Geometer's Sketchpad - Trig Ratio Generator

When using the Geometer's Sketchpad (for both computer and iPad) it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students can practice two very specific skills dealing with trigonometry. The first is simply being able to correctly place the names of the sides of a right triangle (opposite, adjacent and hypotenuse). Students drag the side names and then can check their answers and then randomly generate another triangle to try again. The second is one where a random triangle is generated that shows information about two sides and one angle. Students then drag parts of an equation to create a trig ratio equation. They can check their answer and then randomly generate other right angled triangle to try again. 

This is not meant to be something that a student uses for a long length of time but instead just some quick practice to re enforce the basic ideas from trig ratios.

• MFM2P, MPM2D - determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios.
• MCR3U, MCF3M, MBF3C - As review

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch

• TrigGenerator.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Combining Velocity Vectors

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students will walk through a demonstration of how the combination of two linear motions can create a complex two dimensional motion (in this case circular motion). Some things that I think are important here are the fact that the two motions are completely independent of each other and the idea of how the look of a velocity vector changes as you speed up and slow down. The sketch is meant for students to walk through and answer questions as they go. You could also use it in the calculus part of the course to talk about velocity increasing/decreasing and what that looks like for motion.

• A1.1 - describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)
• C1.2 - represent a vector in two-space geometrically as a directed line segment, with direction expressed in different ways (e.g., 320º; N 40º W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors
• C2.1 - perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two space, and on vectors represented in Cartesian form in two-space and three-space

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch

• CircleVector.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Practice Line of Best Fit

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students practice placing the line of best fit on a linear set of data. It's not meant to be really difficult but just to reenforce the idea of what the line of best fit is. Students can check their answer and try as many as they like. Clicking the Medium or Hard buttons will spread the points out more randomly to make the line a bit harder to determine. This is not meant to be really hard but just a quick way to determine if students have the basic concept of what a line of best fit is

• MPM1D, MFM1P - construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources
• MAP4C - D1.4 - create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology
• MDM4U - D2.4 - generate, using technology, the relevant graphical summaries of two-variable data (e.g., scatter plots, side-by-side boxplots) based on the type of data provided (e.g., categorical, ordinal, quantitative)

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch

• Line of Best Fit.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my look at the dynamic web sketch tab above

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Investigate Parallel Lines

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students investigate angle relationships in parallel lines cut by a transversal. The sketch has some dynamic investigation as well as embedded quizzes and ends with the definition of the theorems. So this sketch fits very well with the fact that the expectation for grade 8 is via investigation.

• Gr8NS - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, protractor) and strategies (e.g., paper folding), the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle;
• MFM1P - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the angles formed by parallel lines cut by a transversal, and apply the results to problems involving parallel lines
• MPM1D - As review

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch.

• 4_ParalellLinesV5.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Practice the Pythagorean Theorem

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). 
In this activity students can download a GSP sketch that allows them to practice determining the hypotenuse (on the first page) or a leg (on the second page). The sketch will generate an infinite number of questions and give a full solution for each.
Note: Although Pythagorean Theorem is introduced in grade 8, it is only supposed to be relating more to the area model so these practice problems may not fit that. 

• MPM1D, MFM1P: D, C2.2 - solve problems using the Pythagorean theorem, as required in applications
• MPM2D, MFM2P: C,A2.2 - determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem;  

• All that is needed are the electronic downloads (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch. The first page can be used for determining the hypotenuse and the second page can be used for determining a leg. Both will randomly generate an infinite number of problems.

• Pythagoras_Generator.gsp 
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Practice Midpoint of a Line Segment

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). 
In this activity students can download a GSP sketch that allows them to practice determining the midpoint of a line segment on the first page (this part could also be used to check answers) and then to be quizzed with randomly generated sets of points on the second page.

• MPM2D: B2.1 - develop the formula for the midpoint of a line segment, and use this formula to solve problems

• All that is needed are the electronic downloads (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch. The first page can be used for discovery or for checking problems and the second page can be used for quizzing students as it will generate an infinite number of random segments to find the midpoint of.

• MidtermPractice.gsp (iPad/V5) (V4)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Perfect Square Practice

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). One of the advantages of doing this is that the bulk of the time spent on the software is actually doing math rather than building something. 

In this sketch students can practice recognizing perfect squares up to 144. It is a very simple sketch not meant to take much time but to just familiarize students with the first 12 perfect squares as well as to remind them that perfect squares can also be defined by physical squares.

• Gr7NS1.6 - represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
• Gr8 - could be used as review or see our square root guesser sketch instead

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

This sketch randomly selects a number under 150 and asks students whether it is a perfect square. They can make a mental guess and check their answer. Or, before the check their answer,  if they want to test it out they can try to create a square that has area equal to the given number. Once done they can generate another random number and try again. The hope is that this will help them become familiar with the first 12 perfect squares. Watch this video to see a demonstration of how it works.

• PerfectSquares.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Square Root Number Line Guesser

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). One of the advantages of doing this is that the bulk of the time spent on the software is actually doing math rather than building something. In this sketch students can practice their knowledge of estimating the square root of numbers up to 500. There are several levels of difficulty: perfect squares up to 100, perfect squares up to 500, square roots up to 100 and square roots up to 500. The intent was that this was built as a practice file for grade 8 students but grade 7 students could use it to practice perfect squares.

• Gr7NS - represent perfect squares and square roots, using a variety of tools
• Gr8NS - estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how the sketch works

• SquareRootNumberlineGuesser.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Percent Guesser

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do). We think this is a really simple and fun activity that helps students get a feel for how big a percent of a whole is. In the sketch the whole is shown and a percent is given and the user has to drag the green dot to where they think that percent is.

• Gr7NS - solve problems that involve determining whole number percents, using a variety of tools
• Gr8NS - as review  
• MPM1D - as review
• MFM1P - as review

• All that is needed is the electronic download
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch.

• Web sketch here

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks