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CCRS StandardStandard IDEvidence of Student AttainmentTeacher VocabularyKnowledgeSkillsUnderstandingResources
1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.Operations and Algebraic ThinkingUse the four operations with whole numbers to solve problems.4.OA.1Students:Given a multiplication equation,
l Create and explain a corresponding verbal multiplicative comparison statement (Table 2).
Given a verbal (written or oral) representation of a multiplicative comparison,
l Write and solve the related multiplication equation (e.g., given "Johnny has 7 cards and Shawna has 5 times as many cards as Johnny," the student will write 5 x 7 and accurately find the number of cards Shawna has to be 35). l Multiplicative comparison
l See Table 2 for problem types.Students know:
l Characteristics of multiplicative comparisons (Table 2). Students are able to:
l Use mathematical language to communicate the relationship between verbal representations of multiplicative comparisons and the related multiplication equations,
l Write multiplication equations that correspond to given multiplicative comparison statements,
l Write verbal multiplicative comparison descriptions given a multiplication equation.Students understand that:
l Multiplicative comparisons relate the size of two quantities and a scale factor,
l Factors in multiplication problems have different roles from each other in the context of comparison problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53708" \t "_blank" ALEX Resources2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 (1 See Appendix A, Table 2.)Operations and Algebraic ThinkingUse the four operations with whole numbers to solve problems.4.OA.2Students:Given multiplication and division problems involving multiplicative comparisons,
l Find, explain and justify solutions using connections between pictorial representations and related equations involving a single unknown.
Given a mixture of multiplicative comparison and additive comparison problems,
l Apply their understanding of operations and a variety of representations to explain and justify the choice of operation in solving the problem. l Multiplicative comparison
l Additive comparison
l See (Tables 1 and 2) for problem types.Students know:
l Characteristics of multiplicative comparison problems and additive comparison problems,
l Addition, subtraction, multiplication, and division strategies.Students are able to:
l Compare and contrast mathematical contexts in order to determine the types of mathematical comparisons present,
l Represent multiplicative comparison contexts physically, pictorially, or symbolically,
l Strategically choose and apply a variety of representations to solve multiplicative comparison problems,
l Use symbols to represent unknown quantities in multiplicative comparison equations,
l Accurately compute products and quotients,
l Use mathematical language to communicate the connections among contexts involving all four operations and related physical, pictorial, or symbolic representations and justify solutions/solution paths.Students understand that:
l The operation of multiplication represents contexts of putting together equal sized groups or multiplicative comparisons,
l The operation of division represents contexts of partitioning into equal-sized shares or contexts of partitioning equally among a given number of groups or contexts involving multiplicative comparisons,
l The operation of subtraction represents taking apart, taking from, and additive comparison contexts,
l Mathematical problems (four basic operations) can be solved using a variety of strategies, models, representations,
l Variables represent unknown quantities when modeling mathematical situations algebraically.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53709" \t "_blank" ALEX Resources3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.Operations and Algebraic ThinkingUse the four operations with whole numbers to solve problems.4.OA.3Students:Given a variety of multistep word problems involving all four operations on whole numbers (including problems in which remainders must be interpreted),
l Explain and justify solutions using connections between the problems and related equations involving a single (letter) unknown,
l Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions. l "Problems in which remainders must be interpreted"Students know:
l Characteristics (see Table 1 and 2) of addition, subtraction, multiplication and division contexts,
l Addition, subtraction, multiplication, and division strategies,
l Strategies for mentally computing and estimating sums, differences, products, and quotients.Students are able to:
l Represent quantities and operations (addition, subtraction, multiplication, and division of whole numbers) physically, pictorially, or symbolically,
l Strategically choose and apply a variety of representations to solve addition, subtraction, multiplication, and division multi-step word problems,
l Use symbols to represent unknown quantities in equations that represent multi-step word problems,
l Use logical reasoning and connections between physical/pictorial representations to justify solutions and solution paths and to interpret remainders,
l Estimate answers in addition, subtraction, multiplication and division problems,
l Evaluate the reasonableness of answers by comparing actual answers to estimates.Students understand that:
l The operation of addition represents both putting together and adding to contexts,
l The operation of subtraction represents taking apart, taking from, and additive comparison contexts,
l The operation of multiplication represents contexts of putting together equal sized groups,
l The operation of division represents contexts of partitioning into equal-sized shares or contexts of partitioning equally among a given number of groups,
l The interpretation of the remainder in a division problem is dependent upon the original context and question,
l Variables represent unknown quantities when modeling mathematical situations algebraically,
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=53710" \t "_blank" ALEX Resources4. Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1100 is prime or composite.Operations and Algebraic ThinkingGain familiarity with factors and multiples.4.OA.4Students:Given any whole number from 1-100,
l Use knowledge of multiplication and division, models for multiplication, and logical reasoning to decompose the given number into all possible factor pairs,
l Determine if it is a multiple of a given single-digit number,
l Use knowledge and vocabulary of factors, factor pairs, and multiples to justify the classification of numbers as prime and composite.l Factor
l Factor pair
l Multiple
l Prime
l CompositeStudents know:
l Strategies for finding factor pairs,
l Vocabulary: factor, multiple, factor pair, prime, composite.Students are able to:
l Use models and logical reasoning to determine all possible factor pairs for a whole number between 1 - 100,
l Accurately compute products and quotients,
l Use an understanding of prime and composite to classify numbers.Students understand that:
l A whole number is a multiple of each of its factors,
l Numbers can be classified as prime, composite, or neither, based on their properties and characteristics.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53712" \t "_blank" ALEX Resources5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example: Given the rule Add 3 and the starting number 1, generate terms in the resulting sequence, and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.Operations and Algebraic ThinkingGenerate and analyze patterns.4.OA.5Students:Given a number or shape pattern in the form of a rule,
l Generate successive members of the pattern and identify apparent features of the pattern that were not explicit in the rule itself, (e.g., given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers),
l Explain informally why the numbers will continue to alternate in this way.
Students know:
l Strategies for generating and recording number or shape patterns from rules,
l Strategies for identifying and communicating shape and number patterns.Students are able to:
l Generate and record number and shape patterns from rules,
l Use logical reasoning and informal language to explain relationships between successive terms in a pattern.Students understand that:
l Patterns in the number system can be used with logical reasoning to make conjectures and solve problems,
l Identifying patterns in the number system leads to a deeper understanding of numbers, their characteristics, and their properties.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53714" \t "_blank" ALEX Resources6. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that 700 70 = 10 by applying concepts of place value and division.Number & Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.1Students:
l Explain, when asked, how the value of a digit differs in two successive place values, 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 modelsStudents are able to:
l Use logical reasoning to explain the relationship between two successive place values.Students understand that:
l Values of digits in any multi-digit number are based on patterns within a base-10 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=53717" \t "_blank" ALEX Resources7. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Number & Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.2Students:Given multi-digit whole numbers orally or in written form,
l Represent quantities in a variety of ways including words, base-ten numerals, and expanded form,
l Explain relationships among representations.
Given two numbers less than 1000,
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 form
l <, =, and > symbolsStudents know:
l Place values,
l Meanings and appropriate use of the mathematical symbols: <, =, >.Students are able to:
l Represent quantities in a number of forms including words, base-ten numerals, and expanded form,
l Compare whole numbers in equalities and inequalities.Students understand that:
l The same quantity can be represented with words, mathematical models, and expanded form based on the place value of the digits,
l The value of a digit in a multi-digit 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=53719" \t "_blank" ALEX Resources8. Use place value understanding to round multi-digit whole numbers to any place.Number & Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.3Students:Given any whole number,
l Justify the rounding of the number to a designated place value using models and place value vocabulary (e.g., 3,456 rounded to the nearest ten is 3460 because it is between the two tens 3450 and 3460, but closer to 3460).Students know:
l Place value vocabulary: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions,
l Place value models (e.g., number lines, place value blocks),
l Place value strategies for comparing and ordering numbers. Students are able to:
l Count by 10s, 100s, 1000s, 10,000s, etc.,
l Determine what is halfway between two consecutive multiples of powers of 10 (360 and 370, 36,000 and 37,000),
l Compare whole numbers,
l Use place value vocabulary, models, and logical reasoning to justify solutions to rounding problems.Students understand that:
l Rounding aids estimation of 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=53720" \t "_blank" ALEX Resources9. Fluently add and subtract multi-digit whole numbers using the standard algorithm.Number & Operations in Base TenUse place value understanding and properties of operations to perform multi-digit arithmetic. 2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.4Students:Given a context which calls for the addition or subtraction of two whole numbers,
l Choose the most appropriate strategy for computing the answer,
l Produce accurate results efficiently using the standard algorithm when appropriate. l Standard algorithms (addition and subtraction)Students know:
l Strategies for computing answers to addition and subtraction problems.Students are able to:
l Strategically choose and apply appropriate methods for adding and subtracting,
l Accurately find sums/differences using the standard addition and subtraction algorithms.Students understand that:
l Mathematical problems can be solved using a variety of strategies, models, and representations,
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 addition and subtraction 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 multi-digit 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=53722" \t "_blank" ALEX Resources10. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Number & Operations in Base TenUse place value understanding and properties of operations to perform multi-digit arithmetic. 2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.5Students:Given multiplication problems (four-digit whole number by one-digit whole number, or two-digit numbers by two-digit numbers),
l Use strategies based on multiplication models (e.g., rectangular arrays, open arrays, area models), place value and properties of operations to find and justify solutions and solution paths.Students know:
l Place value models for multiplying numbers (e.g., area models, open arrays, place value blocks),
l Strategies for finding products based on place value and properties of operations.Students are able to:
l Use strategies based on an understanding of place value and properties of operations to find products,
l Use a variety of place value models of multiplication problems to justify solutions and solution paths.Students understand that:
l Multiplication problems can be solved using a variety of strategies, models, and representations.
l Efficient application of multiplication computation strategies is based on the numbers and operations in the problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53723" \t "_blank" ALEX Resources11. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Number & Operations in Base TenUse place value understanding and properties of operations to perform multi-digit arithmetic. 2(2Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000)4.NBT.6Students:Given division problems (up to four-digit dividends and one-digit divisors),
l Find whole-number quotients and remainders using strategies that involve using 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.Students 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 numbers and operations in the problems,
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=53724" \t "_blank" ALEX Resources12. Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.Number & OperationsFractionsExtend understanding of fraction equivalence and ordering. 3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.1Students:Given a fraction a/b,
l Use visual models to create equivalent fractions and explain the generalized pattern, a/b = (n x a) / (n x b),
l Use the generalized pattern to generate equivalent fractions.Students know:
l Strategies for partitioning wholes,
l Strategies for representing fractional parts of a whole,
l Multiplication and division strategies.Students are able to:
l Represent fractional quantities using visual models,
l Write fractions related to visual models,
l Generate equivalent fractions by modeling the original fraction and further partitioning shares,
l Explain the equivalence of fractions and the generalization a/b = (n x a) / (n x b) using logical reasoning, patterns, and visual models,
l Generate equivalent fractions using the generalization a/b = (n x a) / (n x b).Students understand that:
l Two fractions are equivalent if they are the same size share (represent the same amount) of the same whole or name the same point on a number line.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53726" \t "_blank" ALEX Resources13. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.Number & OperationsFractionsExtend understanding of fraction equivalence and ordering. 3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.2Students:Given two fractions (having denominators of 2,3, 4, 5, 6, 8, 10, 12, 100),
l 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 extra-large pizza or "Susie said her 1/6 pizza was bigger than my 1/2 pizza. Is she correct?").l Benchmark fractionStudents know:
l Strategies for representing fractional quantities,
l Strategies for comparing fractions (e.g., comparing numerators of like fractions, comparing denominators of fractions with like numerators, creating common denominators, and comparing to landmark fractions such as 1/2).Students are able to:
l Strategically choose and apply representations to compare two fractions,
l Record the comparison of two fractions using <, =, and > notation,
l Use mathematical language and logical reasoning to justify solutions.Students understand that:
l Two fractions are equivalent if they are the same size share (represent the same amount) of the same whole or name the same point on a number line,
l Comparisons of fractions are valid only when the two fractions refer to the same whole.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53727" \t "_blank" ALEX Resources14. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.Number & OperationsFractionsBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.3Students:Given any fraction or mixed number,
l Connect their understanding of unit fractions and their understanding of addition to decompose the given fraction or mixed number into the sum of smaller fractions/mixed numbers, including unit fractions.
Given a variety of addition and subtraction word problems involving fractions with like denominators,
l Explain and justify solutions using connections among unit fractions, pictorial representations, and related equations involving a single unknown.Students know:
l Characteristics of addition and subtraction contexts for whole numbers and like fractions,
l Strategies for representing and solving addition and subtraction problems involving 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 like fractions,
l Use symbols to represent unknown quantities in addition and subtraction equations and solve such equations,
l Accurately compute sums and differences of fractions,
l Use logical reasoning and connections among representations to justify 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 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,
l Mathematical problems (addition and subtraction of fractions) can be solved using a variety of strategies, models, representations,
l Variables represent unknown quantities when modeling mathematical situations algebraically.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53729" \t "_blank" ALEX Resources15. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. Example: Use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Example: Use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. Example: If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?Number & OperationsFractionsBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.4Students:Given any fraction,
l Use their knowledge of multiples of whole numbers to connect a visual representation of a non-unit fraction to a product of a whole number and a unit fraction.
Given a multiplication problem involving a whole number and a fraction,
l Use a visual representation of the problem, understanding of unit fractions, and properties of the operation of multiplication to justify n x (a/b) = (n x a)/b,
Given a word problem involving the multiplication of a fraction by a whole number,
l Explain and justify solutions and the reasonableness of solutions using connections among unit fractions, visual representations, and an understanding of multiplication.l MultipleStudents know:
l Associative Property 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 Represent and rename fractional quantities as multiples of whole numbers and unit fractions,
l Strategically choose and apply a variety of representations to solve multiplication word problems involving whole numbers and fractions,
l Apply knowledge of the Associative Property of Multiplication with knowledge of unit fractions to accurately compute products of whole numbers and fractions,
l Use logical reasoning and connections among representations to justify solutions, reasonableness of solutions, and solution paths.Students understand that:
l A fraction a/b is a multiple of the unit fraction 1/b, (e.g.., a/b = a x 1/b),
l Multiplication may be viewed as putting together equal-sized groups,
l Mathematical problems (multiplication of whole numbers and fractions) can be solved using a variety of strategies, models, and representations,
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=53735" \t "_blank" ALEX Resources16. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)Number & OperationsFractionsUnderstand decimal notation for fractions, and compare decimal fractions.3(3xyl
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QR`acd'()+/125?@ACFGHKNPQTYZ@]@ZA}}}}}{U&h;"B*CJH*OJQJ^JaJph&h;"B*CJH*OJQJ^JaJphh;"CJaJ'h;"0JB*CJOJQJ^JaJph,jh;"B*CJOJQJU^JaJph)h;"5B*CJOJQJ\^JaJph#h;"B*CJOJQJ^JaJph*cd@@( $Ifgd,6kd$$If *#*29D 0/0-$$$$2-4ayt;" Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.5Students:Given a fraction with a denominator of 10,
l Use visual models and the generalized pattern, a/b = (n x a) / (n x b) to find the equivalent fraction with a denominator of 100.
Given an addition problem with two fractions with respective denominators of 10 and 100,
l Compute the sum by expressing the fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and then adding.Students know:
l Strategies for generating equivalent fractions,
l Strategies for adding fractions with like denominators.Students are able to:
l Represent fractional quantities using visual models,
l Write fractions related to visual models,
l Generate equivalent fractions using the generalization a/b = (n x a) / (n x b).
l Accurately add fractions.Students understand that:
l Addition may be viewed as joining or adding to,
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 The operations of addition and subtraction are performed on counts with like names/denominators and that the sum or difference retains the same name/denominator.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53743" \t "_blank" ALEX Resources17. Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.Number & Operations FractionsUnderstand decimal notation for fractions, and compare decimal fractions.3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.6Students:Given a fraction with a denominator of 10 or 100,
l Write the equivalent fraction using decimal notation.
Given a fraction in decimal notation (tenths or hundredths),
l Write the equivalent fraction.
Given a fraction in decimal notation,
l Create a number line diagram and justify the placement of the fraction on the number line.Students know:
l Decimal place value,
l Decimal notation,
l Fraction notation.Students are able to:
l Represent fractional quantities including decimals using visual models,
l Write fractions including decimals related to visual models.Students understand that:
l Two fractions are equivalent if they are the same size share (represent the same amount) of the same whole or name the same point on a number line.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53745" \t "_blank" ALEX Resources18. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.Number & Operations FractionsUnderstand decimal notation for fractions, and compare decimal fractions.3(3 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)4.NF.7Students:Given two decimals,
l Use logical reasoning and a variety of models to represent and order the decimals (using <, =, >) and justify their answers,
l Communicate the reason why it is not valid to make a comparison between decimals that refer to different wholes (e.g., why it may not be valid to say 0.5 > 0.25 if 0.5 refers to a small pizza and the 0.25 refers to an extra-large pizza, or "Susie said her 0.25 pizza was bigger than my 0.5 pizza. Is she correct?").Students know:
l Strategies for representing decimal quantities,
l Strategies for comparing decimals (e.g., comparing numerators of like decimals creating common denominators, comparing to landmark fractions such as 1/2).Students are able to:
l Strategically choose and apply representations to compare two decimals,
l Record the comparison of two decimals using <, =, and > notation,
l Use mathematical language and logical reasoning to justify solutions.Students understand that:
l Two fractions (decimals) are equivalent if they are the same size share (represent the same amount) of the same whole or name the same point on a number line,
l Comparisons of fractions (decimals) are valid only when the two fractions (decimals) refer to the same whole.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53747" \t "_blank" ALEX Resources19. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. Example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...Measurement & DataSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.4.MD.1Students:Given a measurement in a relatively large unit (e.g., km, m, kg, lb., l, hr., min.),
l Accurately convert the measurement to an equivalent measurement using smaller units (e.g., m, cm, g, oz., ml, min., sec.) within the same measurement system through the use of a two column table. (e.g., Express the length of a 4 ft. snake as 48 inches by generating a conversion table for feet and inches listing the number pairs (1,12), (2,24), etc.).Students know:
l Relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec.,
l Strategies for converting from relatively large units of measure to smaller units of measure within the same system including multiplication and two-column tables.Students are able to:
l Multiply or use repeated addition to accurately generate number pairs for conversion tables,
l Interpret tables to solve problems.Students understand that:
l The relationships among units within a system of measurement (e.g., metric length, time, standard mass, etc.) are multiplicative comparisons.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53749" \t "_blank" ALEX Resources20. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.Measurement & DataSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.4.MD.2Students:Given word problems involving distances (km, m, cm), intervals of time (hr., min., sec.), liquid volumes (l, ml), mass (kg, g, lb., oz.), and money, including problems involving simple fractions or decimals and problems involving measurements in different units (within the same measurement system, conversions from larger to smaller units only),
l Justify choices of units, solve the problem, and justify solutions. Students know:
l Relative sizes of measurement units within one system of units including: km, m, cm; kg, g; lb., oz.; L, mL; hr., min., sec.,
l Strategies for converting from relatively large units of measure to smaller units of measure within the same system including multiplication and two-column tables,
l Strategies for solving word problems involving measurement including number line representations.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 justify solution paths.Students understand that:
l The relationships among units within a system of measurement (e.g., metric length, time, standard mass, etc.) are multiplicative comparisons,
l The size of the unit of measurement and the number of units are inversely related,
l Addition and subtraction of measurements require measurements in the same unit and that the unit is maintained in the answer.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53751" \t "_blank" ALEX Resources21. Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. Example: Find the width of a rectangular room given the area of the flooring and the length by viewing the area formula as a multiplication equation with an unknown factor.Measurement & DataSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.4.MD.3Students:Given real world and mathematical problems involving area and perimeter of rectangular regions,
l Use a variety of representations (e.g., models, drawings, and equations) based on area and perimeter formulas to find and justify solutions and solution paths.l Area
l PerimeterStudents know:
l Strategies for representing contexts involving area and perimeter of rectangular regions,
l Strategies including standard formulas (A = L x W, P = 2L + 2W, P = L + L + W + W or P = 2 (L +W)) for computing measurements related to the area and perimeter of rectangular regions.Students are able to:
l Discriminate between contexts asking for perimeter and those asking for area measurements,
l Strategically choose and apply appropriate methods for representing and calculating ,
l Accurately compute measurements within area and perimeter of rectangular region problems.Students understand that:
l Perimeter is measured in length units and is the distance around a 2-D figure,
l The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure and the formula for the area of a rectangle is a result of this understanding,
l The length and width of a rectangular region are related to both the area and the perimeter of that region,
l Addition and subtraction of measurements require measurements in the same unit and that the unit is maintained in the answer,
l The multiplication and division of measurements result in the units also being multiplied or divided and that a new unit is created for the answer.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53752" \t "_blank" ALEX Resources22. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. Example: From a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.Measurement & DataRepresent and interpret data.4.MD.4Students:
l Make and use line plots (with the scale matching the unit of measure) to represent data generated by measuring lengths (to the nearest eighth inch) of several objects or by making repeated measurements,
l Use information from data displays to generate questions and solve problems including problems that involve addition and subtraction of fractions.l Line plotStudents know:
l Techniques for constructing line plots,
l Standard units and related tools for measuring length,
l Strategies for adding and subtracting fractions.Students are able to:
l Use standard units and related tools to measure length to the nearest eighth inch,
l Organize and represent length measurement data on a line plot,
l Choose and apply appropriate strategies to solve problems generated by conjectures from examining data displays,
l Apply strategies for solving problems involving adding and subtracting fractions.Students understand that:
l Questions concerning mathematical 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=53755" \t "_blank" ALEX Resources23. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint of the rays by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.Measurement & DataGeometric measurement: understand concepts of angle and measure angles.4.MD.5Students:
l Justify the result of measuring angles (in isolation and as parts of polygons) as a number of one-degree angles contained between the rays that define the angle and including language to describe the number of degrees through which the angle has "turned." l Angle
l Circular arc
l Ray
l EndpointStudents know:
l Measurable attributes of geometric shapes, specifically angle size,
l Units of measurement, specifically one-degree angle (degrees).Students are able to:
l Communicate the process of measuring angles and the relationship of the measurement to a one-degree angle as the unit of measure. Students understand that:
l The rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53758" \t "_blank" ALEX Resources24. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Measurement & DataGeometric measurement: understand concepts of angle and measure angles.4.MD.6Students:Given a variety of angles,
l Accurately measure the angles in whole number degrees using a protractor.
Given a variety of angle measurements,
l Use a protractor and ruler to sketch the corresponding angles.l Angle
l ProtractorStudents know:
l Measurable attributes of geometric shapes, specifically angle size,
l Units of measurement, specifically one-degree angle (degrees),
l Procedures for using a protractor.Students are able to:
l Use a protractor to measure angles in whole number degrees,
l Use a protractor and ruler to sketch angles of a given measure.Students understand that:
l The rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53761" \t "_blank" ALEX Resources25. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.Measurement & DataGeometric measurement: understand concepts of angle and measure angles.4.MD.7Students:Given real world and mathematical problems involving angle measurement,
l Use a variety of representations (including diagrams and single unknown equations) to show angle measure as additive and to find and justify solutions and solution paths. l AngleStudents know:
l Measurable attributes of geometric shapes, specifically angle size,
l Units of measurement, specifically one-degree angle (degrees),
l Strategies for representing and solving real world problems,
l Strategies for finding sums, differences, products, and quotients of whole numbers.Students are able to:
l Strategically choose and apply methods for finding sums, differences, products, and quotients of whole numbers,
l Accurately compute sums, differences, products and quotients of whole numbers.Students understand that:
l The rotation of an angle is measured by the number of one-degree angles that exactly cover the rotation of the angle,
l Representations for solving problems are chosen 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=53762" \t "_blank" ALEX Resources26. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.GeometryDraw and identify lines and angles, and classify shapes by properties of their lines and angles.4.G.1Students:Given a written or an oral prompt,
l Strategically choose and use tools to draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, and parallel lines to specifications.
Given 2-D figures,
l Trace or highlight specific components such as angles, line segments, rays, perpendicular lines, and parallel lines.l Lines
l Line segments
l Rays
l Angles
l Perpendicular
l ParallelStudents know:
l Defining characteristics of geometric figures: points, lines, line segments, angles (right, acute, and obtuse), parallel lines, and perpendicular lines.Student are able to:
l Strategically choose and use tools to draw 2-D geometric figures,
l Decompose 2-D figures in a variety of ways in order to name and identify component parts.Students understand that:
l Shapes are categorized based on attributes they possess in common such as; angle size, side length, side relationships (parallel and perpendicular).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53764" \t "_blank" ALEX Resources27. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.GeometryDraw and identify lines and angles, and classify shapes by properties of their lines and angles.4.G.2Students:Given a variety of 2-D figures,
l Justify the classification of the shapes based on the presence or absences of parallel lines or perpendicular lines, or the presence or absence of angles of a specified size.l Parallel
l Perpendicular
l Right triangleStudents know:
l Defining characteristics of geometric figures: quadrilateral, trapezoid, rhombus, parallelogram, rectangle, square, right triangle, acute triangle, obtuse triangle, angles (right, acute, and obtuse), parallel lines, and perpendicular lines.Students are able to:
l Justify classification of shapes based on the characteristics of their attributes.Students understand that:
l Shapes are categorized based on attributes they possess in common such as: angle size, side length, side relationships (parallel and perpendicular).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53765" \t "_blank" ALEX Resources28. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.GeometryDraw and identify lines and angles, and classify shapes by properties of their lines and angles.4.G.3Students:Given a variety of 2-D figures,
l Justify the existence or non-existence of line symmetry within the figures by drawing the lines of symmetry.l Line symmetryStudents know:
l Defining characteristics of line symmetry.Students are able to:
l Draw lines of symmetry and justify their placement.Students understand that:
l A line of symmetry divides a shape into two parts such that when folded on the line the two parts match.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53766" \t "_blank" ALEX Resources
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
Grade 4 Mathematics CCRS Standards and Alabama COS
Franklin County Schools
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