Playing Around with Pythagoras- Day 9

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Objective

SWBAT apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Big Idea

Now that students are developing proficiency with applying the Pythagorean Theorem to solve problems, they are now ready to apply their conceptual knowledge to a coordinate plane.

Warm Up

7 minutes

For today's Warm Up problems, I included a real-life application of the Pythagorean Theorem to build on the previous day's lesson.  I intentionally used larger numbers to see if students recognized the Pythagorean triple disguised as a larger number (300 vs. 3 and 400 vs. 4).  It will also provide information about my students' abilities to manipulate larger base-ten numbers.

For the second problem, I have asked students to plot three points on a coordinate grid.  This skill is essential to today's lesson, so I wanted to provide practice to jog students' memories. If students struggle with this skill, I will make strategy partner changes before the lesson begins to provide additional support.

The second problem also leads directly to the lesson's focus as the three plotted points will form a right triangle. I will then ask students to find the length of xy and zy.  I will then ask if it is possible to find the length yz. This should lead us to the launch of today's work time.

Applying the Pythagorean Theorem to the Coordinate Plane

8 minutes

Because students have spent eight days applying the Pythagorean Theorem, I only provide two examples for students to attempt in guided practice. I want to see if students can transfer their knowledge to a new skill: finding the distance between two points on a coordinate grid. If students seem to struggle with this concept, I provide additional practice problems. Otherwise, I launch directly into work time.

Work Time: Error Analysis

25 minutes

Today's work time involves working with six coordinate grid distance problems that have already been solved.  Student pairs must analyze each answer and decide if they agree or disagree with the student's solution. If they disagree, they must explain why. Students record their thinking in their journals individually. After 20 minutes of analysis, I ask the pairs to share their findings to gain class consensus.

Ticket Out the Door

5 minutes

To measure individual understanding of this new skill, I ask students to complete today's Ticket Out the Door, which mimics today's work time samples. I am interested to see if students are able to transfer the knowledge gained from analysis during work time to this independent task. Students who struggle with the concept will be brought in for additional support.