Mathematics Grade 6
Educational Links

Strand: GEOMETRY (6.G)

Solve real-world and mathematical problems involving area, surface area, and volume (Standards 6.G.1-4).

Standard 6.G.2

Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (for example, 3½ x 2 x 6), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = kWh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams.)

• Banana Bread
  The purpose of this task is two-fold. One is to provide students with a multi-step problem involving volume. The other is to give them a chance to discuss the difference between exact calculations and their meaning in a context.
• Boxed In and Wrapped Up
  This lesson asks students to find the volume and surface area of a rectangular box and then convert it into a cubical box with the same volume.
• Chapter 5 - Mathematical Foundations (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Geometry.
• Chapter 5 - Student Workbook (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Geometry.
• Computing Volume Progression 1
  This is the first in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.
• Computing Volume Progression 2
  This is the second in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. In this iteration, we do away with the lines that delineate individual unit cubes (which makes it more abstract) and generalize from cubes to rectangular prisms. However, the calculations are the same as in 6.G Computing Volume Progression 1.
• Computing Volume Progression 3
  This is the third in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height.
• Computing Volume Progression 4
  This is the last in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on Archimedes Principle that the volume of an immersed object is equivalent to the volume of the displaced water.
• Geometry (6.G) - 6th Grade Core Guide
  The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 6 - Geometry.
• Grade 6 Math Module 5: Area, Surface Area, and Volume Problems (EngageNY)
  In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. Extending skills from Module 3 where they used coordinates and absolute value to find distances between points on a coordinate plane, students determine distance, perimeter, and area on the coordinate plane in real-world contexts
• Grade 6 Unit 5: Area and Volume (Georgia Standards)
  In this unit students will: Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals. Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes. Solve real-world and mathematical problems involving area. Decipher and draw views of rectangular and triangular prisms from a variety of perspectives. Recognize and construct nets for rectangular and triangular prisms. Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets.
• Surface Area and Volume
  An online activity is the focus of this lesson plan to help students understand the concepts of surface area and volume.
• Surface Area of a Rectangular Prisms
  This lesson will help students understand surface area and solve problems using the surface area of a rectangular prism.
• The Largest Container: Problems Using Volume and Shape
  By using a single sheet of paper this interactive leads students to construct shapes, calculate volume, and think about the relationships between different shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Volume of Prisms
  This is a lesson designed to help students understand how to solve problems for the volume of triangular prisms.
• Volume of Rectangular Prisms
  This lesson is designed to help students understand how to solve for the volume of rectangular prisms.
• Volumes with Fractional Edge Lengths
  The purpose of this task is to introduce students to fractional units for volume.

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http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.