Math.HSF-IF.A.1

Common core State Standards

  • Math:  Math
  • HSF-IF:  High School: Functions
  • A:  Interpreting Functions
  • 1:  Understand the concept of a function and use function notation

    Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Download Common Core State Standards (PDF 1.2 MB)

Using a Lottery to Illustrate Functions
Lesson Objective: Using a lottery to see the uniqueness of functional relationships
Grades 9-12 / Math / Functions
Math.HSF-IF.A.1

Thought starters

  1. Why does Mr. Persaud introduce the lottery scenario without using the word 'function'?
  2. How does the term 'one-to-one correspondence' help students understand functions?
  3. Why is it important to revisit functions in this manner even though students were introduced to functions in previous courses?
10 Comments
This is a teacher centered...Even thought the idea is great, how ever you want to have the students interact with each-other.
Recommended (0)
LOVE LOVE LOVE this. I used this in my class to teach functions, and the students kept going back to the idea that it's okay to "share a car" but it's not okay to "have two cars" in order to help them determine whether or not the examples I showed were functions.
Recommended (0)
I love this idea of lottery to make "one to one" correspondence more relatable. I am going to add this idea to my usual way of using hackey sack to explain the idea with functions. Thanks for sharing. Many x's can share the same y but many y's may not share the same x.
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What was the purpose of the clarification? He wasn't only saying "one-to-one." He was saying "one-to-one correspondence," which implies one-to-one and onto (I watched the first 1:40 minute). Does he use the phrases interchangeably in the video?
Recommended (0)
Just for clarification one-to-one is an injection. One-to-one and onto is a bijection. I like this idea for introducing the definition of a function.
Recommended (1)

Transcripts

  • TEACHING CHANNEL
    INTERVIEW WITH CHRISTOPHER PERSAUD

    CHRISTOPHER PERSAUD:
    So, we have a little situation. There was a lottery. Right now I

    TEACHING CHANNEL
    INTERVIEW WITH CHRISTOPHER PERSAUD

    CHRISTOPHER PERSAUD:
    So, we have a little situation. There was a lottery. Right now I need six winners to see who's gonna get a car. Six winners, let's see them.
    (interview)
    My name is Christopher Persaud. This was a discovery lesson about a lottery, and it was used to introduce functions to them. The objective of today's lesson is to have the students see functions from a completely different perspective, how it can be related to a real-life application, and actually let them be the winners of the lottery. So it had six keys to cars, and after they randomly selected students that raised their hand, they went up to the board and put their name up there.
    (class)
    All right. What I want right now are the six winners to come on up and write what they want on the board. Come on down.
    (interview)
    I transition into it without them even knowing what is a function. I never use the word function. But I was giving them a scenario: six winners, six cars, and each winner now has a car in their possession.
    (class)
    All right, guys. Take a look at the cars that we have and the winners. So first we had the silver Ferrari Spyder. Who had the Ferrari Spyder? Number three, who had the black Mustang? Erica. Blue Porsche? The question is, do you think that there is a one-to-one correspondence between the winners and the cars? However you interpret that phrase, one-to-one correspondence.
    (interview)
    Just that phrase, one-to-one correspondence, it's great to hear their input, what does it mean? None of them really knowing if anything's right or wrong, but just their reasoning. What’s the reason for their answer.
    (class)
    Andrew.
    ANDREW:
    In terms of the money value, it's not a one-to-one correspondence exactly, but in terms of the material to the person, yes it is.
    CHRISTOPHER PERSAUD:
    So, one to one meaning for each person there is one car. For each winner there is one prize. Each person has a car. Do we agree with that? So, we're looking at the person to the car...
    (interview)
    My objective there was to see if they understood the one-to-one correspondence part of it.
    (class)
    Let’s say Andrew's driving, and this time as he's driving he sees the ice cream truck and he gets distracted.
    (interview)
    After going through some reasoning as far as what it means to be a one-to-one correspondence, we went through different scenarios: what happened if someone lost their car, what happened if one of the winners shared a car with another winner, what happened if one of the lottery winners now has two cars.
    (class)
    Liz had good luck. She ends up winning a Honda. We initially looked at where we had six winners, six cars. We changed up a few things where Andrew lost his car, shared a car. At that point, was it still a one-to-one correspondence. Yes. OK. Liz lost her car. Was that a one-to-one correspondence? No. Now Liz has another car, so two cars total for Liz only. They’re still sharing a car. Is this still a one-to-one correspondence? No. OK. What we're looking at right now, the lottery, the fact that we have a one-to-one correspondence is called something. It begins with...f. Yes, functions. There we go. Functions.
    (interview)
    The students need to understand that a function has a one-to-one correspondence from a set A to a set B, because if they don't understand that, they don't know what a function is.
    (class)
    So our function here is the lottery. OK? So when you're looking at the winners and the prize, that's a part of your function. What are the two major components for every function? Domain and range. OK? Who can tell us, in our lottery, what represented our domain? What represented our domain? James?
    JAMES:
    The winners.
    CHRISTOPHER PERSAUD:
    The winners. And our range would be...Britney?
    BRITNEY:
    The cars.
    CHRISTOPHER PERSAUD:
    The cars.
    (interview)
    Now it makes sense. They seen the real-life application, which they will take with them for a long time, versus just remembering, here's the definition, know it, here's the definition, know it.

    * * *END OF AUDIO* * *
    * * *END OF TRANSCRIPT* * *

School Details

Elmont Memorial High School
555 Ridge Road
Elmont NY 11003
Population: 1715

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