Sketchpad Demos
Algebra
Topic/Last Updated |
Description |
| Circles - Pythagorean Relationship (August 25, 2007) |
This demo helps students derive and discover how the Pythagorean Theorem and the standard form of the equation of a circle are related.
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Conic Sections |
This demo allows students to use sliders to manipulate the traditional r, h, k, a & b values in the standard forms for circles, ellipses and hyperbolas. The change in each values affects the graph of the given conic. The document is divided into 4 tabs at the bottom for each conic section.
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| Direct Variation (August 25, 2007) |
This demo is used in conjunction with Lesson 10 from chapter 1 in my Algebra Two crriculum. On the first tab, it animates a rectangle whose height varies varies directly as its base varies. On the second tab, it animates a rectangle whose height does not vary directly as its base varies. Because the table of values and the rectangles can be hidden independently with buttons, you can beg the question of "If we can't see proportionality when we are looking at the table, how can we tell if their is direct variation?" It is at this point in the lesson that I introduce the notion of a constant by showing the y/x calculation for the rectangles.
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| Discriminant (March 2, 2009) |
This demo allows teacher to use sliders to manipulate a quadratic function of the form y=ax2+bx+c. The sliders change the values of a, b & c. It focuses on the Discriminant and the value of b2-4ac is always visible. The discriminant is also tabled with the real root values for the current function. There are also 7 examples of functions that are Perfect Square Trinomials that are preprogrammed
and accessed by buttons labeled PST down the left side of the document.
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| Domain and Range (April 13, 2008) |
This demo allows teachers to demonstrate the domain and range for 10 different functions & relations.
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| Factor Theorem (April 20, 2009) |
This demo is used in conjunction with a lesson that demonstrates the Factor Theorem for Polynomial Functions.
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| Equation of a Line Given Two Points (August 25, 2007) |
This demo allows the user to click and drag two points (with integer values) around the Cartesian plane. As they do the line they connect is shown. At the touch of a button they can show the slope and y-intercept in visual and numeric form.
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Graphs of Horizontal and Vertical Lines |
This demo allows you to animate a point on a series of horizonal or vertical lines. There one graph per tab. When the point is in motion, double clicking the table will collect values from the point.
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Inequalities Investigation (June 9, 2012) |
This demo allows the user to explore what we mean by a "test point" with regard to a linear inequality in two variables. The lines of two examples are graphed on separate sheets and the user can evaluate the inequality for the test point and examine if the point makes the inequality true or false.
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| Intercepts Discovery (August 3, 2008) |
This demo animates a line by way of its intercepts. Students are presented with the essential questions: What do all point on the x-axis have in common? What do all points on the y-axis have in common? Building on this, students should be able to discover how to graph an equation of the form Ax+By=C by quickly finding its x & y intercepts. This demo is used in conjunction with Lesson 3 from Chapter 1. |
| Midpoint, Slope and Distance (June 30, 3008) |
This demo gives teachers access to a visual representation of the midpoint, distance and slope formulas. It is basic, but very handy. It is good for checking problems that students have done.
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| Parallel and Perpendicular Lines (A Slope Discovery) (August 25, 2007) |
This demo is meant to helps students discover the relationship between parallel lines and their slopes. (Similar for Perpendicular Lines). There are 4 tabs at the bottom of the main document when it opens.
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| Perfect Square Trinomials (August 25, 2007) |
This demo helps students derive and discover the (L+R)2=L2+2LR+R2 relationship. It takes a square whose side is L+R and by animation shows that it can be split infinitely into two unique squares and two identical rectangles.
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| Perimeter, Area and Volume (June 18, 2009) |
This demo shows how n-tupling a given side of a figure impacts its perimeter, area and volume.
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| Quadratics - Five Point Graphing (February 21, 2009) |
This demo illustrates how to construct the graph of a quadratic function of the form f(x)=x2+bx+c given that there is at least one real root. The 5 points highlighted in this method are: the roots, the vertex, the y intercept and the reflected y-intercept. The function is also shown in factor form to illustrate the roots using the zero-product property.
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| Quadratics - Forms (General, Vertex and Factored) (May 22, 2010) | This demo illustrates the three forms of Quadratic functions: General Form f(x)=ax2+bx+c, Vetex Form f(x)=a(x-h)2+k and Factored Form f(x)=a(x-r1)(x-r2). Each of these forms is represented on a separate tab in the Sketchpad document. The user can manipulate the values in bold using a slider to investigate how changes in these values in the equation affect changes in their graphs.
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Quadratics - Vertex Discovery |
This demo uses sliders for the values of a, b & c in conjunction with the standard form of f(x)=ax2+bx+c for the purpose of showing a variety of quadratic graphs. The demo shows how x=0 and x=-b/a are zeros for the quadratic function when c=0. From this students should be able to see that the axis of symmetry is half way to this zero, thus being x=-b/2a.
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Slope |
This demo allows students to interact with the slope of a line by controlling rise and run independently. Each of the seven pages asks students to create a specified slope by moving an endpoint of a line segment.
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Transformations |
This is one of my favorite demos. Through the use of sliders, the teacher or student can manipulate the values a, h & k to affect the graph of 10 given parent functions (linear, quadratic, absolute value, greatest integer function, square root, cubics, 1/x, 1/x2, 2x, 1/2x. There is a tab dedicated for each of these functions.
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| Transformations 2 (April 8, 2008) |
This is much like the demo called Transformations. Through the use of sliders, the teacher or student can manipulate the values a, b, h & k to affect the graph of 10 given parent functions (quadratic, absolute value, greatest integer function, square root, cubics, 1/x, 1/x2, sin(x), cos(x) and tan(x). There is a tab dedicated for each of these functions.
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Geometry
Topic |
Description |
| Area - Doubling the Radius of a Circle | This demo helps students derive and discover what happens to the area of a circle when the radius is doubled. Two circles are given. The size of either can be changed, but one will always have twice the radius of the other. The tabulate feature can be used to track changes in the areas of the two circles.
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| Exterior-Angle Theorem for Triangles (March 2, 2009) |
This demo give a quick illustration of how the sum of the measures of two angles of a triangle is equal to the meausre of exterior angle of the third angle.
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| Interior Angles of an n-gon | This demo demonstrates the
how any given polygon can be broken in to a series of triangles.
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| Parallel Lines Cut By Transversal | This demo introduces the vocabulary of corresponding angles, alternate-interior angles, same-side (consecutive) interior angles and alternate-exterior angles. The algebraic relationships for these angles can also be demonstrated.
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| Parallelogram Family | This demo is meant to introduce the five properties of a parallelogram. The special parallelograms of rectangle, rhombus and square are also presented. Each of which is shown to have the properties of a parallelogram along with unique properties as well. Each parallelogram is represented on a whole page and accessed at the tabs in the bottom left of the document window.
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| Points of Concurrency (February, 25, 2008) |
This demo takes students through the construction of how to determine the incenter, circumcenter, centroid and orthocenter for a triangle. There is a tab dedicated to each of these as well as one tab where small versions of all four can be show. This is one of my favorite demos.
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Quadratic Exploration |
This demo was gifted to me by a colleague. It allows students to explore the following conjecture. "Do the sum of the of the squares of the sides of a quadrilateral equal the sum of the squares of the diagonals of the quadrilateral?" Students are able to investigate this for a quadrilateral, rectangle, rhombus, and square. |
| Scale Factor Similarity (April 1, 2008) |
This demo allows students to adjust the dimensions in a series of figures to experiment with scale factor and statements of proportionality. The students are also required to use the Sketchpad calculator to demonstrate the ratios involved in the statement of proportionality.
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| Triangle Congruence - HL | This demo help students discover the HL Congruence Theorem for right triangles.
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| Triangle Congruence - SSS | This demo helps students discover the SSS Congruence Theorem.
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| Triangle Congruence - SAS | This demo helps students discover the SAS Congruence Theorem.
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| Triangle Congruence - AAS | This demo helps students discover the AAS Congruence Theorem.
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| Triangle Congruence - ASA | This demo helps students discover the ASA Congruence Theorem.
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| Triangle NON-Congruence - AAA | This demo helps students investigate whether or not three sets of corresponding congruent angles is sufficient information to prove congruence.
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| Triangle NON-Congruence - SSA | This demo helps students investigate whether or not two sets of corresponding congruent sides and a pair of non-included corresponding congruent angles is sufficient information to prove congruence.
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| Volume/Surface Area of a Cone | This demo investigates the volume and surface area of a cone. The user can control the height and the radius of the base in the cone to change its dimensions. The user can also display a hint as to what they need to type on their calculator to get the answer.
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Trigonometry
Topic |
Description |
| Arc Length (March 26,2008) |
This demo helps students visualize the creation of the arc when a point is rotated in a circle around a central angle. |
| Special Reference Angles |