Simplifying Expressions and Solving Equations Tower Challenge

This is a review activity on simplifying expressions and solving equations for grade 9 applied where students answer questions and are rewarded with building materials for each correct answer. The building materials (spagetti & marshmallows) are then used with the goal being the creation of tallest tower. This is based originally on a TIPS activity on quadratics for MBF3C (Unit 3, Day 6).  We have a similar activity for grade 9 academic that can be found here.

MPM 1P

• substitute into and evaluate algebraic expressions involving exponents 
• describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x²; volume, which is three dimensional,can be represented by (x)(x)(x), (x²)(x),or x³]
• add and subtract polynomials involving the same variable up to degree three using a variety of tools
• multiply a polynomial by a monomial involving the same variable to give results up to degree three using a variety of tools
• solve first-degree equations with nonfractional coefficients, using a variety of tools
• substitute into algebraic equations and solve for one variable in the first degree

• 1 bag of spaghetti and 1-2 bags of small marshmallows (or 1 box of straws and 1-inch pieces of tape)  
• a question sheet for each student
• a teacher answer sheet 
• Optional - a whiteboard for each student to work out their solutions
• Optional - prize for the group with the tallest tower

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 spagetti & 3 marshmallows, 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 a tower with the goal to create the tallest free standing tower.
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.

• Gr9AppliedSimplifyingExpression&SolvingEquationsTowerChallengeQuestions (pdf, doc)
• Gr9AppliedSimplifyingExpression&SolvingEquationTowerChallengeTeacherAnswerSsheet (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

Number Sense and Algebra Tower Challenge

This is a review activity on number sense and algebra for grade 9 academic where students answer questions and are rewarded with building materials for each correct answer. The building materials (spagetti & marshmallows) are then used with the goal being the creation of tallest tower. This is based originally on a TIPS activity on quadratics for MBF3C (Unit 3, Day 6).  We have a similar activity for grade 9 applied that can be found here. 

MPM 1D

• substitute into and evaluate algebraic expressions involving exponents
• describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x²; volume, which is three dimensional,can be represented by (x)(x)(x), (x²)(x),or x³]
• derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents
• extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents.
• relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations
• add and subtract polynomials with up to two variables
• multiply a polynomial by a monomial involving the same variable
• expand and simplify polynomial expressions involving one variable
• solve first-degree equations, including equations with fractional coefficients, using a variety of tools
• rearrange formulas involving variables in the first degree, with and without substitution
• solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods

• 1 bag of spaghetti and 1-2 bags of small marshmallows (or 1 box of straws and 1-inch pieces of tape)  
• a question sheet for each student
• a teacher answer sheet 
• Optional - a whiteboard for each student to work out their solutions
• Optional - prize for the group with the tallest tower

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 spagetti & 3 marshmallows, 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 a tower with the goal to create the tallest free standing tower.
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

• Gr9AcademicNumberSense&AlgebraTowerChallengeQuestions (pdf, doc)
• Gr9AcademicNumberSense&AlgebraTowerChallengeTeacherAnswerSheet (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

Simplifying Expressions with Algebra Tiles Matching Cards

This is a very simple matching activity where students are given a bunch of algebraic expressions (in one variable) and simplified expressions (both in algebraic and algebra tile form) and all they have to do is match up each expression with their simplified form. This is not meant to be a long or complex activity and could best be used as a warm up or end of class review or possibly just in the middle of a long class to switch up the period.

• MPM1D - add and subtract polynomials with up to two variables [e.g., (2x – 5) + (3x + 1), (3x²y + 2xy²) + (4x²y – 6xy²)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);
• MFM1P - add and subtract polynomials involving the same variable up to degree three [e.g., (2x + 1) + (x²– 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);

• There are four sets of cards (each group would get a set so they aren't all working on the same questions). Each set of cards will have answers that have the same characteristics (Set 1 - answer is a trinomial, Set 2 - answer is a binomial with no squared term, Set 3 answer is a binomial with no x term, Set 4 - answer is a binomial with no constant term). A set should contain 12 cards. Four long expressions, four algebraic answers and four algebra tile answers.
• Print and cut out the cards (we suggest laminating them to). Note that each card has what set number it belongs to so that if you mix them up you can easily sort them back into their sets. You may wish to put each set in an envelope or ziplock bag for easy distribution.
• You will probably want to have physical algebra tiles for students to use while doing the actual simplification.
• Note that because there doesn't seem to be a consensus on which colour algebra tiles represent positive or negative, there are two sets. One that assumes red is positive and one that assumes red is negative. Keep which ever is the protocol for your class and discard the other.

1. Students could be put into groups or do this individually. Ether way, since there are only four sets you will need to have multiple copies of each set. 
2. Give each group an envelop and tiles and ask them to match the unsimplified expression with the simplified expression and algebra tile representation. 
3. Once each group is done, have groups switch their envelopes. (1 gives to 2, 2 gives to 3 etc). You can do this 4 times. 

• SimplifyingPolynomialsMatching (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

I Have, Who Has - Simplifying Expression

An I Have, Who Has game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an expression dealing with a polynomial and a "Who has" statement which is the simplified form. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has -3d²?". Someone else will have a card where their expression equals -3d² so they would say " I have 4d² - 9d² - d² + 3d²". Who has 3x + 2y?" That is, they read their expression that equals -3d² and then asks their "Who has" statement. Then someone else will have an expression that matches 3x + 2y and the game continues. If done correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.

• MPM1D - add and subtract polynomials with up to two variables, using a variety of tools
• MFM1P - add and subtract polynomials involving the same variable up to degree three, using a variety of tools 

• There are two sets of cards that you could download here. One set (pictured here) has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). Depending on the size of class you have you might want to use this set multiple times (ie groups of 9) or use the larger set of 27. Either way, in order for the game to work, all cards need to be passed out. So some students may need to have more than one card.
• Regardless. Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.
• Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.

1. Distribute the cards one per student. All cards must be handed out so some students might need more than one card.
2. Tell each person to simplify their "I have" expression and check their answer with at least one other person. 
3. Once students are confident with their simplification all students should stand and then you choose one to read their "Who has" statement. The person who's simplified answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started. 
4. A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.

• IHaveWhoHas-Simplifying-9cards (pdf) (doc)
• IHaveWhoHas-Simplifying-27cards (pdf) (doc)
• IHaveWhoHas-BlankTemplate (doc)

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