## Monday, 25 May 2015

### Gr 8 Algebra and EquationsTower Challenge

This is a review activity on algebra and solving simple linear equations for grade 8 where students answer questions and are rewarded with building materials for each correct answer. The building materials (straws & tape) are then used to create the tallest tower that can hold a cup with a ball.  In this activity students have a different tower challenge than our 9 academic and 9 applied versions.
Gr8 Patterning and Algebra
• translate statements describing mathematical relationships into algebraic expressions and equations
• evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables
• solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model
• make connections between solving equations and determining the term number in a pattern, using the general term
• describe different ways in which algebra can be used in real-life situations
• 1-2 boxes of straws and 1-inch pieces of tape
• a small container with ping pong ball
• a question sheet for each student
• Optional - a whiteboard for each student to work out their solutions
• Optional - prize for the group with the tallest tower that can hold the cup

1. Place students in groups (ideally no bigger than 3 per group)
2. Hand out question sheets (and optional whiteboards) to each student.
3. Have students answer questions from their sheet in any order they want. For every correct answer they will get some building materials (eg: 2 straws & 2 pieces of tape, the amount of each reward is indicated on the student question sheet ). The harder the question the more materials they will get. Eventually the building materials will be used to create the tallest free standing tower that can hold the cup with ball.
4. Students work in groups to answer the questions and bring their solutions up to you to be checked. Only one member from each group can come up at a time. Each group can answer each question only once. To keep track of this, use the teacher answer sheet to check off which questions each group has answered as they come up.
5. Leave about 20 min at the end of the class for students to create their towers (students can no longer answer questions)
6. Take lots of pictures and celebrate the group with the tallest free standing tower.

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.

• Gr8AlgebraTowerChallengeQuestions (pdf, doc)
Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

### Increasing Order of Steepness

In this activity, students will get a set of 7 linear equations and they must start by placing them in increasing order of steepness.  Once their cards are sorted they will be paired with another group with different cards and sort all their cards together as well as answering other questions about their equations.  This is a good activity for rearranging linear equations in the form "y=mx+b" and understanding relative size of slope.

MPM1D
• express the equation of a line in the form y = mx + b, given the form Ax+By+C=0
• identify, through investigation, the equation of a line in any of the forms y=mx+b, Ax + By + C = 0, x = a, y = b
• 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
• solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion
MFM2P
• express the equation of a line in the form y = mx + b, given the form Ax+By+C=0.
• identify, through investigation, y = mx + b as a common form for the equation of a straight line, and identify the special cases x = a, y = b
• 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

• a set of 7 linear equations for each group of 3 - colour copies on cardstock and folded (if you don't have a colour copier, each set of linear equations could be copied on different colour cardstock)
• There are 6 complete sets of cards.  Depending on how big your class is you may need to make 2 complete sets and some groups will have the same set.  We recommend groups no larger than 3.
• 3 blank cards for each set
• a question card for each group
• small stickies for each group (so you can reuse the equation cards - students can write on stickies and attach to the equation card)
• 1 teacher reference sheet - colour copy on cardstock

1. Place students in groups of 3.
2. Give each group a set of linear equation cards, three blank cards, stickies and a question card.
3. Each group starts by putting their set of linear equations in increasing order of steepness (not slope, that will come later).  Tell students that they will be paired up with another group so they may want to include something on their equation card using the stickies.  Use the teacher reference sheet to check the order of steepness quickly.
 teacher reference sheet
4. When 2 groups are finished pair them up and they must now put all their equations in increasing order of steepness.  Make sure when pairing groups that they have different colour cards. While students are waiting to be paired up with another group they could start on answering the other questions from the question card.
5. The paired groups will then continue answering questions from the question card.
Prompt questions from question card:
1. Arrange the linear equations in increasing order of steepness.
2. Each student in the group must create a new linear equation that can be placed between any two of the original equations.  Place them using the blank cards.
3. Each student in the group chooses one card and creates a line that is parallel and perpendicular to their equation.
4. Each student chooses a different card and creates a line that has the same y-intercept as their equation.
5. Each student chooses a different card and finds the x and y intercepts of that line.
6.  Arrange the linear equations in increasing order of slope.  Would the line up look the same?  Discuss with your group.
Note:  In some cases, some groups did not pass putting the equations in increasing order of steepness so they were never paired up with another group.  Not all groups finished all the prompting questions. As an extension, you may consider having all the groups put their equations on a single continuum.

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.

Increasing Order of Steepness complete (pdf) (doc)

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

## Friday, 8 May 2015

### 9 Applied Solving Equations Continuum

When students are given a solving equations worksheet, most will become disengaged quickly. But during this activity, we heard a student say "Am I sick because I think this is fun".  In the above envelopes there are equations that need to be solved that increase in complexity as you go from left to right.  Students start in a particular envelope based on a formative assessment (eg. exit card) and move themselves along the continuum at their own pace.  As an added bonus rather than checking answers at "the back of the book", they will check using an ultraviolet "magic" pen on the answer cards.  Solving equations is like finding that mystery number.

• solve first-degree equations with nonfractional coefficients, using a variety of tools and strategies
• 20 copies of each of the question cards in different colour cardstock, cut and laminated (use colours that allow seeing the magic pen writing)
• 6 envelopes of the same colour as question cards (made from cutting cardstock, taped and laminated)
• 3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, ,,, - use the homework sheet to see the answers to the questions) To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back.
• 3 "magic" pens can be purchased at Chapters/Indigo or we found these at a Scholastic's book fair. We have since purchased some on eBay.

1. For this activity to be successful, students must start at the appropriate envelope.  If they start in one that is too hard they will be frustrated and if they start in one that is too easy they will be bored.  Use an exit card to help you decide which envelope each student should start in. When given back the exit card write down the colour of the envelope they will start in. Note: After doing this activity a few times, I needed an envelope with no integer solutions so I created the purple (1st) envelope.
2. Tape the envelopes to the wall in order of difficulty and set up three stations for the answer cards.
3. Students will get a card and answer the first 5 questions.  To check their answers, they will go to a station to use the magic pens.  Students may decide to do one question at a time and then go check their answer or they may do all 5 and then check.  Students are monitoring themselves so they decide.  If they get the first 5 right, they have a level of mastery to move themselves to the next envelope.  If not there are more questions on the card until they master that type.
4. As they move through the continuum, the hope is that they reach the white envelope that matches the 9 applied curriculum.  Since our goal is to get them to the white card, students should solve ALL equations on that card instead of just the first five.
5. The last 2 envelopes are set up to challenge students who are moving forward quickly.  They should solve all questions in these envelopes. We had a few students that were able to solve all the questions in the pink envelope so to challenge them further the yellow envelope has equations with fractions.  These are not part of the 9 applied curriculum but they can use their prior knowledge to try to solve these equations.
6. The assigned homework handout are just the questions from the cards. Student would just continue from where they left off on the continuum.
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. Note this video is from an academic class which has slightly different envelopes

• 9 Applied Solving Equations Continuum Cards (pdf) (doc)
• 9 Applied Solving Equations Continuum Homework (pdf) (doc)
• Solving Equations Continuum Exit Card (pdf) (doc)
Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

### 9 Academic Solving Equations Continuum

When students are given a solving equations worksheet, most will become disengaged quickly. But during this activity, we heard a student say "Am I sick because I think this is fun".  In the above envelopes there are equations that need to be solved that increase in complexity as you go from left to right.  Students start in a particular envelope based on a formative assessment (eg. exit card) and move themselves along the continuum at their own pace.  As an added bonus rather than checking answers at "the back of the book", they will check using an ultraviolet "magic" pen on the answer cards.  Solving equations is like finding that mystery number.

• solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies
• 20 copies of each of the question cards in different colour cardstock, cut and laminated (use colours that allow seeing the magic pen writing)
• 7 envelopes of the same colour as question cards (made from cutting cardstock, taped and laminated)
• 3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, ...- use the homework sheet to see the answers to the questions) To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back.
• 3 "magic" pens can be purchased at Chapters/Indigo or we found these at a Scholastic's book fair. We have since purchased some on eBay.

1. For this activity to be successful, students must start at the appropriate envelope. If they start in one that is too hard they will be frustrated and if they start in one that is too easy they will be bored. Use an exit card to help you decide which envelope each student should start in. When given back the exit card write down the colour of the envelope they will start in.
2. Tape the envelopes to the wall in order of difficulty and set up three stations for the answer cards.
3. Students will get a card and answer the first 5 questions.  To check their answers, they will go to a station and use the magic pens. Students may decide to do one question at a time and then go check their answer or they may do all 5 and then check. Students are monitoring themselves so they decide.  If they get the first 5 right, they have a level of mastery to move themselves to the next envelope.  If not there are more questions on the card until they master that type.
4. As they move through the continuum, the hope is that they reach the yellow envelope that matches the 9 academic curriculum.  Since our goal is to get them to the yellow card, students should solve ALL equations on that card instead of just the first five.
5. The last 2 envelopes are set up to challenge students who are moving forward quickly.  They should solve all questions in these envelopes. We had a few students that were able to solve all the questions in the purple envelope so to challenge them further I created the brown envelope with quadratic equations.  These would not formally be taught but instead let them use something like guess and check.
6. The assigned homework are just the questions from the cards. Student would just continue from where they left off on the continuum (up to the 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

• 9 Academic Solving Equations Continuum Cards (pdf) (doc)
• 9 Academic Solving Equations Continuum Homework (pdf) (doc)
• Solving Equations Continuum Exit Card (pdf) (doc)
Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks