Objective
By the end of this lesson, you will be able to understand the concept of calculus and apply it to solve Christmas-themed math problems.
Materials and Prep
- Pen/pencil
- Blank paper
- Calculator (optional)
No prior knowledge of calculus is required for this lesson.
Activities
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Activity 1: Santa's Sleigh Speed
Imagine Santa Claus delivering presents on Christmas Eve. Determine Santa's average speed in miles per hour by using the calculus concept of finding the derivative. Calculate the time it takes for Santa to travel a certain distance, and then divide that distance by the time to find the average speed. You can choose a distance and time interval that makes sense to you.
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Activity 2: Reindeer's Acceleration
Explore the concept of acceleration with Santa's reindeer. Assume that one of the reindeer starts from rest and accelerates uniformly to a certain speed. Use the calculus concept of finding the integral to determine the distance the reindeer travels during the acceleration period. You can choose a specific acceleration value and time interval for this activity.
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Activity 3: Present Wrapping Optimization
Imagine you have a rectangular box that needs to be wrapped with the least amount of wrapping paper. Apply the calculus concept of optimization to find the dimensions that minimize the surface area of the box. Calculate the minimum surface area and determine the dimensions that achieve it.
Seventh Grade Talking Points
- "Calculus is a branch of mathematics that deals with rates of change and accumulation."
- "It helps us understand how things change over time and how we can find the maximum or minimum values of functions."
- "In Activity 1, we use calculus to find Santa's average speed by calculating the derivative, which tells us how his position changes with respect to time."
- "Activity 2 involves finding the distance traveled by a reindeer during its acceleration period. We use the concept of integration, which is the reverse process of differentiation."
- "Optimization, as seen in Activity 3, is about finding the best possible outcome. In this case, we are minimizing the surface area of a box to save wrapping paper. Calculus helps us find the dimensions that achieve this."