DCSD Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. : 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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. We will interpret a multiplication equation as a comparison. We will interpret a verbal comparison and turn it into an equation. equation factor interpret multiple multiplicative comparison product The following links can be useful for all CCSS: http://www.dpi.state.nc.us/acre /standards/common-coretools/#unmath https://www.georgiastandards. org/common- Core/Pages/Math-K-5.aspx http://illuminations.nctm.org/le ssons.aspx http://catalog.mathlearningcen ter.org/free Valuable CCSS resource: Teaching Student-Centered Mathematics 3-5 Van de Walle Textbook ISBN 0205408443 Unit 1,3, 8, 9 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. : 4.OA.2 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. (See Glossary, Table 2.) We will solve word problems using multiplication. We will solve word problems using division. We will represent word problems and/or equations with drawings and symbols. We will understand the difference between multiplicative and additive comparisons. additive comparison multiplicative comparison symbol unknown Unit 1,3, 8, 9 Douglas County School District Page 1 June 2013
DCSD Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. : 4.OA.3 Solve multistep word problems posed with whole numbers and having wholenumber 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. We will add, subtract, multiply and divide with or without remainders within word problems. We will identify key words to decide which operation(s) to use to solve a word problem. We will explain and interpret remainders. We will write an equation to solve a word problem using a letter to represent the unknown number. We will determine if an answer is reasonable based on the question for the problem. *Ongoing all year equation estimation estimation strategies mental math quantity remainders rounding unknown number Unit 1,3, 8, 9 We will justify our answers using mental math and estimation including rounding. Douglas County School District Page 2 June 2013
DCSD Operations and Algebraic Thinking Gain familiarity with factors and multiples. : 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 a multiple of a given one-digit number. Determine whether a given whole number in the range 1 100 is prime or composite. We will find factor pairs for any whole number up to 100. We will recognize that a whole number is a multiple of each of its factors. We will determine if a whole number is a multiple of another number. We will determine if a whole number is prime or composite. composite factor factor pairs multiple prime Unit 1,3, 8, 9 Numbers and Operations in Base Ten Generalize place value for multi- digit whole numbers. whole numbers less than or equal to 1,000,000) : 4.NBT.1 Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division. We will recognize that a digit in one place represents 10 times what it represents in the place to its right. base ten system place value place value positions (hundreds, ten thousands, millions, etc.) Units 2, 3, 4, 5, 6, 7, 8, 9 Douglas County School District Page 3 June 2013
DCSD Numbers and Operations in Base Ten Generalize place value for multi- digit whole numbers. whole numbers less than or equal to 1,000,000) : 4.NBT.2 Read and write multi-digit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. We will use the symbols <, >, and = to record the correct relationship between two numbers up to one million. We will read and write whole numbers up to one million in base-ten numerals, expanded, and word form. equal, = expanded form greater than, > less than, < numeral place value positions (ten thousands, millions, etc.) Units 2, 3, 4, 5, 6, 7, 8, 9 Numbers and Operations in Base Ten Generalize place value for multi- digit whole numbers.. : 4.NBT.3 Use place value to round multi-digit whole numbers to any place. We will use place value to round multi-digit whole numbers. We will determine whether the digit being rounded increases or stays the same based on the value of the digit to the right. estimate place value positions (hundred thousand, million, etc.) round/rounding ten thousand value whole number Units 2, 3, 4, 5, 6, 7, 8, 9 whole numbers less than or equal to 1,000,000) Douglas County School District Page 4 June 2013
DCSD Numbers and Operations in Base Ten Use place value and properties of operations to perform multi-digit arithmetic. : 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm We will add and subtract multi-digit whole numbers. addition algorithm difference inverse operation regrouping (borrowing, carrying) standard algorithm subtraction sum Units 2, 3, 4, 5, 6, 7, 8, 9 whole numbers less than or equal to 1,000,000) Douglas County School District Page 5 June 2013
DCSD Measurement and Data Geometric measurement: understand concepts of angle and measure angles. : 4.MD.5a Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:. 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. We will understand that an angle is made up of two rays that share a common endpoint. We will understand that a circle has a total of 360 degrees and can be broken into separate angles. We will understand that all of the separate angles within a circle will add up to 360 degrees. We will understand that an angle that turns through 1/360 degree is called a "one degree" angle. Common endpoint Vertex Ray Angle Geometric shapes central angle circular arc degree endpoint equidistant line segment point quadrant turn Units 4, 5, 6, 7, 8, 9 Measurement and Data Geometric measurement: understand concepts of angle and measure angles. : 4.MD.5b Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through n one-degree angles is said to have an angle measure of n degrees. We will understand that larger angles are composed of many one-degree angles. We will understand that an angle that turns through "n" one-degree angles has a measure of "n" degrees. We will understand that "n" can stand for any number between and including 1 and 360. angle counterclockwise "n" degrees one-degree angle turn Units 4, 5, 6, 7, 8, 9 Douglas County School District Page 6 June 2013
DCSD Measurement and Data Geometric measurement: understand concepts of angle and measure angles. : 4.MD.6- Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. We will measure angles in degrees from 0-360 using a protractor. We will draw an angle of a specific measurement. angle degree protractor ray Units 4, 5, 6, 7, 8, 9 Measurement and Data Geometric measurement: understand concepts of angle and measure angles. : 4.MD.7 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 and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. We will understand that the interior angles (inside angles) of a triangle add up to 180 degrees. We will understand that the interior angles (inside angles) of a quadrilateral add up to 360 degrees. I know an angle can be decomposed into parts. We will decompose an angle into angle parts and add the angles parts to get the sum of the whole angle. acute angle additive angle decomposed non-overlapping obtuse angle right angle straight angle Interior angles Units 4, 5, 6, 7, 8, 9 We will use addition and subtraction to find the unknown angles of a triangle or quadrilateral in a real world problem. We will write an equation to solve for a missing angle. Douglas County School District Page 7 June 2013
DCSD Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. : 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. We will draw. points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines (fill in as appropriate) We will identify in two-dimensional figures. points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines (fill in as appropriate) acute angle angles degrees line segment obtuse angle parallel lines perpendicular lines point ray right angle straight angle Unit 4 Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. : 4.G.2 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. We will classify two dimensional figures using angles, parallel or perpendicular lines. We will recognize and identify right triangles. angle (right, obtuse, acute and straight) classify lines (parallel, perpendicular) two-dimensional triangle (acute, obtuse, right) Unit 4 Douglas County School District Page 8 June 2013
DCSD Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. : 4.G.3 Recognize a line of symmetry for a twodimensional 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. We will recognize and draw lines of symmetry for twodimensional figures. line of symmetry symmetry Unit 4 Measurement and Data Geometric measurement: understand concepts of angle and measure angles. : 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement We will understand that an angle is made up of two rays that share a common endpoint. Common endpoint Vertex Ray Angles Geometric shapes Units 4, 5, 6, 7, 8, 9 Douglas County School District Page 9 June 2013
DCSD Numbers and Operations in Base Ten Use place value and properties of operations to perform multi-digit arithmetic. whole numbers less than or equal to 1,000,000) : 4.NBT.5 Multiply a whole number of up to four digits by a onedigit 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. We will use strategy for multiplying a whole number up to four digits by a one-digit number. (Use the strategies that are in the vocabulary column) We will apply the strategy for multiplying two two-digit numbers. (Use the strategies that are in the vocabulary column) Trimester 2 Strategies include: (rectangular array, area model, partial productbreaking apart equal groups) equation place value row column -Identity property of Multiplication -Commutative Property of Multiplication -Distributive Property of Multiplication over Addition (working knowledge rather than the formal term) Units 2, 3, 4, 5, 6, 7, 8, 9 Douglas County School District Page 10 June 2013
DCSD Number and Operations- Fractions Extend of fraction equivalence and ordering. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x 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. We will identify equivalent fractions and create fraction models to show why they are equal. We will explain why two fractions are equivalent but have different denominators. (Generate equivalent fractions using visual models developing the prior to the standard algorithmmultiplying the numerator and denominator by the same number) Trimester 2 numerator denominator equivalent fraction Unit 6, 7 Douglas County School District Page 11 June 2013
DCSD Number and Operations- Fractions Extend of fraction equivalence and ordering. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.2 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. We will compare fractions using <, >, and = by finding common denominators and justify answer through a visual model. We will compare fractions to a benchmark fraction. We will understand that the size of the whole matters when comparing fractions. Trimester 2 benchmark fraction common denominator comparison symbols (<, >, =) denominator equivalent fraction fraction numerator visual model Unit 6, 7 Douglas County School District Page 12 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous s of operations on whole numbers. : 4.NF.3a Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. We will understand that a fraction is the result of two other fractions being added (composed) or subtracted (decomposed). Trimester 2 compose decompose denominator fraction numerator parts unit fraction whole Unit 6, 7 Denominators 2,3,4,5,6,8,10, 12, and 100) Douglas County School District Page 13 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous s of operations on whole numbers. : 4.NF.3b Understand a fraction a/b with a > 1 as a sum of fractions 1/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. We will understand that a fraction is the result of fractions that are decomposed (smaller) and added together. We will justify a decomposed answer through a visual model. Trimester 2 decompose denominator equation fraction justify numerator Unit 6, 7 Denominators 2,3,4,5,6,8,10, 12, and 100) 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. Douglas County School District Page 14 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous s of operations on whole numbers. : 4.NF.3c Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 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. We will add and subtract mixed numbers with like denominators. We will add and subtract mixed numbers by changing mixed numbers into an improper fraction. We will change an improper fraction into a mixed number. Trimester 2 denominator equivalent fraction improper fraction mixed number numerator properties of operations (working knowledge rather than knowing the formal name) Unit 6, 7 Denominators 2,3,4,5,6,8,10, 12, and 100) Douglas County School District Page 15 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous s of operations on whole numbers. : 4.NF.3d Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fractions models and equations to represent the problem. We will solve word problems using addition and subtraction with like denominators using equations and visual models. Trimester 2 denominator equation fractions numerator visual fraction model whole Unit 6, 7 Denominators 2,3,4,5,6,8,10, 12, and 100) Douglas County School District Page 16 June 2013
DCSD Number and Operations- Fractions Understand decimal notation for fractions, and compare decimal fractions. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.5 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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (Students 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.) We will understand that decimals can be written as fractions. We will generate equivalent decimal fractions. We will show a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 in order to add the two fractions. Trimester 2 decimal fraction denominator fraction hundredths numerator power of 10 tenths Unit 6, 7 Douglas County School District Page 17 June 2013
DCSD Number and Operations- Fractions Understand decimal notation for fractions, and compare decimal fractions. : 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 We will use decimals to show fractions with denominators of 10 and 100. Trimester 2 conversion convert decimal fraction hundredths tenths Unit 6, 7 Denominators 2,3,4,5,6,8,10, 12, and 100) Number and Operations- Fractions Understand decimal notation for fractions, and compare decimal fractions. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.7 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 fraction model. We will read and write decimals through the hundredths. We will compare two decimals (to hundredths) by reasoning about their size. We will understand comparisons are valid when the two decimals refer to the same whole. We will justify conclusions about the comparison of decimals using visual models and other methods. Trimester 2 comparison symbols (<, >, =) decimals hundredths symbols tenths visual models for decimals (grid paper, number line, etc.) whole Unit 6, 7 Douglas County School District Page 18 June 2013
DCSD Measurement and Data Represent and interpret data. : 4.MD.4 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. We will represent fraction data on a line plot and solve problems involving addition and subtraction of fractions. Trimester 2 data fraction (1/2, 1/4, 1/8) line plot Units 4, 5, 6, 7, 8, 9 Operations and Algebraic Thinking Generate and analyze patterns. : 4.OA.5 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. We will create and explain a number or shape pattern that follows a given rule. We will identify additional features of a pattern. Trimester 3 *Ongoing all year features pattern rule sequence Unit 1,3, 8, 9 For 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. Douglas County School District Page 19 June 2013
DCSD Numbers and Operations in Base Ten Use place value and properties of operations to perform multi-digit arithmetic. whole numbers less than or equal to 1,000,000) : 4.NBT.6 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. We will find whole-number quotients and remainders using rectangular arrays and/or area models. We will find whole-number quotients and remainders using strategies based on place value. We will find whole-number quotients and remainders using equations. We will find whole-number quotients and remainders using properties of operations and the relationship between multiplication and division. Trimester 3 dividend divisor product properties of operations (working knowledge rather than formal terms). remainder quotient Units 2, 3, 4, 5, 6, 7, 8, 9 Douglas County School District Page 20 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous of operations on whole numbers. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.4a Apply and extend previous s of multiplication to multiply a fraction by a whole number. 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 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4). We will understand that multiplication is repeated addition. We will understand that adding unit fractions is the same as multiplying a unit fraction by a whole number. We can explain how a fraction is a multiple of another fraction using models, drawings, or equations. Trimester 3 denominator multiple numerator Unit 6, 7 Douglas County School District Page 21 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous of operations on whole numbers. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.4b Apply and extend previous s of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this to multiply a fraction by a whole number. For 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.) We will explain the relationship between unit fractions and their multiples We will show the multiplication of fractions using a visual model. We will multiply a whole number by a fraction. Trimester 3 common denominator multiples Unit 6, 7 Douglas County School District Page 22 June 2013
DCSD Number and Operations- Fractions Build fractions from unit fractions by applying and extending previous of operations on whole numbers. Denominators 2,3,4,5,6,8,10, 12, and 100) : 4.NF.4c Apply and extend previous s of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fractions models and equations to represent the problem. For 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? We will connect a visual fraction model to an equation that represents the problem. We will solve word problems involving the multiplication of a fraction by a whole number. Trimester 3 denominator fraction multiples numerator visual model Unit 6, 7 Douglas County School District Page 23 June 2013
DCSD Measurement and Data Solve problems involving measurement and conversation of measurements from a larger unit to a smaller unit. : 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. - Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurements in a larger unit in terms of small 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 table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... We will identify real world examples relating the size of a unit of measure within a single system which includes length, weight/mass, volume, and time. We will show the measurements of a larger unit in terms of smaller units and record them in a table. We will convert customary units of measure such as feet, gallons and pounds to smaller units such as inches, quarts and ounces and record them in a two-column table. We will convert metric units of measure such as meters, kilograms, and liters to centimeters, grams, and milliliters and record them in a two-column table. Trimester 3 *Ongoing all year benchmark centimeter (cm.) customary system estimate gram (g.) kilogram (kg.) kilometer (km.) liter (l.) meter (m.) metric system millimeter (ml.) minute (min.) ounce (oz.) pound (lb.) second (sec.) Convert equivalent system of measurement two-column table unit Units 4, 5, 6, 7, 8, 9 Douglas County School District Page 24 June 2013
DCSD Measurement and Data Solve problems involving measurement and conversation of measurements from a larger unit to a smaller unit. : 4.MD.2 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. We will use the four operations (+, -, x, ) to solve word problems involving measurement; including simple fractions or decimals and converting measurements from larger units to smaller units. We will use a number line diagram to represent or compare measurement quantities. Trimester 3 *Ongoing all year convert distance intervals mass measurement volume line diagram measurement scale number line scale Units 4, 5, 6, 7, 8, 9 Measurement and Data Solve problems involving measurement and conversation of measurements from a larger unit to a smaller unit. : 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For 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. We will use what we know about area and perimeter to solve real world problems involving rectangles. Trimester 3 area composite figure distance formula length perimeter product rectangle side square unit sum surface two-dimensional figure width Units 4, 5, 6, 7, 8, 9 Douglas County School District Page 25 June 2013