8th Grade Standard - 8.NS.A.2
The Number System
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.
1. Play Treasure Hunt Act 1 Video, whole class.
2. Restate the question: How far away is the final map point?
3. Ask students: "What are your ideas to help the Professor?"
4. Facilitate classroom discussion.
1. Print the data artifact page, cut into halves, and distribute to students.
2. Allow students work time. Then ask students "Does your answer make sense?"
3. Consider using a sharing protocol to lead to mathematical insights and/or highlight misconceptions.
4. Allow students to revise their work.
1. Play Treasure Hunt Act 3 Video, whole-class.
2. Allow students final revisions to their work, if necessary.
3. Give Student Reflection Assignment.
Answer: The final map point and treasure is approximately 1.41 miles away!
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 and finish the Day 1 Student Reflection Assignment.
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 3-Act Math Task.