Lesson 15 | Shapes and Angles | 4th Grade Mathematics

Objective

Draw triangles from given criteria.

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

Draw triangles using a protractor and ruler on grid paper (MP.1, MP.2, MP.5, MP.6).
Draw triangles using a protractor and ruler on blank paper (MP.1, MP.2, MP.5, MP.6).
Analyze statements regarding the classification of triangles (e.g., a right triangle is always scalene) (optional) (MP.3).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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)

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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

Draw three points on the grid below so that when connected they form a triangle. Use your straightedge to connect the three points to form a triangle.

a. How can you classify your triangle?

b. What attributes does your triangle have that led you to that classification?

c. What tools did you use to help you draw your triangle and classify it?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic D > Lesson 14 — Application Problem

Grade 4 Mathematics > Module 4 > Topic D > Lesson 14 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 2

Draw an example of each of the following shapes or explain why it’s not possible to draw one.

a. Right isosceles triangle

b. Acute scalene triangle

c. Obtuse equilateral triangle

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic D > Lesson 14 — Concept Development Problem 1

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In #3, explain why you answered true or false.
Discuss your answer to #5. How are these two triangles closely related?
In #1 and #2, which of the triangles was most challenging to draw? Why?
In #1, when did you need to use your ruler to make sure side lengths were or were not the same length? When was it not necessary to use a ruler?
When you were drawing a triangle that had two attributes, how did you determine what to draw first—the side length or the angle measure?
Why is it important to verify our triangles’ attributes after we have drawn them?

Target Task

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

Problem 1

Draw a right scalene triangle.

Problem 2

Draw an acute isosceles triangle.

Problem 3

True or false: all triangles have at least 2 acute angles.

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 14

Lesson 16

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 Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Problem 3

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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