NAME: Stephanie Kent
TOPIC: Graphing lines
GRADE LEVEL: 9th grade Pre-Algebra
FOCUS QUESTIONS: “How does getting on my feet and working collaboratively change how I learn math? What do I need to know about a line to be able to graph it?”
EDUCATION STANDARDS:
Non-arts Context TEK/S:
§111.39. Algebra I
(c) Knowledge and Skills
(1) 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
(3) Linear functions, equations, and inequalities. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
C: Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real world problems.
Theatre TEK/S:
§117.315. Theatre, Level I, Adopted 2013.
(c) Knowledge and skills.
(1) Foundations: inquiry and understanding. The student develops concepts about self, human relationships, and the environment using elements of drama and conventions of theatre. The student is expected to:
A: understand the value and purpose of using listening, observation, concentration, cooperation, and emotional and sensory recall;
SEL GOAL I Secondary:
Objective B
Recognizes one’s personal learning style and finds ways to employ it
MATERIALS NEEDED:
-
Room with desks and chairs pushed out of the way
-
Two portable white boards (individual size)
-
Index cards with numbers on them, enough for all students (numbers can be positive, negative, fractions, decimals depending on your students’ abilities)
-
Blue tape
-
Permanent marker to write on the tape
-
Gridded floor (or a gridded paper on the floor with at least 1’ by 1’ squares)
-
8.5 by 11 paper with “3x+2y=12” written on it
-
String
1. DATA PROCESSING:
“This activity will help us continue to get better at working collaboratively. We’re going to begin by silently lining up by height. I will time you to see how long it takes.”
Delineate the space where they will line up, pointing out where the shortest person will stand and where the tallest person will stand. Side-coaching: Remind students to remain silent.
“Nice work!”
Reflect (have students remain standing): How did that go? What was hard? How did you communicate?
Break students into two groups by splitting the line down the middle. If possible, have a teacher monitoring each group.
“I’m going to give you each a number. Your job is to line up in your group from smallest to largest. The smallest (or negative) numbers will be at the right and the largest numbers will be at the left.”
Hand out numbers and have students line up from smallest to largest numbers in their groups.
Reflect: How did that go? What was hard? How did you communicate? How does this relate to problem solving in class?
Note: Depending on time, you can combine the groups and have the whole class line up with their numbers from smallest to largest.
Transition: We’re going to continue learning how to problem solve together over the next couple of days. Let’s work together to learn something about what is written on this sheet of paper.”
2. ARTIFACT
“I want you to begin by describing what you see on this paper as if you know nothing about algebra. Just describe exactly what you see without interpretation. For example, if I were to describe this marker, I wouldn’t say it’s a marker. I’d say it’s red, and shiny and plasticky, this top part comes off etc.”
Show the sheet with the equation. Allow for a number of responses to each of the following questions.
“What do you see (describe)?”
-
Side coaching: What letters do you see? Are there any other symbols?
“What does that tell you (analyze)?” Note: Some terminology should start to come in here.
-
Side coaching: What do the symbols tell you?
-
Have a student keep track of terminology on the white board.
“How can we model what you see here (relate)?”
-
Side coaching: How do you know what type of an equation it is (what it represents on the graph)? Do you see any exponents for the variables? What does that tell you? Note: At this point, there may need to be some instruction to get the students to understand why this equations represents a line and not, for example, a circle. Depending on the group, you may choose to skip this conversation.
-
Terms to use: variable, linear equation, degree
Transition: “We have our coordinate plane of the floor. What do we need to know about this linear equation to graph it?”
-
Side coaching: Can we plug numbers in to give us information? Can we change the form of the line for more information?
-
Terms to use: slope, slope-intercept form, standard form
3. SHARING INFORMATION/ HUMAN GRAPH:
“We talked about what makes a point earlier in the lesson. How can we find a point that falls on this line? Check in with the person next to you and see what they think. Does anyone want to show us?”
-
Side coaching: We talked about inputs earlier. What does the word input mean? Do we need to change the scale of our graph for this point?
Have a student show the steps of plugging in a value for x or y to find the second coordinate of a point. This can happen on one of the individual white boards.
“Thank you! Can someone else show us where this point goes on the coordinate plane?”
-
Side coaching: Remember which axis represents x and which represents y! Are there some points that are easier to work with than others (think intercepts!)?
“After we have one point, what can we do to find the line? Check in with your neighbor.” Either a second point or the slope.
-
Side coaching: How do we find the slope from the equation?
Have another student use an individual whiteboard to show finding a second point or finding the slope.
“Nice work! Can someone show us, using this string, how we can use that information to put the line on our coordinate plane?”
-
Side coaching: Remember what slope represents?
-
“Terms” to use: “Rise over run”
Have the students who represent points hold a piece of string to create the line. Set the string down on the plane.
Note: If students graph the line with two points, make sure to ask how to find the slope from the equation.
“How can we find the slope of the line on the graph?”
Transition: “Awesome work today. Look at our beautiful line! Let’s sit back in a circle.”
4. REFLECTING ON THE LESSON:
What did we do today? What terms did we use?
How was this activity different from the ways you’ve learned math before? Did any of those differences make learning easier? Harder?