## Note Card Activity - Section 3: Writing Functions to Model the Scenario

# The Tortoise and The Hare Project Day 1

Lesson 12 of 24

## Objective: Students will be able to write and evaluate functions modeling a race between the tortoise and the hare.

## Big Idea: Will the tortoise win again? Students will not only find out but write a mathematical story about it.

*60 minutes*

#### Warm up and Homework Review

*10 min*

I include **warm ups **with a **rubric **as part of my daily routine. My goal is to allow students to work on **Math Practice 3 **each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Tortoise and Hare Project Day 1 which asks students to evaluate the accuracy of an equation modeling linear data.

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**To see this part of the lesson unfold, watch: Classroom Video: Vertical Alignment**

I begin by asking my students how many of them know the story of The Tortoise and The Hare. Often, I find that many are unfamiliar with it. I then give the students a quick retelling of the story. This is the hook into the lesson. Here is a nice short retelling of the story.

This lesson is adapted from a free Math Projects Journal lesson*. I am impressed with their products and encourage you to check them out. This and the next two lesson share how I put this project into action since with my students this project takes three days. While I love the depth and multiple representations in the project, by itself it does not reach deeply enough into CCSS Algebra 2 standards. With that in mind, I added a fourth day and piece-wise function extension that extends the project to CCSS the [Algebra 2] functions students will study this year. This extension also addresses the fact that situations modeled mathematically often need to be simplified for increased clarity .

web reference: The Math Projects Journal

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**To see this part of the lesson unfold, watch: Classroom Video: Checks for Understanding**

I tell students that the goal of this project is to write a mathematical story about the tortoise and the hare "rematch". I have students do a think-pair-share to describe the speed of a runner. The goal is for the students to realize that speed is variable. Once that has been discussed, I tell them that this makes some situations hard to model therefore we will be simplifying the situation and I ask them what we could do to simplify this situation [to make it easier to model]. You may need to guide the class response so they conclude we'll need to use average speed.

The mathematical premise we then use as a class becomes:

*The Tortoise and the Hare finally have their **long awaited rematch. The Tortoise gets a 1000 foot lead and runs at 9 inches per second. The Hare begins at the starting line and runs at a rate of 6 feet per second. There is also a rat in this race. The Rat starts 1,200 feet ahead of the Hare and runs back towards the starting line at a rate of 2 feet per second*.

We discuss this as a class and then, in pairs, they work to write equations for the distance traveled by each of the runners, the one minute mark, and the finish line using *d* for distance and *t *for time (**Math Practice 4**). These constitute the first activity on the worksheet from Math Projects Journal.

Some students get these quickly while others struggle (**Math Practice 1**). I walk around during this time and provide guidance as needed. Often, all it takes is walking though one of the animal distance problems for the students to feel more comfortable. If too many groups are struggling, we may stop and discuss one of the problems as a class. The key is to use students to build the model rather than doing it personally. I will do the **Note Card Activity** to go over all of the equations. All five equations will be placed on a single note card and all the variations to each will go up on the white board at the same time. It is important for the success of the rest of the project that all of the students have the correct equations at this point.

NOTE: you will need copies of page 2-3 from the Activity-Tortoise and Hare Project as these will be used for the first three days of the project.

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**To see this part of the lesson unfold, watch: Classroom Video: Developing a Conceptual Understanding**

The remainder of the class will be spent determining a variety of information about the race using the equations written in the last section (**Math Practice 2**). These questions are located in Activity-Tortoise and Hare Project located in Section 3. This information will be important for the story that the students will be writing about the race. As they work, I walk around providing direction for students who are struggling. Any unfinished portions will be completed for homework if students need the extra time.

In the next lesson, the students will finish finding any information relevant to the race and then graph the scenario in preparation to write a chronological story based on all portions of these functions.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test