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1 Fourth Grade 4.NOP.1 Multiplication and division; Find the factor pairs for a given whole number less than or equal to 100; recognize prime numbers as numbers greater than 1 with exactly one factor pair. Example: The factor pairs of 42 are {42, 1}, {21, 2}, {14, 3}, {7, 6}. 4.NOP.2 Problem solving with the four operations; Solve multistep word problems involving the four operations with whole 4.NOP.3 Problem solving with the four operations; Solve problems posed with both whole numbers and fractions. Understand that while quantities in a problem might be described with whole numbers, fractions, or decimals, the operations used to solve the problem depend on the relationships between the quantities regardless of which number representations are involved. 4.NOP.4 Problem solving with the four operations; Assess the reasonableness of answers using mental computation and estimation strategies including rounding to the nearest 10 or 100. M5N1.ab. Students will further develop their understanding of whole a. Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite). b. Find multiples and factors. M3N2. Students will further develop their skills of addition and subtraction and apply them in problem M4N4.ab. Students will further develop their a. Know the division facts with understanding and fluency. b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). M4N7.a. Students will explain and use properties of the four arithmetic operations to solve and check problems. a. Describe situations in which the four operations may be used and the relationships among them. M4N2.ae. Students will understand and apply the concept of rounding a. Round numbers to the nearest ten, hundred, or thousand. e. Represent the results of computation as a rounded number when appropriate and estimate a sum or difference by rounding March 15, 2010 Page 39 of 119

2 4.NBT.1 Numbers up to 100,000; Understand that a digit in one place represents ten times what it represents in the place to its right. For example, 7 in the thousands place represents 10 times as many as than 7 in the hundreds place. 4.NBT.2 Multiplying and dividing in base ten; Read, write and compare numbers to 100,000 using baseten notation, number names, and expanded form 4.NBT.3a Multiplying and dividing in base ten; The product of a one-digit number times a multi-digit number is the sum of the products of the one-digit number with the summands in the expanded form of the multi-digit number. Illustrate this numerically and visually using equations, rectangular arrays, area models, and tape diagrams. 4.NBT.3b Multiplying and dividing in base ten; Algorithms for multi-digit multiplication can be derived and explained by writing multi-digit numbers in expanded form and applying the distributive property. 4.NBT.4 Multiplying and dividing in base ten; Fluently multiply and divide within 100. By end of Grade 4, know from memory products of one-digit numbers where one of the factors is 6, 7, 8, or 9. M4N1.a. Students will further develop their understanding of how whole numbers and decimals are represented in the base-ten numeration system. a. Identify place value names and places from hundredths through one million. M4N1.b. Students will further develop their understanding of how whole numbers and decimals are represented in the base-ten numeration system. b. Equate a number s word name, its standard form, and its expanded form. (See frameworks.) M3N3.c. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem c. Use arrays and area models to develop understanding of the distributive property and to determine partial products for multiplication of 2- or 3-digit numbers by a 1-digit number. (See frameworks.) M3N3.c. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem c. Use arrays and area models to develop understanding of the distributive property and to determine partial products for multiplication of 2- or 3-digit numbers by a 1-digit number. M4N4.a. Students will further develop their a. Know the division facts with understanding and fluency. M3N3.b. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem b. Know the multiplication facts with understanding and fluency to 10 x 10. March 15, 2010 Page 40 of 119

3 4.NBT.5 Multiplying and dividing in base ten; Mentally calculate products of one-digit numbers and one-digit multiples of 10, 100, and 1000 (e.g., ). Mentally calculate whole number quotients with divisors of 10 and NBT.6 Multiplying and dividing in base ten; Compute products and whole number quotients of two-, three-or four-digit numbers and one-digit numbers, and compute products of two two-digit numbers, using strategies based on place value, the properties of operations, and/or the inverse relationship between multiplication and division; explain the reasoning used. M4N4.d. Students will further develop their d. Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. ( yields the same answer as 205 5). M3N3.a. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem a. Understand the effect on the product when multiplying by multiples of 10. M4N4. Students will further develop their c. Understand the relationship between dividend, divisor, quotient, and remainder. d. Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. ( yields the same answer as 205 5). M3N3.def. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem d. Understand the effect on the product when multiplying by multiples of 10. e. Apply the identity, commutative, and associative properties of multiplication and verify the results. f. Use mental math and estimation strategies to multiply. M3N4.aeg. Students will understand the meaning of division and develop the ability to apply it in problem a. Understand the relationship between division and multiplication and between division and subtraction. e. Divide a 2 and 3-digit number by a 1-digit divisor. g. Use mental math strategies to divide. March 15, 2010 Page 41 of 119

4 4.NBT.7 Multiplying and dividing in base ten; Explain why multiplication and division strategies and algorithms work, using place value and the properties of operations. Include explanations supported by drawings, equations, or both. A range of reasonably efficient algorithms may be covered, not only the standard algorithms. 4.NBT.8 Multiplying and dividing in base ten; Compute products of two-digit numbers using the standard algorithm, and check the result using estimation. 4.NBT.9 Multiplying and dividing in base ten; Given two whole numbers, find an equation displaying the largest multiple of one which is less than or equal to the other. For example, given 325 and 7, the equation 325 = shows the largest multiple of 7 less than or equal to NF.1a Operations on fractions; Understand addition of fractions: Adding or subtracting fractions with the same denominator means adding or subtracting copies of unit fractions. For example, 2/3 + 4/3 is 2 copies of 1/3 plus 4 copies of 1/3, or 6 copies of 1/3 in all, that is 6/3. 4.NF.1b Operations on fractions; Sums of related fractions can be computed by replacing one with an equivalent fraction that has the same denominator as the other. For example, the sum of the related fractions 2/3 and 1/6 can be computed by rewriting 2/3 as 4/6 and computing 4/6 + 1/6 = 5/6. M4N4. Students will further develop their a. Know the division facts with understanding and fluency. b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). c. Understand the relationship between dividend, divisor, quotient, and remainder. d. Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. ( yields the same answer as 205 5). M4N4.c. Students will further develop their c. Understand the relationship between dividend, divisor, quotient, and remainder. M4N6.b. Students will further develop their understanding of the meaning of decimal fractions and common fractions and use them in computations. b. Add and subtract fractions and mixed numbers with like denominators. (Denominators should not exceed twelve.) M5N4.cg. Students will continue to develop their c. Find equivalent fractions and simplify fractions. g. Add and subtract common fractions and mixed numbers with unlike denominators. March 15, 2010 Page 42 of 119

5 4.NF.2 Operations on fractions; Compute sums and differences of fractions with like denominators, add and subtract related fractions within 1 (e.g., 1/2 + 1/4, 3/10 + 4/100, 7/8 1/4), and solve word problems involving these operations. 4.NF.3 Operations on fractions; Understand that the meaning of multiplying a fraction by a whole number comes from interpreting multiplication by a whole number as repeated addition. For example, 3 2/5 = 6/5 because 3 2/5 = 2/5 + 2/5 + 2/5 = 6/5. 4.NF.4 Operations on fractions; Solve word problems that involve multiplication of fractions by whole numbers; represent multiplication of fractions by whole numbers using tape diagrams and area models that explain numerical results. 4.NF.5 Operations on fractions; Understand that fractions give meaning to the quotient of any whole number by any non-zero whole number. For example, 3 4 = 3/4, because 3/4 multiplied by 4 equals 3. (The division 3 4 means the number which yields 3 when multiplied by 4.) 4.NF.6 Operations on fractions; Solve word problems that involve non-whole number quotients of whole numbers; represent quotients of whole numbers using tape diagrams and area models that explain numerical results. M4N6.b. Students will further develop their understanding of the meaning of decimal fractions and common fractions and use them in computations. b. Add and subtract fractions and mixed numbers with like denominators. (Denominators should not exceed twelve.) M5N4.cg. Students will continue to develop their c. Find equivalent fractions and simplify fractions. g. Add and subtract common fractions and mixed numbers with unlike denominators. M5N4.d. Students will continue to develop their d. Model the multiplication and division of common fractions. M5N4.d. Students will continue to develop their d. Model the multiplication and division of common fractions. M5N4.a. Students will continue to develop their a. Understand division of whole numbers can be represented as a fraction (a/b= a b). M4N4.b. Students will further develop their b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). March 15, 2010 Page 43 of 119

6 4.NF.7 Decimal concepts; Understand that a twodigit decimal is a sum of fractions with denominators 10 and 100. For example, 0.34 is 3/10 + 4/ NF.8 Decimal concepts; Use decimals to hundredths to describe parts of wholes; compare and order decimals to hundredths based on meanings of the digits; and write fractions of the form a/10 or a/100 in decimal notation. Use > and < symbols to record the results of comparisons. 4.MD.1 The number line and units of measure; Understand that the unit length on a number line (interval from 0 to 1) can be divided into parts of equal fractional length. Draw number line representations of problem situations involving length, height, and distance including fractional or decimal units. For example, show distances along a race course to tenths of a mile on a number line, by dividing the unit length into 10 equal parts to get parts of length 1/10; the endpoint of the segment of 1/10 length from 0 represents 1/10 of a mile from the starting point of the race. In Grade 4, all numbers lines begin with zero. 4.MD.2 Perimeter and area; Understand that if a region is decomposed into several disjoint pieces, then the area of the region can be found by adding the areas of the pieces (when these areas are expressed in the same units). M4N5.a. Students will further develop their understanding of the meaning of decimals and use them in computations. a. Add and subtract both one and two digit decimals. M3N5. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations. M3N5.ab. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations. b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3). M4N5. Students will further develop their understanding of the meaning of decimals and use them in computations. b. Understand the relative size of numbers and order two digit decimals. M3N5.ab. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations. b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3). M3M2. Students will measure length choosing appropriate units and tools. M5M1f. Students will extend their understanding of area of geometric plane figures. f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes. March 15, 2010 Page 44 of 119

7 4.MD.3 Perimeter and area; Apply the formulas for area of squares and rectangles. Measure and compute whole-square-unit areas of objects and regions enclosed by geometric figures which can be decomposed into rectangles. Limit to situations requiring products of one-or two-digit 4.MD.4 Perimeter and area; Find one dimension of a rectangle, given the other dimension and the area or perimeter; find the length of one side of a square, given the area or perimeter. Represent these problems using equations involving a letter for the unknown quantity. M5M1f. Students will extend their understanding of area of geometric plane figures. f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes. M5M1d. Students will extend their understanding of area of geometric plane figures. d. Find the areas of triangles and parallelograms using formulae. M5A1a. Students will represent and interpret the relationships between quantities algebraically. a. Use variables, such as n or x, for unknown quantities in algebraic expressions. 4.MD.5a Angle measurement; Understand what an angle is and how it is measured: a. An angle is formed by two rays with a common endpoint. 4.MD.5b Angle measurement; Understand what an angle is and how it is measured: b. An angle is measured by reference to a circle with its center at the common endpoint of the rays. The measure of an angle is based on the fraction of the circle between the points where the two rays intersect the circle. 4.MD.5c Angle measurement; Understand what an angle is and how it is measured: c. A one-degree angle turns through 1/360 of a circle, where the circle is centered at the common endpoint of its rays; the measure of a given angle is the number of one-degree angles turned with no gaps or overlaps. 4.MD.6 Angle measurement; Measure angles in whole-number degrees using a protractor; sketch angles of specified measure; find the measure of a missing part of an angle, given the measure of the angle and the measure of a part of it, representing these problems with equations involving a letter for the unknown quantity. M4M2. Students will understand the concept of M4M2. Students will understand the concept of M4M2b. Students will understand the concept of b. Understand the meaning and measure of a half rotation (180 ) and a full rotation (360 ). M4M2a. Students will understand the concept of a. Use tools, such as a protractor or angle ruler, and other methods such as paper folding, drawing a diagonal in a square, to measure angles. March 15, 2010 Page 45 of 119

8 4.MD.7 Representing and interpreting data; Make a dot 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 dot plots. For example, from a dot plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 4.G.1 Lines and angles; Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines; identify these in plane figures. 4.G.2 Lines and angles; Identify right angles, and angles smaller than or greater than a right angle in geometric figures; recognize right triangles. 4.G.3 Lines and angles; Classify shapes based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size. 4.G.4 Line symmetry; Understand that a line of symmetry for a geometric figure is a line across the figure such that the figure can be folded along the line into matching parts 4.G.5 Line symmetry; Identify line-symmetric figures; given a horizontal or vertical line and a drawing that is not a closed figure, complete the drawing to create a figure that is symmetric with respect to the given line. M4D1ae. Students will gather, organize, and display data according to the situation and compare related features. a. Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs. e. Determine and justify the range, mode, and median of a set of data. M4M2. Students will understand the concept of M3G1b. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. b. Identify and compare the properties of fundamental geometric figures. M4G1a. Students will define and identify the characteristics of geometric figures through examination and construction. a. Examine and compare angles in order to classify and identify triangles by their angles. M3G1c. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. c. Examine and compare angles of fundamental geometric figures. M4G2b. Students will understand fundamental solid figures. b. Describe parallel and perpendicular lines and planes in connection with the rectangular prism. M6G1a. Students will further develop their understanding of plane figures. a. Determine and use lines of symmetry. M6G1a. Students will further develop their understanding of plane figures. a. Determine and use lines of symmetry. March 15, 2010 Page 46 of 119

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