# Teacher Sample

### 8th Grade Standard - 8.NS.A.2

#### The Number System

#### 8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

# LESSON: TREASURE HUNT

### How far away is the final map point?

The best way to visualize and use irrational numbers is to approximate them with a decimal. In Treasure Hunt, Caterina Fenn hires Tiberius Picklebottom to help her find her grandfather’s hidden treasure. Based on a map and a few calculations, Tiberius determines the distance to the treasure is √2 miles. They must approximate this distance in order to use the theodolite (the measuring device), and want to be as accurate as possible to minimize their digging efforts.

# Day 1

#### 1. Immersion

- Play Treasure Hunt Immersion video, whole-class.
- Restate the question:
**How far away is the final map point?** - Facilitate classroom discussion, ask students: "What are your ideas to help the Professor?"

#### 2. Data & Computation

- Print the Data Artifact, cut into halves, and distribute to students.
- Allow students work time. Then ask students "Does your answer make sense?"
- Consider using a sharing protocol to lead to mathematical insights and/or highlight misconceptions.
- Allow students to revise their work.

#### 3. Resolution

- Play Treasure Hunt Resolution video, whole-class.
- Prepare and give brief lecture (Direct Instruction).
- Assign Simulation Trainer, as available.

Answer: The final map point and treasure is approximately 1.41 miles away!

# Day 2

1. Have your students go to midschoolmath.com/clicker.

2. Click on Launch Clicker Quiz and note Clicker Quiz #.

3. Have students enter quiz code on their screens.

4. Launch Clicker Quiz.

5. Review Clicker Quiz results and prompt students to make connections to the Math Simulator.

# Day 3

1. Print and distribute the Practice Printable to your students.

2. Print the Teacher Answer Key.

3. Give a short 5-7 minute teacher lecture on the concept of the standard.

4. Have students complete the Practice Printable.

5. Have students complete the Student Reflection Assignment.

# ADD: