The Superhero 1: A Math Lesson for the First Day of School
The number one is a fascinating number! So why not celebrate it on the first day of school!
Why is 1 so important? For a lot of reasons:
It’s the first of the set of counting numbers. After all you can’t count to one hundred without starting at one. It’s part of the Multiplicative Identity Property, which is so essential for students in Pre-algebra and Algebra 1 as the backbone of equivalence. In fact, one of the first lessons I used to do every school year centered around equivalence. So why not celebrate 1 the superhero! In addition to middle school and Algebra, this lesson can also be useful for fraction equivalency in Grades 3-5.
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How to Count to 1
How to Count to 1 by Casper Salmon is a fun way to launch your math class celebrating the number 1. It’s a funny picture book about counting to 1. The reason I like it as a first day of school activity is that it’s not only lighthearted and funny, but it helps ease math anxiety because everyone can count to 1! Or can they?
The Invisible 1
When teaching middle school and Algebra, I had a cape with the numeral 1 on the back. When I wore the cape, I told the students I was a math superhero. My secret identity was one (x * 1 = x or 1x = x), and I had the power of invisibility and to take on other forms (e.g., 3/3). I even had one of my students make me an animation of the “Invisible 1” to share with my students.
So, after reading How to Count to 1, slip behind your door or out into the hallway and throw on your superhero cape and emerge as the “Invisible 1”. Then write an equation on the board such as x + 3x + 4b = 16 and challenge students to find the invisible ones lurking in the equation.
Preventing Misconceptions: One of the most helpful places to find the “Invisible 1” is in front of the first term, x. Point out to students that an x can be written as 1x because of the Multiplicative Identity Property. Having students find the invisible 1 coefficients before combining like terms (1x + 3x + 4b = 16) helps students avoid common errors such as x + 3x = 3x2. As soon as they write the coefficient before the variable, they usually realize that they need to add the coefficients instead of combining variables (1x + 3x = 4x).
But there are other places that 1’s can hide. They can be found in denominators, for example x + 3x + 4b = 16 can be written as (x/1) + (3x/1) + (4b/1) = 16/1 or (x + 3x + 4b)/1 = 16/1.
Another tricky thing that ones can do is appear as fractions and these 1’s can appear in all sorts of crazy forms (e.g., 1/1, 3/3, 4/4, 100/100, -2/-2, 3.75/3.75, (x+2)/(x+2)). Now let’s look at our original equation. Where can we find some invisible 1s? Here is one example: (5/5)x + (2/2)3x + (2.5/2.5)4b = (-3/-3)16. It’s good for kids to practice adding invisible ones all over the place. But then talk about which invisible ones are useful and which are not. For example when adding (¾)x +(2/3)x, it would be useful to rewrite the equation using invisible 1’s in the form of 12/12 getting (12/12)(3/4)x + 12/12(2/3)x. If grade-level appropriate this could lead to a useful conversation about clearing fractions from equations. Why can you clear fractions from equations? Because of the invisible 1’s of course!
You can also use the concept of invisible 1’s to discuss why the Multiplicate Inverse Property works. Why does 2/3 * 3/2 = 1 because there are two other invisible 1’s hiding as the equation can be rewritten as (2/2)(3/3) = 1. Look at all those sneaky ones!
Equivalency Challenge
Write the number 1 on the board and ask students to write as many equivalent expressions to 1 as they can. You may even want to give a prize to the winner. This is also a good time to integrate the Additive Identity Property as well. Here are some examples: 1 = 5/5 = 1 + 3 – 4 = 2.65/2.65 = a + 1 – a = (3x + 2b + 4)/(3x +2b + 4), etc.
Conclusion
The first day of school can be hard for students with math anxiety, so why not try to lighten the mood with a zany superhero! But even if you want to stick with your normal first day of school routine, you can do “Invisible 1 Day” any day of the year to reinforce equivalency and prevent common misconceptions!
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More Math Lessons
If you like this lesson, check out some of my other math and STEM activities.
- Improve Test Scores and Student Engagement by Starting Your Year Teaching Statistics
- Using Patterning to Explore Powers and Exponents | Free Math Lessons
- Using Understanding to Teach Linear Equations |Free Math Lessons
- Increase Student Engagement by Using Picture Books to Launch the Notice & Wonder Routine
- Fostering Estimation Strategies Using The Best Mouse Cookie by Laura Numeroff
- A Mathematical Journey through Zero & Infinity-Part 1: A Mystery Box, Some Books, and a Contest
- Using a Picture Book and Magnetic Tiles To Teach Integers
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Ladder and Friends Learn to Pray
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Many of the Christian resources I found for young children had cute little kids and cuddly animals. This was not appealing at all to my son; he wanted trucks and wheel and trains! So, I scoured Amazon looking for Christian books aimed at young boys, but I couldn’t find anything. Therefore, I decided to write my own. It should be available late Summer 2026. Join my pre-order mailing list today to get the latest updates about when the book will be available. (Note: There is NO financial obligation at this time!)
