4th grade mathematics curriculum map for common...

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4th Grade Mathematics Curriculum Map For CommonCore State Standards (CCK12)

§ Content Standards

1 Place Value• Ones, Tens, Hundreds, Thousands• Ten-Thousands, Hundred-Thousands• Millions• Comparing Numbers Using Place Value

4.NBT.1.: Recognize that in a multi-digit whole number, a digit in oneplace represents ten times what it represents in the place to its right. Forexample, recognize that 700 / 70 = 10 by applying concepts of placevalue and division. (SBAC Summative Assessment Target: 1.09, 4.03)

4.NBT.2.: Read and write multi-digit whole numbers using base-tennumerals, number names, and expanded form. Compare two multi-digitnumbers based on meanings of the digits in each place, using >, =, and. symbols to record the results of comparisons. (SBAC SummativeAssessment Target: 1.06, 1.09, 4.03)

2 Comparing and Rounding Numbers• Comparing Numbers• Introduction to Rounding• Concepts of Rounding• Understanding Rounding

4.OA.4.: Find all factor pairs for a whole number in the range 1-100.Recognize that a whole number is a multiple of each of its factors.Determine whether a given whole number in the range 1-100 is amultiple of a given one-digit number. Determine whether a given wholenumber in the range 1-100 is prime or composite. (SBAC SummativeAssessment Target: 1.07, 1.08, 2.01, 3.01, 4.01, 4.02)


4.NBT.3.: Use place value understanding to round multi-digit wholenumbers to any place. (SBAC Summative Assessment Target: 1.10)

3 Money and Decimals• Decimals, Dimes, and Pennies• Introduction to Money• Making Change• Adding Money

4.NBT.1.: Recognize that in a multi-digit whole number, a digit in oneplace represents ten times what it represents in the place to its right. Forexample, recognize that 700 / 70 = 10 by applying concepts of placevalue and division. (SBAC Summative Assessment Target: 1.09, 4.03)


4.MD.2.: Use the four operations to solve word problems involvingdistances, intervals of time, liquid volumes, masses of objects, andmoney, including problems involving simple fractions or decimals, andproblems that require expressing measurements given in a larger unit interms of a smaller unit. Represent measurement quantities usingdiagrams such as number line diagrams that feature a measurementscale. (SBAC Summative Assessment Target: 2.03, 3.04)


4 Column Addition and Subtraction• Column Addition• Column Addition of Three Numbers• Column Subtraction• Inverse Operations

4.OA.3.: Solve multistep word problems posed with whole numbers andhaving whole-number answers using the four operations, includingproblems in which remainders must be interpreted. Represent theseproblems using equations with a letter standing for the unknownquantity. Assess the reasonableness of answers using mentalcomputation and estimation strategies including rounding. (SBACSummative Assessment Target: 2.01, 3.01)

4.NBT.4.: Fluently add and subtract multi-digit whole numbers using thestandard algorithm. (SBAC Summative Assessment Target: 1.11)


5 Translating Words into Expressions• Translating Words to Expressions• Order of Operations• Unknown Numbers• Working with Number Sentences

4.OA.2.: Multiply or divide to solve word problems involvingmultiplicative comparison, e.g., by using drawings and equations with asymbol for the unknown number to represent the problem, distinguishingmultiplicative comparison from additive comparison. (SBAC SummativeAssessment Target: 1.05, 1.06, 4.01)




6 Introduction to Multiplication• Multiplication as Repeated Addition• Multiples of 2, 4, and 8• Multiples of 3, 6, and 9• Multiples of 5, 7, and 10




4.NBT.5.: Multiply a whole number of up to four digits by a one-digitwhole number, and multiply two two-digit numbers, using strategiesbased on place value and the properties of operations. Illustrate andexplain the calculation by using equations, rectangular arrays, and/orarea models. (SBAC Summative Assessment Target: 1.11, 3.02, 4.03)


7 Understanding Multiplication• Multiplication using Area• Variables in Multiplication• Distributive Property of Multiplication• Multiplying on a Number Line






4.NBT.6.: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on placevalue, the properties of operations, and/or the relationship betweenmultiplication and division. Illustrate and explain the calculation by usingequations, rectangular arrays, and/or area models. (SBAC SummativeAssessment Target: 1.11, 3.02, 4.03)



8 Multiplication with Partial Products• Multiplying by 10, 100, and 1,000• Distributive Property of Multiplication• Creating Partial Products• Multiplying 1-Digit by 2-Digit Numbersusing Partial Products







9 Multiplication with Regrouping• 1-Digit by 3- and 4-Digit Multiplication withPartial Products• 1-Digit by 2-Digit Multiplication withRegrouping• 1-Digit by 3- and 4-Digit Multiplication withRegrouping• Regrouping Review






10 2-Digit by 2-Digit Multiplication• 2-Digit by 2-Digit Multiplication Review• Multiplication of Multiples of 10 byMultiples of 10 and 100.• Introduction to 2-Digit by 2-DigitMultiplication• 2-Digit by 2-Digit Multiplication Practice






11 Money, Decimals, & Story Problems• Multiplying Money and Decimals• Solving Story Problems• Solving Multi-Step Story Problems• Multi-Step Story Problem Practice





12 Introduction to Division• Understanding Division• Fact Families• Division Facts• Division Facts





13 Concepts of Division• Dividing by Multiples of 10, 100, and 1,000• Remainders• Introduction to Long Division (Partial-Quotient Division Algorithm)• Long Division with Multiples of 10





14 Long Division• Long Division with 3-Digit Dividends• Long Division with 3-Digit Dividends• Long Division with Remainders• Dividing Decimals and Money





15 Understanding Long Division• Long Division with 4-Digit Dividends• Long Division with 4-Digit Dividends withRemainders• Long Division with 2-Digit Divisors• Testing Your Results with InverseOperations




16 Introduction to Fractions• Parts of a Whole• Counts of Unit Fractions• Improper Fractions• Adding Fractions with Like Denominators

4.NF.3(a): Understand addition and subtraction of fractions as joiningand separating parts referring to the same whole. (SBAC SummativeAssessment Target: 1.12, 1.14, 2.02, 3.03, 4.04)

4.NF.3(b): Decompose a fraction into a sum of fractions with the samedenominator in more than one way, recording each decomposition by anequation. 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. (SBAC Summative Assessment Target: 1.12, 1.14, 2.02,3.03, 4.04)

4.NF.3(d): Solve word problems involving addition and subtraction offractions referring to the same whole and having like denominators, e.g.,by using visual fraction models and equations to represent the problem.(SBAC Summative Assessment Target: 1.12, 1.14, 2.02, 3.03, 4.04)

4.NF.4(a): Understand a fraction a/b as a multiple of 1/b. For example,use a visual fraction model to represent 5/4 as the product 5 x (1/4),recording the conclusion by the equation 5/4 = 5 x (1/4). (SBACSummative Assessment Target: 1.14, 2.02, 3.03, 4.04)


17 Fraction Addition and Subtraction• Adding Fractions with Like Denominators• Subtracting Fractions with LikeDenominators• Adding and Subtracting Mixed Numbers• Mixed Numbers

4.NF.1.: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n xb) by using visual fraction models, with attention to how the number andsize of the parts differ even though the two fractions themselves are thesame size. Use this principle to recognize and generate equivalentfractions. (SBAC Summative Assessment Target: 1.12)

4.NF.2.: Compare two fractions with different numerators and differentdenominators, e.g., by creating common denominators or numerators,or by comparing to a benchmark fraction such as 1/2. Recognize thatcomparisons are valid only when the two fractions refer to the samewhole. Record the results of comparisons with symbols >, =, or , andjustify the conclusions, e.g., by using a visual fraction model. (SBACSummative Assessment Target: 1.13)


4.NF.3(b): Decompose a fraction into a sum of fractions with the samedenominator in more than one way, recording each decomposition by anequation. 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. (SBAC Summative Assessment Target: 1.12, 1.14, 2.02,3.03, 4.04)

4.NF.3(c): Add and subtract mixed numbers with like denominators, e.g.,by replacing each mixed number with an equivalent fraction, and/or byusing properties of operations and the relationship between addition andsubtraction. (SBAC Summative Assessment Target: 1.12, 1.14, 2.02,3.03, 4.04)




18 Equivalent Fractions• Equivalent Fractions• Complicating Fractions• Simplifying Fractions• Simplifying Fractions





19 Common Denominators• Comparing Fractions• Comparing Fractions by Getting aCommon Denominator• Adding Fractions with UnlikeDenominators• Adding Fractions with UnlikeDenominators







20 Fraction Multiplication• Fractions in Story Problems• Multiplying Fractions by Whole Numbers• Multiplying Fractions by Whole Numbers• Fractions in Story Problems



4.NF.3(c): Add and subtract mixed numbers with like denominators, e.g.,by replacing each mixed number with an equivalent fraction, and/or byusing properties of operations and the relationship between addition andsubtraction. (SBAC Summative Assessment Target: 1.12, 1.14, 2.02,3.03, 4.04)



4.NF.4(b): Understand a multiple of a/b as a multiple of 1/b, and use thisunderstanding to multiply a fraction by a whole number. For example,use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizingthis product as 6/5. (In general, n x (a/b) = (n x a)/b.) (SBAC SummativeAssessment Target: 1.14, 2.02, 3.03, 4.04)

4.NF.4(c): Solve word problems involving multiplication of a fraction by awhole number, e.g., by using visual fraction models and equations torepresent the problem. For example, if each person at a party will eat3/8 of a pound of roast beef, and there will be 5 people at the party, howmany pounds of roast beef will be needed? Between what two wholenumbers does your answer lie? (SBAC Summative Assessment Target:1.14, 2.02, 3.03, 4.04)


21 Fractions and Decimals• Ordering Fractions on a Number Line• Relationship Between Decimals andFractions• Adding Decimals• Ordering Decimals on a Number Line


4.NF.5.: Express a fraction with denominator 10 as an equivalentfraction with denominator 100, and use this technique to add twofractions with respective denominators 10 and 100. For example,express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (SBACSummative Assessment Target: 1.12)

4.NF.6.: Use decimal notation for fractions with denominators 10 or 100.For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters;locate 0.62 on a number line diagram. (SBAC Summative AssessmentTarget: 1.12)

4.NF.7.: Compare two decimals to hundredths by reasoning about theirsize. Recognize that comparisons are valid only when the two decimalsrefer to the same whole. Record the results of comparisons with thesymbols >, =, or , and justify the conclusions, e.g., by using a visualmodel. (SBAC Summative Assessment Target: 1.13)

22 Lines and Angles• Lines, Line Segments, and Rays• Angles• Measuring Angles• Adding Angles

4.MD.5(a): An angle is measured with reference to a circle with itscenter at the common endpoint of the rays, by considering the fractionof the circular arc between the points where the two rays intersect thecircle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. (SBAC SummativeAssessment Target: 1.17, 3.05)

4.MD.5(b): An angle that turns through n one-degree angles is said tohave an angle measure of n degrees. (SBAC Summative AssessmentTarget: 1.17, 3.05)

4.MD.6.: Measure angles in whole-number degrees using a protractor.Sketch angles of specified measure. (SBAC Summative AssessmentTarget: 1.17, 3.05)

4.MD.7.: Recognize angle measure as additive. When an angle isdecomposed into non-overlapping parts, the angle measure of thewhole is the sum of the angle measures of the parts. Solve addition andsubtraction problems to find unknown angles on a diagram in real worldand mathematical problems, e.g., by using an equation with a symbol forthe unknown angle measure.

4.G.1.: Draw points, lines, line segments, rays, angles (right, acute,obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. (SBAC Summative Assessment Target: 1.17, 3.05)


23 Polygons• Introduction to Polygons• Quadrilaterals• Triangles• Perimeter

4.MD.3.: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. For example, find the width of arectangular room given the area of the flooring and the length, byviewing the area formula as a multiplication equation with an unknownfactor. (SBAC Summative Assessment Target: 1.16, 2.03, 2.04, 3.04)

4.G.2.: Classify two-dimensional figures based on the presence orabsence of parallel or perpendicular lines, or the presence or absenceof angles of a specified size. Recognize right triangles as a category,and identify right triangles. (SBAC Summative Assessment Target: 1.17,3.05)

24 Area and Volume• Area of Rectangles• Splitting Areas• Surface Area• Volume

4.MD.3.: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. For example, find the width of arectangular room given the area of the flooring and the length, byviewing the area formula as a multiplication equation with an unknownfactor. (SBAC Summative Assessment Target: 1.16, 2.03, 2.04, 3.04)

25 Symmetry and Congruence• Reflection Symmetry• Rotational Symmetry• Congruence and Similarity• Turn, Flip, and Slide

4.G.3.: Recognize a line of symmetry for a two-dimensional figure as aline across the figure such that the figure can be folded along the lineinto matching parts. Identify line-symmetric figures and draw lines ofsymmetry. (SBAC Summative Assessment Target: 1.17, 3.05)

26 Graphs• Pictographs and Bar Graphs• Line Plots• Interpreting Line Graphs• Making Line Graphs

MP.4.: Model with mathematics.

4.MD.4.: Make a line plot to display a data set of measurements infractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition andsubtraction of fractions by using information presented in line plots. Forexample, from a line plot find and interpret the difference in lengthbetween the longest and shortest specimens in an insect collection.

27 Length, Weight, Capacity• Measuring Lengths• Adding and Subtracting Lengths• Measuring Weight• Measuring Capacity

4.MD.1.: Know relative sizes of measurement units within one system ofunits including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within asingle system of measurement, express measurements in a larger unitin terms of a smaller unit. Record measurement equivalents in a two-column table. For 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 tablefor feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...(SBAC Summative Assessment Target: 1.15)

28 Time and Temperature• Units of Time• Adding and Subtracting Lengths of Time• Elapsed Time• Temperature

29 Metric Length• Converting Metric Lengths• Converting between Metric andCustomary Lengths• Fractions and Decimals• Metric Prefixes



30 Mass and Capacity• Grams and Kilograms• Comparing Decimal Masses• Liters and Milliliters• Comparing Decimal Liters

4.NF.7.: Compare two decimals to hundredths by reasoning about theirsize. Recognize that comparisons are valid only when the two decimalsrefer to the same whole. Record the results of comparisons with thesymbols >, =, or , and justify the conclusions, e.g., by using a visualmodel. (SBAC Summative Assessment Target: 1.13)


31 Statistics• Range• Median• Mode• Mean

32 Probability• Impossible, Unlikely, Likely, Certain• Simple Events• Joint Probability• Predictions

33 Factors• Greatest Common Factor• Least Common Multiple• Prime and Composite Numbers• Factor Trees



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