Article
Courtesy of Yaowu Yuan (Top Yellow Flower, Top Red Flower, Yuan)
Math,

The Colorful Life of Flowers

Scientist Yaowu Yuan uses math models to study flowers

By Jeanette Ferrara
From the March 2021 Issue

Learning Objective: Students will identify and draw one or more lines of symmetry in flowers.

Lexile: 880L; 800L
Focus Area: Geometry,
Standards
  • MATHEMATICAL PRACTICES: MP3, MP4, MP6 CCSS: 4.G.A.3 TEKS: 4.6B

Presentation View
See Student View

Lexile® measure

  • 880L
  • 800L
horizontal

Parallel to the base
vibrant

Bright and colorful
traits

Qualities that an individual has, such as a person’s hair color
variety

A selection of different types of the same thing
symmetry

When something has one side or half that can fit exactly on top of the other half

Example: A square is a symmetrical shape because each side is the same as its opposite side.
biologist

A scientist who studies living things
range

A set of different things of the same general type

Example: Flowers have a wide range of patterns, from stripes to dots.
hues

Colors
vertical

Perpendicular to the base
landing strips

Long runways used by airplanes to take off or land
pollinators

Things that spread pollen from flower to flower—often insects such as bees

Courtesy of Yaowu Yuan (Top Yellow Flower, Top Red Flower, Yuan)

Different monkeyflower species and varieties

Heather Angel/NPL/Minden Pictures

Freckle-like dots, blobs of color, spirals! The petals of wild monkeyflowers show a dazzling variety of color combinations. They have more than 100 possible patterns!  

Why so many varieties? These vibrant hues help with pollination, the act of spreading a plant’s pollen so it can reproduce. The petal patterns act like landing strips for pollinators such as bees. They guide the insects into the flower so the bugs will pick up pollen and spread it to other flowers. Scientists know why these flowers look so different—but they want to know how.

Dots like freckles. Blobs of color. Spirals! The petals of wild monkeyflowers show an amazing variety of color combinations. These petals can show more than 100 possible patterns!

Why so many varieties? The vibrant hues help with pollination. Pollination happens when pollen from a plant spreads to other plants. Pollination is how plants reproduce. The petal patterns act like landing strips for bees and other pollinators. The patterns guide the insects into the flower. Pollen sticks to the bugs. Then the bugs spread the pollen to other flowers. Scientists know why these flowers look so different. But they want to know how.

Courtesy of Yaowu Yuan

Yaowu Yuan studies flowers at his lab in Connecticut. 

That’s where Yaowu Yuan comes in. He’s a biologist at the University of Connecticut. Yuan looks at the flowers’ genes, material that’s passed down from generation to generation. Genes determine traits such as hair color and eye color in humans. In monkeyflowers, genes determine petal colors and patterns.

Yuan uses laboratory techniques to turn off specific genes in a developing plant. Then he records how each change affects the plant’s appearance as it grows. 

“We are trying to figure out how to change a single gene so that the petal pattern changes,” says Yuan. For example, “we’re studying how to change a spot to a stripe.” 

Yaowu Yuan is a biologist at the University of Connecticut. Yuan looks at the genes of monkeyflowers. Genes are material that is passed down from generation to generation. Genes determine traits such as hair color and eye color in humans. Genes determine petal colors and patterns in monkeyflowers.

Yuan uses laboratory techniques to turn off specific genes in a developing plant. Then he records how each change affects the way the plant looks as it grows.

“We are trying to figure out how to change a single gene so that the petal pattern changes,” says Yuan. For example, “we’re studying how to change a spot to a stripe.”

Yuan hopes his research helps scientists better understand the relationship between genes and physical traits in a wide range of plants and animals. 

“Understanding the beauty in nature is incredibly satisfying,” says Yuan. “And nature is, of course, full of math.”

Yuan hopes his research will help scientists understand more about how genes and physical traits are related to each other. He hopes his research will be useful in studying a wide range of plants and animals.

“Understanding the beauty in nature is incredibly satisfying,” says Yuan. “And nature is, of course, full of math.”

Math Talk

What other patterns do you notice in nature?

Math Talk

What other patterns do you notice in nature?

Fractions to Decimals

What to Do

A line of symmetry divides an object into 2 equal parts that are mirror images of each other. Yuan has to think about lines of symmetry often when studying the petal patterns.

Some objects have 1 line of symmetry.

Some objects have more than one line of symmetry. Weʼve marked 4 lines of symmetry on this star, including a horizontal line and a vertical line.

Some objects have no lines of symmetry, like this key.

Shutterstock.com

Example

Does the monkeyflower below have a line of symmetry?

Marybeth Rivera

Yes, you can draw 1 vertical line of symmetry. The parts on each side of the line are mirror images.

Fractions to Decimals

What to Do

A line of symmetry divides an object into 2 equal parts that are mirror images of each other. Yuan has to think about lines of symmetry often when studying the petal patterns.

Some objects have 1 line of symmetry.

Some objects have more than one line of symmetry. Weʼve marked 4 lines of symmetry on this star, including a horizontal line and a vertical line.

Some objects have no lines of symmetry, like this key.

Shutterstock.com

Example

Does the monkeyflower below have a line of symmetry?

Marybeth Rivera

Yes, you can draw 1 vertical line of symmetry. The parts on each side of the line are mirror images.

Now You Try It

A. This monkeyflower has 1 line of symmetry. Draw a line on the flower to show its symmetry.

B. What type of line did you draw above? 

A. This monkeyflower has 1 line of symmetry. Draw a line on the flower to show its symmetry.

B. What type of line did you draw above? 



Draw the line(s) of symmetry on this flower. How many does it have?

Draw the line(s) of symmetry on this flower. How many does it have?



Circle the flower that has 1 line of symmetry.

Circle the flower that has 1 line of symmetry.



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

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



Draw a flower that has at least 1 line of symmetry. Use dotted or dashed lines to mark the line(s) of symmetry.

Draw a flower that has at least 1 line of symmetry. Use dotted or dashed lines to mark the line(s) of symmetry.

Continue Your Learning

  • Rewatch the video “Powerful Plants!” above. Then draw your own flower and label each of its parts using what you learned from the video. Circle the part of the flower where photosynthesis occurs.
  • Play a symmetry drawing game! Number a set of note cards 3, 4, 5, 6, and 8 and shuffle them. Pick a card. This will tell you how many sides the shape you draw must have. Then flip a coin. If the coin lands on heads, draw your shape with at least 1 line of symmetry. If the coin lands on tails, draw your shape with no lines of symmetry. Take turns playing with a friend or family member. 

Continue Your Learning

  • Rewatch the video “Powerful Plants!” above. Then draw your own flower and label each of its parts using what you learned from the video. Circle the part of the flower where photosynthesis occurs.
  • Play a symmetry drawing game! Number a set of note cards 3, 4, 5, 6, and 8 and shuffle them. Pick a card. This will tell you how many sides the shape you draw must have. Then flip a coin. If the coin lands on heads, draw your shape with at least 1 line of symmetry. If the coin lands on tails, draw your shape with no lines of symmetry. Take turns playing with a friend or family member. 
video (1)
Activities (8)
Question & Answer Sheets
Skills Activities
Answer Key (1)
Text-to-Speech