This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

In this lesson, students complete several activities that involve coordinates and graph paper given the following invitation to learn: "Suppose you are having a birthday party and a friend you have invited has asked you for directions from the school to your house. You tell them it is five blocks away. Is this enough information for them to find your house?"

This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

This activity allows the user to plot points on the coordinate plane and to read the coordinates of a point plotted by the computer.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students will continue to explore surface area, looking at more complex solids made up of cubes. Students will look at the 2-D views of these solids to see all of the surfaces and to find a shorter method to calculate the surface area.Key ConceptsThe 2-D views of 3-D figures (front top and side) show all of the surfaces of the figure (the area of the three views is doubled or the back, bottom, and other side) and so can be used to calculate surface area. The only exception is when surfaces are hidden or blocked and must be accounted for.GoalsExplore the relationship between 2-D views of figures and their surface area.Find the surface area of different solids.

This lesson unit is intended to help teachers assess how well students are able to: recognize and visualize transformations of 2D shapes; and translate, reflect and rotate shapes, and combine these transformations. It also aims to encourage discussion on some common misconceptions about transformations.

This resource is part of Tools4NCTeachers.

This packet contains exit tickets for the Kindergarten, Cluster 4 geometry standards. Exit tickets are written responses to questions posed at the end of a lesson. They are brief assessments which allow the teacher to determine student understanding of the concepts and skills taught that day. At the Kindergarten level, a blank copy of the exit ticket should be displayed on the board and read aloud to students. As teacher reads, students work independently on their own copy of the exit ticket.

This resource is part of Tools4NCTeachers.

This file contains a sample image of a geometry anchor chart, as well as an image of a composing shapes activity. Directions and descriptions are included.

This resource is part of Tools4NCTeachers.

In this task, students identify shapes, describe attributes of shapes, and compare a two-dimensional and three-dimensional shape. This task may be used for instructional or assessment purposes.

This resource is part of Tools4NCTeachers.

Students are asked to draw a set of two-dimensional shapes, and build three-dimensional shapes from clay. This task may be used for instructional or assessment purposes.

This resource is part of Tools4NCTeachers.

In this task, students identify the names of two and three-dimensional shapes regardless of orientation. This task may be used for instructional or assessment purposes.

This resource is part of Tools4NCTeachers.

Based on a series of teacher directions, students select stated shapes and place them in specified locations. Students must recognize the names of shapes and position words. This task may be used for instructional or assessment purposes.

This resource is from Tools4NCTeachers. This file contains a set of 3 tasks (including scoring rubric and recording sheets).  The tasks may be used for instruction or assessment.The focus of standard G.1 is on recognizing/drawing 2D shapes and recognizing/describing 3D shapes.  Please remix this resource to help create additional tasks - especially for 3D shapes! 

In this lesson, students will graph translations (slides) and reflections (flips) on a coordinate plane. The lesson is introduced by having students move across the room to demonstrate translations and reflections.

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

In this activity, a student challenges a partner to recreate his quadrilateral or other shape on a geoboard by calling out the ordered pairs of the quadrilateral's vertices.