2015-2016 Curriculum Blueprint
Grade: 5
Course: Mathematics
Topic 10 – Understand Volume Concepts
Flexible Time
Line
7 days
Topic Overview
Topic 10 focuses on deep understanding of the measureable attribute of volume and using numbers and operations to describe and compute the volume of
rectangular prisms and compatible shapes.
Vertical Progression
4th Grade: The students apply formulas to solve perimeter and area problems.
6th Grade: The students will be able apply their understanding of formulas to solve real world volume problems.
Learning Goal
Essential Question
Students will be able to describe the meaning of volume and determine the
What is the meaning of volume of a solid?
volume of a prism.
How can the volume of a rectangular prism be found?
Topic 10 Scale
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards
Step 1: Problem-Based Learning “Solve and Share”
 cube
within the topic. Lessons and problems used for instruction
Problem-Based Learning Lesson Flow Map
 cubic unit
and assessment should be determined through collaborative
Conceptual understanding is developed when mathematics is
 formula
unit planning.
introduced in the context of solving a real problem in which
 rectangular prism
ideas related to the new content are embedded. Conceptual
 unit cube
Topic 10: Understand Volume Concepts
understanding results because the process of solving a problem
 volume
Lesson 10-1: Model Volume
requires students to connect their prior knowledge with the new
Lesson 10-2: Develop a Volume Formula
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Lesson 10-3: Volume of Prisms
Lesson 10-4: Combine Volume of Prisms
Each lesson in the book begins with a Solve and Share. See the
Lesson 10-5: Solve Word Problems Using Volume
links below for additional tasks to be used as needed:
Lesson 10-6: Math Practices and Problem Solving: Use
Appropriate Tools
Math Formative Assessment System (MFAS) Tasks by Standard
Illustrative Mathematics Tasks by Standard
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
lesson through the use of the worked-out problem in the
textbook.
Deconstructed Standards
MAFS.5.MD.3.3 (DOK 1) Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a) 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.
b) 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.
 Recognize that volume is the measurement of the space inside a solid three-dimensional figure.
 Recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes.
 Recognize any solid figure packed without gaps or overlaps and filled with n unit cubes indicates the total cubic units or volume.
MAFS.5.MD.3.4 (DOK 1) Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
 Measure volume by counting unit cubes, cubic cm, cubic in, cubic ft, and improvised units.
MAFS.5.MD.3.5 (DOK 2) Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a) 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.
b) 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.
c) Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems
 Identify a right rectangular prism.
 Multiply the three dimensions in any order to calculate volume (Commutative and Associative Properties.)
 Know that “B” is the area of the base.
 Recognize volume as additive.
 Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the
base, or when multiplying the edge lengths (L x W x H)
 Apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems:
Volume = length x width x height, Volume = area of base x height.
 Solve real world problems by decomposing a solid figure into two non-overlapping right rectangular prisms and adding their volumes.
 Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.
MAFS.K12.MP.5.1 Use appropriate tools strategically.
Additional Resources & Links
Higher Order Questions & Writing Connections
Georgia Units
Link to Webb’s DOK Guide
Unit 6 – Volume and Measurement
*Higher order questions should be utilized to foster a deep,
Differentiating Area and Volume
conceptual understanding of the topic. Encouraging students to
How Many Ways
express their mathematical thinking in writing helps them solidify
Rolling Rectangular Prisms
their learning.
*NOTE: most of Georgia Unit 6 pertains to this Topic.
EngageNY - Module 5
Topic A: Lessons 1-3
Topic B: Lessons 4-7
www.PearsonRealize.com:
Home School Connection
Reteach to Build Understand Pages
Professional Development Videos
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Why is volume represented with cubic units?
How can you find the volume of cubes and rectangular prisms?
How can you find the combined volume of two or more rectangular
prisms?
How do you determine if your solution is correct?
How is volume related to multiplication? To addition?
Explain why multiplying b x w x h is the correct way to find volume
of a rectangular prism or cube.
Marzano Proficiency Scales Bank
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks and rubrics that the teacher can implement with
their students.
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks, videos, lesson plans,
and curriculum modules.
Common Core Flip Books: Provides additional information and sample problems
for every standard
FSA Test Item Specifications
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
www.pearsonrealize.com
Daily Review 10-1 through 10-6