Shapes and Angles

Lesson 1

Objective

Identify and draw points, lines, line segments, rays, and angles. 

Common Core Standards

Core Standards

?

  • 4.G.A.1 — Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

  • 4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Foundational Standards

?

  • 3.G.A.1

Criteria for Success

?

  1. Label geometric objects in order to make it easier for them to be identified, located, and differentiated.
  2. Understand that a point is a precise location in space. It has no dimension.
  3. Understand that a line is a straight path with no thickness, extending in both directions infinitely. It is one-dimensional. The notation for a line through points $$A$$ and $$B$$ is $$\overleftrightarrow{AB}$$.
  4. Understand that a line segment is a part of a line that has two endpoints. It does not extend in either direction infinitely. The notation for a line segment through points $$C$$ and $$D$$ is $$\overline{CD}$$.
  5. Understand that a ray is a part of a line that has one endpoint. It extends in one direction infinitely. The notation for a ray through points $$E$$ and $$F$$ is $$\overset{\rightharpoonup}{EF}$$ or $$\overrightarrow{EF}$$.
  6. Understand that an angle is the union of two rays that share a common endpoint. The notation for an angle formed by rays  $$\overset{\rightharpoonup}{HG}$$and $$\overset{\rightharpoonup}{HJ}$$ that meet at the point $$H$$ is $$\angle GHJ$$.
  7. Understand that the vertex of an angle is the point where the two rays meet.
  8. Draw points, lines, line segments, rays, and angles using a ruler or straightedge (MP.5).
  9. Identify points, lines, line segments, rays, and angles using a ruler or straightedge in two-dimensional figures (MP.2).

Tips for Teachers

?

  • The following materials are needed for today's lesson: Straightedge Blank Paper

In Criteria for Success #5 you will notice there are two different notations for a ray. Students are welcome to use either notation, but for the remainder of this unit we will use the notation $$\overrightarrow{AB}$$.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Tasks

?

Problem 1

Silently pick a point from the following image:

Write a description of where your point is located.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Dan Meyer Pick a Point

Pick a Point by Dan Meyer is made available at dy/dan under the CC BY 4.0 license. Accessed Feb. 12, 2018, 1:29 p.m..

Problem 2

  1. Draw two points and label them $$A$$ and $$B$$.
  2. Draw a line between the two points. Label it $$\overleftrightarrow{AB}$$.
  3. Draw another point that is not on $$\overleftrightarrow{AB}$$ and label it $$C$$.
  4. Draw a line segment between $$A$$ and $$C$$. Label it $$\overline{AC}$$.
  5. Draw another point that is not on $$\overleftrightarrow{AB}$$ or $$\overline{AC}$$ and label it $$D$$.
  6. Draw a ray from $$B$$ to $$D$$ and label it $$\overrightarrow{BD}$$.
  7. Draw a point that is not on any of the existing objects. Label it $$E$$.
  8. Draw an angle between $$D$$, $$B$$, and $$E$$, and label it $$\angle DBE.$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic A > Lesson 1Concept Development

Grade 4 Mathematics > Module 4 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 3

Identify any points, lines, line segments, rays, and angles in the following figures.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic A > Lesson 1Concept Development

Grade 4 Mathematics > Module 4 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • Compare your figure to your partner’s for Problem #1. How are they alike? How are they different? 
  • A point indicates a precise location with no size, only position. Points are infinitely small. Why do we mark them with a dot? Won’t our pencil marks have width? Won’t our pencil marks actually cover many points since the dots we draw have width and points do not?
  • Just like a point, a line has no thickness. Can we draw a line that has no thickness, or will we always have to imagine that particular attribute? Why do we draw it on paper with thickness?
  • How many corners does a triangle have? A square? A quadrilateral? How does that relate to the number of angles a polygon has?
  • How are a ray and a line similar? How are they different?
  • How are angles formed? Where have you seen angles before? 
  • Why is it hard to find real-life examples of lines, points, and rays?
  • How does your understanding of a number line connect to this lesson on lines?

Target Task

?

Problem 1

Draw a line segment to connect the word to its picture. 

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic A > Lesson 1Exit Ticket, Question #1

Grade 4 Mathematics > Module 4 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

How is a line different from a line segment?

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic A > Lesson 1Exit Ticket, Question #2

Grade 4 Mathematics > Module 4 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Mastery Response

?

Create a free account or sign in to view Mastery Response

Additional Practice

Unit Practice

With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.

View Preview