Playing with Palindromes

Happy 5/21/25! Until May 29th, we’ll be celebrating mathematical palindromes, and sharing easy and fun ways for you to incorporate them into your child’s daily life.

What is a palindrome?

A palindrome is a word, phrase, or sentence that reads the same backwards and forwards. It comes from the Greek word palindromos, meaning “running back again”. You may be familiar with some palindromic phrases—“Madam, I’m Adam” and “a man, a plan, a canal, Panama” immediately come to mind—but numerical palindromes are also found all around us.

By linking a linguistic idea like palindromes to a mathematical idea like symmetry, you can help your child make connections between the two and strengthen their math confidence.

According to Common Core Math Standards, children begin learning about topics like symmetry and mirroring as early as first grade. Building an early understanding can help your child develop the building blocks for using these concepts later in geometry, function interpretation, and trigonometry.

Below are some simple activities for you and your child to explore, this week and beyond!

For the artist: Butterfly Symmetry

An easy analogy for palindromes is that they show "reflectional" symmetry, where an image is reflected over a line, like a mirror.

For this activity, you’ll need a pencil, paints or paint pens, and this butterfly outline PDF.

1. Fold your butterfly page in half along the dotted line, with the butterfly image on the outward-facing sides of the paper.

2. Use a pencil to create a design inside the wing on ONE half of your butterfly.

3. Unfold your paper and fold it the other direction, with the wings facing inward. Crease the paper, so it can fold back and forth easily. Unfold and lay the paper flat on the table.

4. Use paints or a paint pen to trace ONE line or fill in ONE shape you drew with the pencil.

5. Fold the butterfly in half so that the wings are on the inside. Press firmly so that the paint transfers from one wing to the other. Fold carefully to avoid smudging!

6. Unfold the butterfly. You should now see the shape that you colored reflected on the other side!

7. Repeat steps 1 – 3 with each of the shapes you drew.

For the adventurer: Symmetrical Scavenger Hunt

Reflectional symmetry can be found in nature, too! On a walk to the bus stop or while playing in the backyard, look for symmetrical objects all around you. Leaves, house windows, and cars are all great places to look for symmetry.

Recognizing numerical palindromes is another great way to build your child’s number sense. Try looking for car license plates, building addresses, and times on a digital clock. Have your child read out the numbers from left to right, then from right to left. Encourage them to not just recognize palindromes, but be able to explain why some numbers are palindromes and others aren’t.

For the writer: Palindrome Poetry

If your child is interested in writing, using palindromes is a great way to teach pattern concepts like rhythm and meter. Kids can count words, syllables, or sentences to make poems that follow a palindromic format.

Here are a few prompts for palindrome poetry for different age ranges:

For early elementary, focus on simple palindromic words.

Start with words like “level”, “rotor”, or “madam”. Spell these words out, and encourage your child to explain why these are palindromic words.

Then, use these words to make silly sentences! Notice the shapes your mouth makes when you say these words.

i.e. “Rotor spins around and around.”

For late elementary, challenge kids to create poems where entire sentences are palindromes.

This requires more planning, creativity, and patience. Remember that the words don’t need to have an identical number of letters, and that the middle of the palindrome can be one letter or two.

i.e. “Race fast, safe car”; “Was it a car or a cat I saw?”

For middle schoolers, create poems where the structure is palindromic.

When the poem’s structure mirrors itself, the number of lines or syllables in each line might be palindromic, as in the poem Dammit I’m Mad by Demetri Martin. Each line could also mirror each other, as in the poem Doppelgänger by James A Lindon.

i.e. this syllabic palindrome “Cry / when I / find that my / best friend has / left once / more”

For high schoolers, challenge them to use palindromic words, sentences, and structures all at once.

This requires advanced planning, and a strong understanding of poetic structure. Don’t be afraid to start from an existing palindromic poem. For example, how could we expand on the palindrome “A man, a plan, a canal: Panama.”? Could we add some information before and after about the Panama Canal? Or who the man was?

Don’t be afraid to mess with the internal meter and structure. Once you’ve practiced all these skills, nothing’s stopping you from making an amazing palindromic poem!

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We hope this has given you some ideas to talk about reflectional symmetry and palindromes with your family!

If you’re interested in exploring more mathy concepts with us, check out our Events Calendar to find an event near you. Happy Palindrome Week!