Easter Analytic Geometry Review Activity

This is an Easter review activity where students will answer analytic geometry questions and collect eggs on the Smartboard. (This is the Easter version to a Halloween activity post. If teaching in the spring this context makes more sense otherwise in the fall use the Halloween activity instead at this link - they are the same questions in both activities)

MPM1D

• determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations
• identify, through investigation, the equation of a line in any of the forms y = mx + b,             Ax + By + C = 0, x = a, y = b
• express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0
• determine, through investigation, various formulas for the slope of a line segment or line and use the formulas to determine the slope of a line segment or a line
• identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b
• identify, through investigation, properties of the slopes of lines and line segments
• graph lines by hand, using a variety of techniques
• determine the equation of a line from information about the line
• describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation
• construct tables of values, graphs, and equations, using a variety of tools to represent linear relations derived from descriptions of realistic situations

• 51 plastic Easter eggs (find at a Dollar store)
• 2 Easter baskets (find at a Dollar store)
• analytic geometry questions
• solution handout
• Smartboard
• Smart Notebook file with score board
• whiteboard and markers (optional)
• Easter decorations (optional)
• prizes for winning team (optional)

1. Print questions in colour.  Cut out questions and place one in each of the 51 eggs.
2. Place eggs in an Easter basket.
3. Bring up the scoreboard on the smartboard.  (Could create your own scoreboard if a smartboard is not available)
4. Place students is groups and give each student a whiteboard and marker.
5. Have each group choose an Easter basket from the scoreboard.
6. One student from the group will come up and choose an egg.  They will bring it back to their group where all members will answer the question inside.
7. One person will then come and check their answer with the teacher.
8. The teacher will check off that the group has answered that question.  
9. The student will then drag an egg to their Easter basket on the smartboard.  Based on difficulty, questions with no eggs on the card students collect 1 egg, questions with  2  eggs on the card students collect 2 eggs and the same with 3 eggs.
10. Have students place the question back in the egg and choose another one.  (Answered questions with egg should be put in a separate basket and put back in circulation when eggs get low.)
11. The group who collects the most eggs will win.  

Note:  There are some special cards that students will find. I call these the golden eggs (they are not always in yellow eggs but the card is yellow).

To see the activity in action with an applied class (with proportional reasoning), go to this post (ie it runs the same way but with different questions) 

• Analytic Geometry Egg Hunt questions (pdf) (doc)
• Analytic Geometry Egg Hunt solutions (pdf) (doc)
• Egg Hunt scoreboard (Smart Notebook file) (not)

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

Halloween Analytic Geometry Review Activity

This is a Halloween review activity where students will answer analytic geometry questions and collect candy on the Smartboard.  (This is the Halloween version to an Easter activity post. If teaching in the fall this context makes more sense otherwise in the spring use the Easter activity instead at this link - they are the same questions in both activities)

 MPM1D

• determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations
• identify, through investigation, the equation of a line in any of the forms y = mx + b,             Ax + By + C = 0, x = a, y = b
• express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0
• determine, through investigation, various formulas for the slope of a line segment or line and use the formulas to determine the slope of a line segment or a line
• identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b
• identify, through investigation, properties of the slopes of lines and line segments
• graph lines by hand, using a variety of techniques
• determine the equation of a line from information about the line
• describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation
• construct tables of values, graphs, and equations, using a variety of tools to represent linear relations derived from descriptions of realistic situations

• 49 Halloween containers (find at a Dollar store)
• analytic geometry questions
• solution handout
• Smartboard
• Smart Notebook file with score board
• whiteboard and markers (optional)
• Halloween decorations (optional)
• prizes for winning team (optional)

1. Cut out questions and place one in each of the 49 containers.
2. Spread out containers on a table and add some Halloween decorations (optional).
3. Bring up the scoreboard on the smartboard.  (Could create your own scoreboard if a smartboard is not available)
4. Place students is groups and give each student a whiteboard and marker.
5. Have each group choose a Halloween bag from the scoreboard.
6. One student from the group will come up and choose a container.  They will bring it back to their group where all members will answer the question inside.
   
7. One person will then come and check their answer with the teacher.
8. The teacher will check off that the group has answered that question.  
9. The student will then drag a candy to their bag on the smartboard.  Questions with no pumpkins are worth 1 candy, questions with 2 pumpkins are worth 2 candies and questions with 3 pumpkins are worth 3 candies.
10. Have students place the question back in the container and choose another one.  (Answered questions with container should be put to the side and put back in circulation when containers get low.)
11. The group who collects the most candy will win.  

 Note:  There are some special cards that students will find. Tap bags 1, 3, 6 or 8 on the Smartboard to play Halloween music.

To see the activity in action with an applied class (with proportional reasoning), go to this post (ie it runs the same way but with different questions) 

• Analytic Geometry Halloween questions (pdf) (doc)
• Analytic Geometry Halloween solutions (pdf) (doc)
• Halloween scoreboard (Smart Notebook file) (not)

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

Easter Proportional Reasoning Review Activity

This is an Easter review activity where students will answer proportional reasoning questions and collect eggs on the Smartboard.  (This is the Easter version to a previous Halloween activity post. If teaching in the spring this context makes more sense otherwise in the fall use the Halloween activity instead at this link - they are the same questions in both activities)

 MFM1P

• illustrate equivalent ratios, using a variety of tools 
• represent, using equivalent ratios and proportions, directly proportional relationships arising from realistic situations
• solve for the unknown value in a proportion, using a variety of methods
• make comparisons using unit rates – solve problems involving ratios, rates, and directly proportional relationships in various contexts using a variety of methods
• solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

• 51 plastic Easter eggs (find at a Dollar store)
• 2 Easter baskets (find at a Dollar store)
• proportional reasoning questions
• solution handout
• Smartboard
• Smart Notebook file with score board
• whiteboard and markers (optional)
• Easter decorations (optional)
• prizes for winning team (optional)

1. Print questions in colour.  Cut out questions and place one in each of the 51 eggs.
2. Place eggs in an Easter basket.
3. Bring up the scoreboard on the smartboard.  (Could create your own scoreboard if a smartboard is not available)
4. Place students is groups and give each student a whiteboard and marker.
5. Have each group choose an Easter basket from the scoreboard.
6. One student from the group will come up and choose an egg.  They will bring it back to their group where all members will answer the question inside.
7. One person will then come and check their answer with the teacher.
8. The teacher will check off that the group has answered that question.  
9. The student will then drag an egg to their Easter basket on the smartboard.  Based on difficulty, questions with no eggs on the card students collect 1 egg and questions with  2  eggs on the card students collect 2 eggs.
10. Have students place the question back in the egg and choose another one.  (Answered questions with egg should be put in a separate basket and put back in circulation when eggs get low.)
11. The group who collects the most eggs will win.  

Note:  There are some special cards that students will find. I call these the golden eggs (they are not always in yellow eggs but the card is yellow).

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.

• Proportional Reasoning Egg Hunt questions (pdf) (doc)
• Proportional Reasoning Egg Hunt solutions (pdf) (doc)
• Egg Hunt scoreboard (Smart Notebook file) (not)

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

Geometry Board Game

This is a geometry review activity where students will find missing angles formed by lines, in triangles and in polygons. The game is loosely based on the Candyland board game where students move pieces around a board and answer questions based on the colour they land on.

• MPM1D, MFM1P - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons
• 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

For each group (groups of two or four - playing against each other or in teams of two)

• up to four game pieces 
• one die
• one game board printed in colour on card stock (laminated if possible). If you wish, one group can play on the Smartboard.
• one instruction sheet printed on card stock (laminated if possible) with answer sheet on the back (preferably printed in colour)
• one set of question cards. Each set consists of five types of questions that are colour coded. Print each on colour card stock (there is one page with 8-10 questions for each colour) and laminate (if possible) then cut them out. The colour of the cards loosely group the types of questions to supplementary, complementary, opposite angles (yellow), angles in triangles (blue), parallel lines (red), angles in polygons (green), more challenging questions that may require algebra (white). 

Game Setup

1. Separate the cards by colour. Shuffle each colour and make a face down pile for each.
2. Decide on teams (or play individually) and place a marker on START for your team.
3. Keep the answer card face down at all times until checking your answers. 

Game Play

1. Each team takes turns rolling the die and moving your markers.
2. When you land on a colour, choose the appropriate card and answer the question (determine the values of the unknown variables). You have up to 2 minutes to answer your question.
3. A player from the opposing team uses the answer key to quickly check your answer. If you do not answer your question correctly, move back to your last position.  Remember: the answer sheet must remain face down at all times except for checking solutions.
4. If you land on a Mystery spot (marked with a ?) you will have 3 minutes to answer (since these are tougher questions). If you answer correctly, you get a free die roll and move to the appropriate spot without having to answer another question. If you answer incorrectly move back to your last position as before.

Ending the game

1. To win the game, you must land exactly on the “You Win!” spot.
2. Once there, the opposing team will choose a question (but not a Mystery question) from one of the piles (without looking).
3. If you answer correctly, you win. If you answer incorrectly, move back to your last spot. 

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.

• GeometryBoardGameQuestions (pdf) (doc)
• GeometryBoard (Notebook)

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

The Area Representation of Pythagorean Theorem

In Grade 8 here in Ontario, Pythagorean Theorem is introduced for the first time. It is pretty common for students to only see a² + b² = c² and they move on. This can be a problem for students since if they only see that formula, they can't get past the a's, b's & c's and often get them mixed up because they don't understand them (so many kids can recite a² + b² = c² proudly but that's where their expertise stops). But if you examine the expectations, you will see that really the focus is on the conceptual nature of the relationship. So we developed this activity to focus on the area representation of PT. The premiss is that students are given six sets of three numbers. The numbers come in the form of the side lengths of squares. Three of the sets are Pythagorean Triples the others are not (students are not told this). They then use the given squares to construct triangles (using the squares as the side lengths) and (hopefully) discover that right angled triangles have a special relationship with the areas of the squares.
A NEW ADDITION is an Explain Everything version. In this version students manipulate the squares right in the app.

• Gr8NS1.4 - determine the Pythagorean relationship, through investigation using a variety of tools (e.g., dynamic geometry software; paper and scissors; geoboard) and strategies; 
• MPM1D, MFM1P - relate the geometric representation of the Pythagorean theorem and the algebraic representation a² + b² = c² ;

• Print (on card stock preferably), laminate (optional) and cut out the squares. Note that the squares should be cut out as tightly to the edge as possible. Each group of 6 should have one set of cards. 
• Each group should have 1-2 pieces of chart paper
• Markers 
• whiteboards (optional)

1. Place students in groups of six (or in any group size that could be split in two).  Three students will construct triangles using squares with the following side lengths:     1) 5, 10, 12     2)  9, 10, 17   3) 12, 13, 15  (this group will create non right angled triangles - don't tell them this). The other three students will construct triangles using squares with side lengths:  4) 5, 12, 13   5) 6, 8, 10      6) 8, 15, 17 (this group will create right angled triangles - don't tell them this). Regardless, each set of students should trace the triangles and the squares that form them on their own chart paper (if they don't trace them, they won't have enough squares).
2. Ask the group of six if they notice anything different between triangles in groups 1, 2, 3 compared to groups 4, 5, 6 (hopefully they they will notice that in one set the triangles are right)
3. Ask students to find the area of each square and see if they can find any relationship in the squares in each of groups 4, 5 & 6 compared to groups 1, 2 & 3 ( you may need to steer some groups towards the sum of the areas with gentile questioning)
4. Discuss, as a group, what they discovered.
5. Give students a whiteboard and ask them to find the missing sides in triangles. A Smartboard file is attached with several more triangles.
6. As an extension students can investigate how general the area relationship is using this WebSketch.

Note: if using the Explain Everything version, all six groups are on the same file. So depending on how many iPads you have, you may group students differently. 

• Square Templates (pdf) (doc)
• Explain Everything (xpl)
• Pythagorean Relationship practice (not) (pdf) 
• Geometer's Sketchpad Area Relationship (WebSketch) (GSP file)

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