Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 15
Math
Unit 6
7th Grade
Lesson 15 of 21
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Lesson Notes
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Determine if conditions describe a unique triangle, no triangle, or more than one triangle.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Your group should have a few copies of Handout #2 and a set of cards from Handout #1.
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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..
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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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.
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.
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Identify and describe two-dimensional figures that result from slicing three-dimensional figures.
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary relationships.
Standards
7.G.B.5
Use vertical, complementary, and supplementary angle relationships to find missing angles.
Use equations to solve for unknown angles. (Part 1)
Use equations to solve for unknown angles. (Part 2)
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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.
Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
Determine the relationship between the area and radius of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.
Solve problems involving area and circumference of two-dimensional figures (Part 1).
7.G.B.47.G.B.6
Solve problems involving area and circumference of two-dimensional figures (Part 2).
Topic C: Building Polygons and Triangles
Draw two-dimensional geometric shapes using rulers, protractors, and compasses.
7.G.A.27.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.
Topic D: Solid Figures
7.G.A.3
Find the surface area of right prisms.
7.G.B.6
Find the surface area of right pyramids.
Find the volume of right prisms and pyramids.
Solve real-world and mathematical problems involving volume.
Distinguish between and solve real-world problems involving volume and surface area.
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