Standards in Unit:
Draw, construct, and describe geometrical figures and describe the relationships between them.
- Building an understanding that angle measures remain the same and side lengths are proportional.
- Using a scale factor to compute actual lengths and areas from a scale drawing.
Solve real-world and mathematical problems involving angle measure, area, surface area, and volume, including cylinders, cones, and spheres
- Understand the relationships between the radius, diameter, circumference, and area.
- Apply the formulas for area and circumference of a circle to solve problems.
- Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
- Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
• NC.8.G.9 Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.
• NC.8.G.3 Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the x-axis and y-axis on two-dimensional figures using coordinates.
- Verify experimentally the properties of rotations, reflections, and translations that create congruent figures.
- Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
- Given two congruent figures, describe a sequence that exhibits the congruence between them.
- Verify experimentally the properties of dilations that create similar figures.
- Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
- Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Summary of Unpacking for Each Standard:
NC.7.G.1 -In learning proportionality, students will learn about scaled figures and how to determine missing side lengths and areas using proportional reasoning. This provides a geometric rationale for the RP work from earlier units. They will understand that scale drawings have equal angle measures and proportional corresponding sides related by a scale factor. They will use this scale factor to solve problems and create scale drawings.
NC.7.G.4 -Students have learned the basics of circles in the past, but in this unit, they will dive deep and be exposed to the Π (pi) ratio for the first time. They will derive the formulas for area and circumference of circles based on ratio reasoning and decomposing the area, and they will use them to solve problems. (See the unpacking document for specific examples.) They will also integrate this standard with the coordinate plane, finding radius and diameter using the plane and applying them to solve problems. (This is a review from the 6th Honors course, but for 2018-19, some students may not have learned this standard.)
NC.7.G.6 -Students will build on their learning from previous grades, specifically composing and decomposing rectangles and parallelograms, to find the measurements of more two and three-dimensional figures. They will need to solve equations for lengths using formulas, and they can derive the formulas for volume and surface areas of prisms and pyramids. All of these measurements can be found in mathematical or real-world context. (This is a review from the 6th Honors course, but for 2018-19, some students may not have learned this standard.)
NC.8.G.9- Students will derive the formulas for the volumes of cones, cylinders, and spheres in this standard and apply them in real-world and mathematical contexts. Merely memorizing formulas is not the goal for this standard. Students should build on their work with rectangular prisms and pyramids, applying what they have learned about circles, to understand how to determine the volumes of cones, cylinders, and spheres conceptually.
NC.8.G.3- Students will understand the difference between rigid transformations, which preserve congruence, and non-rigid transformations (mainly dilations), which do not preserve congruence. They will also explore transformations on the coordinate plane and discover the effects each transformation has on the coordinates of shapes.
NC.8.G.2 -The focus of this standard is the idea of congruence, and students should be able to define congruence, identify congruent shapes, and use measurements to prove congruence. They will also understand which transformations preserve congruence and which do not, and they will be able to identify which transformation has occurred between two congruent shapes.
NC.8.G.4- Students will understand the concept and definition of similarity and how certain sequences of transformations create similar figures. They will also understand similarity in terms of scale factor and explore how side lengths are related by dilations of various scale factors.
Prerequisite Skills:
Future Skills:
Key Vocabulary:
Cornerstone Task
Popcorn Box Problem: Teacher Version (Links to an external site.)Links to an external site. Student Version (Links to an external site.)Links to an external site.
MTSS/Remediation Resources
Math Topic/DPI Bucket: Circles/Geometry
Engage NY F2F Intervention: Grade 7, Module 3 (Links to an external site.)Links to an external site., Topic C, Lessons 16-18
Edgenuity Online Intervention: Grade 7 Two-Dimensional Geometry Unit, Lessons 5-8
Math Topic/DPI Bucket: 3D Shapes/Geometry
Engage NY F2F Intervention: Grade 7, Module 6, Topic D, E
Edgenuity Online Intervention: Grade 7 Three-Dimensional Geometry Unit