6.G.2 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Learning Targets (I can)

• Find the volume of a prism with fractional lengths.
• Apply the formulas for volume.
• Apply the Associative Property of Multiplication to find the volume of a prism efficiently.
• Estimate volume to determine if calculations are reasonable. 
• Reason about volume as dimensions change.

About the Math

Students learning Grade 6 mathematics standards build on their work with area in the previous grades by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 mathematics by drawing polygons in the coordinate plane. Essential vocabulary for this standard includes: base, cube, edge, formula, fraction, height, prism, rectangular prism, right rectangular prism, unit cube, unit fraction, volume, and width. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

TASKS

These tasks can be used with small group or whole group instruction.

• A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with the dimensions of 12 in x 4 1/2 x 3 1/2 in. How many toys can be packed into the larger box for shipping?
• What is the relationship between area of a rectangle and volume of a rectangular prism?
• Give students two pieces of paper (8 1/2 x 11) and ask them to fold one piece of paper into a short rectangular prism (with a square base) and the other into a tall rectangular prism (with a square base). Which prism will have the largest volume?
• A pack of notebook paper (8 1/2 x 11) is 3/8 inch high. Estimate and then calculate what the volume would be if we stack eight packs of paper.
• Troy has a compost bin with the dimensions 2 ft x 1 1/2 ft x 3 2/3 ft. The bin is 3/4 full. What amount of volume does Troy have left in his compost bin?
• A prism has a volume of 200 cm3. What could the dimensions (length, width, and height) be? What is another possibility? Is it helpful to know the volume formula for rectangular prisms when solving this problem?

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Additional Tasks

  These links provide instructional ideas connected to this standard. 

• Computing Volume Progression 1 (Links to an external site.)  Links to an external site.(Illustrative Math)
• Computing Volume Progression 4 (Links to an external site.) Links to an external site. (Illustrative Math)
• Banana Bread (Links to an external site.)  Links to an external site.(Illustrative Math)
• Computing Volume Progression 2 (Links to an external site.) Links to an external site. (Illustrative Math)
• Computing Volume Progression 3 (Links to an external site.) Links to an external site. (Illustrative Math)
• Christo’s Building (Links to an external site.)  Links to an external site.(Illustrative Math) 
• Volume of Rectangular Prisms Download Volume of Rectangular Prisms (HCPSS Lesson Collection) 

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	6-8	Boxed Comparison- Cubic Units, Activity 14.18, Page 320
	Groundworks: Measurement	4   5	112-119 (Boxed In)   104-111 (Find the Dimensions)
	Groundworks: Geometry	5   6	56-63 (Block of Cubes)   56-63 (Block of Cubes)
	Problem-Driven Math	6	20 (Boxing Jewelry)

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• How Much Will Fit Inside? Download How Much Will Fit Inside?
  (HCPSS-adapted resource)
• WAR: Volume Edition Download WAR: Volume Edition
  (HCPSS-adapted resource)
• Volume: Least to Greatest Download Volume: Least to Greatest
  (HCPSS-adapted resource)
• Volume: Working Backwards Download Volume: Working Backwards
  (HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

• Apply the Formulas for Volume to Solve Problems Links to an external site.
• Apply the Formulas for Volume to Solve Problems _2 (performance task) Links to an external site.
• Use Volume to Find Unknown Dimensions Links to an external site.
• Apply the Formulas for Volume to Estimate and Solve Problems Links to an external site.
• Apply the Formulas for Volume to Solve Problems Involving Fractional Dimensions Links to an external site.
• Apply the Formulas for Volume to Solve Problems Involving Fractional Dimensions_2 Links to an external site.
• Apply the Formulas for Volume to Reason About Rectangular Prisms Links to an external site.

Learning Targets

• Find the volume of a prism with fractional lengths.
• Apply the formulas for volume.
• Apply the Associative Property of Multiplication to find the volume of a prism efficiently.
• Estimate volume to determine if calculations are reasonable. 
• Reason about volume as dimensions change.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.