Do you recognize this object? It’s a pop-up card! Well, it’s the foundation of a pop-up card—without any decorations. Watch how all the shapes move together when the card is opened and closed. What could we turn this card into? A dinosaur, like the one in Matthew Reinhart’s video, perhaps?
In the time-stamped version of the video below, Reinhart explains two of the support structures he uses frequently, the v-fold and the layer. these support structures are called pop-up mechanisms: elements that cause movement on the surface of the page. In this activity, he will build v-bend mechanisms and explore the geometry that makes them pop. you will explore the layering mechanism in a later activity.
You are reading: Making pop up books
materials
- Light Cardstock
- One copy of the Pop-up Template
- Two copies of the Card Template
Remember to be careful when using sharp tools and always cut on a cutting mat or other layer to protect your table.
note: copy paper can be used instead of cardstock, but is more likely to tear if popups are repositioned.
prepare and create your first popup card
- cut out the shapes from the popup template by cutting along the solid lines. On the card template, create two cards by cutting along the labeled cut line. Fold each card and unfold back and forth along the dotted lines so each fold is neat. At the end of this step, you should have four cards and eight shapes. these eight shapes will be our popups and we will refer to them by the number printed on the shape. Tip: Stack your cards and popups by type to work on later.
- Use a protractor to measure angles a and b on one copy of popups #1, #2, and #3. write each angle measure in table i on your pop-up observation sheet. how are angles a and b related in each popup? notice a pattern?
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create your remaining popups
Now that you’ve created your first pop-up card, grab the remaining card stacks. Follow the instructions below to build three different pop-up cards. as you work, record your measurements in table ii on the pop-up observation sheet.
observe
- does each popup stay inside the card when the card is closed?
- how do the measures of angles c1 and d1 compare?
- how measures are compared how many angles c2 and d2 are compared?
- how does line 1 and line 2 make each popup look different?
When you’re done, your three popup cards should look like this:
Credit: Jamie Back Note: You will have one extra copy of Card 2, this is for later.
elaborate your theory: how do popups work?
Mathematicians, like scientists, use observations to make educated guesses. In mathematics, these informed guesses are called guesses. Let’s look at your popup observation sheet and your completed three cards to make guesses about the geometry that causes the v-fold mechanisms to explode. start by focusing on symmetry. parts of objects have symmetry when one part is the same size and shape as another after flipping, rotating, or sliding.
- where do you notice symmetry in your popups and cards? what data from table i or table ii supports your observations?
- can you describe how symmetry might be important to the motion of popups?
Your guesses about symmetry might look like this:
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v-folds have an axis of symmetry. the dotted line on each v-fold mechanism is a line of symmetry. this explains why the angles a and b in each v-fold mechanism have the same measure: the axis of symmetry divides each pop-up window into two parts of the same size and shape.
cards have a line of symmetry. the center fold of the card is a line of symmetry. closing the card reflects line 1 to the other side of the card, making angles c and d the same measure.
In popups, the axis of symmetry of the card and the v-fold are aligned. when we placed our v-folds on the card, the v-fold’s line of symmetry was directly over the center fold of the card. when the two lines of symmetry are aligned, the card and popup open and close together.
other ideas you should think about:
- what could be controlling the height of a popup?
- if a popup extends outside the closed card, what changes could you make to the popup or card to keep the popup inside the card?
what else can you do?
With these observations in mind, play around with how the v-fold mechanisms are attached to your three cards. you can try reattaching the popups to lines that are drawn at different angles or lines that extend in a different direction from the center of the card. you can change the size or shape of the popup. you can even try other ways to attach the popup to the card. while playing, try:
- modify the height of a popup.
- make a large part of a popup extend outside the closed card.
- make two popups lock each other when the card is opened or closed.
- Notice what happens when you position a popup so that its fold is not directly over the center of the card.
v-folds are just one of many types of mechanisms used by emerging artists. In the next activity, we’ll use a layering mechanism to help build our popup. watch the video below to learn how to create simple layers.
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