Algebra Tiles

Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

Copyright 2011, National Council of Teachers of Mathematics

Conic Section Explorer

Explore the different conic sections and their graphs. Use the Cone View to manipulate the cone and the plane creating the cross section, and then observe how the Graph View changes.

Copyright 2011, National Council of Teachers of Mathematics

Interactive Calculus Tool

Master calculus concepts in an interactive environment. Explore graphs of polynomial functions. Approximate tangent lines, derivative curves, and areas. Then, see the actual result of each. Modify graphs and parameters as you work to see if you can improve your approximations.

Copyright 2011, National Council of Teachers of Mathematics

Vector Investigation: Boat to the Island

Move the boat around the water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Try to land the boat on the island — but be careful not to hit the walls!

Copyright 2011, National Council of Teachers of Mathematics

Algebraic Transformations

This applet allows you to transform a plus sign in eight different ways: rotate it ¼, ½, ¾, or a full turn, or flip it vertically, horizontally, or diagonally.

Copyright 2011, National Council of Teachers of Mathematics

The Mathematics of Garlic

Nathan T. Moore and John C. Deming

August 2010, Volume 104, Issue 1, Page 22

More than vegetables—proportional reasoning skills and an understanding of sophisticated statistical concepts—can grow from a backyard plot.

The Mathematics of Garlic.pdf The Mathematics of Garlic.pdf
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Mathematics Teacher, National Council of Teachers of Mathematics

Alternative Approaches to Traditional Topics in Algebra

John W. Coburn

August 2010, Volume 104, Issue 1, Page 34

These new approaches to algebra, although atypical, can bring unreachable students into the classroom mix.

Mathematics Teacher, National Council of Teachers of Mathematics

Funny Face Contest: A Formative Assessment

Yong S. Colen

August 2010, Volume 104, Issue 1, Page 50

Algebra students create their own funny faces onscreen after studying several parent functions and their transformations.

Funny Face Contest, A Formative Assessment.pdf Funny Face Contest, A Formative Assessment.pdf
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Mathematics Teacher, National Council of Teachers of Mathematics

Activities for Students: How Long Does It Take for a Person to Sober Up? Some Mathematics and Science of DUI

August 2010, Volume 104, Issue 1, Page 58

How many hours after consuming a six-pack of beer has the alcohol been flushed from one’s system? An activity module integrates health education, biology, physics, chemistry, social studies, driver education, and mathematics.

Mathematics Teacher, National Council of Teachers of Mathematics

Mathematical Knowledge for Teaching in Planning and Evaluating Instruction: What Can Preservice Teachers Learn?

Anne K. Morris, James Hiebert, and Sandy M. Spitzer

November 2009, Volume 40, Issue 5, Page 491

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one’s teaching.

Journal for Research in Mathematics Education, National Council of Teachers of Mathematics

Area Tool

Use this tool to determine how the length of the base and the height of a figure can be used to determine its area. Can you find the similarities and differences between the area formulas for trapezoids, parallelograms, and triangles?

Copyright 2011, National Council of Teachers of Mathematics

Cyclic Figures

Students will recognize rotation symmetry in figures and examining various rotation symmetries.

Copyright 2011, National Council of Teachers of Mathematics

Dihedral Figures

Use this activity to recognize dihedral symmetry and reflections in figures and examining various symmetries.

Copyright 2011, National Council of Teachers of Mathematics

Free Ride

This applet allows you to vary the gear ratio of a bike. The distance traveled by a half-pedal is determined by the ratio of gears. Can you capture all five flags on a course?

Copyright 2011, National Council of Teachers of Mathematics

Geometric Solids

This tool allows you to learn about various geometric solids and their properties. You can manipulate and color each shape to explore the number of faces, edges, and vertices, and you can also use this tool to investigate the following question:

For any polyhedron, what is the relationship between the number of faces, vertices, and edges?

What other questions can this tool help you answer?

Copyright 2011, National Council of Teachers of Mathematics

"A Study of Proof Conceptions in Algebra"

Lulu Healy and Celia Hoyles

Journal for Research in Mathematics Education

This resource surveys the different conceptions algebra students have regarding proof.

A Study of Proof Conceptions in Algebra.pdf A Study of Proof Conceptions in Algebra.pdf
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JSTOR

"Focusing on Informal Strategies When Linking Arithmetic to Early Algebra"

Barbara A. Van Amerom

Educational Studies in Mathematics

Modeled on studies of students' own productions, a prototype pre-algebra learning strand was designed which takes students' informal (arithmetical) strategies as a starting point for solving equations.

JSTOR

"Predicting Eighth-Grade Algebra Achievement"

Barbara K. Flexer

Journal for Research in Mathematics Education

The relative importance of a group of cognitive variables in explaining the algebra achievement of high-ability eighth graders was investigated in this article.

JSTOR

"Do not worry about your difficulties in mathematics, I assure you that mine are greater"

Albert Einstein (1879-1955)

"Mighty is geometry; joined with art, resistless"

Euripides (485-406 B. C. E)

 to i: Get real! 
i to 
: Get rational!

Volker Runde, Math Jokes

Teacher: What is 2k + k

Student: 3000!
Volker Runde, Math Jokes

Trigonometry for farmers: swine and coswine...

Volker Runde, Math Jokes

Q: How does a mathematician induce good behavior in her children? 
A: "I've told you n times, I've told you n
+1 times..."

Volker Runde, Math Jokes

Q: What is the first derivative of a cow? 
A: Prime Rib!

Volker Runde, Math Jokes

Congruence Theorems

Investigate congruence by manipulating the parts (sides and angles) of a triangle. If you can create two different triangles with the same parts, then those parts do not prove congruence. Can you prove all the theorems?

Copyright 2011, National Council of Teachers of Mathematics

Function Matching

See how well you understand function expressions by trying to match your function graph to a generated graph. Choose from several function types or select random and let the computer choose.

Copyright 2011, National Council of Teachers of Mathematics

Limits

A geometric series is a sum of numbers such that the ratio between consecutive terms is constant. For instance, 1/2 + 1/4 + 1/8 + … is a geometric series. In this activity, you can see a representation of several geometric series and their limits.

Copyright 2011, National Council of Teachers of Mathematics

A Geometric Investigation of (a + b)2

What is the value of (a + b)2? You might think it's a2 + b2, but it's not! Use this geometric demonstration to find out what it really is.

Copyright 2011, National Council of Teachers of Mathematics

Angle Sums

Examine the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon. Can you find a relationship between the number of sides and the sum of the interior angles?

Copyright 2011, National Council of Teachers of Mathematics

Transforming the Way We Teach Function Transformations

Eileen Durand Faulkenberry and Thomas J. Faulkenberry

August 2010, Volume 104, Issue 1, Page 29

Using transparencies helps students learn function transformations—through understanding, not memorization.

Mathematics Teacher, National Council of Teachers of Mathematics

Cosby’s Rule: Connecting Summation Operations, Definite Integrals, and the Fundamental Theorem of Calculus

Margaret H. Sloan

August 2010, Volume 104, Issue 1, Page 45

What happened when a student in an AP Calculus class in a small school in rural Georgia discovered a way to bypass some laborious computations.

Mathematics Teacher, National Council of Teachers of Mathematics

Mathematical Lens: Looking for Slope in All the Wrong Places

August 2010, Volume 104, Issue 1, Page 18

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month the photographs focus on slopes of roadways and trigonometry.

Mathematics Teacher, National Council of Teachers of Mathematics

Delving Deeper: A Problem in Probability

August 2010, Volume 104, Issue 1, Page 71

The authors take the old dart-board problem and examine why the density of random hits seems to be greater nearer the bull’s-eye.

Delving Deeper, A Problem in Probability.pdf Delving Deeper, A Problem in Probability.pdf
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Mathematics Teacher, National Council of Teachers of Mathematics

Knowledge Needed by a Teacher to Provide Analytic Scaffolding During Undergraduate Mathematics Classroom Discussions

Natasha M. Speer and Joseph F. Wagner

November 2009, Volume 40, Issue 5, Page 530

Using case study analysis and a cognitive theoretical orientation, the authors examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. Examples of classroom teaching and interview data demonstrate that, despite having extensive teaching experience and possessing strong content knowledge, some instructors may still face challenges when trying to provide analytic scaffolding to move whole-class discussions toward a lesson’s mathematical goals.

Journal for Research in Mathematics Education, National Council of Teachers of Mathematics

Compound Interest Simulator

This applet will allow you to investigate savings account earnings, credit card debt, and a stock market simulation.

Copyright 2011, National Council of Teachers of Mathematics

Diagonals to Quadrilaterals

Two line segments can be drawn to intersect in various ways — they could be perpendicular, they could bisect one another, or both. Depending on the arrangement of these segments, various quadrilaterals can be formed by connecting the endpoints of the segments.

This activity allows you to discover what types of quadrilaterals can be formed when the diagonals meet in various ways.

Copyright 2011, National Council of Teachers of Mathematics

Flowing Through Mathematics

Simulate water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.

Copyright 2011, National Council of Teachers of Mathematics

Frieze Patterns

Students can experiment with the seven classes of Frieze patterns with this activity. They can explore the transformations that constitute each of the seven categories.

Copyright 2011, National Council of Teachers of Mathematics

Half Angle

If you want to inscribe a circle within a triangle, where will the center of the circle lie? This applet allows you to find the incenter of a triangle, as well an a visual explanation of why it occurs where it does.

Copyright 2011, National Council of Teachers of Mathematics

"The Effects of a Graphing-Approach Intermediate Algebra Curriculum on Students'Understanding of Function"

Jeannie C. Hollar and Karen Norwood

Journal for Research in Mathematics Education

In this study, we investigate the effects of a graphing-approach curriculum employing the TI-82 graphing calculator in an algebra classroom.

JSTOR

"Effects of Standards-Based Mathematics Education: A Study of the Core-plus Mathematics Project Algebra and Functions Strand"

Mary Ann Huntley, Chris L. Rasmussen, Roberto S. Villarubi, Jaruwan Sangtong, James T. Fey

Journal for Research in Mathematics Education

To test the vision of Standards-based mathematics education, a comparative study was conducted of the effects of the Core-Plus Mathematics Project (CPMP) curriculum and more conventional curricula on growth of student understanding, skill, and problem-solving ability in algebra.

JSTOR

"There are things which seem incredible to most men who have not studied Mathematics"

Archimedes of Syracus (287-212 B. C. E)

"There is no royal road to geometry"

Euclid of Alexandria (325-265 B.C.E)

"Mathematics is the queen of the sciences and number theory is the queen of mathematics"

Carl Friedrich Gauss (1777-1855)-German

An infinite crowd of mathematicians enters a bar. 
The first one orders a pint, the second one a half pint, the third one a quarter pint... 
"I understand", says the bartender - and pours two pints.

Volker Runde, Math Jokes

Q: What does the zero say to the eight? 

A: Nice belt!
Volker Runde, Math Jokes

Life is complex: it has both real and imaginary components.

Volker Runde, Math Jokes

Math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x].

Volker Runde, Math Jokes

Q: Why do you rarely find mathematicians spending time at the beach? 
A: Because they have sine and cosine to get a tan and don't need the sun!

Volker Runde, Math Jokes

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