Shapes and Angles

Lesson 1

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Objective

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

Common Core Standards

Core Standards

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  • 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

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  • 3.G.A.1

Criteria for Success

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  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

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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 $$\overrightarrow{AB}$$.

Lesson Materials

  • Blank Paper (1 sheet per student)
  • Ruler (1 per student) — This can be any tool used to draw a straight line, e.g., a straightedge, a ruler, etc.

Fishtank Plus

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

 

Anchor Tasks

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Problem 1

Silently pick a point from the following image:

Write a description of where your point is located.

Guiding Questions

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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

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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 Fishtank Learning, Inc.

Problem 3

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

Guiding Questions

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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 Fishtank Learning, Inc.

Problem Set & Homework

  • Problem Set

    • Problem Set Answer Key
  • Homework

    • Homework Answer Key

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

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Problem 1

Match each term in Column A with a corresponding picture in Column B. One item is missing in each column, which should be filled in to create the remaining pairs. 

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Problem 2

What makes a line different from a line segment? 

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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.

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