Common Core State Standards 1 st Edition Math Pacing Guide Fourth Grade 4 th Nine Week Period


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1 Common Core State Standards 1 st Edition Math Pacing Guide Fourth Grade 4 th Nine Week Period 1 st Edition Developed by: Christy Mitchell, Amy Moreman, Natalie Reno `````````````````````````````````````````````````````````````````````````````````````` Mr. Stan Rounds, Superintendent Dr. Steven Sanchez, Associate Superintendent for Learning, Teaching & Research Prepared By: Lydia Polanco, Director of Elementary Instruction
2 Math Pacing Guide Las Cruces Public Schools Understanding Mathematics: The standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. 1 Mathematical understanding and procedural skill are equally important. 2 Description of the Pacing Guide: A pacing guide is an interval based description of what teachers teach in a particular grade or course; the order in which it is taught, and the amount of time dedicated to teaching the content. Purpose of a Pacing Guide: The purpose of a pacing guide is to ensure that all of the standards are addressed during the academic year. Each pacing guide is nine weeks in duration. Components of the Pacing Guide: Critical Areas Each grade level has identified Critical Areas. These areas are woven throughout the standards and should receive additional time and attention. Mathematical Practice Standards (8) Based on the NCTM Process Standards, these standards describe the variety of "processes and proficiencies" students should master while working with the Grade Level Content Standards. Domains are larger groups of related Content Standards. Standards from different domains may sometimes be closely related. 3 Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. 4 Grade level standards define what students should know and be able to do by the end of each grade level. Unpacked standards provide a clear picture for the teacher as he/she implements the CCSS Resources includes but not limited to current district core resources Depth of Knowledge (DOK) Criteria for systematically analyzing the alignment between standards and standardized assessments. 1 Mathematics, Introduction, p. 4 2 See #1 3 See #1 4 Mathematics, Introduction, p. 5
3 Based on analysis of SBA data from 2013, standards on the following pages should be reviewed and reinforced during the 4 th quarter.
4 Grade Level: 4 Quarter: 4th Nine Weeks Domain: Number and Operations Fractions 3 Standard Q1 Q2 Q3 Q4 4.NF.4a X X I/P R 4.NF.4b X X I/P R 4.NF.4c X X I/P R Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Critical Areas: #1: No Connection #2: Strong Connection #3: No Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 4.NF.4a 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). 4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding 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), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b) MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7. Look for and make use of structure. MP.8. Look for and express regularity in repeated reasoning. MP.4. Model with mathematics. MP.7. Look for and make use of structure. 4.NF.4c 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. 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? Unpacked Content Standard: 4.NF.4a builds on students work of adding fractions and extending that work into multiplication. Example: 3/6 = 1/6 + 1/6 + 1/6 = 3 x (1/6) MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. MP.6. Attend to precision.
5 Number line: Area model: 4.NF.4b This standard extended the idea of multiplication as repeated addition. For example, 3 x (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 6 x (1/5). Students are expected to use and create visual fraction models to multiply a whole number by a fraction. 4.NF.4c When introducing this standard make sure students use visual fraction models to solve word problems related to multiplying a whole number by a fraction. Vocabulary: no new vocabulary Resources: envision Math 4.NF.4a Topic 13: Extending Fraction Concepts 131 Fractions as Multiples of Unit Fractions: Using Models 4.NF.4b Topic 13: Extending Fraction Concepts 132 Multiplying a Fraction by a Whole Number: Using Models Depth of Knowledge 4.NF.4a DOK 1: Use the rectangles below to model 5 x ¼. 4.NF.4a DOK 1: Show 1 ¼ on the number line below 4.NF.4c Topic 13: Extending Fraction Concepts 133 Multiplying a Fraction by a Whole number: Using Symbols
6 4.NF.4a DOK 2: Model 7 x 1/3 and show your answer as a mixed number and an improper fraction. 4.NF.4b DOK 1: List the next four multiples of the following fraction. ⅖ : 4/10, 6/15, 8/20, 10/25 4.NF.4b DOK 2: Melissa fills a measuring cup with ¾ cup of juice 3 times. Write and solve a multiplication equation with a whole number and a fraction to show the total amount of juice she uses. 4.NF.4c DOK 1: I m joining five groups of ¾ of a pint. What multiplication equation can be used to describe how to join the pints? ¾ + ¾ + ¾ + ¾ + ¾ = (5 x ¾)
7 Grade Level: 4 Quarter: 4th Nine Weeks Domain: Measurement and Data (4.MD) Standard Q1 Q2 Q3 Q4 4.MD.1 P R R R 4.MD.2 P R R R 4.MD.3 I/P I/P R R Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Critical Areas: #1: Strong Connection #2: No Connection #3: No Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; Ib., oz.; I, ml; 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 twocolumn 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), MP.5. Use appropriate tools strategically. MP.6. Attend to precision 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. 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. (1 st quarter focus=perimeter; 2 nd quarter focus will be area). MP.5. Use appropriate tools strategically. MP.6. Attend to precision MP.5. Use appropriate tools strategically. MP.6. Attend to precision Unpacked Content Standard: 4.MD.1 involves working with both metric and customary systems some of which have been introduced in the previous grades. However, conversions should be within only one system of measurement. Students should have ample time to explore the patterns and relationships in the conversion tables that they create. Example: Customary length conversion table
8 Foundational understandings to help with measurement concepts: Understand that larger units can be subdivided into equivalent units (partition). Understand that the same unit can be repeated to determine the measure (iteration). Understand the relationship between the size of a unit and the number of units needed (compensatory principal). 4.MD.2 includes multi step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems. Example: Charlie and 10 friends are planning for a pizza party. They purchased 3 quarts of milk. If each glass holds 8oz will everyone get at least one glass of milk? possible solution: Charlie plus 10 friends = 11 total people 11 people x 8 ounces (glass of milk) = 88 total ounces 1 quart = 2 pints = 4 cups = 32 ounces Therefore 1 quart = 2 pints = 4 cups = 32 ounces 2 quarts = 4 pints = 8 cups = 64 ounces 3 quarts = 6 pints = 12 cups = 96 ounces If Charlie purchased 3 quarts (6 pints) of milk there would be enough for everyone at his party to have at least one glass of milk. If each person drank 1 glass then he would have 1 8 oz glass or 1 cup of milk left over. Example: At 7:00 a.m. Candace wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed and 17 minutes to eat breakfast. How many minutes does she have until the bus comes at 8:00 a.m.? Use the number line to help solve the problem. 4.MD.3 calls for students to generalize their understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization. Example: Mr. Rutherford is covering the miniature golf course with an artificial grass. How many pieces of 1foot long fencing will he need to go around the entire
9 outer edge of the course? Vocabulary: kilometer, meter, centimeter, kilogram, gram, pound, ounce, liter, milliliter, hour, minute, second, equivalent, distance, time, liquid, rectangles, area, perimeter, formula volumes, mass, money, measure, metric, customary, convert/conversion, relative size, liquid volume, mass, length, distance, kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), liter (L), milliliter (ml), inch (in), foot (ft), yard (yd), mile (mi), ounce (oz), pound (lb), cup (c), pint (pt), quart (qt), gallon (gal), elapsed time, hour, minute, second Resources: Depth of Knowledge envision Math 4.MD.3 Topic 15: Solving Measurement Problems 151 Solving Perimeter and Area Problems 4.MD.1 DOK 1: 3ft. = inches 4.MD 2 DOK 2: Damian wants to buy a video game that costs $ He has $17.36 in his piggy bank. If his grandma gives him $25.00 for his birthday, how much more money does he need to be able to buy the game? 4.MD.3. DOK 1: What is the perimeter of the given shape (with all side lengths labeled). 4.MD.3. DOK 2: Find the perimeter of an irregular polygon with missing side lengths. 4.MD.3. DOK 2: Sally wants to plant a square garden. The perimeter is 16in. How long is each side. Explain how you know.
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