Volume: 5 th Grade Style

1. Volume: 5th Grade Style A measurement topic for intermediate grade 5

2. 5th Grade Measurement Standards • 1.0 Students understand and compute the volumes and areas of simple objects: 1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram). 1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects. 1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm 3], cubic meter [m3], cubic inch [in 3], cubic yard [yd3]) to compute the volume of rectangular solids. 1.4 Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects (i.e., find the perimeter, area, volume). • 2.0 Students identify, describe, and classify the properties of, and the relation­ ships between, plane and solid geometric figures: 2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). 2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems. 2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

3. Measurement:Leading up to volume • Earlier today Megan introduced volume in terms of capacity younger students tend to use nonstandard units. • When working with capacity making guesses or estimating is a major part of learning about volume until the fifth grade. • Perimeter and Area were already covered been covered using standard units by Sabrina and Bevlee in their respective grade levels. • Once all these topics have been introduced to students, 5th grade is ready to explore volume.

4. Formal Volume • Volume shape development and formula use are analogous to area. • Summing the area of all sides of a solid is not equal to the volume, that is the surface area. • A cylinder is solid with 2 congruent parallel bases and sides that are parallel elements. 2 special classes of cylinders that we focus on in 5th grade are cubes and rectangular prisms. • All of these special prisms all have the same volume formula and follow parallelogram area formulas where Volume = Base xHeight

5. Activity 1 • Build 1 square rectangular prism. • Build 4 square rectangular prism with open lid • Show that 4 of the 1 square prism fit into the 4 square prism. • Now take what was learned from the 1 in 4 square prism and estimate how many would 4 square prisms would fit in a 32 square prism.

6. Activity 1 extended • Activity 2 is a computer simulation program that will show how to create prisms on a computer. • Cubes and Prisms from a 2d workmat 3d solid • http://illuminations.nctm.org/ActivityDetail.aspx?ID=6

7. Activity 2 • Circular Cylinder made up of coasters. • Coaster Dimensions: • Diameter = 3.5 inches • Height = . 0.03125 inches. • Number of coasters = 32 • Each Coaster is 1/32 shifted along the diameter creating a sheer or slanted cylinder. • What is the volume.

8. Questions for End • How is developing volume formulas for prisms related to developing area formulas for parallelograms ? How can you prove that ? • How could a square prism’s volume be used to provide a good approximation for a circular cylinder’s volume ? What would need to be the same and explain why this would work?