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| In this unit, students build on their prior work with area and explore ways to find the area of rectangles with fractional side lengths. Students also learn about volume as an attribute of solid figures. Using improvised units, they explore volume and build toward using cubic units and volume formulas. The following big ideas will be covered in this unit:
- Tiling can be used to find the area of rectangles with fractional side lengths. - Volume typically refers to the amount of space an object takes up but is also used for the size of three-dimensional shapes. - Volume is measured with units such as cubic inches or cubic centimeters- units that are based on linear measures. - Volume can be expressed in both customary and metric units. - Formulas, (v = length x width x height or v = base x height), can be used to calculate the volume for rectangular prisms. - When changing from smaller units to larger related units within the same measurement system, there will be fewer larger units. |
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| Number & Operations—Fractions 5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.B.4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.MD.A. Convert like measurement units within a given measurement system. 5.MD.A.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 5.MD.C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.C.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.C.3a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. 5.MD.C.3b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.C.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.C.5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.C.5a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. 5.MD.C.5b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 5.MD.C.5c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: Make mathematical conjectures and arguments. (MP. 3) Make sense of others’ mathematical thinking. (MP. 3) Model real-world situations using graphs, drawings, tables, symbols, numbers, diagrams, and other representations. (MP. 4) Use mathematical models to solve problems and answer questions. (MP. 4)
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| - Area is the two-dimensional space inside a region. - When finding the area of a rectangle, the dimensions represent the factors in a multiplication problem. - A rectangle whose sides have length w units and l units, can be partitioned into w rows of unit squares with l squares in each row. - Liquid volumes can be measured using mL and Liters. - The larger the unit, the smaller the number you obtain as you measure. | - Fractional side lengths can be multiplied to find the area of a rectangle. - Measurements can be expressed in larger or smaller units within a measurement system. - Formula for volume can be applied to solve real world math problems. - Base-ten system supports conversions within the metric system. |
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| 1.2- Area, unit square. square units, length, width, area, rectangle 1.5- 3-dimensional, volume, conjecture, length, width, height, attributes 1.6- rectangular prism 1.7- unit cube, cubic unit, rows, layers, base 1.11- mathematical model Bold: Listed in teacher's EDM4 edition Normal Font: not listed in teacher’s edition as a vocabulary word but will be helpful for students in explanations |
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| The following lesson plan sequence is obtained from Everyday Mathematics 4. Each lesson is aligned with a learning objective to inform the teachers on what students should be able to at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day. |
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| The following language supports are for English Language Learners but could also be used to support any struggling learner in mathematics. The strategies are obtained from the SIOP model. The language objectives will support students' academic language development. The sentence stems and starters provides the support many students need to be able to participate in discussions and writing about mathematics. |
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