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Traveling Sound
Learners explore how sound waves move through liquids, solids and gases in a series of simple sound energy experiments. They describe how sound needs molecules to move and that changing the medium that it travels through changes the...
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Sort it Out
Learners identify and sort a variety of two- and three-dimensional objects and compare and contrast their attributes. They identify shapes, locate shapes on the faces of solids, sort real objects and explain the sorting rule, and...
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DEAD MAN'S CURVE
Ninth graders, after being given a unique scenario and a task sheet on Dead Man's Curve, calculate and explain the force needed to keep a car on a curve using a set of formulas and a geometric property of circles. They utilize and create...
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Arithmagons
Fifth graders explore patterns and relationships among the numbers that form arithmagons. They create and attempt different rules that can be used to solve arithmagons. Students use linear algebra to solve arithmagons.
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Gougu Rule or Pythagoras' Theorem
Fifth graders explore Pythagoras' Theorem. They examine the pattern linking the length of the hypotenuse of a right angled triangle and the length of the other two sides. Students find an unknown side in right angled triangles.
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Consecutive Numbers
Like all of the Problem Solving units, this one aims to introduce students to the underlying ideas of mathematics through a problem. The problem here requires a knowledge of arithmetic and the use of some algebra. In this unit we see how...
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Rotation Symmetry
Middle schoolers investigate the concept of symmetry by using various examples and performing independent practice with scaffolding provided by the teacher. They review reflection symmetry and cover the new rotation symmetry using...
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Babylonian Mathematics 2
Students research Babylonian mathematics. They calculate simple surd numbers. Students find the fractional form of rational numbers expressed as decimals. They work with numbers in base 60.
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Guzzinta
Students explore strategies to solve number problems. They study divisibility rules. Students examine and practice multiples, factors, and palindromes. In groups, students play a "number property" game.
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The Distributive Property
Students review how to solve problems using the Distributive Property of Mathematics. They solve problems using the paper and pencil method and then use the graphing calculator to discover the property over addition while making a visual...
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Relating Division and Subtraction
Third graders relate the process of division to subtracting equal groups. Through guided practice and teacher demonstration, they complete division problems using a subtraction method. Students complete problems independently for...
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Dividing By 3 and 4
Third graders are introduced to how to divide by 3 and 4. They are told that are going to use the same procedures as they did on yesterday, except with new divisors. Students turn their attention to the Paddle Problem on page 206 of...
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Four Color Theorem
Students identify and interpret how the Free Response questions are graded on an AP Exam. They also discuss coloring the included map, placing several examples on the board to determine the number of colors necessary to color each....
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Got Complements? with Cabri Jr.
Learners use the axes and measure angle tool to explore and calculate complementary angles with Cabri Jr. They also identify what happens to the calculation as they drag the endpoint into a different quadrant. Finally, they label each...
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Sum of Angles
In this sum of angles worksheet, 6th graders solve and complete 6 different types of problems. First, they identify different alternate and corresponding angles. Then, students state what the angles of a triangle add up to and how they...
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Pape's Theorems
In this math worksheet, learners find the length of the side of a regular hexagon whose area is numerically equal to its perimeter.
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Worksheet 4
In this math learning exercise, students write down five exact differential equations in symmetric form. Then they test the statements concerning differential equations.
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Worksheet 1
In this math worksheet, students give an example of a function which is continuous but not differentiable. They also write a definition for differentiable.
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Complex Analysis: Cauchy's Integral Formula and Integral Examples
In this integral formula worksheet, students examine Cauchy's formula and higher derivatives of analytic functions. They use this provided information to solve eight problems.
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Complex Analysis: Harmonic Functions
In this harmonic function worksheet, students explore harmonic functions and construct a harmonic conjugate. This three-page worksheet contains three problems, with explanations and examples.
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Linear Systems: Applications of Eiginvalues
In this Eigenvalue and Eigenvector learning exercise, students examine the applications of matrix exponentiation. This four-page learning exercise provides explanations and examples, as well as three problems to complete.
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Linear Systems: Symmetric Matrices
In this symmetric matrices worksheet, students explore the characteristics of symmetric matrices. This two-page worksheet contains examples and explanations concerning symmetric matrices. Two problems are provided to solve.
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The Product and Quotient Rules
In this product and quotient rules worksheet, students use Taylor's Theorem to rewrite functions in a given form. They determine the derivatives of functions. This three-page worksheet contains explanations, examples, and seven problems.
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Derivatives of Elementary Functions
In this derivatives worksheet, students sketch the graphs of four functions. They write the derivatives of eight functions. Students complete two derivative tables.
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