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U n t er r i ch t spl a n
Ne t s o f R e c t ang ul ar Pris ms
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .14 , 5 .8b,
5 .8c , 6.10d
Virginia - Mathematics Standards of Learning (2016): 5 .8.a, 5 .8.b,
5 .9.b
Fairfax County Public Schools Program of Studies: 3 .14 .a.3 ,
3 .14 .a.4 , 5 .8.b.1, 5 .8.b.2, 5 .8.b.3 , 5 .8.c .3 , 6.10.d.1
Online-Ressourcen: P ush t he E nv e l o pe , C ast yo ur N e t W i de
T eacher
present s
St udent s
pract ice
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10
5
6
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min
min
min
min
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Opening
Class
discussion
T eacher
present s
St udent s
pract ice
Closing
5
min
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
rectangular prisms
P r ac t i c e constructing a rectangular prism from a net, and vice
versa
L e ar n to connect nets (2-dimensions) with rectangular prisms
(3-dimensions)
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De v e l o p strategies for correctly coloring the faces of a net or
solid
Ope ni ng | 8 min
Prepare for the opening with two or more identical objects that are
rectangular prisms, that can be unfolded into nets. The example that follows
will use cereal boxes.
Show a cereal box in its 3-dimensional prism form.
A sk: What is the name of this shape?
While many students will likely say “box,” encourage them to find
another, more mathematical name. Ideally, they reach the
conclusion of “right rectangular prism,” though it may require
some guidance.
S ay: Each side of the cereal box has unique features to it. Some
sides have pictures, one side has nutritional information, and other
sides are mostly blank. There are other features too. For example,
the front and the back faces do not share any edges. All of these
ideas will be important.
Show a cereal box in its 2-dimensional net form.
A sk: What does it look like if we cut along some of the edges to
flatten out the rectangular prism--the box--so that we can see all of
the unique faces?
Your students may say it looks like a bunch of rectangles. While
this is true, dive a little deeper into why.
Namely, each face of the cereal box is a rectangle (2dimensional), so flattening the box should not change that.
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If you have another cereal box, consider showing a different
version of how that net could be created. A generic example of
two nets for the same rectangular prism is shown below.
Flip one of the nets over so that only the brown cardboard is
showing. Write on a couple of the faces to denote which face of
the box they correspond to, such as “front” and “nutritional
information.”
Note that your choice of faces may require you to include
directional information like “up” to avoid the prospect of multiple
correct solutions (since you will eventually flip the net back over
to see if the faces are correctly labeled). One such example is
using “front” and “back.”
A sk: Use the box to help determine how the remaining faces should
be labeled.
Invite several students to offer up suggestions, while also
explaining why. Encourage arguments in support or against the
choice of labels.
Write down the consensus answers, even if you know they will be
incorrect. Looking back and discussing why the faces were
incorrectly labeled can be just as powerful as getting them right
in the first place.
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T e ac he r pr e se nt s M at h game : C ast yo ur N e t W i de C ubo i ds | 8 min
Present Matific ’s episode C a s t y o u r N e t W id e - C u b o 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 rectangular prism. Each screen requires your students to select
the correct colors for each face of the net, so that they align with the prism
shown. The first screen uses a cube, as shown below.
The cube on the right is rotating, but clicking on the cube will pause the
rotation. Additionally, clicking and dragging will rotate the shape in any
desirable direction. Below are two rotations of the same cube from the
above screen.
The net can be folded back into the prism (and vice versa), as shown below.
This allows your students to compare the coloring of the net with the
intended coloring of the prism as they progress.
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For some nets, there may be more than one correct coloring. For the cube
above, the red faces are opposite each other, meaning any two faces of the
net that end up opposite each other could be red (provided red is colored
first). The light and dark blue have the same property, but once red is
selected, there will be a fixed relationship to which faces must be light or dark
blue.
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.
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 C ubo i ds | 10 min
Have the students play C a s t y o u r N e t W id e - C u b o id s on their personal
devices. Encourage your students to spend some time exploring the
relationship between the nets and the prisms 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.
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C l ass di sc ussi o n | 5 min
A sk: What was challenging about coloring the nets?
The relationship between 2-dimensional objects and 3dimensional objects is often challenging at first, so it is
important to address that challenge.
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 C ubo i ds | 6 min
Present Matific ’s episode Pu s h t h e E n v e lo p e - C u b o 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 prism. This time, the colored net is provided. Each screen
requires your students to select the correct color for only one face of the
rectangular prism, while the other faces are already colored.
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At the start of the first screen only, the colored net at right will fold into a
rectangular prism, then unfold back into the net. Subsequent screens will only
provide the static net.
Notice that, in the above screen, orange is a tempting color to use.
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 red?
How many of you think we should color the face purple?
How many of you think we should color the face orange?
Ask a few students to explain why they have chosen that color. In particular,
the discussion about using orange or purple 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.
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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 C ubo i ds | 6 min
Have the students play Pu s h t h e E n v e lo p e - C u b o 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.
C l o si ng | 5 min
A sk: We saw two different types of scenarios today. First, we were
given the rectangular prism and had to color the net. Then, we were
given the net and had to color the prism. 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 prism can take some time
to get accustomed to, but that these challenges provide
opportunities for growth.
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