Lesson 16 | Shapes and Angles | 4th Grade Mathematics

Objective

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

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.G.A.2 — Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Geometry

4.G.A.2 — Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

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

Make sense of a three-act task and persevere in solving it (MP.1).
Classify/sort quadrilaterals according to their attributes like side length, angle measure, and presence of parallel/perpendicular sides (MP.2, MP.5).
Understand that a quadrilateral is a closed shape with four straight sides.
Understand that a trapezoid is a quadrilateral with at least one pair of parallel sides. (See Notes/Tips for Teachers section.)
Understand that a parallelogram is a quadrilateral with exactly two pairs of parallel sides.
Understand that a rectangle is a parallelogram with perpendicular sides.
Understand that a rhombus is a parallelogram with four sides of equal length.
Understand that a square is a parallelogram with perpendicular sides of equal length.
Understand that shapes can be classified into more than one category.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students have learned all of the vocabulary used in today’s lesson in prior grade levels. Thus, today’s lesson serves to refine the definitions of that vocabulary and engage with this content more deeply, given students’ new understanding of angles from work throughout this unit.
“In the U.S., that the term ‘trapezoid’ may have two different meanings. In their study The Classification of Quadrilaterals (Information Age Publishing, 2008), Usiskin et al. call these the exclusive and inclusive definitions:
- T(E): a trapezoid is a quadrilateral with exactly one pair of parallel sides
- T(I): a trapezoid is a quadrilateral with at least one pair of parallel sides.

These different meanings result in different classifications at the analytic level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. Both definitions are legitimate. However, Usiskin et al. conclude, ‘The preponderance of advantages to the inclusive definition of trapezoid has caused all the articles we could find on the subject, and most college-bound geometry books, to favor the inclusive definition.’” (Geometry Progression, p. 3). Thus, the inclusive definition is used below and throughout the curriculum.

Lesson Materials

Ruler (1 per student) — This can be any tool used to verify equal lengths, e.g., the edge of a piece of paper, etc.
180° Protractor (1 per student)
Template: Quadrilaterals (1 per student or small group) — This material should be cut into pieces before the lesson.

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Anchor Tasks

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

Problem 1

Act 1: Watch the video: Investigating Quadrilaterals.

a. What do you notice? What do you wonder?

b. How is this person sorting the cards each time? Make a prediction.

Guiding Questions

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References

101Questions Investigating Quadrilaterals

Investigating Quadrilaterals by Jenise Sexton is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 5, 2018, 12:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to determine how they sorted them in their first and second sorts –

First sort:

Second sort:

Guiding Questions

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References

101Questions Investigating Quadrilaterals

Investigating Quadrilaterals by Jenise Sexton is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 5, 2018, 12:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Reveal the answer.

The shapes were first sorted according to whether they had at least one set of parallel sides or not.
The shapes with at least one set of parallel sides were then sorted according to whether they had two pairs of parallel sides or not.

Was your answer reasonable? Why or why not?

First sort:

Second sort:

Guiding Questions

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References

101Questions Investigating Quadrilaterals

Investigating Quadrilaterals by Jenise Sexton is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 5, 2018, 12:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 4

Act 4 (the sequel): Sort the quadrilaterals from Template: Quadrilaterals in a different way from how they were sorted in the three-act task above.

Guiding Questions

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References

101Questions Investigating Quadrilaterals

Investigating Quadrilaterals by Jenise Sexton is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 5, 2018, 12:05 p.m..

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

How is it possible for the shape in #1 to be a trapezoid, but no side to be parallel to side $$r$$?
What was the most specific word you used for each part of #2? What other terms would work?
For #3, what makes a square different from a rectangle? Why is it important to define a square as a rectangle with four equal-length sides and not as a quadrilateral with four equal-length sides?
What is the most specific term you could use to describe the shape you chose in #6? Are there other answer choices that could be described with the same word?
What are some attributes that every square has in common? How is a square a special case of a rectangle, a parallelogram, and a trapezoid?
If your teacher asked you to draw a trapezoid and you drew a parallelogram, explain to your teacher why a parallelogram is also a trapezoid.

Target Task

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

Problem 1

For each figure in the table below, determine whether each statement describes the figure. If so, place an X in the box. You may mark more than one box for each figure.

	Appears to have at least one pair of parallel sides	Appears to have all sides of equal length

Problem 2

Based on the properties identified in the table above and any other properties you can identify, name each shape, being as specific as possible. Write the name of each shape below.

Shape A: ______________

Shape B: ______________

Shape C: ______________

Student Response

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

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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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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

Lesson 15

Lesson 17

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

Geometry

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 4

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

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