NAME: Stephanie Kent
TOPIC: Inputs and outputs; graphing points
GRADE LEVEL: 9th grade Pre-Algebra
FOCUS QUESTION(S): “How do I approach math (how am I asked to approach math) and how does this affect how I learn? How do I graph real-world data?”
EDUCATION STANDARDS:
Non-arts content TEK/S:
§111.39. Algebra I
(c) Knowledge and Skills
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Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
C: Select tools, including real objects, manipulatives, and technology as appropriate, and techniques including mental math, estimation, and number sense as appropriate, to solve problems.
D: Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs and language as appropriate.
G: Display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
Theatre TEK/S:
§117.64. Theatre, Level I
1A: understand the value and purpose of using listening, observation, concentration, cooperation, and emotional and sensory recall.
SEL GOAL I Secondary:
Objective A
Identifies personal emotions as valid regardless of other’s opinions
Identifies the event or thought that triggered an emotion
Objective B
Recognizes one’s personal learning style and finds ways to employ it
MATERIALS NEEDED:
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Room with desks and chairs in a large circle
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Two portable white boards (individual size)
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Two sheets of poster paper with the phrases:
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“When I hear the word math, I think . . .”
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“I learn best when . . .”
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Markers
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Two balls or bean bags
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Blue tape
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Permanent marker to write on the tape
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Gridded floor (or a gridded paper on the floor with at least 1’ by 1’ squares)
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Post it notes
1. POSTER DIALOGUE “In class today, we’re going to think about our relationships to learning math and what different kinds of activities we can use to learn math that will activate us in different ways. We all learn differently, we all have strengths and challenges, and we want to explore what styles of learning work for us. To help me get to know you, I invite you to finish the following statements:”
Hold up the posters with the questions and read them aloud.
“Remember that when I’m asking you how you feel about math, I want to know how you feel about the material, not about any specific instances or teachers (though I know you wouldn’t have anything bad to say about (name of cooperating teacher). He’s awesome.)”
Put the posters up on the board. Hand out markers.
“Take your marker and write at least one word, phrase or sentence on each poster. If you see something you agree with, put a checkmark next to it. Multiple people can be working on a poster at the same time. You may want to come back to a poster more than once to see what has changed.”
Give about five minutes. Side coaching: If students are struggling to answer a question, give them the option of writing I don’t know. They may also need to be reminded to take the prompts seriously and to not use profanity. Ask them to cross out anything that doesn’t fall into these boundaries. For the prompt, “When I hear the word math, I think . . .” they can write what math does, what it involves and how they feel about it.
“Let’s take a moment to stand up and silently read what is on each poster. Now let’s all sit back down.”
Read off the answers to “When I hear the word math, I think . . .”
Reflect:
“What themes do you see occurring in this poster (are there any repeated statements or statements that seem to be saying similar things)?”
Have a student circle the words or write them up if they aren’t already there.
“How do most of us feel about math? Does anyone want to give an explanation of why (Remember we’re not naming specific teachers)?”
Read off the answers to “I learn best when . . .”
Reflect:
“What themes do you see occurring in this poster (are there any repeated statements or statements that seem to be saying similar things)?”
Have a student circle the words or write them up if they aren’t already there.
“Can we come up with some ways to make these things happen in the math classroom? We can try any of these methods, but we’ll stop using them if learning isn’t happening.”
Transition: “We may not have answers to this question yet, but this is why I’m here. We’re trying to integrate the things on the second poster into the classroom in order to change the negative feelings on the first poster. Keep this in mind, because I’m going to ask you later to reflect on activities we do to tell me if they’re ______________, ________________ and ________________. (words or phrases from the poster). These will be our goals.”
Keep the second poster up, but take down the first.
2. THREE (OR IN THIS CASE, TWO) BALL TOSS: “We’re going to play a game that involves moving balls around the circle. This game will create data that we can use to explore graphing. Let’s stand up in our circle, close enough that we can hand this ball to our neighbor. Let’s start by handing the ball around the circle and counting up by ones. You say the next number when you have the ball. Let’s start with one.”
Have the ball go around the circle once.
“Nice work. Now we’re going to introduce a second ball (name each ball by an identifying factor, ex. the blue ball and the red ball). This one you throw (with a gentle underhand toss) to a person who is not next to you. Make sure you say their name and look at them before you throw it so they know it’s coming. You want them to catch it. I’m trusting you all to be good at this part, because it’ll be hard for me. I’m still learning your names! We will continue counting and sending the other ball around the circle. If someone drops a ball or loses count, we’ll have to start all over again! ”
Play once or twice. Side coaching: I once had a class get to 40! Do you think we can get there? Can we pick up the pace?
Note: You can appoint someone other than yourself to introduce the second ball.
“Let’s introduce a time limit. Maybe twenty seconds? (Name of cooperating teacher) could you time us?”
Play once or twice. Have a student write 20 seconds on the individual white board, and what number(s) we counted up to. Note: See how this time limit works with the group. Adjustments may be needed.
“Let’s try with 15 seconds.”
Play twice. Have a student record these numbers as well.
“Nice work. Let’s all sit back in a circle.”
3. SHARING INFORMATION:
Have the students sit back down at their desks. All information should be written on individual white boards that remain in the circle. Have one board for the math and one board for terminology.
“How could we write this information in a table? Can someone do that for us? How can we write this information as points? What would we have to decide to do so?”
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Side coaching: How are we using numbers in this game? Points have two coordinates; do we have two different kinds of information? What are they? How do we decide which is the x and which is the y?
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Possible terms to use: input and output, independent and dependent, domain and range
Have a student write the points on one board and the terms used on another board. Include as many students as possible in this process. Note: The following information can be introduced through questions from the teacher instead of direct instruction depending on the content knowledge of the students.
“So points have x-coordinates and y-coordinates. The x is usually the one we call the input, or the thing that we are changing. Here, we change the time constraint, so the time became the x-coordinate. What was our unit of time? It’s important to know that, otherwise we wouldn’t know if the time was in milliseconds or years. The thing that changes as a result of the input (or the time constraint) is the output, or the y-coordinate. In this case, that is the number we counted to. But was the time constraint the only thing that affected the number we got to?"
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Possible terms to use: causation and correlation
4. HUMAN GRAPH:
“Now let’s graph these points. But we’re going to be the points, so we need a human sized graph. I have some tape here; can we make a coordinate plane on the floor? What does a coordinate plane look like? What do we need to label before we can plot points? What does our scale need to be to plot the points we have up here?”
Note: Have students help make the coordinate plane. Make the scale by ones or twos if possible. Otherwise, the students will be standing very close to one another on the graph. The desks may need to be moved out of the way for this.
If the students don’t come up with these, side coach them to:
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Make sure the axes are placed on the seams of tiles so the tiles can represent the graph.
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Have students decide which directions are positive and which axes are x and y.
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Have students label the axes with a scale (you may want to label this with post it notes so we can change it later)
“Can someone stand where our first point would be on the graph? How do we know that’s where to stand?”
Repeat with a few more points.
Transition: “Great work. We now have our coordinate plane set; we’ll use this in our next two lessons.”
5. REFLECTING ON THE LESSON:
What did we do today? What terms did we use?
Which processes from the “I learn best when . . .” poster did we use?
How were these activities different from the ways you’ve learned math before? Did any of those differences make learning easier? Harder? How?
Which other processes from the “I learn best when . . .” poster would you like to try?