Lesson 15 | Geometry | 7th Grade Mathematics

Objective

Determine if conditions describe a unique triangle, no triangle, or more than one triangle.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Geometry

7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Criteria for Success

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

Given three conditions about a triangle, determine if a unique triangle can be made, and if so, then draw the triangle.
Explain why three given conditions about a triangle may result in more than one or no triangles.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson requires some preparation work for Anchor Problem #1: Using Handout #1, cut out the cards at the bottom of the page. Each pair or group will need a set.
This article from SERP Poster Problems nicely breaks down the 7.G.2 standard language and is a valuable read prior to the lesson.

Lesson Materials

180° Protractor (1 per student)
Compass (1 per student)
Ruler (1 per student)
Blank Paper (2-3 sheets per student)

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Your group should have a few copies of Handout #2 and a set of cards from Handout #1.

Draw three cards and place them in the appropriate places on the Handout #2 form. This represents three conditions about a triangle. Once you’ve placed them on the form, do not change the order.
Determine if the set of conditions will make one unique triangle, more than one triangle, or no triangle.
- If you can make one unique triangle, draw and label the triangle.
- If more than one or no triangle can be made, be prepared to explain your reasoning.
Choose another three cards and repeat the activity.

Guiding Questions

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References

SERP Poster Problems Triangles to Order — Handout #1 and #2

Triangles to Order from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed March 11, 2018, 11:57 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

Two triangles are described below. Determine if each description results in one unique triangle, more than one triangle, or no triangle. Explain your reasoning or draw images to support your conclusion.

a. Triangle $${EFG}$$ is an isosceles triangle with two angles measuring 35°. Side length $${EG}$$ measures 10 cm.

b. Triangle $${{PQ}R}$$ is an isosceles triangle with $${\angle P}$$ and $${\angle Q}$$ measuring 22°. Side length $${PQ}$$ measures 8 cm.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

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

Starting at the origin, a ladybug walked 4 units east. Then she walked a distance of 3 units in an unknown direction. At that time, she was 30 degrees to the north of her original walking direction.

The diagram shows one possibility for the ladybug’s final location. Find a different final location that is also consistent with the given information, and draw the ladybug there.

References

Illustrative Mathematics A task related to standard 7.G.A.2

A task related to standard 7.G.A.2, accessed on March 11, 2018, 11:55 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

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 following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

SERP Poster Problems Triangles to Order — Handout #4
EngageNY Mathematics Grade 7 Mathematics > Module 6 — Lessons 8-12
MARS Formative Assessment Lessons for Grade 7 Describing and Defining Triangles — Great set of problems determining triangles based on three given conditions

Lesson 14

Lesson 16

Lesson Map

Topic A: Angle Relationships

Identify and determine values of angles in complementary and supplementary relationships.

7.G.B.5

Use vertical, complementary, and supplementary angle relationships to find missing angles.

7.G.B.5

Use equations to solve for unknown angles. (Part 1)

7.G.B.5

Use equations to solve for unknown angles. (Part 2)

7.G.B.5

Topic B: Circles

Define circle and identify the measurements radius, diameter, and circumference.

7.G.B.4

Determine the relationship between the circumference and diameter of a circle and use it to solve problems.

7.G.B.4

Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.

7.G.B.4

Determine the relationship between the area and radius of a circle and use it to solve problems.

7.G.B.4

Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.

7.G.B.4

Solve problems involving area and circumference of two-dimensional figures (Part 1).

7.G.B.4 7.G.B.6

Solve problems involving area and circumference of two-dimensional figures (Part 2).

7.G.B.4 7.G.B.6

Topic C: Building Polygons and Triangles

Draw two-dimensional geometric shapes using rulers, protractors, and compasses.

7.G.A.2 7.G.B.5

Determine if three side lengths will create a unique triangle or no triangle.

7.G.A.2

Identify unique and identical triangles.

7.G.A.2

Determine if conditions describe a unique triangle, no triangle, or more than one triangle.

7.G.A.2

Topic D: Solid Figures

Identify and describe two-dimensional figures that result from slicing three-dimensional figures.

7.G.A.3

Find the surface area of right prisms.

7.G.B.6

Find the surface area of right pyramids.

7.G.B.6

Find the volume of right prisms and pyramids.

7.G.B.6

Solve real-world and mathematical problems involving volume.

7.G.B.6

Distinguish between and solve real-world problems involving volume and surface area.

7.G.B.6

Geometry

Objective

Common Core Standards

Core Standards

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Target Task

References

Student Response

Additional Practice

Lesson Map

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