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 - 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

Sort Students into Groups using Linear Representations

In this activities students are each given one card. The card will either have a graph, table of values or equation of a linear relation. Their job is to find the two other students who have the other two representations of the same linear relationship. This shouldn't take too long and could be repeated every couple of days to solidify conversion between representations

MPM1D, MFM2P  - 

• graph lines by hand, using a variety of techniques
• identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b

• Download the cards and cut them out (you may want to laminate them)

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. Students will find the other people who have the same linear relationship

• GraphTableLineMatch (doc) (pdf)

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

Linear Scavenger Hunt

The linear scavenger hunt is an activity where there are sets of four representations of linear relations on cards (graphical, tabular, algebraic and word problem) that students have to search for and match.

• MPM1D, MFM1P, MFM2P
• determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation
• determine other representations of a linear relation, given one representation
• describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation 
• determine the equation of a line from information about the line

• Linear Scavenger Hunt Cards (printed 1 sided)
• Linear Scavenger Hunt Question Cards (printed back to back)
• Tape/stick tack
• Beach Ball (optional)
• Whiteboard markers (optional)

1. Each group of 3 students gets 1 representation of a linear relationship  - either a story, equation, table or graph.  Students will complete a scavenger hunt by roaming around the room to find the other 3 representations of their linear relationship. The other three cards in each set are randomly distributed around the class before hand.
2. Once all four cards are together, each group must fill in missing information on the graph (title and axes labels) and in the table (column titles and table values -  CAUTION:  yellow rows are out of step in the pattern). Teacher can check missing information quickly using reference card.
3. Each group will tape their equation in the middle of their desks.
4. Each group will now tape their story to the beach ball.  Students will throw the ball and each group will select a card (not their own).  That group must now find the equation of the new story they got off the beach ball.  One member will then circulate to check if the equation is correct with the original group for their new story and return it to that group.
5. Repeat step 4 with the tables.
6. Repeat step 4 with the graphs.
7. Each group should now have the original 4 representations of their linear relationship.  Students will now answer 5 questions related to their relationship found on the Question Cards.  

Other possible uses

• give a story or equation to each student and have them find their partner
• give each group of 3 an equation and have them describe several situations that could be modelled by the given linear equation.
• give students a card and have them identify as a direct or partial variation
• give a student a table or graph - have them find the rate and explain its meaning

The video, below is only visible in the WECDSB domain. That is, only teachers in our school board can see the video if they are logged into their MyTools2Go accounts.

• Linear Scavenger Hunt Cards (doc) (pdf)
• Linear Scavenger Hunt Question Cards (doc) (pdf)
• Note that if you print these out on card stock and laminate them, students can use whiteboard markers or whiteboard crayons to do their work on them and can be reused.

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