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U n t er r i ch t spl a n
Id e nt if y ing Ne t s o f 3-Dime ns io nal
F ig ure s
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .14 , 6.10d
Virginia - Mathematics Standards of Learning (2016): 6.7 .c
Fairfax County Public Schools Program of Studies: 3 .14 .a.3 ,
3 .14 .a.4 , 6.10.d.1
Online-Ressourcen: A S af e t y N e t
Opening
T eacher
present s
Mat h game
St udent s
pract ice
Mat h game
Class
discussion
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Mat h game
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Mat h game
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Closing
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M at h Obj e c t i v e s
E x pe r i e nc e nets as a 2-dimensional representation of 3dimensional figures
P r ac t i c e deconstructing a prism or pyramid into a net
L e ar n to connect nets (2 dimensions) with prisms and
pyramids (3 dimensions)
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De v e l o p strategies for correctly identifying the net that
corresponds to a solid
Ope ni ng | 10 min
Have your students get into small groups.
Provide each group with a printout of the nets below, or project an
image of the nets on the board.
A sk: What 3-dimensional figure can we create from each 2dimensional net?
Give each group some time to explore the nets.
Encourage discussions amongst the groups about why these nets
produce different 3-dimensional figures.
Take a minute or two to discuss the names of each of the figures.
These shapes both have triangular bases, but the first becomes a
prism, while the second becomes a pyramid. This difference is
important to note.
Try to have your students lead the conversation about how to tell
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the difference between the two figures, as well as their nets.
Next, provide each group with a 3-dimensional figure (or project an
image of figure, like the one below, onto the board).
While this figure has no coloring, you could consider coloring the
faces as an added challenge.
A sk: What kind of figure is this?
Use this as an opportunity to discuss briefly why the figure is a
pentagonal prism, and also why the figure is not a pyramid or
other type of prism.
S ay: Draw a net for this figure.
After a couple of minutes, have each group show the net they
drew.
A sk: Do all of the nets look the same?
Most likely, some will differ, which is good. This will emphasize
the multiplicity of solutions.
A sk: How can we be sure our nets are correct?
The simplest solution is to fold them. If time allows, consider
letting your students cut out and folding the nets they have
drawn.
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T e ac he r pr e se nt s M at h game : A S af e t y N e t - R e c t angul ar
P r i sms and C ube s | 5 min
Present Matific ’s episode A S a f e t y N e t - R e c t a n g u la r Pr is m s a n d
C u b e s to the class, using the projector. The examples shown in this section
result from the episode being in “Preset” mode.
The goal of this episode is to connect 3-dimensional figures with their
corresponding 2-dimensional nets. Each screen requires your students to
select the correct net for the rectangular prism shown. While most screens
will show prisms with different colorings, the prism on the first screen is one
color.
The primary challenge of this episode is that the nets cannot be manipulated.
Rather, your students must visualize folding the net (or unfolding the
rectangular prism into its net). While your students can simply guess which
net is correct, ask them to explain why they are making each selection.
Once a net is selected--whether it is correct or incorrect--an animation will
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show the net being folded into a figure. Shown above is the net in the top left
of the first screen. While there are several reasons why this net does not
yield the desired prism, the animation allows your students to visualize that
the figure would have at least one open face.
Subsequent screen will involved rectangular prisms with colored faces, as
shown below.
The colors can increase complexity, but they can also help your students
orient themselves. For the prism above, opposite faces share the same
color, so the bottom right net can be ruled out quite easily.
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S t ude nt s pr ac t i c e M at h game : A S af e t y N e t - R e c t angul ar
P r i sms and C ube s | 8 min
Have your students play A S a f e t y N e t - R e c t a n g u la r Pr is m s a n d
C u b e s on their personal devices. Encourage your students to develop
strategies for determining which net is correct. Of similar benefit is deductive
reasoning (i.e., discussing why nets are not correct).
Advanced students can continue on to play A S a f e t y N e t - Pr is m s . While
the first episode contains only prisms with rectangular bases, this episode
includes some prisms with non-rectangular bases.
In the example above, only one net yields a triangular prism. However, it is
possible that more than one net forms the correct 3-dimensional figure,
meaning the coloring of the faces will determine which of those nets actually
aligns with the figure on the left.
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C l ass di sc ussi o n | 5 min
A sk: What was challenging about choosing the right net?
Obviously one of the greatest challenges is not being able to
physically manipulate the nets. Selecting the correct net requires
some ability to visualize that folding, as well as some
understanding of the relationship between 2-dimensional objects
and 3-dimensional objects.
A sk: How did you overcome those challenges? What strategies did
you try?
As with nearly all obstacles in math, there are multiple paths to
success. Sharing the strategies developed by a few students will
help other students realize the multitude of possible solutions. In
turn, this will hopefully result in more resilient problem solving in
the future.
Consider also addressing some strategies that did not pan out.
See if those strategies can be revised in order to make them
more fruitful for the second episode of this lesson.
T e ac he r pr e se nt s M at h game : A S af e t y N e t - P yr ami ds | 5
min
Present Matific ’s episode A S a f e t y N e t - Py r a m id s to the class, using
the projector. The examples shown in this section result from the episode
being in “Preset” mode.
Again, the goal is to connect 3-dimensional figures with their corresponding
2-dimensional nets. The added challenge is that the provided figures are
pyramids. The first screen shows a square pyramid.
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As before, encourage your students to voice their opinions about which net
is correct and why . It may also be beneficial to take a poll by a show of
hands. This may help you uncover misconceptions that your students have.
Remember that elimination is a powerful tool for your students, particularly if
they are struggling with where to start. In the example below, the top left net
has five faces, but the figure should only have four, so this option can be
eliminated. Notice the two nets on the bottom are identical in configuration,
but the colors differ. The figure requires blue to be next to orange (shown on
the left), meaning the bottom right net is eliminated. The decision between
the two remaining nets returns to visualizing how the nets actually fold.
As before, once a net is selected, an animation will show the net being folded
into a figure. If an incorrect net is chosen, this animation will give your
students a better sense of why that net does not yield the desired pyramid.
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S t ude nt s pr ac t i c e M at h game : A S af e t y N e t - P yr ami ds | 8
min
Have your students play A S a f e t y N e t - Py r a m id s on their personal
devices. Encourage your students to develop repeatable strategies for
determining which net can be folded to yield the desired pyramid.
C l o si ng | 5 min
A sk: Was finding the correct nets for pyramids easier or harder
than finding the correct nets for prisms?
On the one hand, your students may find a challenge in the
expansion from nets with only rectangles to nets with other
polygons. However, they may have also had a chance to refine
their strategies for nets.
Take a few minutes to discuss the remaining struggles your
students experienced, using insight from other student to help
offer solutions.
Remind your students that converting information between the 2dimensional net and the 3-dimensional figure (and vice versa) can
take some time to get accustomed to, but that these challenges
provide opportunities for growth.
Address the challenges of visualizing folding nets.
If your students are still struggling a great deal with connecting
nets and their corresponding figures, consider providing a few more
physical nets for them to manipulate.
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