Lesson 10.2Math is Beauty
Start hereWords, worked example, and sentence starters
Learning target I can use bilateral symmetry to describe structure in nature and in human creations.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| symmetricSpanish: simétrico | Having two halves that match — one side is a mirror image of the other. | A butterfly: the left wing is the mirror of the right. |
| mirror imageSpanish: imagen reflejada | A copy of a figure flipped across a line, so the two halves face each other. | Fold the layer down the middle: each leaf lands on its partner. |
| bilateral symmetrySpanish: simetría bilateral | Reflective symmetry in plants and animals — the two sides of the body mirror each other. | All 17,000+ butterfly species have it — two sides, one mirror line. |
| line of symmetrySpanish: eje de simetría | The line you can draw through a figure so each side is a reflection of the other. | The line straight down the butterfly's body. |
| balanceSpanish: equilibrio | An even, steady arrangement — neither side feels heavier than the other. | Two matching halves — neither side feels heavier than the other. |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
I look at the two sides of the butterfly, and they look like mirror images — the butterfly is symmetric.
- All butterflies have reflective symmetry. In plants and animals, this is called bilateral symmetry.
- To show it, I draw a line down the middle of the butterfly's body: everything on the left is reflected on the right.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
This plant grows in layers, and each layer is made up of two leaves — so 3 layers hold 3 × 2 = 6 leaves.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- has a line of symmetry because the two halves are .
- I have seen symmetry in .
- The two sides .
- A has bilateral symmetry.
Word bank symmetricmirror imagebilateral symmetryline of symmetrybalance
Watch outA common mistake
Thinking a figure lacks bilateral symmetry just because its line of symmetry is not vertical — the mirror line can run in any direction, and the test is whether the two sides match across it.
Lesson 10.2Math is Beauty
Version ASupported practice
Learning target I can use bilateral symmetry to describe structure in nature and in human creations.
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1Circle the letter of the best answer. Show how you know.
What does it mean that a butterfly is symmetric?
- AThe butterfly has exactly two wings
- BThe two sides of the butterfly look like mirror images
- CThe butterfly's wings are very colorful
- DThe butterfly is larger than most insects
Hint Think about what you see on the left wing versus the right wing.
Show your work
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2Circle the letter of the best answer. Show how you know.
In plants and animals, reflective symmetry is called:
- Arotational symmetry
- Ba mirror image
- Cbilateral symmetry
- Dbalance
Hint The word starts with 'bi-', meaning two.
Show your work -
3Circle the letter of the best answer. Show how you know.
A plant grows in layers, and each layer is made up of 2 leaves. How many leaves does the plant have after growing 4 layers?
- A4 leaves
- B6 leaves
- C8 leaves
- D16 leaves
Hint How many leaves are in ONE layer?
Show your work -
4Circle the letter of the best answer. Show how you know.
How can you SHOW that a layer of two leaves has bilateral symmetry?
- ACount the total number of leaves on the plant
- BMeasure how tall the plant is
- CDraw a line down the middle of the layer and check that each side mirrors the other
- DColor the two leaves different colors
Hint Symmetry is about two sides matching.
Show your work
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5Answer in complete sentences.
Where have you seen symmetry before? Name one place and describe it.
Sentence starter I have seen symmetry in ___ .
The two sides ___ .Write your answer -
6Answer in complete sentences.
Name one animal besides a butterfly that has bilateral symmetry.
Sentence starter A ___ has bilateral symmetry.
Its line of symmetry runs ___ .Write your answer
Explain your thinkingFind something in this room that you think has bilateral symmetry and your partner thinks does not. Where exactly would the line of symmetry go, and what makes the two halves mirror images rather than just similar?
Sentence starter ___ has a line of symmetry ___ because the two halves are ___.
Lesson 10.2Math is Beauty
Version BCore practice
Learning target I can use bilateral symmetry to describe structure in nature and in human creations.
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1Circle the letter of the best answer. Show how you know.
Why do people find symmetry pleasing?
- AOur brains are wired to favor balance, and bilateral symmetry provides balance
- BSymmetric things are always brightly colored
- CSymmetry only appears in rare and expensive objects
- DSymmetric shapes are always larger than non-symmetric ones
Show your work -
2Circle the letter of the best answer. Show how you know.
There are over 17,000 species of butterflies, and ALL butterflies have reflective symmetry. About how many of those species have reflective symmetry?
- AAbout half of them
- BOnly the most colorful ones
- CNone — symmetry is only in plants
- DAll 17,000+ of them
Show your work -
3Circle the letter of the best answer. Show how you know.
A plant grows 2 leaves at a time, one layer per week. How many leaves has it grown after 6 weeks?
- A6 leaves
- B8 leaves
- C12 leaves
- D36 leaves
per 1 -
4Circle the letter of the best answer. Show how you know.
Which is the best test for whether a figure has bilateral symmetry?
- ACheck whether the figure has an even number of parts
- BFind a line where one side is the mirror image of the other
- CCheck whether the figure is found in nature
- DCheck whether the figure looks beautiful to you
Show your work
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5Answer in complete sentences.
Are the two leaves in a real plant layer EXACTLY symmetric? Why might this be?
Write your answer -
6Answer in complete sentences.
Where else do you see bilateral symmetry — in nature OR in something humans made?
Write your answer
Explain your thinkingFind something in this room that you think has bilateral symmetry and your partner thinks does not. Where exactly would the line of symmetry go, and what makes the two halves mirror images rather than just similar?
Lesson 10.2Math is Beauty
ChallengeExtension
Learning target I can use bilateral symmetry to describe structure in nature and in human creations.
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1Write the letter of the matching item on each line.
Match each transformation idea to its description.
- Reflection
- Rotation
- Translation
- Rotational symmetry
- AFlip across a mirror line
- BTurn around a center point
- CSlide without turning or flipping
- DFits onto itself in less than a full turn
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2Circle the letter of the best answer. Show how you know.
Your friend insists that only ONE of two flowers has bilateral symmetry, but both pass the mirror-image test — just across lines pointing in different directions. What is the best response?
- AYour friend is right, because a real line of symmetry must always be vertical
- BBoth flowers have bilateral symmetry — a line of symmetry does not have to point the same direction in every figure
- CNeither flower has bilateral symmetry, because flowers are not animals
- DAgree with your friend, because two people should not disagree about math
Show your work -
3Circle the letter of the best answer. Show how you know.
A symmetric garden design puts the same planting on each side of a center path. One side uses 14 tulips and 9 daisies. How many flowers does the WHOLE symmetric design use?
- A23 flowers
- B28 flowers
- C46 flowers
- D126 flowers
Show your work
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4Answer in complete sentences.
You and a friend are studying a building for an art project. The building's left half mirrors its right half. What can you say about the building in terms of bilateral symmetry?
Write your answer -
5Answer in complete sentences.
The lesson says math CREATES the beautiful designs we find in nature. Someone argues back: 'Nature is beautiful, but that has nothing to do with math.' Use the butterfly, the plant, or symmetry in your answer to respond.
Write your answer