enVision Mathematics Topic 8
7th Grade; February – March (5 weeks); 3rd Quarter
Embedded Files
Topic Title(s):
Solve Problems Involving Geometry
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
Standard(s):
4. Geometry
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
7.G.A. Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)
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. (CCSS: 7.G.A.2)
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in cross sections of right rectangular prisms and right rectangular pyramids. (CCSS: 7.G.A.3)
7.G.B. Geometry: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
State the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (CCSS: 7.G.B.4)
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (CCSS: 7.G.B.5)
Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (CCSS: 7.G.B.6)
Investigate what side and angle measurements are necessary to determine a unique triangle. (Entrepreneurial Skills: Inquiry/Analysis)
Reason abstractly by deconstructing three-dimensional shapes into two-dimensional cross-sections. (MP2)
Describe, analyze, and generalize about the resulting cross-section of a sliced three-dimensional figure and justify their reasoning. (MP3)
Appropriately use paper, pencil, ruler, compass, protractor, or technology to draw geometric shapes. (MP5)
Solve problems involving angle measure, area, surface area, and volume. (Entrepreneurial Skills: Inquiry/Analysis)
Persevere with complex shapes by analyzing their component parts and applying geometric properties and measures of area and volume. (MP1)
Model real-world situations involving area, surface area, and volume. (MP4)
Reason accurately with measurement units when calculating angles, circumference, area, surface area, and volume. (MP6)
Inquiry Questions
How are proportions used to solve problems involving scale drawings?
What are some examples of cross-sections whose shapes may be identical but are from different three-dimensional figures?
How can the formula for the area of a circle be derived from the formula for the circumference of the circle?
What are the angle measure relationships in supplementary, complementary, vertical, and adjacent angles?
What are some examples of real-world situations where one would need to find (a) area, (b) volume, and (c) surface area?
Coherence Connections
This expectation is in addition to the major work of the grade.
In Grade 6, students solve real-world and mathematical problems involving area, surface area, and volume.
In previous grades, students understand concepts of angle, measure angles, and solve real-world and mathematical problems involving area, surface area, and volume.
In Grade 7, this expectation connects with analyzing proportional relationships and using them to solve real-world and mathematical problems.
In Grade 8, students understand the connections between proportional relationships, lines, and linear equations, and understand congruence and similarity using physical models, transparencies, or geometry software. In high school, students use geometric constructions as a basis for geometric proof.
In Grade 8, students understand congruence and similarity using physical models, transparencies, or geometry software, and understand and apply the Pythagorean Theorem. Students also use the formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.
Academic Vocabulary & Language Expectations:
Scale drawing, adjacent angles, complementary angles, supplementary angles, vertical angles, circumference, cross section, composite figure
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 8
Let's Investigate! Tasks
Let's Investigate! What's the Angle? (TE) (relates to Lesson 8-4)
Let's Investigate! Target the Area (TE) (relates to Lesson 8-6)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: None since this Unit Plan is in addition to the major work of the grade
Coherence Map/Concept Progressions: 7.G.A.1, 7.G.B.4, 7.G.B.6
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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