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Laabri

(U2) - Lesson 1 Piggies and Pools

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Lesson Summary:

In this lesson, we learned that the possible inputs for a function are called the domain. We found that some situations are best described using a discrete model and others are represented better with a continuous model. Arithmetic sequences are part of the linear family of functions and geometric sequences are part of the exponential family of functions.

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Today's Learning Goal:

  • Surface the difference between a discrete and continuous model for a given context.

  • Introduce continuous exponential functions.

  • Recognize that arithmetic sequences are linear functions by examining the constant rate of change.

  • Recognize that geometric sequences are exponential functions by examining the constant ratio of values over equal intervals.

  • Introduce the concept of the domain of a function defining the possible input values.

Today's Materials:

  1. Laptop

  2. Pencil

  3. Guided Note Sheet

  4. Binder

Please complete the Jump Start (activator). This is independent it should be silent.

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1.

Describe what a discrete function would look like on a graph.

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2.

Describe what a continuous function would look like on a graph.

Launch, Explore, Discuss

We are beginning on the guided notes paper. Problems 1-4.

Launch, Explore, Discuss

Lets compare the problem 1-4 to find similarities and differences with each other.

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6.

Closure - Debreif: What is the mathematical reason that the dots are connected on some graphs and not on others?

Independent Practice

Instructions:

Predict the next two terms in the sequence. State whether the sequence is arithmetic, geometric, or neither.

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7.

Predict the next two terms in the sequence.

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Predict the next two terms in the sequence.

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Independent Practice

Instructions:

Identify whether the following statements represent a discrete or a continuous relationship.

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12.

The hair on your head grows 1/2 inch per month

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13.

The city of Buenos Aires adds 6,000 tons of trash to its landfills every day.

Independent Practice

Instructions:

Show your work!

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8.

State whether the sequence is arithmetic, geometric, or neither.

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9.

State whether the sequence is arithmetic, geometric, or neither.

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11.

State whether the sequence is arithmetic, geometric, or neither.

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14.

Apples are on sale at the market at 4 pounds for $2.00. What is the price for 1 pound?

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15.

One dozen (12) eggs cost $1.98. How much does 1 egg cost? (Round to the nearest cent.)

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16.

Best Shoes had a back to school special. The total bill for 4 pairs of shoes came to $69.24 (before tax). What was the average price for each pair of shoes?

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