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NC.5.NF.4 Which Room is Larger?DomainNumber and Operations - FractionsClusterApply and extend previous understandings of multiplication and division to multiply and divide fractions. Standard(s)NC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers.Use area and length models to multiply two fractions, with the denominators 2, 3, 4.Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number.Solve one-step word problems involving multiplication of fractions using models to develop the algorithm.MaterialsTask handout, Graph paper (optional) TaskWhich Room is Larger?Newfield Elementary School is a brand new school. When the fifth grade teachers first saw the school, they talked about which rooms were larger. The dimensions of the rooms are below: RoomsWidthLengthRoom A12 yards1513 yardsRoom B34 the width of Room A1513 yardsRoom C114 the width of Room A1513 yardsRoom D113 the width of Room A1513 yardsRoom E23 the width of Room A1513 yardsPart 1: Which rooms are larger than Room A? Which rooms are smaller than Room A? How do you know? Part 2: Without calculating, order the rooms in ascending order based on area (smallest room to largest room). Write an explanation about how you determined the order of the rooms. Part 3: Find the area of each of the rooms. Does your order match the order in Part 2?Write an explanation about how you calculated the size of the rooms. RubricLevel INot YetLevel IIProgressingLevel IIIMeets ExpectationsStudent is not yet able to reason about which rooms were larger and smaller than Room A.Student is not yet able to identify the actual area of each room.Student is independently able to complete one or two of the parts of this task:Part 1: Student identifies which students are larger and smaller than Room A. Student explains that Room C and Room D are larger than Room A because their widths were more than the whole width of Room A and their lengths were the same as Room A. Student explains that Room B and Room E were smaller than Room A because their widths were less than the whole width of Room A and their lengths were the same as Room A.Part 2: Student lists rooms in order from smallest to largest: Room E, Room B, Room A, Room C, Room D. Student explains we know that Room E and Room B are smaller than Room A from Part 1. Room E is 23 the width of Room A, which is smaller than Room B, which is 34 the width of Room A (since 23 is 13 from a whole and 34 is only 14 from a whole). Room A is next because we know it is smaller than Rooms C and D and larger than Rooms B and E from Part 1.Student explains we know that Room C and Room D are larger than Room A from Part 1. Room C is 114 the width of Room A, which is smaller than Room D, which is 113 the width of Room A since 14 is smaller than 13. That makes Room D the largest room. Part 3: Student finds the exact area of each room and explains how they found the area and how their answer relates to their answer in Part 2.Room E – 12223sq yardsRoom B – 138 sq yardsRoom A – 184 sq yardsRoom C – 230 sq yardsRoom D – 24513sq yardsStudent is independently able to complete all three parts of this task: Part 1: Student identifies which students are larger and smaller than Room A. Student explains that Room C and Room D are larger than Room A because their widths were more than the whole width of Room A and their lengths were the same as Room A. Student explains that Room B and Room E were smaller than Room A because their widths were less than the whole width of Room A and their lengths were the same as Room A.Part 2: Student lists rooms in order from smallest to largest: Room E, Room B, Room A, Room C, Room D. Student explains we know that Room E and Room B are smaller than Room A from Part 1. Room E is 23 the width of Room A, which is smaller than Room B, which is 34 the width of Room A (since 23 is 13 from a whole and 34 is only 14 from a whole). Room A is next because we know it is smaller than Rooms C and D and larger than Rooms B and E from Part 1.Student explains we know that Room C and Room D are larger than Room A from Part 1. Room C is 114 the width of Room A, which is smaller than Room D, which is 113 the width of Room A since 14 is smaller than 13 . That makes Room D the largest room. Part 3: Student finds the exact area of each room and explains how they found the area and how their answer relates to their answer in Part 2.Room E – 12223sq yardsRoom B – 138 sq yardsRoom A – 184 sq yardsRoom C – 230 sq yardsRoom D – 24513sq yards*Level IV: student uses multiple models to support their reasoning (i.e., equations, arrays, etc.). Student also notices additional patterns.Standards for Mathematical Practice1. Makes sense and perseveres in solving problems.2. Reasons abstractly and quantitatively.3. Constructs viable arguments and critiques the reasoning of others.4. Models with mathematics.5. Uses appropriate tools strategically.6. Attends to precision.7. Looks for and makes use of structure.8. Looks for and expresses regularity in repeated reasoning.Which Room is Larger?Newfield Elementary School is a brand new school. When the fifth grade teachers first saw the school, they talked about which rooms were larger. The dimensions of the rooms are below: RoomsWidthLengthRoom A12 yards1513 yardsRoom B34 the width of Room A1513 yardsRoom C114 the width of Room A1513 yardsRoom D113 the width of Room A1513 yardsRoom E23 the width of Room A1513 yardsPart 1: Which rooms are larger than Room A? Which rooms are smaller than Room A? How do you know? Part 2: Without calculating, order the rooms in ascending order based on area (smallest room to largest room). Write an explanation about how you determined the order of the rooms. Part 3: Find the area of each of the rooms. Does your order match the order in Part 2?Write an explanation about how you calculated the size of the rooms. ................
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