Untitled Document

Alphabetical

Absolute Value Equations : given an absolute value function and the graph, change the variables to see the changes in the graph. There is a page with 4 challenge problems for the students to complete that can be sight checked.

Animation Lesson : gives directions on how to do basic animations. Three samples are shown also.

Area & Perimeter on Graph : given a shape on a grid, use the grid patterns to determine the area of the overall shape. Click to see the shape broken down into rectangles and triangles or rectangles, triangles and trapezoids. Double check area using Sketchpad. Repeat for Perimeter.

Circumference : drag a point around a circle to show the arc. The length is shown as well as a segment of the same length. Drag to change the radius of the circle.

Classifying Angles by Degrees : drag a point around a semi-circle to see acute, right, obtuse and straight angles.

Conditional Statements : uses a Venn diagram and the 4 conditional statements. The truth of each statement is explored as user moves the circles amongst each other.

Congruence vs. Similarity : triangle and polygon sections. Explore congruence relationships. Explore similarity by controlling the shape and/or the scale factor. Includes proportions and grids to make the ratios easier to understand.

Constructions : goes through 13 basic constructions, with directions, on sketchpad.

Domain & Range : drag a point on a function and the domain and range is traced on a number line at the side. Change the function, the graph controls and/or animate the point.

Ellipses : given an ellipse, verify d₁ + d₂ remains constant and equate that to the major axis length. The ellipse can be manipulated all possible ways.

Equidistant : discover a perpendicular bisector of a segment and an angle bisector by moving points to make the lengths of the segments equal. Animate to see the locus of all points where the lengths are equal. Answer what the locus of points is called. Hints are given.

Flag : sample of a flag project. Students choose a flag, copy and paste the flag picture and then re-create the flag using proportions to generate a scalable model in Sketchpad. We then had our students print out the flags at a given size and find the area of each shaded portion by hand. We could check using the sketchpad files. Great opportunity for interdisciplinary work using the countries of the flags.

Evaluating Functions : given f(x) and its graph, drag a point on the graph. The coordinates are shown as well as the value of f at that point.

Geometric Mean : given a right triangle with altitude to the hypotenuse, click to separate the three triangles with animation to more easily see the similarity. Drag vertices to see the changes in all. Click to show the angle measurements and the ratios to verify similarity. Includes a proof of the Pythagorean Theorem and verification of ratios with side lengths.

Graphing by Roots : given 2 roots, click to change the roots and see the difference in the graph. Click to add a 3rd or 4th root. Equation is given in root form - click to see the expanded form also.

Graphing Inequalities : graph 1, 2 or 3 inequalities. Show all shading or just the solution set.

Hidden polygons : highlight triangles to form the polygons listed on the screen.Answers

Hyperbolas : given a hyperbola that can be fully manipulated, choose to show the distances and verify that d₁ - d₂ remains constant and relates the shortest distance between branches. Choose to show the asymptotes and a, b and c lengths to relate to the equation.

Intercepts : given a line, drag points to change the line. The y- and x-intercepts are shown. Click to also see the standard or slope-intercept form of the line to see where the intercepts can be seen in the equations.

Intersection of Planes : demonstrates the intersection of 2 "vertical" planes. Option to add a third and/or a horizontal plane. Includes animation of one plane..

Introduction Lesson : step-by-step directions for students to make a stick figure as an introduction to Sketchpad tools and menus.

Inverse Graphs : given a function, a point on the function and y=x, drag the point on the function to see the inverse graphed. Function is able to be changed.

Isosceles Triangles : given a triangle with all angles measured and side lengths shown, manipulate the triangle to answer the questions presented. Leads into triangle inequalities.

Linear Quiz : given an equation, change the equation so that it matches a given graphed line. 6 questions per page. Pages lead through y=b, x=k, y=x+b, y=mx, y=mx+b.

Linear Systems : given two lines with slope-intercept equations, the intersection point and cooredinate is shown. Manipulate the lines separately or click to have them represent one solution, no solution, or infinite solution.

Linear Transformations : given a graph of f(x), drag another line and see the equation in f(x) + __ format.

Medians, Altitudes and Angle Bisectors in a Triangle : separate pages, including leading questions, for each individual items. Special points formed by each item are also included. One page incorporates all to discover unique situations with a regular triangle.

Number Lines : control the symbol and number graphed. The resulting expression is graphed on a number line complete with appropriate shading.

Parabola & Distance : given a parabola with directrix and focus graphed, move a point on the parabola. When the point is colinear with the focus, the square related to a shows.

Parabola Equations : choose standard or vertex form. Given an equation and the graph, change the variables to see the changes in the graph. y= and x= are included. There is a page with 4 challenge problems in y= format for the students to complete that can be sight checked.

Parallel Lines and Angles : has students create a transversal, identify and measure the angles. 10 questions are asked with room to answer on the screen. Can be graded electronically

Perpendicular Lines : given two intersecting lines with all 4 angles measured, drag the lines to see the change in angles. Right angle shown when lines are perpendicular. Questions about congruent, right and straight angles.

Point-Slope : change the slope and/or the coordinates of the point. Line is graphed. Equation shown in point-slope and slope-intercept forms.

PosNegBoard : adapted from Keypress Chipboard using + and - signs instead.

Reilly : demonstrating using a picture in Sketchpad. Given a face, draw what would be the line of symmetry for the halves of the face. Mimick one half of the face using Sketchpad tools and reflect across the line to see whether the face is truly symmetry or not.

Remote Exterior Angles : given a triangle with 2 angles and the remote exterior measured, verify that the sums are equal. Manipulate the triangle to see the relationship holds. Click to show the other two relative remote exterior angles with all measurements and calculations shown.

Sketchpad Tutorial : step-by-step directions for any learner.

Slope : control the graphed equation. Coordinates of 2 points are shown. The rise/run triangle is shown. Distance is shown on the graph. Slope is calculated by distance and subtraction of points. Change the coordinates to see that the slope remains the same. Click to add a second set of 2 points that can be dragged.

Slope-Intercept Form : show a line with 2 points shown where students can only change the slope by moving the points. Show a line where students can only alter the intercept. Slope with rise/run can be shown on the graph.

Special Parallelograms : given a parallelogram, choose to show angle measures, side measures and/or diagonals. Complete a chart leading students to the classification of parallelograms.

Sum of Angles in a Triangle : given a triangle and the angle measurements, drag the vertices to see that the sum remains the same. Questions students to relate it to a straight line and provides animation translating copies of the triangle to demonstrate.

Sum of Exterior Angles : Regular and non-regular. Given a regular polygon with each exterior angle drawn, control the number of sides to see the sum remains the same. Sum is also shown as completing a circle to visually reinforce. 2nd page has non-regular triangle and quadrilateral.

Sum of Interior Angles : Regular and non-regular. Given a regular polygon, control the number of sides to explore the idea of breaking the shape into triangles to find the sum. Students fill in a chart on the screen to help discover the formula. Click to show the triangle divisions for up to a 20-sided polygon.

Trapezoids : given a trapezoid on the screen, measure angles and sides. Then answer questions (how many congruent angles, how many congruent sides, etc.) about the figure. Change it to an isosceles trapezoid and answer questions about that. Challenge is to create a trapezoid using sketchpad.

Middle School

Circumference : drag a point around a circle to show the arc. The length is shown as well as a segment of the same length. Drag to change the radius of the circle.

Classifying Angles by Degrees : drag a point around a semi-circle to see acute, right, obtuse and straight angles.

CongruenceSimilarity : triangle and polygon sections. Explore congruence relationships. Explore similarity by controlling the shape and/or the scale factor. Includes proportions and grids to make the ratios easier to understand.