Article
Courtesy of Vivian Moy
Math,

Pop-up Designer

Matthew Reinhart makes art that leaps off the page

By Stephanie Warren Drimmer
From the Special Collections Issue

Learning Objective: Students will identify and draw lines of symmetry in 2-D drawings based on the designs of 3-D pop-up art. 

Lexile: 830L; 670L
Focus Area: Geometry,
Standards
  • CCSS: 4.G.A.3, MP3, MP4, MP6 TEKS: 4.6B

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Lexile® measure

  • 830L
  • 670L

Matthew Reinhart works at a table covered with paper scraps in his studio in New York City. He cuts, folds, glues, and tapes pieces together to create a flat shape. Then he pulls a paper tab. Suddenly, the flat shape springs to life. It unfolds into a 3-D sculpture of a monster that waves its claws and gnashes its teeth.

Reinhart designs pop-up books. He helps bring stories to life with dinosaurs that “roar” and fairy-tale princesses that spin. Reinhart combines science, engineering, and art to make his amazing paper creations.

Matthew Reinhart works at a table covered with paper scraps. He has a studio in New York City. He cuts, folds, glues, and tapes paper pieces together. First, the creation is a flat shape. Then Reinhart pulls a paper tab. Suddenly, the flat shape springs to life. It unfolds into a 3-D sculpture of a monster. It waves its claws and gnashes its teeth.

Reinhart designs pop-up books. He helps bring stories to life. He makes dinosaurs that "roar" and fairy-tale princesses that spin. Reinhart combines science, engineering, and art to make his amazing paper creations.

Making a new pop-up book takes a lot of planning. Reinhart first writes an outline showing what will be on each page. For example, to make a dinosaur book that includes a T. rex, “I think: What’s the coolest way for readers to encounter a T. rex?” says Reinhart. “Maybe it tries to bite them!”

Next is the engineering stage. “That’s when I cut and fold paper to figure out how to make a T. rex that bites,” he says. He uses different folding techniques to create various effects in a pop-up. 

Making a new pop-up book takes a lot of planning. Reinhart first writes an outline. This shows what will be on each page. For example, to make a dinosaur book that includes a T. rex, "I think: What's the coolest way for readers to encounter a T. rex?" says Reinhart. "Maybe it tries to bite them!"

Next is the engineering stage. "That's when I cut and fold paper to figure out how to make a T. rex that bites," he says. He uses different folding techniques. This creates various effects in a pop-up. 

Courtesy of Matthew Reinhart

Every pop-up Reinhart creates is unique—he goes through a lot of trial and error. He builds each piece as many as 20 times until it works exactly right. 

“I go through a lot of paper!” he says. “But failing is OK. That’s how I discover ways to make a piece move in a really new and cool way.”

Every pop-up Reinhart creates is unique. He goes through a lot of trial and error. He builds each piece as many as 20 times until it works exactly right.

"I go through a lot of paper!" he says. "But failing is OK. That's how I discover ways to make a piece move in a new and cool way."

MATH TALK:

Must a book’s pop-ups be symmetrical?  Why or why not? 

MATH TALK:

Must a book’s pop-ups be symmetrical?  Why or why not? 

Lines of Symmetry

Lines of Symmetry

Now You Try It

Reinhart has to think about lines of symmetry often when creating his folding pop-ups. Can you find the lines of symmetry in each pop-up illustration that follows? Some may have more than one line of symmetry. Others may have none.

Reinhart has to think about lines of symmetry often when creating his folding pop-ups. Can you find the lines of symmetry in each pop-up illustration that follows? Some may have more than one line of symmetry. Others may have none.

1A. This lizard has one line of symmetry. Draw a line through the lizard to show its symmetry.

1A. This lizard has one line of symmetry. Draw a line through the lizard to show its symmetry.

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1B. What type of line did you draw above?

1B. What type of line did you draw above?

2. Draw all the lines of symmetry on this snowflake. How many does it have?

2. Draw all the lines of symmetry on this snowflake. How many does it have?

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3. Circle the castle that has one line of symmetry.

3. Circle the castle that has one line of symmetry.

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4. Circle the part of this lizard that would have to change for it to have a line of symmetry.

4. Circle the part of this lizard that would have to change for it to have a line of symmetry.

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5. Draw an image that has at least one line of symmetry. Mark the line(s) of symmetry with dotted line(s).

5. Draw an image that has at least one line of symmetry. Mark the line(s) of symmetry with dotted line(s).

video (1)
Activities (1)
Skills Activities
Answer Key (1)
video (1)
Activities (1)
Skills Activities
Answer Key (1)
Step-by-Step Lesson Plan
Download the Lesson Plan

1. SPARK ENGAGEMENT.

Play the video “Engineering the Perfect Pop-up”. Before or after reading the article, spark a discussion based on the following questions as a whole group, in small groups, or with a partner:

  • Do you think the images in a pop-up book are more engaging than pictures in a traditional book? Why or why not? 
  • What math skills do you think Matthew Reinhart uses when making a pop-up art image?

2. INTRODUCE THE MATH CONCEPT AND VOCABULARY.

Engage students with the following questions to discuss the meaning of symmetry:

  • With your partner or group, discuss, draw, and list types of lines. (straight lines, number lines, perpendicular lines, parallel lines, right angles, etc.) 
  • Fold an 8 in. x 11 in. piece of paper in half vertically.  
  • The fold in this paper represents symmetry. 
  • Write down what the word symmetry means to you. Have students share their definitions aloud. 
  • Discuss and create a working definition for symmetry as a class. 

3. WORK THROUGH A SAMPLE PROBLEM AS A CLASS.

  • Give each student a square sticky note.   
  • Do you see a line of symmetry? (Yes.) Is there more than one line of symmetry? (Yes.) 
  • Fold your sticky note to show all the lines of symmetry. Then go over those lines by creating dash marks with your pencil.
  • How many lines of symmetry are there? (4 lines) 
  • How do you know this? (Possible answer includes: I was able to fold my sticky note 4 times so that the 2 sides were congruent, or the same.)
  • Draw your own shape. Switch with a partner and have them find all the lines of symmetry for your shape.  
  • Have a few pairs of volunteers share their shapes and lines of symmetry that they found. Discuss any misconceptions as a class.

MATH COACH’S TIP:

Folding paper 2-D shapes is a great way for students to identify lines of symmetry. It’s important to remember that the entire cross-sectional line represents one line of symmetry. Sometimes students will count each individual line coming from the central point. − Melinda Villalovos, District Math Coach, Arizona

MATH COACH’S TIP:

Folding paper 2-D shapes is a great way for students to identify lines of symmetry. It’s important to remember that the entire cross-sectional line represents one line of symmetry. Sometimes students will count each individual line coming from the central point. − Melinda Villalovos, District Math Coach, Arizona

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