships among categories and subcategories of shapes to explain the attributes of the given shapes (e.g.,(1) given a triangle, a student would be able to describe it as having three sides, and then because all triangles are polygons, also describe it as being a closed figure with straight sides, or (2) given a square, a student would be able to describe it as a special rectangle having four right angles but also having four congruent sides).l Categories
l SubcategoriesStudents know:
l Characteristics of categories and subcategories of 2D figures (a variety of polygons including; triangles, quadrilaterals, pentagons, hexagons, etc.),
l The unique categories of triangles (acute, obtuse, scalene, isosceles and equlateral) and quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid).Students are able to:
l Justify the classification of shapes based on their attributes,
l Explain the relationship among categories and subcategories of shapes.Students understand that:
l Shapes may be classified based on their attributes,
l Attributes belonging to a category of 2D figures also belong to all subcategories of that category.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53826" \t "_blank" ALEX Resources26. Classify twodimensional figures in a hierarchy based on properties.GeometryClassify twodimensional figures into categories based on their properties.5.G.4Students:Given a variety of 2D figures,
l Use the attributes of the shapes to explain their classification in as many categories and subcategories as possible (e.g., students will describe the attributes that allow a square to be classified as a polygon, a parallelogram, a rectangle, a rhombus, and a square, while the rhombus fits in the heirarchy of polygon and parallelogram, but not rectangle).l HierarchyStudents know:
l Characteristics of categories and subcategories of 2D figures (a variety of polygons including; triangles, quadrilaterals, pentagons, hexagons, etc.),
l The unique categories of triangles (acute, obtuse, scalene, isosceles and equlateral) and quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid).Students are able to:
l Justify the classification of a shape into a category and successive subcategories based on the identification of additional or specific attributes,
l Explain the relationship among categories and subcategories of shapes.Students understand that:
l Shapes are classified based on the properties of their attributes,
l Attributes belonging to a category of 2D figures also belong to all subcategories of that category.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53828" \t "_blank" ALEX Resources
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
Grade 5 Mathematics CCRS Standards and Alabama COS
Franklin County Schools
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