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

Sort students into groups using Quadratic Representations

In this activity students are each given one card. The card will either have a graph, table of values or equation of a quadratic relation. Their job is to find the two other students who have the other two representations of the same quadratic relationship. This shouldn't take too long and could be repeated every couple of days to solidify conversion between representations.
New: Alternatively, you could have students just work individually on this Desmos card sort 

• MPM2D - A3.3 determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y = a(x – r)(x – s);
• MBF3C - A1.8 determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation
• MCF3M - A1.5 determine, through investigation, and describe the connection between the factors used in solving a quadratic equation and the x-intercepts of the graph of the corresponding quadratic relation
• MCR3U - As review

• Download the cards and cut them out (you may want to laminate them)
• If you are doing the Desmos Cardsort instead, students should have devices to do the sort on (note that phones have screens that are too small)

1. Shuffle the cards and distribute one per student. Note that there are 11 sets of 3 cards so you may want to remove sets to more closely match your student population.
2. Instruct students to find the two other people that have different representations for the same quadratic relation. 
3. Once students find their partners they will be in groups of three

If doing the Desmos Cardsort instead, have students (or pairs of students) complete each page of the cardsort. You may wish to consolidate on the last page of the card sort.

• GroupQuadratics (Googledoc) (pdf)
• Desmos CardSort 

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 - Practice Distance Between Points

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 distance between two points (this part could also be used to check answers) and then to be quizzed with randomly generated sets of points.

• MPM2D - develop the formula for the length of a line segment, and use this formula to solve problems (e.g., determine the lengths of the line segments joining the midpoints of the sides of a triangle, given the coordinates of the vertices of the triangle, and verify using dynamic geometry software);

• All that is needed are the electronic downloads
• 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 points to find the distance between.

• DistancePractice.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