Mathematics Curricular Guide Common Core State Standards Transitional Document FOURTH GRADE 2013-2014 SCHOOL YEAR MATHEMATICS SCOPE & SEQUENCE
Unit Title Days 1. Unit 5: Landmarks and Large Numbers 13 2. Unit 1: Factors, Multiples, Arrays 20 3. Unit 3: Multiple Towers and Division Stories 32 4. Unit 4: Size, Shape, and Symmetry/Measurement Conversion 35 5. Unit 6: Fraction Cards and Decimal Squares 40 6. Unit 8: How Many Packages? How Many Groups? 10 7. Unit 9: Penny Jars and Plant Growth 18 RESOURCES FOR PERFORMANCE TASKS http://www.georgiastandards.org/common-core/pages/math-k-5.aspx http://schools.nyc.gov/academics/commoncorelibrary/tasksunitsstudentwork/default.htm **Pages listed in the tan common core adaptations on snap ins are used to meet the listed standards. ***Common Core connections to Units begin with Unit 3, as Units 5 and 1 were taught before this guide changed.
Unit 5 Landmarks and Large Numbers 4.NBT.1 MP.1 Make sense of problems and persevere in solving them MP.3 Construct viable arguments and critique the reasoning of others MP.8 Look for and express regularity in repeated reasoning.
Unit 1: Factors, Multiples, and Arrays 4.OA.1 Interpret a multiplication equation as a comparison -Sessions 1.6A, 3.2, 3.3, 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison -Sessions 1.6A, 3.2, 3.3 4.OA.3 Solve multi-step word problems posed with whole numbers and having whole number answers using four operations, including problems in which remainders must be interpreted. -Investigation 1, Sessions 3.2, MP.1 Make sense of problems and persevere in solving them MP.3 Construct viable arguments and critique the reasoning of others MP.8 Look for and express regularity in repeated reasoning. 4.OA.4 Find factors, multiples, prime and composite numbers -Investigation 1 (not 1.6A), Investigation 2, Investigation 3
Unit 3: Multiple Towers and Division Stories 4.OA.1 Interpret a multiplication equation as a comparison Sessions: 3.1, 3.2, 3.3, 4.1, 4.3 *Note: Investigation 3 needs to use multiplicative comparison language 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison Sessions: 3.1, 3.2, 3.3, 4.1, 4.3 *Note: Investigation 3 needs to use multiplicative comparison language 4.OA.3 Solve multi-step word problems posed with whole numbers and having whole number answers using four operations, including problems in which remainders must be interpreted. Sessions: 1.1, 2.2, 2.3, 2.4, 2.5, 2.6 4.OA.4 Find factors, multiples, prime and composite numbers Sessions: 1.4, 1.5, 3.1., 3.2, 3.3 4.NBT.5 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 Sessions: 1.1, 1.3, 1.4, 1.5, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4 *Note: Unit does not have large enough numbers to meet whole standard 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. Sessions: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 4.1 *Note: Unit does not have large enough numbers to meet whole standard MP.1 Make sense of problems and persevere in solving them Sessions: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 4.3, 4.4, 4.5 Sessions: 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 4.5 MP.3 Construct viable arguments and critique the reasoning of others Sessions: 2.3, 2.4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 3.2 Sessions: 1.1, 2.1, 3.1, 3.2 Sessions: 4.3, 4.4, 4.5 Sessions: 1.1, 1.2, 2.4, 2.5, 2.6, 3.1, 3.2, 3.4, 4.1, 4.2, 4.3 MP.8 Look for and express regularity in repeated reasoning. Sessions: 3.3, 3.4, 4.1, 4.2, 4.3, 4.8
Unit 4: Size, Shape and Symmetry 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm Sessions 1.3, 4.5, 4.6, 4.7 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. *Note: Investigation 1 only addresses linear 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. Sessions: 1.3, 1.5 *Note: Investigation 1 only addresses linear 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. Sessions 1.3 (perimeter, apply the area and perimeter formulas of rectangles), 1.4 (perimeter), 1.5 MP.1 Make sense of problems and persevere in solving them Sessions 4.7 Sessions: 4.7 MP.3 Construct viable arguments and critique the reasoning of others Sessions: 2.4, 2.5 Sessions: All sessions in Investigations 1, 3, 4 Sessions: 1.4, all sessions in Investigation 2 and 3 MP.8 Look for and express regularity in repeated reasoning. 4.MD.5.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. Sessions 2.3A, 3.4A 4.MD.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Session 3.4A (Continued on next page)
4.MD.6 Measure angles in whole-number degrees using a protractor *Note: Investigation 3 teaches how to use a protractor; measures angles of power polygons should introduce how to use a protractor in Session 3.1. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Sessions: 3.1, 3.2, 3.3 *Note: Read Common core Adaptation for Investigation 3. 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines Sessions: 3.4A, 2.3A Introduction *Note: Introduces perpendicular/parallel. 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel and perpendicular lines, or the presence or absence of angles of a specified size. Sessions: All of Investigation 2, 4.1, 4.2, 4.3, 4.4 *Note: Look at Common Core Adaptations for Investigations 4.1, 4.2, 4.3, 4.4 4.G.3 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. Sessions 4.1, 4.2, 4.3
Unit 6: Fraction Cards and Decimal Squares 4.NF.1 Explain why a fraction is equivalent to a fraction 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. -Sessions 1.1, 1.2, 2.1, 2.5, 2.6 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 -Sessions 1.2, 1.5, 2.1, 2.2, 2.3, 2.4, 2.6 4.NF.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole -Sessions 1.5, 1.6, 1.8A 4.NF.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation -Sessions 1.6 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 by using properties of operations and the relationship between addition and subtraction -Sessions 2.7A MP.1 Make sense of problems and persevere in solving them Sessions 1.1, 1.2, 1.5, 1.8A, 3.7 Sessions: 1.1, 1.2, 1.5, 1.6, 1.7, 3.7 MP.3 Construct viable arguments and critique the reasoning of others Sessions: 2.1, 2.2, 2.3 Sessions: 1.3, 1.4, 1.5, 1.8A, 3A.1, 3A.2, 3A.3, 3.4, 3.5, 3.6 Sessions: 2.6, 3.1, 3.2, 3.3, 3.4 Sessions; 3.1, 3.2 Sessions: 2.4, 3.3 MP.8 Look for and express regularity in repeated reasoning. 4.NF.3.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 -Sessions 1.4, 1.7, 1.8A (Continued on next page)
4.NF.4.a Understand a fraction a/b as a multiple of 1/b. -Sessions 3A.1, 3A.2, 3A.3 4.NF.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. -Sessions 3A.1, 3A.2, 3A.3 4.NF.4.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. -Sessions 3A.1, 3A.2, 3A.3 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 Sessions: 3.1, 3.3 4.NF.6 Use decimal notation for fraction with denominators 10 or 100 Sessions: 3.2, 3.3 4.NF.7 Compare 2 decimals to hundredths by reasoning about their size Sessions: 3.2, 3.4, 3.5, 3.6, 3.7 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. Sessions: 3.4, 3.5, 3.6 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (,, ). Session: 2.7A
Unit 8: How Many Packages? How Many Groups? 4.NBT.5 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. -Sessions 1.2, 1.3, 1.4, 1.5, Investigation 2, 3.1, 3.4, 3.5, 3.6 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 Investigation 3 4.OA.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. -Sessions 1.5, 2.1, 2.2, 2.4A, 3.3., 3.5 MP.1 Make sense of problems and persevere in solving them -Sessions 1.1, 1.2, Investigation 3 -Session 3.6 MP.3 Construct viable arguments and critique the reasoning of others -Sessions 2.1, 2.2, 2.3, 2.4 -Sessions 3.2, 3.3, 3.4 (300 chart) -Sessions 1.3, 1.4, 1.5 MP.8 Look for and express regularity in repeated reasoning. -Sessions 2.2, 2.3, 2.4, 2.5, 3.4 4.OA.5 generate a number or shape pattern that follows a give rule. -Sessions 1.4, 1.5, 3.2 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. -Sessions 2.4A practice sheet 31C
Unit 9: Penny Jars and Plant Growth 4.OA.5 Generate a number or shape pattern that follows a given rule. -Sessions 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 4.NBT.5 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. -Sessions 2.1 (C65-CCSS), 2.2, 2.4, 2.5, 2.6 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. -Sessions 2.1 (C65-CCSS), 2.2, 2.4, 2.5, 2.6 MP.1 Make sense of problems and persevere in solving them -Sessions 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 MP.3 Construct viable arguments and critique the reasoning of others -Sessions 1.1, 1.2, 2.1, 2.2, 2.3, 2.4 -Sessions 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 MP.8 Look for and express regularity in repeated reasoning. 4.MD.1 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. *Investigations says this standard is addressed, we don t agree.