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  • Geometry
2D Representations of 3D Objects
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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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
2D Rotation Using Matrices
Conditional Remix & Share Permitted
CC BY-NC-SA
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This Demonstration illustrates the concept of rotating a 2D polygon. The rotation matrix is displayed for the current angle. The default polygon is a square that you can modify.

Material Type:
Activity/Lab
Diagram/Illustration
Homework/Assignment
Interactive
Simulation
Teaching/Learning Strategy
Provider:
Wolfram Research
Provider Set:
Wolfram Demonstrations Project
Author:
Mito Are and Valeria Antohe
Date Added:
09/04/2013
AAS Congruent Triangles
Read the Fine Print
Rating

An interactive applet and associated web page that shows how triangles that have two angles and a non-included side the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two angles and non-included side are outlined in bold to show they are the same measure and are the elements being used to prove congruence. The web page describes all this and has links to other related pages. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Material Type:
Reading
Simulation
Provider:
Math Open Reference
Author:
John Page
Date Added:
02/16/2011
A-CED Regular Tessellations of the plane
Unrestricted Use
CC BY
Rating

This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
Analyzing Congruence Proofs
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Angle Hunting
Conditional Remix & Share Permitted
CC BY-NC-SA
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In this activity, learners use a hand-made protractor to measure angles they find in playground equipment. Learners will observe that angle measurements do not change with distance, because they are distance invariant, or constant. Note: The "Pocket Protractor" activity should be done ahead as a separate activity (see related resource), but a standard protractor can be used as a substitute.

Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Application of Derivatives
Conditional Remix & Share Permitted
CC BY-SA
Rating

We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.

Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
Date Added:
03/12/2012
Applying Angle Theorems
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Are Random Triangles Acute or Obtuse?
Conditional Remix & Share Permitted
CC BY-NC-SA
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This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strange
Date Added:
06/02/2012
Bank Shot
Unrestricted Use
CC BY
Rating

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/21/2012
Battleships
Only Sharing Permitted
CC BY-NC-ND
Rating

This activity explores the main algorithms that are used as the basis for searching on computers, using different variations on the game of battleships. This activity demonstrates three search methods for finding information in data: linear searching, binary searching and hashing. It also includes an optional introductory activity as well as a video showing a fun demonstration related to the same content.

Material Type:
Activity/Lab
Game
Lesson Plan
Simulation
Provider:
Computer Science Unplugged
Science and Math Informal Learning Educators (SMILE)
Provider Set:
Computer Science Unplugged
SMILE Pathway: Science and Math Activities in One Search
Author:
Brian Mason Scientific and Technical Trust
Computer Science Unplugged
Google Inc.
Ian Witten
Jane McKenzie
Mike Fellows
Robyn Adams
Tim Bell
Date Added:
01/02/2002
CTE Architecture: Access Ramp
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/05/2012
CTE Architecture: Framing a House
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/05/2012
CTE Architecture: Storage Sheds
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/05/2012
CTE Health Sciences: Range of Motion
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type:
Activity/Lab
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
07/27/2012
Calculating Volumes of Compound Objects
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Congruent Segments
Unrestricted Use
CC BY
Rating

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Designing: Candy Cartons
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: Select appropriate mathematical methods to use for an unstructured problem; interpret a problem situation, identifying constraints and variables, and specify assumptions; work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area; and communicate their reasoning clearly.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Determinants
Conditional Remix & Share Permitted
CC BY-SA
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This dynamic worksheet illustrates the relationship between the DETERMINANT, the Area of the pre-image, and the Area of the image.

Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
Date Added:
04/26/2012
Determinants
Conditional Remix & Share Permitted
CC BY-SA
Rating

Ana Donevska Todorova Humboldt Universitハt zu Berlin Mathematisch-Naturwissenschaftliche Fakultハt II Institut f゚r Mathematik, Didaktik der Mathematik ??? ?????????? ?????? ???????? ?? ???????????? ????? ? ????

Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
Date Added:
03/12/2012
Determinants and Analytic Geometry
Conditional Remix & Share Permitted
CC BY-SA
Rating

Ana Donevska Todorova Humboldt Universitハt zu Berlin Mathematisch-Naturwissenschaftliche Fakultハt II Institut f゚r Mathematik, Didaktik der Mathematik

Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
Date Added:
03/12/2012
Dilating a Line
Unrestricted Use
CC BY
Rating

This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Drawing to Scale: Designing a Garden
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Equations of Circles 1
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Equations of Circles 2
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Estimating: Counting Trees
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

Material Type:
Assessment
Lecture Notes
Lesson Plan
Teaching/Learning Strategy
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Author:
http://map.mathshell.org/
Date Added:
04/26/2013
Estimations and Approximations: The Money Munchers
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Evaluating Statements About Enlargements (2D and 3D)
Only Sharing Permitted
CC BY-NC-ND
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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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Evaluating Statements About Length and Area
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Everything Maths: Grade 11
Unrestricted Use
CC BY
Rating

This is a comprehensive math textbook for Grade 11. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: language of mathematics, exponents, surds, error margins, quadratic sequences, finance, quadratic equations, quadratic inequalities, simultaneous equations, mathematical models, quadratic functions and graphs, hyperbolic functions and graphs, exponential functions and graphs, gradient at point, linear programming, geometry, trigonometry, statistics, independent variables, dependent events. This book is based upon the original Free High School Science Text series.

Material Type:
Textbook
Provider:
Siyavula
Date Added:
04/12/2012
Experimenting with Symmetry
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

In this activity, learners use pattern blocks and mirrors to explore symmetry. Learners work in pairs and build mirror images of each other's designs. In doing so, learners will examine principles of symmetry and reflection.

نوع المادة:
Activity/Lab
Provider:
متحف Exploratorium لدعم التعليم
المؤلف:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Exploring Tessellations (Grades 6-8)
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

In this activity, learners design unique tiles and make repeating patterns to create tessellations. This activity combines the creativity of an art project with the challenge of solving a puzzle. This lesson features three investigations, in which learners make tessellations by translating, rotating, and reflecting the patterns.

Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Fabulous Fractals and Difference Equations
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Laura Zager
Date Added:
07/12/2014
Fabulous Fractals and Difference Equations
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

Material Type:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
Author:
Laura Zager
Date Added:
06/02/2012
Figure This! Math Challenges for Families
Restricted Use
Copyright Restricted
Rating

This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge. Resources for further investigations are suggested as well. From the Printing the Challenges link on the homepage, PDF files are available for all 80 challenges in English, the first 15 challenges in Spanish, and the family resource materials in English and Spanish.

Material Type:
Activity/Lab
Homework/Assignment
Provider:
National Council of Teachers of Mathematics
Provider Set:
Figure This!
Date Added:
01/01/2002
Find the Missing Angle
Unrestricted Use
CC BY
Rating

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Floor Plan
Unrestricted Use
CC BY
Rating

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012