Line Segments & Distance

Learning Objectives

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

Instructional Rationale

How will you access students’ prior knowledge and incorporate that into the lesson?

This lesson begins by engaging students in a brief warm up activity in which they are asked to brainstorm on when it would be useful to calculate distance using a formula rather than use traditional measuring tools. Students are then asked to free-associate real world examples of situations where this might be practical such as rough terrain or bodies of water.

By the end of the lesson students will be able to:

Calculate the distance between two points on a coordinate plane.
Make a connection between the distance formula and the Pythagorean Theorem.
Identify real world situations in which the distance formula could be useful.

How are you integrating UDL (multiple means of engagement, representation, and action & expression) into your lesson?

Information is presented in several different manners such as text, visual imagery, and audio recordings. The teacher can add their own voice recording to any slide easily in Nearpod by clicking the microphone button on the bottom of the slide.
Students can engage both independently or collaboratively based on need.
Students can engage both live (in-person and synchronously) or asynchronously.
Students can provide responses to independent practice and assessments in multiple ways such as typing, drawing, writing, uploading images, or with a recording of their voice.
Open-ended response questions and scaffolded with fading response stems.

What evidence do you have that you are connecting teaching to the CRP tenets (academic success, cultural competence and critical consciousness)?

Lesson material is rigorous and scaffolded, including guided procedures to promote academic success. Examples #1, #2 and #3 are intended to be used as instructional models by the teacher.
Cultural competence and critical consciousness are considered during the introduction or hook to the lesson. Allowing students to free-associate to develop examples from their own lives of situations when using traditional measurement tools may not be practical will help construct a safe, comfortable environment for learning. In addition, free association can help promote relationship building, which will also reinforce a safe learning environment.
The images in the practice problems can be replaced by teachers with images that are more relevant to the particular class this lesson is being presented in.

Assessments

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.

Materials & Resources

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

Procedures & Implementation

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

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.

Standards & Indicators

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.

Trajectory

Acknowledged

Engages in discussions and activities around representative diversity and individual differences without grappling with structural oppressions. Culture is externalized and the focus is on the abstract. Minor discomfort may be felt and tensions are largely avoided.

Throughlines

Multiple Ways of Knowing and Doing

The knowledge and wisdom of the students, families, and communities are centered in content and materials to promote equitable and inclusive learning experiences.

Standards

Social Justice

Identity 5 - Students will recognize traits of the dominant culture, their home culture and other cultures and understand how they negotiate their own identity in multiple spaces.

Diversity 8 - Students will respectfully express curiosity about the history and lived experiences of others and will exchange ideas and beliefs in an open-minded way.

ISTE NETS

Empowered Learner 1c - Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

Creative Communicator 6c - Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.

Global Collaborator 7b - Students use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoints.