CK-12 Foundation's Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.
This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year. It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story. This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
CK-12's Geometry - Second Edition is a clear presentation of the essentials of geometry for the high school student. Topics include: Proofs, Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.
CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.
CK-12 Geometry Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Geometry Student Edition. The solution and assessment guides are available upon request.
Students take on the role of geographers and civil engineers and use a device enabled with the global positioning system (GPS) to locate geocache locations via a number of waypoints. Teams save their data points, upload them to geographic information systems (GIS) software, such as Google Earth, and create scale drawings of their explorations while solving problems of area, perimeter and rates. The activity is unique in its integration of technology for solving mathematical problems and asks students to relate GPS and GIS to engineering.
In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure. They come to understand that the space can be tiled with unit squares without gaps or overlaps. They make predictions and explore which rectangles cover the most area when the side lengths differ. Students progress from using square tile manipulatives to drawing their own area models and manipulate rectangular arrays to concretely demonstrate the arithmetic properties. The module culminates with students designing a simple floor plan that conforms to given area specifications.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter. The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations. Next students explore geometry. Students tessellate to bridge geometry experience with the study of perimeter. Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements. Students solve word problems involving area and perimeter using all four operations. The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
In this 25-day module, students work with two- and three-dimensional figures. Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms. The second half of the module turns to extending students understanding of two-dimensional figures. Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths. They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes. This module fills a gap between Grade 4s work with two-dimensional figures and Grade 6s work with volume and area.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
Measurement in Grade 7 sees us move from simply finding the perimeter and area of a common object, such as a rectangle or triangle, and move into complex shapes that may involve a combination of different shapes or circles. This unit reviews the basics of finding the area of rectangles, triangles, and parallelograms. It concludes with some real-life problems to which these concepts can be applied.This unit is designed for the Alberta Grade 7 Curriculum.
Harry and his students look at various arrangements of classroom desks in this video from Cyberchase.
The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.
A main concern of shoe engineers is creating shoes that provide the right amount of arch support to prevent (or fix) common gait misalignments that lead to injury. During this activity, students look at their own footprints and determine whether they have either of the two most prominent gait misalignments: overpronation (collapsing arches) or supination (high arches). Knowing the shape of a person's foot, and their natural arch movement is necessary to design shoes to fix these gain alignments.
Students teams determine the size of the caverns necessary to house the population of the state of Alabraska from the impending asteroid impact. They measure their classroom to determine area and volume, determine how many people the space could sleep, and scale this number up to accommodate all Alabraskans. They work through problems on a worksheet and perform math conversions between feet/meters and miles/kilometers.
In this classic hands-on activity, learners estimate the length of a molecule by floating a fatty acid (oleic acid) on water. This lab asks learners to record measurements and make calculations related to volume, diameter, area, and height. Learners also convert meters into nanometers. Includes teacher and student worksheets but lacks in depth procedure information. The author suggests educators search the web for more complete lab instructions.
This task asks students to identify which of the six polygons have the same area. Students may complete the task using a variety of techniques including decomposing shapes, using transformations (rotations, reflections, translations) to move one or more parts of the figure to another part to more easily calculate the area, enclosing the polygon inside a larger rectangle and then subtract the areas of the "extra" pieces, etc.
Students will look at examples and non-examples of squares and rectangles to determine properties of the two shapes. Students practice drawing the shapes with specific dimensions and building up to is a square also a rectangle and is a rectangle also a square?
Students will look at examples and non-examples of squares and rectangles to determine properties of the two shapes. Students practice drawing the shapes with specific dimensions and building up to is a square also a rectangle and is a rectangle also a square?
This article is about the isoperimetric theorem. It states the theorem, explains its history and uses examples and exercises to demonstrate it. The resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.