Lesson 1 | Shapes and Angles | 4th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Geometry

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:

Measurement and Data

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

The foundational standards covered in this lesson

3.G.A.1

Geometry

3.G.A.1 — Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Label geometric objects in order to make it easier for them to be identified, located, and differentiated.
Understand that a point is a precise location in space. It has no dimension.
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 $$\overleftrightarrow{AB}$$.
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 $$\overline{CD}$$.
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 $$\overrightarrow{EF}$$.
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 $$\angle GHJ$$.
Understand that the vertex of an angle is the point where the two rays meet.
Draw points, lines, line segments, rays, and angles using a ruler or straightedge (MP.5).
Identify points, lines, line segments, rays, and angles using a ruler or straightedge in two-dimensional figures (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

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

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

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 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

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 1 — Concept Development

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Problem 2

What makes a line different from a line segment?

Student Response

An example response to the Target Task at the level of detail expected of the students.

Create a free account or sign in to view Student Response

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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

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

Lesson 2

Lesson Map

Topic A: Lines and Angles

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

4.G.A.1 4.MD.C.5

Identify and draw right, obtuse, and acute angles.

4.G.A.1

Identify and draw perpendicular lines.

4.G.A.1

Identify and draw parallel lines.

4.G.A.1

Topic B: Measures of Angles

Use iteration with one physical nonstandard unit to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Understand that an angle that turns through $${{1\over360}}$$ of a circle is called a “one-degree angle” and can be used to measure angles. Use a makeshift protractor to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Measure angles that are less than 180° using a 180° protractor. Distinguish angle measure from other attributes.

4.MD.C.5 4.MD.C.6

Sketch angles of specified measure using a 180° protractor.

4.MD.C.5 4.MD.C.6

Identify and measure angles as turns and recognize them in various contexts.

4.MD.C.5 4.MD.C.6

Topic C: Measures of Adjacent Angles

Decompose angles using pattern blocks.

4.MD.C.7

Solve problems involving the measure of two adjacent angles.

4.MD.C.7

Solve problems involving the measure of more than two adjacent angles.

4.MD.C.7

Measure and sketch angles that are greater than 180°.

4.MD.C.5 4.MD.C.6 4.MD.C.7

Topic D: Shapes and Lines of Symmetry

Analyze and classify triangles based on side length, angle measure, or both.

4.G.A.1 4.G.A.2

Draw triangles from given criteria.

4.G.A.1 4.G.A.2

Analyze and classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size.

4.G.A.1 4.G.A.2

Draw quadrilaterals from given criteria.

4.G.A.1 4.G.A.2

Identify and draw lines of symmetry in two-dimensional figures.

4.G.A.3

Shapes and Angles

Objective

Common Core Standards

Core Standards

Geometry

Measurement and Data

Foundational Standards

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy