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U n t er r i ch t spl a n
Ne t s o f Py ramid s
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .14
Virginia - Mathematics Standards of Learning (2016): 6.7 .c
Fairfax County Public Schools Program of Studies: 3 .14 .a.3 ,
3 .14 .a.4
Online-Ressourcen: P ush t he E nv e l o pe , C ast yo ur N e t W i de
Opening
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St udent s
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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
pyramids
P r ac t i c e constructing a pyramid from a net, and vice versa
L e ar n to connect nets (2-dimensions) with pyramids (3dimensions)
De v e l o p strategies for correctly coloring the faces of a net or
solid
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Ope ni ng | 10 min
Have your students get into small groups.
Provide each group with the net below.
A sk: What 3-dimensional shape can we create from this 2dimensional net?
Give each group some time to explore the net and bend the edges
as needed to create the triangular pyramid.
Discuss why the shape is called a triangular pyramid, as well as
any obstacles your students had in folding the net.
Provide each group with scissors and tape.
S ay: Unfold the shape back into the net. Cut at least one of the
faces off and tape it somewhere else, so that you can still fold the
net into the triangular pyramid.
Again, provide your students with some time to discuss and
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explore the possibilities. Some changes will work, while others
will not.
Have the groups share their nets and show what happens when the
nets are folded.
If any groups do not yield the desired pyramid, take some time
to discuss why that happened, encouraging the attempt.
One correct net (left) and one incorrect net (right) are shown
below.
Next, show a triangular pyramid that has colors (or numbers,
pictures, etc.) on the faces.
S ay: Unfold the figure back into the net. Try to color the faces so
that it looks like this pyramid when it is folded.
Allow some time for exploration and discussion amongst the
members of each group. Some groups will realize that they can
fold the shape to align the colors, then unfold again.
Have the groups share their nets, folding the nets into the
pyramid to check the color schemes.
While the base of the pyramid is distinct, the remaining three
faces are identical. As such, coloring the faces may seem
trivial, but it is not. Note that the two colorings below are, in
fact, different (if they are both folded into the page).
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Take a minute to discuss the challenges of coloring the sides, as
well as the strategies your students came up with to overcome
those challenges.
T e ac he r pr e se nt s M at h game : C ast yo ur N e t W i de P yr ami ds | 6 min
Present Matific ’s episode C a s t y o u r N e t W id e - 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.
The goal of this episode is to connect the 2-dimensional net with the 3dimensional pyramid. Each screen requires your students to select the
correct colors for each face of the net, so that they align with the pyramid
shown. The first screen uses a rectangular pyramid.
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The square pyramid on the right is rotating, but clicking on the pyramid will
pause the rotation. Additionally, clicking and dragging will rotate the shape in
any desirable direction. Below are two rotations of the same pyramid from
the above screen.
The net can be folded back into the pyramid (and vice versa), as shown
below. This allows your students to compare the coloring of the net with the
intended coloring of the pyramid as they progress.
For some nets, there may be more than one correct coloring. For the above
pyramid, all triangular faces are the same size. Thus, the only requirement is
that two opposite faces are purple, and the other two opposite faces are
orange. Accordingly, the orange and purple above could be switched, provided
the remaining sides are adjusted as well.
Continue on to one or two more examples, as you see fit. Otherwise, you may
opt to proceed more quickly to the practice portion, where your students can
explore strategies individually. By this time, your students should have
working knowledge of the connection between 2-dimensional nets and 3dimensional figures, such as pyramids.
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S t ude nt s pr ac t i c e M at h game : C ast yo ur N e t W i de P yr ami ds | 8 min
Have the students play C a s t y o u r N e t W id e - Py r a m id s on their
personal devices. Encourage your students to spend some time exploring the
relationship between the nets and the pyramids by folding and unfolding the
net. As they progress through the screens, circulate and ask about what
strategies they are using to find the correct coloring for each net.
C l ass di sc ussi o n | 5 min
A sk: What was challenging about coloring the nets?
While your students should have some experience with the
relationship between 2-dimensional objects and 3-dimensional
objects at this point, there are still spatial and conceptual
challenges to address.
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.
T e ac he r pr e se nt s M at h game : P ush t he E nv e l o pe P yr ami ds | 6 min
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Present Matific ’s episode Pu s h t h e E n v e lo p e - 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.
Once again, the goal of this episode is to connect the 2-dimensional net with
the 3-dimensional pyramid. This time, the colored net is provided. Each
screen requires your students to select the correct color for only one face of
the provided pyramid, while the other faces are already colored.
At the start of the first screen only, the colored net will fold into a pyramid,
then unfold back into the net. Subsequent screens will only provide the static
net. As an added challenge, the pyramid cannot be rotated.
Notice that, in the above screen, yellow, purple, and red are all viable options.
Encourage your students to pause and think about the color for 10 seconds
before responding. Ask your students to raise their hands to show which
color they think is correct:
How many of you think we should color the face purple?
How many of you think we should color the face red?
How many of you think we should color the face yellow?
Ask a few students to explain why they have chosen that color. Your
students can rightfully rule out purple, since it does not share an edge with
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orange in the pyramid. In particular, the discussion about using yellow or red
is an opportunity to discuss how rotations of a 3-dimensional figure affect
the coloring of its net.
Continue on to subsequent screens, inviting the same kinds of explanations
and reasoning as discussed above.
S t ude nt s pr ac t i c e M at h game : P ush t he E nv e l o pe P yr ami ds | 6 min
Have the students play Pu s h t h e E n v e lo p e - Py r a m id s on their
personal devices. While it is possible to simply guess colors until finding the
correct answer, encourage your students to develop strategies for finding
the right color. You can always turn this into a game by asking: who can find
the right color in the fewest number of tries? This encourages thoughtful
reflection on the color of choice, while discouraging guessing.
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C l o si ng | 5 min
A sk: We saw two different types of scenarios today. First, we were
given the pyramid and had to color the net. Then, we were given the
net and had to color the pyramid. Which one was more challenging?
Why?
Take a minute or two to discuss where your students struggled
and why.
A sk: What helped you overcome those challenges?
Revisit some of the useful strategies your students devised.
Remind your students that converting information between the 2dimensional net and the 3-dimensional figure can take some time
to get accustomed to, but that these challenges provide
opportunities for growth.
Address the challenges of visualizing the rotations of the
pyramids and folding the nets (second episode) instead of being
able to actually manipulate them (first episode).
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