2014-2015 Curriculum Blueprint ... Course: MJ1

2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Approximate Time:
10 Days
Unit #11: Problem Solving With Volume and Surface Area
Learning Goal
Students will understand and be able to solve real-world and mathematical problems involving
area, surface area, and volume.
Link to Learning Scale Surface Area and Volume


Essential Question(s)
When you want to find the volume of a rectangular prism that has sides with fractional
lengths, what are some methods you can use?
Why is a net helpful when calculating the surface area of pyramids and prisms?
Focus Standards
Bullets are the deconstructed standards These should be used to develop concise learning
statements/daily objectives/scales. 6th Grade Math Test Item Specifications
Unit Overview
In this unit, students learn how to find volume of rectangular prisms with fractional side
lengths. Students also model 3--‐D figures with nets and use the nets to find surface area.
Students apply their ability to evaluate expressions as they calculate area, surface area, and
volume using appropriate formulas.
As students investigate volume of surface area of 3-D figures, they select and use appropriate
tools—such as formulas, nets, and unit cubes— strategically (MP.5). Understanding how net
models of 3-D figures relate to their surface areas requires that students look for and make use
of structure (MP.7). Applying formulas to find volumes with fractional edge lengths requires that
students attend to the degree of precision appropriate for a given situation (MP.6).
Vertical Progression:
http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine
remediation needs or enrichment opportunities)
5th Grade Students find the area and volume of an object.
MAFS.6.G.1.2 (DOK 2): 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 = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge
lengths in the context of solving real-world and mathematical problems.

Know how to calculate the volume of a right rectangular prism.

Model the volume of a right rectangular prism, with fractional edge lengths by packing it
with unit cubes of the appropriate unit fraction edge lengths.
7th Grade Students draw and determine the actual area based on a scale drawing.
Unit Sequence
Be selective in choosing problems aligned to the
standards within each lesson
MAFS.6.G.1.4 (DOK 2): Represent three-dimensional figures using nets made up of rectangles and Volume of Rectangular Prism with Fractional
Lengths
triangles, and use the nets to find the surface area of these figures. Apply these techniques in the
context of solving real-world and mathematical problems.
 EngageNY Module 5: Lesson 11 – (page 150)

Know that 3-D figures can be represented by nets.
 NC Lessons for Learning Task: “Block Party”
– Performance Task for determining volume

Apply knowledge of calculating the area of rectangles and triangles to a net, and combine the
with fractional edge lengths (page 24)
areas for each shape into one answer representing the surface area of a three-dimensional
figure.
Understanding & Application of the formula V=Bh

Solve real-world and mathematical problems involving surface area using nets.
 EngageNY Module 5: Lesson 12/13 –
(page 170) Collaborative Centers Task is
MAFS.6.EE.1.2 (DOK): Write, read, and evaluate expressions in which letters stand for
included
numbers.
 Holt 9-6
c. Evaluate expressions at specific values of their variables. Include expressions that arise from
formulas used in real- world problems. Perform arithmetic operations, including those involving
whole-number exponents, in the conventional order when there are no parentheses to specify a Representing & Using Nets of 3-D figures
particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the  EngageNY Module 5: Lesson 15/16 –
(page 213)
volume and surface area of a cube with sides of length s = 1/2.

Substitute specific values for variables

Translate written phrases into algebraic expressions.











Essential Vocabulary
Volume
Surface Area
Dimensions
Right Rectangular Prisms
Pyramids
Cube
Fractional Edge Lengths
Nets
Higher Order Questions/Stems
Do we need to know the length and the
width to find the volume of the
rectangular prism? Why or Why Not?
How does the formula relate to the
measure and the figure?
How can you use a net to calculate surface
area?
2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Approximate Time:
10 Days
Unit #11: Problem Solving With Volume and Surface Area
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
Surface Area of 3-D Figures
 EngageNY Module 5: Lesson 17/18
(page 262)
 Holt 9-8 (excluding cylinders)
MAFS.K12.MP.5.1: Use appropriate tools strategically.
MAFS.K12.MP.6.1: Attend to precision
MAFS.K12.MP.7.1: Look for and make use of structure.
Surface Area and Volume - Real World
Applications
 EngageNY Module 5: Lesson 19 - (page 288)

Translate algebraic expressions into written phrases.
Supplemental Resources
6th Grade Flip Book – A user-friendly resource
regarding specifications of the Common Core
State Standards.


Writing Connections
When you want to find the volume of a
rectangular prism that has sides with
fractional lengths, what are some
methods you can use? Explain the
processes.
How is the formula 𝑉=𝑙∙𝑤∙ℎ related to the
formula 𝑉= B∙h?
Writing Template Tasks These template tasks
are designed from the Mathematical Practice
Standards. When filled in, these templates
become teaching tasks that create opportunities
for teaching literacy skills in mathematics.
EngageNY Grade 6 Module 5 – Word documents
Link to Problem Solving Rubric
can be found using this link
Link to Webb’s DOK Guide
o Teacher Materials - The teacher materials
consist of scripted lessons, instructional
strategies, and structured plans.
o Student Materials - The student materials
consist of the student pages for each lesson in
this Module.
o Copy Ready Materials - A collection of the
module assessments, lesson exit tickets and
fluency exercises from the teacher materials.
Georgia Unit 5: Geometry Tasks aligned to
standards 6.G.1.2 and 6.G1.4:
o Finding Surface Area – page 69
o How Many Ways? – page 73
o Banana Bread – page 79
o Volume and Cubes – page 82
o Packaging Our Goods – page 91
o Painting Barns – page 97
o Boxing Bracelets – page 107
o The File Cabinet – page 114
o STEM Fish Tank Foam Packaging Design –
page 119
MARS Task: “Packing It In” – A formative
assessment lesson intended to help students
reason precisely, defend their conclusions, and
use mathematics to model a scenario concerning
volume. PowerPoint to support is found under
the Resources heading at bottom of page
2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Unit #11: Problem Solving With Volume and Surface Area
MARS Task: “Candle Box” – Performance task for
creating a Hexagonal net.
MARS Task: "Smoothie Box" – Performance task
for creating a box to hold 12 bottles (net).
Illustrative Mathematics – 6th grade tasks
developed under the direction of writers of the
CCSS at the University of Arizona. Following is a
series of 4 Tasks Aligned to 6.G.1.2 that gradually
build in complexity:
o Volume#1
o Volume #2
o Volume #3
o Volume #4
Engage NY Module 5 – Short task to scaffold for
understanding of a cube with fractional edge
length (page 161)
RTTT Item Specifications – page 27
Teaching Channel Video 2 min video with focus
on Improving Participation with Talk Moves
(Personalized Learning Opportunity).
Approximate Time:
10 Days