Curriculum  /  Math  /  4th Grade  /  Unit 8: Shapes and Angles  /  Lesson 1

Shapes and Angles

Lesson 1

Math

Unit 8

4th Grade

Lesson 1 of 18

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  $$\overrightarrow{HG}$$ and $$\overrightarrow{HJ}$$ 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

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.
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Anchor Tasks

25-30 minutes

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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Student Response

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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

a.   Draw two points and label them $$A$$ and $$B$$.

b.   Draw a line between the two points. Label it $$\overleftrightarrow{AB}$$.

c.   Draw another point that is not on $$\overleftrightarrow{AB}$$ and label it $$C$$.

d.   Draw a line segment between $$A$$ and $$C$$. Label it $$\overline{AC}$$.

e.   Draw another point that is not on $$\overleftrightarrow{AB}$$ or $$\overline{AC}$$ and label it $$D$$.

f.   Draw a ray from $$B$$ to $$D$$ and label it $$\overrightarrow{BD}$$.

g.   Draw a point that is not on any of the existing objects. Label it $$E$$.

h.   Draw an angle between $$D$$, $$B$$, and $$E$$, and label it $$\angle DBE.$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic A > Lesson 1 — Concept 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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Student Response

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References

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

15-20 minutes

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 each of them 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

5-10 minutes

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.  

Column A   Column B

Line

  

     

Point

  

 
     
   

     

Ray

  

     

Line segment

  

Student Response

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Problem 2

What makes a line different from a line segment? 

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Identify and draw right, obtuse, and acute angles.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Lines and Angles

Topic B: Measures of Angles

Topic C: Measures of Adjacent Angles

Topic D: Shapes and Lines of Symmetry

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