Points, Lines & Planes

1. Students will be able to identify and model points, lines and planes.
2. ​Students will be able to identify the intersections of lines and planes.

Formative – Problem Set: Naming Points, Lines and Planes.

• These practice problems are embedded within the lesson and require 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 identifying and naming points, lines and planes.
• This problem set may be completed independently or in small groups (break out rooms) depending on your classroom needs.  Students can collaborate in small groups or break out rooms prior to answering the questions.

Formative – Problem Set: Drawing Line/Plane Intersections.

• These practice problems are embedded within the lesson and require 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 examples of geometric entities and their intersections as described within each problem.
• This problem set may be completed independently or in small groups (break out rooms) depending on your classroom needs.  Students can collaborate in small groups or break out rooms prior to answering the questions.

Formative – Problem Set: Naming Geometric Entities.

• 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 voice explaining the solutions, allowing them more flexibility in their methods for answering each question. Students will identify, draw, and name the geometric entities and intersections as described.
• This problem set may be completed independently or in small groups (break out rooms) depending on your classroom needs.  Students can collaborate in small groups or break out rooms prior to answering the questions.

Summative – Multiple Choice/Short answer Quiz.

• This quiz is positioned at the end of the lesson and is intended to be a summative assessment. The problems are a mixture of short answers, open-ended questions, and multiple choice questions. For the open-ended questions, students will be able to type, draw, upload an image or record their voices to provide solutions for the problems.  Students will demonstrate their ability to identify and name geometric entities such as points, lines, and planes and their intersections as well as give real world examples.

Time Requirements:

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

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 and asynchronous.  Teachers can choose to launch the lesson live or in student paced mode for remote learning.

https://np1.nearpod.com/sharePresentation.php?code=c4574504855e5dafd802d97daec24c0b-1

Introducing and Facilitating the Lesson

In your introduction, invite students to free-associate with objects that come to mind for each of the geometric terms discussed in this lesson. Encourage students to find examples of each entity that are present in their everyday lives. You can have the students write their methods 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’ 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 Extensions

1.  Students could be broken into small groups or break out rooms and given a few minutes to discuss what was learned during the lesson, any new ideas of real world examples of points, lines or planes, or any questions they may have about the lesson.   
2. In small groups or individually, students can explain why when two cars enter an intersection at the same time on different paths, one or both of the cars must stop to avoid a collision.  However, two airplanes can cross paths while flying in different directions without changing their speeds and not collide.  Students can present their explanations either orally, written out or with a picture.  

Sequence of Events (Total time: 90 Minutes)

• Introduction/Hook – 5 minutes
• Review of Vocabulary, Standards, and Objectives – 5 minutes
• Explanation of Points, Lines, and Planes – 10 minutes
• Example 1 – 5 minutes
• Problem Set #1- 10 minutes
• Example #2 – 5 minutes
• Problem Set #2 – 10 minutes
• Example #3 – 5 minutes
• Problem Set #3 – 10 minutes
• Example #4 (sway) – 10 minutes
• Quiz – 20 minutes

Tying This Lesson to Assessment and Expected Outcomes

• The problem sets and quiz 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 each geometric entity in the hook that is well known and meaningful in the local area.

Indiana State Geometry Standard:

G.LP.2 Use precise definitions for angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line and plane. Use standard geometric notation.

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.