Wentzville School District
Stage 1 – Desired Results
Unit 10 - Volume and Surface Area
Unit Title: Volume and Surface Area
Course: Integrated Math 6
Brief Summary of Unit: In this unit, students will learn to measure volume and surface area of rectangular prisms.
Students will also learn to represent three-dimensional figures using nets made up of triangles and rectangles and to
use those nets to find surface area of prisms and pyramids.
Textbook Correlation: Glencoe Math Course 1 Chapter 10
Time Frame: 3 weeks
WSD Overarching Essential Question
Students will consider…
● How do I use the language of math (i.e.
symbols, words) to make sense of/solve a
problem?
● How does the math I am learning in the
classroom relate to the real-world?
● What does a good problem solver do?
● What should I do if I get stuck solving a
problem?
● How do I effectively communicate about math
with others in verbal form? In written form?
● How do I explain my thinking to others, in
written form? In verbal form?
● How do I construct an effective
(mathematical) argument?
● How reliable are predictions?
● Why are patterns important to discover, use,
and generalize in math?
● How do I create a mathematical model?
WSD Overarching Enduring Understandings
Students will understand that…
● Mathematical skills and understandings are
used to solve real-world problems.
● Problem solvers examine and critique
arguments of others to determine validity.
● Mathematical models can be used to interpret
and predict the behavior of real world
phenomena.
● Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
● Varieties of mathematical tools are used to
analyze and solve problems and explore
concepts.
● Estimating the answer to a problem helps
predict and evaluate the reasonableness of a
solution.
● Clear and precise notation and mathematical
vocabulary enables effective communication
and comprehension.
● Level of accuracy is determined based on the
context/situation.
● How do I decide which is the best
mathematical tool to use to solve a problem?
● How do I effectively represent quantities and
relationships through mathematical notation?
● How accurate do I need to be?
● When is estimating the best solution to a
problem?
● Using prior knowledge of mathematical ideas
can help discover more efficient problem
solving strategies.
● Concrete understandings in math lead to
more abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
know that volume and surface area are attributes of 3-dimensional figures that can be used to solve real
world problems.
Meaning
Essential Questions
● How do you know when to use volume and
surface area formulas?
● How is shape important when measuring a
figure?
● Why is careful use of geometric language
necessary?
● What is the best measurement to use when
solving a problem?
● What are the similarities and differences
among volume and surface area?
● What is the relationship between area and
surface area?
●
When would you use volume in everyday life?
● What are ways that volume can be measured?
● How is volume affected by a change in one
dimension?
● How can you find the surface area of 3D figures?
● How is a net utilized to represent a 3D figure?
● What is a real world application of surface area?
Understandings
● Two dimensional figures can be used to
represent three dimensional objects.
● Measurements can be used to describe,
compare, and make sense of the real-world.
● Three dimensional objects can be described,
classified, and analyzed by their attributes.
● Geometry and spatial sense offer ways to
visualize, to interpret, and to reflect on our
physical environment.
● Volume measures the number of unit cubes of
needed to fill a given space.
● The dimensions of a unit cube must be of equal
length – not necessarily a whole number.
● Surface area is the sum of the areas of each
individual face of the 3D figure
● Three-dimensional figures can be “unfolded” into
flat 2D shapes (nets) which can then be used to
find the surface area
Acquisition
Key Knowledge
Key Skills
Students will know….
Students will be able to….
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
nets
isometric dot paper
base
cubic units
lateral face
slant height
surface area
three-dimensional figure
prism
triangular prism
rectangular prism
pyramid
vertex
volume
three dimensional figures
area of rectangle, triangle and parallelogram
●
●
●
●
●
●
●
●
●
●
●
●
Model the volume of prisms
Use unit cubes to find volume of right rectangular
prisms.
Use a formula to find volume of right rectangular
prisms.
Given the volume of a right rectangular prism,
determine any missing dimensions.
Use appropriate tools to precisely measure the
dimensions of the right rectangular prism.
Calculate the volume of triangular prisms.
Given the volume of a triangular prism, determine
any missing dimensions.
Use nets to represent three-dimensional figures
(rectangular prisms, triangular prisms, pyramids)
Calculate surface area of rectangular prisms.
Calculate the surface of triangular prisms.
Calculate the surface area of pyramids.
Solve real-world problems involving surface area
and volume using multiple strategies.
Standards Alignment
MISSOURI LEARNING STANDARDS
6.G.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 a 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.
6.G.4 Represent three-dimensional figures using nets made up of rectangles and 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.
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 2, 5