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A-CED Regular Tessellations of the plane
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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
Algebraic Equations, Inequalities, and Properties
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This lesson is about trying to get students to make connections between ideas about equations, inequalities, and expressions. The lesson is designed to give students opportunities to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings.The idea is for students to start gathering global information by looking at the whole number string rather than thinking only about individual procedures or steps. Hopefully students will begin to see the symbol strings as mathematical objects with their own unique set of attributes. (7th Grade Math)

Material Type:
Activity/Lab
Lecture
Lesson Plan
Teaching/Learning Strategy
Provider:
Noyce Foundation
Provider Set:
Inside Mathematics
Author:
Disston, Jacob
Date Added:
11/30/2011
Animal Populations
Unrestricted Use
CC BY
Rating

In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Stephen M. Hou
Date Added:
06/02/2015
The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Material Type:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
Author:
Stephen M. Hou
Date Added:
06/02/2012
Bernardo and Sylvia Play a Game
Unrestricted Use
CC BY
Rating

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/21/2013
Braking Distance
Unrestricted Use
CC BY
Rating

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Building and Solving Equations 1
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

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
CTE Health Sciences: BMI Calculations
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
CTE Health Sciences: False Positives
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
CTE Health Sciences: Ivy Smith Grows Up
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
CTE Health Sciences: Medication Dosage
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
Classifying Solutions to Systems of Equations
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear 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
Combined Fuel Efficiency
Unrestricted Use
CC BY
Rating

The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/25/2013
Comparing Investments
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest 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
Comparing Linear Functions
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The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students are given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. (7th/8th Grade Math)

Material Type:
Activity/Lab
Lecture
Lesson Plan
Teaching/Learning Strategy
Provider:
Noyce Foundation
Provider Set:
Inside Mathematics
Author:
Dimas, Cecilio
Date Added:
11/30/2011
Discounted Books
Unrestricted Use
CC BY
Rating

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

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
Equation Grapher (AR)
Unrestricted Use
CC BY
Rating

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

نوع المادة:
محاكاة
Provider:
University of Colorado Boulder
Provider Set:
المحاكاة التفاعلية لموقع PhET
المؤلف:
Michael Dubson
Mindy Gratny
Patricia Loblein
Date Added:
06/01/2004
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
Forming Quadratics
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help teachers identify and help students who have the following difficulties: understanding how the factored form of the function can identify a graphŐs roots; understanding how the completed square form of the function can identify a graphŐs maximum or minimum point; and understanding how the standard form of the function can identify a graphŐs intercept.

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
Generalizing Patterns: Table Tiles
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 identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

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
Generalizing Patterns: The Difference of Two Squares
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.

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
Guess My Number
Unrestricted Use
CC BY
Rating

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/07/2012
Lines and Linear Equations
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

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
Making a Translation Tessellation
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

In this activity, learners slide shapes to create unusual tiled patterns. Learners transform a rectangle into a more interesting shape and then make a tessellation by repeating that shape over and over again. Learners will also calculate the area of a rectangle. This activity works best as a "centers" activity.

Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Modeling Situations With Linear Equations
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

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
Ohm's Law
Unrestricted Use
CC BY
Rating

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

Material Type:
Activity/Lab
Interactive
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
Date Added:
11/16/2007
Ohm's Law (AR)
Unrestricted Use
CC BY
Rating

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

Material Type:
Activity/Lab
Interactive
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
Date Added:
06/02/2008
Playground Patterns of Cracks
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

In this math activity, learners observe and sketch cracking patterns in pavement. Learners use a protractor to measure and label the angles of their sketches and conclude if some angles are more common than others.

Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Profit of a company
Unrestricted Use
CC BY
Rating

This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.

Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Projectile Motion (AR)
Unrestricted Use
CC BY
Rating

Blast a Buick out of a cannon! Learn about projectile motion by firing various objects. Set the angle, initial speed, and mass. Add air resistance. Make a game out of this simulation by trying to hit a target.

Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Wendy Adams
Date Added:
06/02/2008
Properties of Quadrilaterals
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This lesson is about properties of quadrilaterals and learning to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems. Students will: Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them. Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counter examples and indirect proof. Identify, formulate and confirm conjectures. Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others. (9th/10th Grade Math)

Material Type:
Activity/Lab
Lecture
Lesson Plan
Teaching/Learning Strategy
Provider:
Noyce Foundation
Provider Set:
Inside Mathematics
Author:
Humphreys, Cathy
Date Added:
11/30/2011