Everything in one Equation

When I landed my first teaching job, I was excited beyond words. I become consumed when I am passionate about something, soaking up everything about the object of my passion.  On one particular evening, I was reading the employee calendar when something caught my eye. In the bottom left corner of each calendar block were two numbers separated by a slash. For example, 3/2 or 6/12. I was unsuccessful in trying to figure out these numbers so I flipped to the front of the book. I found an explanation.

Numbers in the bottom left corner of each school-day block denote the instructional day. The school year is made up of nine instructional months and 20 days each, for a total of 180 instructional days. For instance, 4/17 on December 2 is the 17th instructional day of the fourth month of school.

After reading this paragraph, I surmised there had to be a way determine the day of school (1-180) using those two numbers. I played around with different equations. My husband and daughter tried when I enlisted their help, but they couldn’t figure out an equation that would work. I can’t remember how long it took me, but I figured it out that evening.

The equation is: (IM-1)20 + ID= Day of School. That is if you take the instructional month subtract 1 and multiply the difference by 20 and add the instructional day, it would yield the day of school. I eagerly shared it with my class that first year. Considering that my students were only 8 and 9 year olds, I knew it might be difficult for them to understand. I did have one student who grasped the equation to my surprise.

As years passed, I shared the equation with my class, albeit later in the year when I had taught more math concepts. I was met with glassy eyes. My explanation didn’t go over any better with teachers. At the beginning of this year, (my 5th year) I made a commitment to teach this equation at the beginning of the year and require that students figure out the day of school every day. My efforts have reaped much fruit. Every day, I write the IM and ID on the board. Students use these numbers to figure out the day of school. This is their morning work. I’ve also added the expectation that they take the day of school, subtract it from 180 days using the standard algorithm or using mental math. Then they have to write the days we have gone and the days we have left as two fractions of the whole. Lastly, they have to draw a graphic illustrating all this. The graphic is a 3 X 3 grid. The 9 squares stand for each of the 9 instructional months. As we reach 20 days, they shade in a box.

From this simple equation, I can teach much of 4th grade math content: Number & Operations, Fractions, Geometry, and Decimals. This equation that came out of curiosity is a fruitful and authentic math resource. I get so much, veritably, everything in 4th grade math, from one equation.