Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle measurements, uniqueness of triangles, and solid figure application problems.
In Unit 6, seventh-grade students cover a range of topics from angle relationships to circles and polygons to solid figures. The seventh-grade Geometry standards are categorized as additional standards, however, there are several opportunities throughout the unit where students are engaged in the major work of the grade. In the beginning of the unit, students use and solve equations to represent relationships between angles and find missing angle measures. Investigating circles, students discover the proportional relationship between the circumference of a circle and its diameter, and understand π as the ratio of these two quantities. Students will also use their expressions skills to write numerical expressions that can be used to find surface area and volume of three-dimensional figures.
Throughout the unit, students encounter several vocabulary words, such as complementary angles, vertical angles, radius, and circumference. Many of these words enable students to be more precise in their communications with each other (MP.6). Students will also encounter complex diagrams of angles and 3-D figures where they will need to understand what information they can glean from the diagram and plan a solution pathway before jumping in (MP.1). Students should have access to several tools they may opt to use throughout the unit, including rulers, protractors, compasses, and reference sheets (MP.5).
The foundational skills for the standards in this unit stem from fourth through sixth grades. In fourth grade, students studied the concepts of angle measurement and understood angle measure to be additive. In fifth grade, students developed an understanding of three-dimensional volume, which they further built on in sixth grade. Sixth-grade students also began to distinguish between the three-dimensional space an object takes up and the surface area that covers it.
In eighth grade, students will zoom in on right triangles and apply the Pythagorean theorem to determine side lengths in right triangles. They will also continue solving real-life applications of surface area and volume, with the addition of cones, spheres, and cylinders.
Pacing: 23 instructional days (21 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
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vertical angles
adjacent angles
radius
diameter
circumference
complementary angles
Triangle Inequality Theorem
cross-section
surface area
volume
supplementary angles
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7.G.B.5
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.4
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
7.G.B.6
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.A.2
7.G.B.5
Draw two-dimensional geometric shapes using rulers, protractors, and compasses.
7.G.A.2
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.3
Identify and describe two-dimensional figures that result from slicing three-dimensional figures.
7.G.B.6
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.
Key: Major Cluster Supporting Cluster Additional Cluster
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