Thanksgiving
Thanksgiving is a harvest holiday in USA, Canada and many other countries. There are historical, religious and cultural reasons for its celebration but it has become mostly a day for families to get together to feast.
Jony is a 15 year old cheerleader. She wants to look fit and attractive. She may have her own reasons to stay fit and trim but she says that she does it to remain attractive for the game audiences.
Jony and her cheerleading friends Dana and Katy were sitting and chatting. The football season would start soon. They and the other girls had been practicing their cheers since beginning of the school year. They felt pretty good about it but were concerned about the upcoming Thanksgiving holiday.
Excess Calorie Intake
Jony: My grandma lives in Dodoville. She hosts the Thanksgiving family gathering every year. We all love grandma. She is also very affectionate towards us. It is also a chance for me to meet my uncles, aunts and cousins. Oh, grandma is a great cook. That’s the problem. We get filled up with the traditional thanksgiving meal.
Dana: Ya, same here. We can’t stop eating. First, the meal is very delicious and second, grandma makes sure that our plate is full.
Katy: Same here. Not only that, we would have no physical activity on Thanksgiving and two travel days – one to get there and the other to get back. We have to find a way to solve this problem. Let’s us ask Mr. Max (science teacher) and figure something out. There’s got to be a way.
The three of them went to Mr. Max and told him their concern.
Mr. Max: Well it is simple. You have to balance the calorie burnt with the calorie intake. How many of you know what your daily calorie intake and burn are ?
Jony: I have a gismo called Fitcal that monitors my daily calorie burn. It comes out to about 2200 calories per day. Last week, I kept a tab of everything I ate and added the calories. It came out on the average to be about the same or just a few calories up or down.
Dana: The concern is that over the Thanksgiving holiday, we will not be as active and we will also overeat.
Mr. Max: What do you think will be your excess intake?
Jony: I don’t know about others but we have some breakfast and evening snacks that day and here is a typical Thanksgiving feast at our grandma’s house.
| Thanksgiving Day Calorie Intake (approximate values) | ||
| Calories | ||
| Maple Roast Turkey and Gravy | 550 | |
| Harvest rice dish | 250 | |
| Mashed pototo, bacon, mushrooms… | 400 | |
| Stuffing | 200 | |
| Maple cranberry sauce | 200 | |
| Mincemeat and Pumpkin Layer Pie | 400 | |
| Corn | 100 | |
| Dinner roll | 200 | |
| Total for the lunch | 2300 | |
| Breakfast, evening snacks and drinks | 2000 | |
| Total for the day | 4300 |
Mr. Max: That adds up to 4300 calories. Since you normally take in 2200 calories per day, you will overeat by 4300 – 2200 = 2100 calories on the Thanksgiving day.
Jony: We also have a barbecue on the day before and a hefty breakfast the day after. These two are travel days and I can control my calorie intake to the normal total of 2200 calories. Dana and Katy, what about you ?
Dana and Katy nodded in affirmation.
No Exercise On The Holiday
Mr. Max: You will all have very little physical activity on Thanksgiving and the two travel days. What is your physical activity on normal days?
Jony: I walk to school and back, exercise in the PhysEd class and then we have the cheerleading practice. My Fitcal shows that these activities add up to 1000 calories. I guess, I burn the other 1200 calories in all other activities including sitting and sleeping.
Mr. Max: So that means that for the three days you would miss burning a 1000 calories per day or a total of 3000 calories.
Jony: Yes and also would have overeaten at least 2100 calories. So it adds up to 5100 calories.
Jony’s friends said that their problem was similar.
Mr. Max: This year Thanksgiving is on November 25. Here are the graphs for (A) your excess calorie intake, (B) Exercise deficit and the (C) the sum of A and B. I have made the graphs starting from November 19.
The New Plan
| Activities vs calories for a 48 kg female (approximate values) | |
| Sitting, standing being active | 60/hour |
| 5 km run | 300 |
| Hiking/walking briskly | 200/hour |
| Playing soccer for 2 hours | 700 |
Dana: Looks like, we will have to increase our activities somehow.
Mr. Max: So what activities can you do on the three day Thanksgiving trip?
Jony: I will call my cousin Tom and ask if we can go for a 2 hour hike and a 5 km run on the day we reach there.
Mr. Max: Your run and walk on Nov. 24 total burn will be 700 calories. You could also walk around the neighborhood and house to make it a total of 1100 calories.
Jony: On Nov. 25, I will try to organize a 2 hour soccer game for the next morning with all my cousins, and I could also go for a 2 hour walk after the lunch.
Mr. Max: That would also add up to 1100 exercise calories.
Jony: On Nov. 26, after coming home, I could go for another 5 k run and a 2 hour walk. So what does that add up to ?
Mr. Max: So that would be another 700 calories. Be active in the car to make it to a total of 800 calories.
Dana: Let me add up the calorie deficit Jony’s activities will make up on Nov. 24, 25 and 26. These add up to 1100 +1100 + 800 = 3000. The excess calorie intake was 5100. That means, she still has 2100 excess calories to burn.
Katy: I have a suggestion. For 5 days before Nov. 24, we can go for a 5 km runs after our cheerleading practice.
Jony: Yes, that would burn 300 x 5 = 1500 extra calories. We can also do the same on Nov. 27 and 28 for another 600.
Mr. Max drew the graph D of the excess calories burned each day on Nov. 19-28. Mind you, these were for the activities over and above their normal daily activities. Jony followed the proposed schedule. Many other cheerleaders also went for the 5 km run after the cheerleading practice. Some others decided to go on diets.
Challenge
For this proposal to make sense the curve C which represents total of excess calorie intake plus exercise deficit should be cancelled out by the calories burnt in curve D. How can you be sure because the curves C and D look so different ?
The question you should ask is if the total calories on different days add up to the same number in C and D. This concept is called Area Under the Curve and you will learn more about it in Calclulus. The story Johnny and Sara’s place would be a good read even if you are not into Calculus (https://mathstories4u.com/calculus-johnnyandsarasplace/).
Here, we will first make a table of calories for each day in Curves C and sum up all the values from Nov 19 to 28. We will repeat the same process for Curve D. If the sums of the two columns are the same, we will say yes the calories in D are sufficient to cancel out the excess calories in C.
| Calories | ||
| nv | C | D |
| 19 | 0 | 300 |
| 20 | 0 | 300 |
| 21 | 0 | 300 |
| 22 | 0 | 300 |
| 23 | 0 | 300 |
| 24 | 1000 | 1100 |
| 25 | 3100 | 1100 |
| 26 | 1000 | 800 |
| 27 | 0 | 300 |
| 28 | 0 | 300 |
| SUM | 5100 | 5100 |
Math Stories For You 