8EE5 Lesson Prepared by Lisa Neubert, Jenn Bott, Brittany Ryan and Daryl Francom

8EE5 Lesson prepared by Lisa Neubert, Jenn Bott, Brittany Ryan and Daryl Francom

8EE5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships in different ways, ie. Distance-time graph to distance-time equation to determine which of two moving objects has greater speed.

Prior knowledge: It is assumed that students have prior knowledge in coordinate planes, including graphing and locating points and addition and subtraction of integers. Exposure to ratios and the relationship between the numerator and denominator and how it affects the magnitude is helpful, but not essential.

Develop: Linear equations

Task: Exploring Houses “Navigating through Algebra in Grades 6-8” 2007 (pg 9)

Goals: To assess students’ - Understanding of pattern development - Ability to use a table to organize information; - Choice of strategy (e.g. draw a picture, use recursion, write an explicit rule) to make a prediction.

Introduces a linear relationship the number of houses and the number of shapes. Since the blocks change by three each time, this will teach the concept of rate-of-change. Encourage use of charts, graphs, drawings, verbal descriptions, and recursive and explicit equations. Introduce house 0 to introduce y-intercept.

Task “Walking Strides” Navigating through algebra (pg 25)

Goals: - Recognize what varies in the experiment - Identify the independent and dependent variables. - Use a table to organize information - Make a graph to display data using correct labels and scales - Consider how the steepness (slope) of a line relates to distance covered in a given time.

Alternate Activity “Building Stairs” www.teachforever.com/2007/12/lesson-idea-teach-slope-by- building.html This will investigate the concept of rise and run

Practice: Worksheet http://www.kutasoftware.com/freeworksheets/alg1worksheets/slope%20from %20a%20graph.pdf ______

Solidify: “Walking Rates” Navigating through Algebra (pg. 44) Goals: Connect the concept of linearity with real-world context - Use a table to organize information - Make a graph to display data, using correct labels and scales - Recognize the relationship among the table, the graph, and the equation and the slope of the line.

Practice: Worksheet Finding Slope in a graph (Kuda) Daryl find alternative http://en.wikiversity.org/wiki/vertical_height_and_horizontal_length_and_slope utube video on slope (The ramp one is not working, but the ski slope is.)

Develop and Solidification: y-intercept and steepness of slope

Task: “Pledge Plans” Navigating through Algebra Pg. 46

Solidify: -Connect the concept of linearity with real-world contexts - Use a table to organize information - Make a graph to display data using correct labels and scales - Recognize the relationship among the table, the graph, the equation, and the slope of the line - Identify the y-intercept from a graph or a table

Anticipating: Students may not write the table or graph from 0-10 Students need a way to identify the particular graph i.e. stars, points boxes Students writing the independent variable and dependent variable on wrong axis Not all values will start at 0.

Questions to ask: How many km is the race? How many km do we have to have on our table? How much do they have at the beginning of the race? Where would the starting point begin? KM what? In your table, what would you label the starting point? How can you tell which student’s pledge would bring in the most money? What does it mean when the lines cross? How can we tell which line represents which student? What would you label the horizontal axis? Why? What would you label the vertical axis? Why? Can you write an equation for these lines? Where does the 4 come from in the equation? What would we put in instead of m? What if another student proposed to begin with $5 then $1 each km? What if Kaden just asked for $10 for the whole race, not just per km? What if we just did the walk and sponsors can just donate any amount they want? (undefined slope)

Develop: http://voices.yahoo.com/ms-algebra-teach-slope-creative-3092326.html

Teaches: 0 and undefined slope

______Practice and solidify:

Online worksheet: http://algebrahelp.com/worksheets/view/graphing/eqfromgraph.quiz Interactive activity: http://www.Itcconline.net/green/java/BasicAlgebra/LineGraph.htm Worksheet: “Graphing Lines” http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Graphing%20lines%20sl.pdf

Option: Video on utube “Hungry Wolf” can lead into discussion on on steepness of slope) ______

Alternate Activity: (Ask if this is a linear equation or not. May lead into scatterplots.)

The Kiss and Noodle Lab

Objective: To fit a line to a set of data. To make projections about real-world situations.

1. Place two desks _____ inches apart. (Your teacher will assign each group a different number of inches).

2. Place one piece of pasta across the gap. Attach a cup to a bent paperclip and hang it from the pasta. Gently place kisses in the cup until the pasta breaks. Record the number of kisses needed to break the pasta in the table below.

3. Continue the experiment, determining the number of kisses need to break 2, 3, 4 and 5 pieces of pasta. Record the data in the table below. When you have all the data recorded, create a scatterplot on the graph provided.

4. Record all of the data on the table in the classroom.

Number of pieces of spaghetti Number of kisses needed to break spaghetti 1 2 3 4 5 Post-Experiment Discussion

1. How did the length of the gap affect the results? ______2. What does the slope represent in this experiment? ______3. What does the y-intercept represent in this experiment? ______4. What factors could have affected the breakage of the pasta? ______Develop: slope for rate of change: