Fist+Size+and+Height+Assignment+Introduction

=How's it organized?= These pages provide a lesson plan, a demonstration of usage of mathematical language that will help student understand the lesson, a brief definition and application of learning theories that are used to this lesson plan, and a few examples of learning theories that applies to this lesson plan to be able to solve the problems. The learning theories that our group has been assigned to work on are constructivism and Inquiry based learning theory for solving a algebraic problems.

These pages are organized as follows: A brief summary of the definition and a description of the constructivist theory and inquiry based learning theory, a link to the actual lesson plan, and a few examples how these learning theories apply.

=Where did this lesson come from?= This lesson plan is based on Algebra -- Activities Sampler in Brahier, Daniel. J. Teaching Secondary and Middle School Mathematics.

Activity#1: Provide students with tape measure or yardstick (meterstick) and ask them to carefully measure (a) the distance across their knuckles when making a fist and (b) their height in inches (or centimeters). Each student should write the measurement on a Post-it note and place it on the chalkboard. Read the measurements to the class and have each student make a scatterplot of the data for everyone in the class. The points should be roughly linear, and this will lead to a discussion of selecting two of the plotted points to use for finding a line of best fit. By counting off the slope between the two selected points, students can find the slope, and by extending the line until it intersects the y-axis, they can find the y-intercept and determine an equation for the line of best fit. Similar explorations can be carried out to compare height with shoe size, length of the forearm with the diameter of the head, and so forth. This activity gives students practice with collecting and representing data while they think about equations that describe line in real settings.

=What is a scatterplot?= Good question. Here is the Wikipedia article on scatterplots: [|Scatterplot Wikipedia Page]

And here is a Youtube video on scatterplots: media type="youtube" key="9Iw3a_LtJVE" height="315" width="560"

And here is a great website called VirtualNerd that gives example of scatterplots and finding best line and predicting the equation of the line with a slope and y-intercept. []

= **STAGE 1 – Desired Results** =

**Established Goals:**

 * Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
 * Use graphs to analyze the nature of changes in quantities in linear relationships.
 * Students verify that a points lies on a line, given an equation of the line. (CA Standard 7.0)
 * Students are able to derive linear equations by using the point-slope formula. (CA Standard 7.0)

**Understandings:**
//Students will understand that…//
 * Students will understand how to plot their data on a scatter plot using the correct intervals in the axis.
 * Students will understand how to draw a line of best fit on a scatter plot.
 * Construct scatterplots of two-variable data
 * Interpret individual data points and make conclusions about trends in data, especially linear relationships
 * Estimate and write equations of lines of best fit

**Essential Questions:** = **STAGE 2 – Assessment Evidence** = As formative assessment and during class period while students are working on the project the teacher will review the questions below with students and gives them feedback on their answers.
 * Do you think there is a direct relationship between the Fist Size and Height measurement? Why or why not?
 * How would you graph the data?
 * Given a data set, will students be able to correctly plot the data onto a scatter plot, and identify X and Y value on the coordinate plane?
 * Given a scatter plot and points, will students be able to draw a line of best fit?
 * Given two points, will students be able to determine the slop and y-intercept to write the slope-intercept equation of the line?

As summative assessment:
 * Quiz the next class session
 * Math lab report based on the class project turn in to teacher next class time
 * Exit ticket, which consist of new graph with data that students will analyze their understanding for class objectives.

= **STAGE 3 – Learning Plan** =
 * Teacher starts the class session by reviewing homework and pervious lesson.
 * Warm up activity: Teacher will ask students what they know about collecting data, graphing data, coordinate plane, X-and Y- Vales, and where they can use them. (Activating prior knowledge).
 * Provide the students with a clear outline/set of directions on the activity as well as a check-list of objects they will be working on.
 * Each pair of students will use meterstick to carefully measure (a) the distance across their knuckles when making a fist and (b) their height inches or centimeters.
 * Teacher will provide clear guidelines describing how to measure the distance across their knuckles and their height to the closest centimeters.
 * Collecting data among each group.
 * Students will turn their data to the teacher.
 * Teacher will collect the data and enter them on the data table.
 * Students will be asked to identify X and Y terms and put data into ordered pair.
 * Students will plot the data into scatter plot.
 * Teacher will ask students to try and choose two or more plotted points from the scatter plot to use for best-fit line.
 * Teacher will ask student if they know the definition of best-fit line based on their graph.
 * Student should be identify the best fit line is a linear line.
 * Teacher will ask students to find the **slope** between the 2 chosen plotted points. Student should be able to use slope formula, Slope = Rise/Run.
 * Teacher will ask each group for the slope, and will make sure everyone has the same result.
 * Teacher will ask students to extend the best-fit line to cross the Y-axis.
 * Teacher will ask students to identify the point of intersection on the Y-axis. Which will be Y intercept.
 * Student will write the y intercept as (0, b) which b is y-intercept.
 * Teacher will ask students to extend the best-fit line to cross X-axis, and identify X intercept.
 * Students will write the X intercept as (a, 0).
 * Teacher will introduce the general form of the linear equation which is y = mx + b, m = Slope and b = y-intercept
 * Teacher will ask student to calculate y-intercept from the equation.
 * Teacher will ask students to find X-intercept.