##
* *Reflection: Checks for Understanding
The Tortoise and The Hare Project Day 2 - Section 1: Warm Up

I received an amazing amount a great responses to this question. I really like open-ended questions like this because they can bring out some misunderstandings that may not pop up otherwise. One interesting issue that came up with several of my students, as seen in Student Work 1, Student Work 2, and Student Work 3, had to do with mixing units within a modeling situation. This let me know that these students were struggling with the concept of linear growth and modeling in general.

A great way to deal with a problem like this is to use an activity like My Favorite No or putting it on the board for a class discussion. I never give the name of the student unless they identify themselves. I also engender a classroom atmosphere of discovery and comfort with the fact that mistakes get made when exploring mathematics. This helps students learn from their mistakes rather than fear making them.

*Checks for Understanding: Mixing Units*

# The Tortoise and The Hare Project Day 2

Lesson 13 of 24

## Objective: Students will be able to graph functions and identify their important features in relationship to a real-life scenario.

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

*50 minutes*

#### Warm Up

*5 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. The Video Narrative explains this lesson’s Warm Up- Tortoise and Hare Project Day 2 which asks students to write a scenario to match a function.

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#### Function Review

*10 min*

This is the second day of the five day project. In the last lesson, the students built functions to model the rematch between the tortoise and the hare, and then used the functions to find important information about the race.

I have student pairs join with a neighboring group to compare their answers. For any discrepancies, the students will review their work and decide upon the correct response (**Math Practice 3**). Once they have had a couple of minutes, we discuss any unresolved problems as a class.

#### Resources

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#### Graphing the Scenario

*32 min*

Students now graph the scenario on a coordinate plane. I provide the following information:

*Graph all of the equations on the same coordinate plane, with a domain of 0 ≤ t ≤ 650 seconds, and a range of 0 ≤ d ≤1500 feet. The graph must show all significant data points.*

Directions are to use the entire sheet of graph paper and a straight edge. Some students might want to used different colored pens/pencils which can be helpful visually.

I find that is it important to walk around at this point to catch serious mistakes in domain or range early on as the graph is crucial to the final portion of this project. Some students may struggle to graph these equations given size of some of the numbers. I like to remind students that they don’t have to use the slope and y-intercept. All they need is two points. I ask them which points on each equation may be the simplest to graph (**Math Practice 2**) and hopefully this will lead them to either the intercepts or the point the animals cross the finish line. I do ask that they show each animal's start/finish point, the one minute mark, and where they meet each animal.

Before they can continue to the final portion of this project, they must check their graphs with me. An incorrect graph will affect the students’ ability to write an accurate story.

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This portion is the key to the entire project. The students will write a story about the race between the tortoise, hare and rat (**Math Practice 4**). It must be in chronological order. They have to use the graph to figure out the proper order (**Math Practice 6**). As it states in the lesson plan from Math Projects Journal, students often want to view the graph as an aerial view of the race rather than a time/distance relationship. One suggestion they give is move a piece of paper across the graph showing the position of each animal at any given second.

We will begin this story during this class period if the students have time and finish it during the next lesson.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to evaluate the easiest and hardest portions of this lesson.

*expand content*

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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