How does a vending machine work?

How does a vending machine work?
Warm Up OBJECTIVE: Students will be able to define function and identify examples and non-examples of functions. LANGUAGE OBJECTIVE: Students will be able to use the definition of function, both orally and in writing, when justifying examples and non-examples of functions. How does a vending machine work? What do you expect to happen when you push a button? (Time on this slide – 5 min) Time passed 5 min In-Class Notes Give students about 3 minutes to answer this question individually on their Warm Up handout Next take 2 minutes and have 2 or 3 students share their responses. Preparation Notes This Warm Up introduces a metaphor for functions that can be used throughout this series of lessons. During the warm up try to get students to say that only 1 type of soda will come out when you press any given button. To show an animation of how a soda machine works click the “Animation” button. Note that students will see this, and other, animations later in the Launch. Animation Agenda

Agenda: 1) Warm Up: How does a vending machine work? (individual)
OBJECTIVE: Students will be able to define function and identify examples and non-examples of functions. LANGUAGE OBJECTIVE: Students will be able to use the definition of function, both orally and in writing, when justifying examples and non-examples of functions. 1) Warm Up: How does a vending machine work? (individual) 2) Launch: A look at three machines and defining functions (group and partner) 3) Explore: Deciding if it’s a function (partner) 4) Summary: Building a function wall (group) 5) Exit Ticket (individual) (Time on this slide – 1 min) Time passed 6 min In-Class Notes Spend a minute going over the objective and agenda for the day. Preparation Notes 6) Homework

Launch: Input-Output Table
(Time on this slide – 2 min) Time passed 8 min In-Class Notes Begin by asking students to think about what an input-output table might be. Encourage them to think back to the warm up and ask them what were the inputs and outputs in that example. Then write down the definition and students should copy it down in their notes. Show students two ways that an input-output table can be drawn (i.e., horizontal and vertical orientations). Let them know that they should be comfortable using both and that they will see both kinds in today’s lesson. Have students copy down the two types in their notes. Preparation Notes It is recommended that you project slides on a whiteboard so you can write on top of the slide. If this is not possible then click the “Answers” button for a filled in version of this slide. Answers Agenda

Launch: Machine A Input (button pressed) Output (soda can) Input
(Time on this slide – 1 min) Time passed 9 min In-Class Notes Tell students that they will observe three different soda vending machines and use the input-output table to describe the behavior of the vending machines (click once to show an input-output). Ask students what is the input and output of a vending machine. Once they give their responses click again to show labels of the input and output. Tell students that they should always label their inputs and outputs with a unit. Have students copy down the skeleton of the input-output table into their notes for Machine A. Preparation Notes Agenda

Launch: Machine A Finished Agenda
(Time on this slide – 2 min) Time passed 11 min In-Class Notes Take student requests for what sodas they want and click the appropriate buttons. Make sure all buttons are clicked at some point. Also make sure to click at least some of the buttons more than once so that students see that the same soda is coming out each time a given button is pressed. When done exploring the behavior of Machine A click the button “Finished” Preparation Notes Please try these vending machines slides before class. When you click for a soda make sure to click the rectangular label of the soda you want and not some other point on the slide. If you click elsewhere on the slide you will advance to the next hidden slide and the behavior of the machine will not work as planned. Make testing the three machines as engaging as you’d like. Perhaps make sure that across the three machines each student gets to pick their favorite soda choice. Finished Agenda

Launch: Machine A Input (button pressed) Output (soda can) Coca-Cola Coca-Cola Diet Coke Diet Coke Dr. Pepper Dr. Pepper Mountain Dew Mountain Dew Describe the behavior of this machine. What do you notice? (Time on this slide – 2 min) Time passed 13 min In-Class Notes After students have seen how Machine A behaves ask them to fill out their input-output table. You can do this in the whole group. Then as a whole group have students share out what they notice about the machine’s behavior. Record the students’ responses and have students copy them down too. Push for students to say that each time a button is pressed (input) you always get the same soda out (output) and that soda matches the label pressed. Emphasize with your students that each input yields only one output. Preparation Notes If there is a disagreement about the output give for a particular input then click the “Back” button which will take you to Machine A. When done checking Machine A’s behavior then click “Finished” to get back to this slide. Back Agenda

Launch: Machine B Finished Agenda
(Time on this slide – 2 min) Time passed 15 min In-Class Notes Take student requests for what sodas they want and click the appropriate buttons. Make sure all buttons are clicked at some point. Also make sure to click at least some of the buttons more than once so that students see that the same soda is coming out each time a given button is pressed. When done exploring the behavior of Machine B click the button “Finished” Preparation Notes Please try these vending machines slides before class. When you click for a soda make sure to click the rectangular label of the soda you want and not some other point on the slide. If you click elsewhere on the slide you will advance to the next hidden slide and the behavior of the machine will not work as planned. Finished Agenda

Launch: Machine B Input (button pressed) Output (soda can) Coca-Cola Diet Coke Diet Coke Mountain Dew Dr. Pepper Coca-Cola Mountain Dew Dr. Pepper Describe the behavior of this machine. What do you notice? (Time on this slide – 2 min) Time passed 17 min In-Class Notes After students have seen how Machine B behaves ask them to fill out an input-output table. You can do this in the whole group. Then as a whole group have students share out what they notice about the machine’s behavior. Record the students’ responses and have students copy them down too. Push for students to say that each time a button is pressed (input) you always get the same soda out (output) but that the soda does not match the label pressed. In other words each input yields only one output but the machine is mislabeled. Preparation Notes If there is a disagreement about the output give for a particular input then click the “Back” button which will take you to Machine B. When done checking Machine B’s behavior then click “Finished” to get back to this slide. If students struggle with the fact that the machine is mislabeled you can do several things. First go through the animation a few more times so that students are convinced that pressing a given button gives you the same soda each time. Next make sure students have the input-output table in their notes. Finally ask students questions like “If I wanted a Coca-Cola, what button would I need to press?”. Once students have answered several questions like these then you can ask them “So if pressing the Dr. Pepper button gives me a Coca-Cola can, what would I have wanted the button say instead of Dr. Pepper? What does this tell me about the machine?” At this point students students should be realizing the machine is mislabeled. If students struggle with coming up with the right word to describe the machine but they understand the concept, then you might just want to give them the word “mislabeled” and have them use it in their description of the machine. Back Agenda

Launch: Machine C Finished Agenda
(Time on this slide – 2 min) Time passed 19 min In-Class Notes Take student requests for what sodas they want and click the appropriate buttons. Make sure all buttons are clicked at some point. Also make sure to click all the buttons more than once so that students see that each button gives more than one soda. When done exploring the behavior of Machine C click the button “Finished” Preparation Notes Please try these vending machines slides before class. When you click for a soda make sure to click the rectangular label of the soda you want and not some other point on the slide. If you click elsewhere on the slide you will advance to the next hidden slide and the behavior of the machine will not work as planned. Also in the case of Machine C make sure to click the left side of the rectangular labels once and the right side of the rectangular labels later on. This will ensure that students see both of the outputs produced by the one input. (Since PowerPoint uses commands that are functions, it was impossible to have the same area clicked do two different things which is why the labels are split in half; if students catch on just let them know that in this machine the entire area of the label counts as the same input). Finished Agenda

Launch: Machine C Input (button pressed) Output (soda can) Coca-Cola Coca-Cola Coca-Cola Mountain Dew Diet Coke Dr. Pepper Diet Coke Diet Coke Dr. Pepper Dr. Pepper Dr. Pepper Coca-Cola Mountain Dew Dr. Pepper (Time on this slide – 2 min) Time passed 21 min In-Class Notes After students have seen how Machine C behaves ask them to fill out an input-output table. You can do this in the whole group. Then as a whole group have students share out what they notice about the machine’s behavior. Record the students’ responses and have students copy them down too. Push for students to say that each time a button is pressed you can’t be sure which of two sodas may come out. (In other words this machine is broken and unreliable). Preparation Notes If there is a disagreement about the output give for a particular input then click the “Back” button which will take you to Machine C. When done checking Machine C’s behavior then click “Finished” to get back to this slide. Mountain Dew Mountain Dew Describe the behavior of this machine. What do you notice? Back Agenda

Launch: Questions Which machine would you MOST want to use? Why?
2) Which machine would you LEAST want to use? Why? 3) Which machine(s) lets you PREDICT the soda that will come out when you push a given button? 4) Which machine(s) DO NOT let you predict the soda that will come out when you push a give button? 5) Machines A and B are examples of functions. What do you think is the definition of a function? (Time on this slide – 10 min) Time passed 31 min In-Class Notes Give students about 6 minutes to discuss with a partner to discuss the five follow-up questions about the three machines. As students answer the questions they can make any notes they want on their handout. Then have students share out in the full group for about 4 minutes. You can write down their responses on the board and students can adjust the notes on their own handout as needed. Students should be the ones doing most of the talking here and sharing their responses, not the teacher. The teacher should only intervene as needed if answers are not correct after the whole class has come to a consensus. Preparation Notes The most important question on this handout is #5 which is asking students to think about what the word “functions” might mean. They are relying on their experience working with function and non-function vending machines. Make sure to give enough time to discuss this question. It is recommended that you project slides on a whiteboard so you can write down the students’ responses on top of the slide. If this is not possible then click the “Answers” button for a possible response to each question. Answers Agenda

Launch: Questions A function is….
a rule that gives you only ONE OUTPUT for each input. Example of a function: (Time on this slide – 2 min) Time passed 34 min In-Class Notes Taking the contextualized definition of function that students came up with, generalize it to mean “a rule that gives you only one output for each input”. Ask for a student to give you an input-output table that is an example of a function. Have the rest of the class agree or disagree with that example and explain why. Make sure that they refer to the definition when agreeing or disagreeing with the example. Students should copy down the example in their handout. Preparation Notes Again it is recommended that you (or the student) writes on the whiteboard an example of a function. If this is not possible then click the button “Answers” to show an example. Answers Agenda

Launch: Questions A function is….
a rule that gives you only ONE OUTPUT for each input. NOT an example of a function: (Time on this slide – 1 min) Time passed 35 min In-Class Notes Ask for a student to give you an input-output table that is NOT an example of a function. Have the rest of the class agree or disagree with that non-example and explain why. Make sure that they refer to the definition when agreeing or disagreeing with the example. Students should copy down the non-example in their handout. Preparation Notes Again it is recommended that you (or the student) writes on the whiteboard an example of a function. If this is not possible then click the button “Answers” to show an example. Answers Agenda

Explore/Practice Agenda
(Time on this slide – 10 min) Time passed 45 min In-Class Notes Have students work with a partner on the Explore handout. Let them know that in the Explore they will be asked to look at several input-output tables and decide (and justify) if it is a function or not. In the explanation make sure students refer back to the definition of a function. Preparation Notes The Explore has different kinds of input-output tables that are not based on the vending machine context. It is important for students to look at both non-mathematical (e.g., table #1) and mathematical (e.g., table #4) examples since this will build their intuition of what is a function across various contexts. Make sure to circulate around the room and help pairs as needed. Having students use the definition of function to explain their reasoning is an example of MP 6: Attend to precisions; specifically, students “use clear definitions in discussion with others and in their own reasoning.” For more advanced students there is an Explore Extension handout that you can pass out. It contains the same problems as the regular handout with the addition of asking students to define what the rule does to the input to give the output. Both the function and non-function tables have well defined rules even if the non-function examples yield multiple outputs for some inputs. Students will have a chance to check their answers during the whole group Function Wall summary activity. Agenda

Summary: Function Wall
Examples of functions Non-examples of functions (Time on slides 47 through min) Time passed 50 min In-Class Notes Slides 47 through 59 are meant to be done together. Introduce the Function Wall to students which is a graphic organizer that students will use at the end of each lesson in this functions series to document what examples they encountered in the day’s lesson that are functions and what examples weren’t functions. The function wall can then be referred to in later lessons. Click through showing each table students worked on in the Explore and ask the class if it is or isn’t a function and to explain why. At the end of the sequence of slides give students a minute to document which tables were and weren’t functions on their own handout. Since the tables might take too long to copy over students might choose to write down the table numbers in the appropriate column. Preparation Notes The teacher should be doing little talking in this activity. Students should be the ones that decide and defend if a table is a function or not. Between all the voices in the class a consensus should be reached. If you see something terribly wrong that is going unchecked then intervene but in general let students do the talking. At the end of each function lesson you may wish to post up some of the examples and non-examples of functions up in your classroom as part of a physical, growing Function Wall. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (month) 12 January 45 February 360 December 160 June See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (number) 5 16 8 25 –2 –5 1 Input (number) Output (month) 12 January 45 February 360 December 160 June See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (month) 12 January 45 February 360 December 160 June Input (number) Output (number) 5 16 8 25 –2 –5 1 See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (month) 12 January 45 February 360 December 160 June Input (word) math function planet book Output (letter) a u o Input (number) Output (number) 5 16 8 25 –2 –5 1 See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (month) 12 January 45 February 360 December 160 June Input (number) Output (number) 5 16 8 25 –2 –5 1 Input (word) math function planet book Output (letter) a u o See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (number) 4 2 25 5 –2 9 –3 3 Input (number) Output (month) 12 January 45 February 360 December 160 June Input (number) Output (number) 5 16 8 25 –2 –5 1 Input (word) math function planet book Output (letter) a u o See notes on slide 47. Agenda

Examples of functions Non-examples of functions Input (word) math function book zebra Output (letter) h n k a Input (word) math function Output (letter) h n m f Input (number) Output (month) 12 January 45 February 360 December 160 June Input (number) Output (number) 5 16 8 25 –2 –5 1 Input (number) Output (number) 4 2 25 5 –2 9 –3 3 Input (word) math function planet book Output (letter) a u o See notes on slide 47. Agenda

Exit Ticket Answer the questions on the Exit Ticket individually.
(Time on this slide – 4 min) Time passed 54 min In-Class Notes Let students complete the Exit Ticket individually. Preparation Notes The exit ticket will give you an idea of what percentage of the class can define function and can determine, given an input-output table, if that table represents a function. Based on the class wide feedback you may want to use the warm up tomorrow as an opportunity to check in with a few individual students that are struggling or you may want to do a larger whole group discussion as part of the warm up debrief or launch in the next lesson. Agenda

Front Back Homework Agenda (Time on this slide – 1 min) Time passed 55
In-Class Notes Assign the homework and let them know that they will be asked to decide if an input-output table is a function or not (see front of handout) and to make their own examples and non-examples of functions (see back of handout). Thank students for their work today. Preparation Notes Agenda

How does a vending machine work?

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