Derivative Matching Cards

This is a very simple matching activity for Calculus. Students are give a set of cards with either a linear, quadratic or cubic function on them. Their job is to pair them up so that one is a function and the other is its derivative. There are a total of 12 functions with 12 derivatives. The first six are all linear or quadratic graphs and the second six are either quadratic or cubic graphs (if you wanted to give students an easier set you could only give them the first six). This is not meant to be a brain buster of an activity but it does help to solidify thinking in terms of the characteristics of the connections between a function and its derivative.
NEW: Desmos has turned this activity into one of their new CardSort activities. You can get that version here

• MCV4U - A2.2 - generate, through investigation using technology, a table of values showing the instantaneous rate of change of a polynomial function, f(x), for various values of x (e.g., construct a tangent to the function, measure its slope, and create a slider or animation to move the point of tangency), graph the ordered pairs, recognize that the graph represents a function called the derivative, f ’(x) or , and make connections between the graphs of f(x) and f ’(x) or y and dy/dx
• MCV4U - B1.1 - sketch the graph of a derivative function, given the graph of a function that is continuous over an interval, and recognize points of inflection of the given function (i.e., points at which the concavity changes)

• As mentioned above, there are 12 cards and their derivatives but you could break them up into sets of 6 cards and their derivatives where the first set was made of linear and quadratic functions and the second set is made of quadratic and cubic functions (or you could just put them all together). On each page there are six graphs. The first column are the functions and the second column are the matching derivatives.
• Print the sheets out on card stock (and laminate if possible). We tend to print each set out on different colours. This way if they get mixed up all you need to do is collect 24 cards of one colour and you will know you have a full set
• You may also want to print a copy of the teacher answer key which has all 24 graphs on one page so you can easily check student's answers.

• Put students in groups of two or three
• Distribute cards and tell them they have to pair the cards up in terms of a function its derivative. 
• Instruct them that every card is paired up and they will likely be correct if they have no cards left over
• Encourage them to use properties of functions and derivatives (zeros, max/mins etc) to speed up the process 

• Derivative Match Cards (Google Doc, PDF)
• Derivative Match Teacher Key (PDF)
• Desmos CardSort version
• For an online version (Flash based) try out this link from the MAA. Thanks to @EulersNephew for pointing this out

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 - Equations

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 a simple equation "Who has" statement which is the answer. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has 7?". Someone else will have a card where their equation has an answer that equals 7 so they would say " I have 2x = 14". Who has negative 4?" That is, they read their equation that has an answer that equals 7 and then asks their "Who has" statement. Then someone else will have an equation that matches -4 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.

• Gr7PA - solve linear equations of the form ax = c or c = ax and ax + b = c or variations such as b + ax = c and c = bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator NOTE - only use the 9 card set if doing this for grade 7 as there are a few multi step equations;
• Gr8PA - 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 
• MPM1D, MFM1P - solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies);

• 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 solve their "I have" equation and check their answer with at least one other person. 
3. Once students are confident with their answer all students should stand and then you choose one to read their "Who has" statement. The person who's equation has the same answer 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-Equations-9cards (pdf) (doc)
• IHaveWhoHas-Equationss-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

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

I Have, Who Has - Making Change in Canada

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 making change with money in Canada. If you are not from Canada, you may not know that here we no longer use pennies. This means that when we buy things and pay cash we actually have to round to the nearest nickel to make change. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has $4.35?". Someone else will have a card where their change equals $4.35 so they would say "I have $20 and it costs $15.63. Who has change of $1.75?" That is, they read their statement that equals $4.35 and then asks their "Who has" statement. Then someone else will have an expression that matches $1.75 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.

• MAT1L - DMS1.03 – round money values to stated accuracies (e.g., the nearest cent, the nearest dollar, the nearest ten dollars, the nearest hundred dollars, the nearest thousand dollars, and the nearest million dollars), in applications drawn from everyday situations; DMS2.01 – make the correct change for an offered amount with and without concrete materials (e.g., change from a $5 bill for an item costing $4.77);
• MAT2L - EMS1.01 – read and interpret money values given in words, write money values as decimals, and round money values appropriately, in solving problems found in everyday contexts;

• This is a small set that 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). You will likely have more than 9 students in your class and so will need multiple sets (ie groups of 9). 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.
• 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. Make sure you have gone over the rounding rules for money first. 
2. Distribute the cards one per student. All cards must be handed out so some students might need more than one card.
3. Tell each person to calculate the change for their "I have" expression and check their answer with at least one other person. 
4. Once students are confident with their answers all students should stand in their groups and then you choose one to read their "Who has" statement. The person who's 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. 
5. 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-MakingChange (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

I Have, Who Has - Integers

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 addition, subtraction, multiplication and division of of integers. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has 2?". Someone else will have a card where their expression equals 2 so they would say " I have -2 + 5 -1. Who has 7?" That is, they read their expression that equals 2 and then asks their "Who has" statement. Then someone else will have an expression that matches 7 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.

• Grade 8 - solve problems involving operations with integers, using a variety of tools
• MPM1D, MFM1P - simplify numerical expressions involving integers and rational numbers, with and without the use of technology 

• 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-Integers-9cards (pdf) (doc)
• IHaveWhoHas-Integers-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