Line Segments & Distance

1.  Students will be able to find the distance between two points using the Distance Formula. 
2. Students will be able to apply the distance formula to exercises and problems.

Formative – Practice Problem #1:  Finding Measurements by Adding or Subtracting

• This practice problem is embedded within the lesson and requires students to draw (or type) the answer on the Nearpod slide. Students can also upload a drawing or file from their computer, allowing them more flexibility in their methods for answering each question. Students will be using addition or subtraction to calculate the length of a line segment.
• This problem may be completed independently or in small groups (breakout rooms) depending on your classroom needs. Students can collaborate in small groups or breakout rooms prior to answering the questions.

Formative – Practice Problem #2: Write and Solve Equations to Find Measurements

• This practice problem is embedded within the lesson and requires students to draw (or type) the answer on the Nearpod slide. Students can also upload a drawing or file from their computer, allowing them more flexibility in their methods for answering each question. Students will draw diagrams to facilitate solving line segment distance problems.
• This problem may be completed independently or in small groups (breakout rooms) depending on your classroom needs. Students can collaborate in small groups or breakout rooms prior to answering the questions.

Formative – Practice Problem #3: Find Distance on a Coordinate Plane

• This practice problem is embedded within the lesson and requires students to draw (or type) the answer on the Nearpod slide. Students can also record their voices explaining the solutions, allowing them more flexibility in their methods for answering each question. Students will use two coordinate points to calculate distance on a coordinate plane.
• This problem may be completed independently or in small groups (breakout rooms) depending on your classroom needs. Students can collaborate in small groups or breakout rooms prior to answering the questions.

Summative – Practice Problems #4-#6:  Real World Examples of Coordinate Plane Distance

• These practice problems are embedded within the lesson and require students to draw (or type) the answer on the Nearpod slide. Students can also record their voices explaining the solutions, allowing them more flexibility in their methods for answering each question. Students will use two coordinate points to calculate distance on a coordinate plane in a real world situation.
• These problems may be completed independently or in small groups (breakout rooms) depending on your classroom needs. Students can collaborate in small groups or breakout rooms prior to answering the questions.

Time Requirements:

• This lesson should take about two 45-minute class periods to allow time for presentation of material with the Nearpod as well as time for independent practice/formative assessments (Practice Problems) and class discourse.

Technology Requirements:

• Teachers and students will need a device with internet connection to access the Nearpod presentation.

All materials have been inserted into a Nearpod lesson. All assessments, both formative and summative, are embedded into the presentation to allow for a quick check for understanding. Basic Nearpod accounts are free for teachers. I have attached a link below that will allow you to make a copy of this Nearpod presentation. Once you have clicked the link and made a copy, you can edit any slide. You can record your own voice reading directions or talking through examples to raise the comfort level of your students.  

This lesson can be utilized for face-to-face, remote, or hybrid learning. Teachers can access reports to collect data on the students’ answers in real time, so this lesson works just as well live as asynchronous.  Teachers can choose to launch the lesson live or in student paced mode for remote learning. 

https://np1.nearpod.com/sharePresentation.php?code=874103e46b1230976a1a0147c60292bb-1

Introducing and Facilitating the Lesson

In your introduction, invite students to free-associate situations that come to mind when it may not be practical to measure a distance with a traditional measuring device.  Encourage students to find examples of such situations that  are present in their everyday lives. You can have the students write their ideas or share them orally.

Since this lesson is designed to work both synchronously, asynchronously and face-to-face, you will choose to launch the lesson live or student paced, based on your class’s needs. A code and/or link will be generated for student entry into the lesson.   A printed handout of the nearpod lesson can be distributed to students to facilitate note taking.

This lesson works well with zoom or google meet when your screen is shared. You can share the link in the chat for students to join the Nearpod for live lessons. Students can pull up the presentation on another tab while in the meet and toggle back and forth for instruction and independent work.

Learning Extension

1. As an extension to this lesson, students can take a photo of an object (e.g. building, tower, house, roadway, etc.) and create a distance formula problem using Kami or a similar program.  Students can trade problems with each other either in person or via email and solve each other’s custom problems.

Sequence of Events (Total Time: 75 Minutes)

• Introduction/Hook/Warm Up – 10 minutes
• Review of Vocabulary, Standards, and Objectives – 5 minutes
• Geogebra Applet – 5 minutes
• Explaining Connection Between Pythagorean Theorem and Distance Formula  – 5 minutes
• Example #1 – 5 minutes
• Practice Problem  #1- 5 minutes
• Example #2 – 5 minutes
• Practice Problem #2 – 5 minutes
• Example #3 – 10 minutes
• Practice Problem  #3 – 10 minutes
• Practice Problems #4-#6  – 10 minutes

Tying This Lesson to Assessment and Expected Outcomes

• The practice problems built into the Nearpod presentation directly ask students to demonstrate skills and expected outcomes that are in line with Indiana Geometry standard G.LP.2 and the given objectives.

Modifications Based on Student Needs

• Student responses can be collected in a variety of ways such as through voice recordings, drawings, images, typing and writing. Responses can also be resubmitted for students whose performances are not at proficiency .  
• Teachers can modify the Nearpod presentation to add voice recordings for directions and explanations in addition to the visual images and text already incorporated into the presentation.
• The lesson can be launched both live and student paced to suit synchronous, asynchronous and in person teaching methods.
• Additional cultural relevance can be added by giving examples of distance formula use in a project meaningful in the local area.

Indiana State Geometry Standard:

G.T.8 Develop the distance formula using the Pythagorean Theorem. Find the lengths and midpoints of segments in the two-dimensional coordinate system. Find measures of the sides of polygons in the coordinate plane; apply this technique to compute the perimeters and areas of
polygons in real-world and mathematical problems.

Indiana State Process Standard:

PS.2 Reason abstractly and quantitatively: Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.