In the excitement of beginning a 5th grade math enrichment club I created a math problem that may have been a bit extreme. I wanted to use something from real life, make it challenging, and leave my students thinking. 

The topic I settled on was sodium; specifically, our salt intake. What 5th grader can resist paying attention to a life and death lesson? They may have already heard about salt consumption severity, but if not, they will! This should make the lesson stick. (see “Explanation” of The Power of Contrast.) As it turned out, I was right. Not only did a few of the 5th graders understand the dangers of salt, but some knew that too much can negatively affect your blood pressure. 

In order to increase the cool-factor of the lesson, I explained the importance of salt in conducting electricity throughout your body. I did this by asking them which is more dangerous during a lightning storm, swimming in a chlorinated pool or a salt water pool. Salt is a much better conductor of electricity than regular, clean water. They were energized by this new information. (For a very easy to read article about salt’s necessary functions in our bodies, check out “Pass the Salt: Sodium’s Role in Nerve Signaling and Stress on Blood Vessels” by Abbey Bigler-Coyne. And, here is an awesome, short read about salt’s dangerous properties during lightning storms: “Ask the Physicists: Swimming in a Lightning Storm“)

I knew that the 5th graders had been working with decimals. I thought it would be fun to make a problem that had them wrestle with decimals in more than one way. We would average our salt intake. 

First, I did some research. According to the American Heart Association, humans would ideally consume 1,500 milligrams (or less) of salt per day. Written in decimal form, this translates to 1.15 g.

American foods are loaded with salt, and our favorites are the worst! For lack of time, I did not burden my math enrichment students with too much detail. They had no trouble understanding what foods are super salty. They mentioned French fries, hot dogs, and chicken fingers. Then, we discussed foods that didn’t seem salty, but definitely had some, like ice cream. 

This set me up for presenting my word problem: While the human body needs some salt (only around 500 mg), too much of it can be harmful. It is recommended to consume around ½ of a teaspoon or less per day. A half of a teaspoon of regular table salt measures about 1.15 grams. 

Some foods are notoriously more salty than others. In the interest of being healthy, one might try to consume less salt on days surrounding heavy intake periods. 

Look at the data to the right. How many days will this person need to consume only 1 gram of salt in order to bring their average down to 1.15 grams per day?

How It Works

Before going over the problems with my 5th grade math enrichment students, I taught what it means to find the average of a few numbers. I pretended that the students had taken a quiz, and I wrote some fake scores on the board. What was the average score? It isn’t necessarily the middle of the range (distance from smallest to greatest). I had written 10, 8, 5, 6, 8, 4, 0. (They insisted that someone get a zero; Rude! I suggested that the zero was probably due to the person failing to put their name on the quiz, and couldn’t get any credit;) 

There were two 8s. That might pull the average up. “You use an algorithm to find the average, and it can adjust,” I explained. I showed them how you add all of the numbers together, and then divide by the number of scores. “There’s more than one 8, so that should cause the average to weigh heavier on the higher end of scores. But, then the zero is going to drag the average down.” 

“It is like tug of war,” I explained. “The higher the scores, the more the rope gets pulled in that direction. If there are more low scores, the rope begins to go to that side.” 

We played with the numbers, changing them a few times. I showed how, when you raise a few grades, the average goes up. I had students make predictions. 

Next, I showed the 5th grade math enrichment team our word problem for the day. I read it to them, and then asked them our Ready Math questions that help us understand word problems:

1. What is this problem about? A. Salt; Adjusting the average consumption.
2. What are we asked to find? A. The number of days necessary to significantly decrease our average amount of salt consumption.
3. What is the important information? A. The amounts of salt we consumed over the weekend, our goal, and the amount of salt we will allow ourselves to eat until we reach our average goal.
4. And finally, what are you going to do? A. Continue figuring out the average of the three weekend amounts, combined with ones (1 gram per day) until you reach an average < 1.15 g.

They understood the story of the problem. We ate way too much salt over the weekend. Now, we feel the need to eat extra healthy to make up for it. 

I walked the class through one or two tries: “If you consume only one gram of salt during the day after the weekend, what happens to the average?” We added up the number of grams, and then divided by the four days in question. 9.61 ÷ 4 = 2.40, still too high.

I had placed the word problem in a Jamboard. When I pushed the lesson out to my 5th graders via their new 5th Grade Math Enrichment Google classroom, I made a copy for each. I let them wrestle with the numbers on their own for a few minutes. I showed them how you can “duplicate” a slide in Jamboard, so that all of the important numbers and word problem get carried over to another clean workspace. I wanted them to try the math a few times, showing me their work. 

I caught a few of them trying to average the three days of the weekend. I told them that this was unnecessary, because we already know that every single day of the weekend was way over our end goal of 1.15 g! “You can go ahead and practice averaging, but this won’t get you to our goal: Finding the day we don’t have to limit our salt intake to only 1 gram.” 

After a while, I wrote the weekend numbers on the dry erase board: 2.56, 3.08, and 2.97. Then I said, “What if you eat only one gram of salt for the next ten days?” I drew ten ones next to the first three numbers. “In order to find the average, you first add all of the numbers together.” I drew plus symbols between every number. “Next, you divide by the number of weights.” I walked them through dividing 18.61 by 13. “The average intake would be 1.43 grams per day. This is still too high, so we have to continue eating only one gram per day a little longer.”

We hadn’t found the answer by the end of our time together, but that was okay. This time of math enrichment was meant to provide teaching that they can bring back to class and use on their own during independent work time. I had hoped that some of the students would continue working on their salt word problem throughout the week, when they finish their other work. 

A few students seemed excited about finding the accurate number of days as they left the classroom. They told me their tries and expressed surprise at not finding the answer yet. I told them to keep going. It was out there!

I found out later that a few students expressed to their math teacher that the problem was a little too hard. This inspired me to include the next part of this blog; The explanation. 

I chose 1 gram to be the new amount that the person consumes each day because you could eliminate one of the steps from the algorithm for solving averages, if you used increments of ten days. More than erase the step, you do it mentally. We already did ten days in class. That wasn’t low enough. Next, try 20 days. If you remember that the three days from the weekend is 8.61 g, all you have to do is stick a two in front of it! Then put a two in the tens place of the number you are dividing by; 23 (twenty more days + the three weekend days). At this point, it would be best to use a calculator to figure out the long division. (I never said that you couldn’t. I modeled using long division, but once you leave the classroom… 😉 Just show your work!! Write down what you did. Document each try, the answer you got, what you did. Be a scientist about it. 

Once you find between what two tens your answer falls, you can begin narrowing your work further. 28.61 ÷ 23 = 1.24 (twenty days of 1 gram of salt per day); 38.61 ÷ 33 = 1.17 average grams of salt per day; close, but not there yet; 48.61 ÷ 43 = 1.13 We made it! …But, we only ate one gram of salt for more days than necessary. We overshot our goal. In order to figure out the exact day, we could go back one or two days at a time. Maybe try the middle; 35 days. 

One student messaged me within the 5th Grade Math Enrichment Google classroom, seeking clarification. She had taken notes on my example of ten days, and couldn’t remember why we added the ten to 8.61. I messaged her back, and a couple of days later, she had it! This student not only figured out the answer, but showed me all of her work. It is beautiful and impressive. 

In addition to this incredible success, however, I am pleased to share that some of the students were still mentioning the problem to me in the hall, days later. A student whom I see riding his bike when I monitor the crosswalk in the mornings queried if anyone had solved the problem, and we talked about possible solutions. I told him that it was more than 30 days. He couldn’t believe it.