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Writer's pictureGilbert Faustin

How to find the slope?

Updated: Aug 24, 2022

Gilbert Faustin

Multimedia Design & Development

Instructor: Dr. Gregor

Course: EDU 630


Youtube Video






Visual Presentation Slideshow



Script


1. Welcome your audience and introduce yourself

Good afternoon, everyone, ladies and gentlemen; I am Gilbert Faustin. Today I would love to

present/ teach everyone about finding the slope of the line in Algebra and show the visual graphs and examples to help everyone understand the material. 

2. Capture their attention

How many of you have ever had trouble understanding a math lesson? That could be because of a lack of visual aid in or during the lesson. Visual aid for math, especially Algebra, involves graphs and formulas. Hence, many math courses require a graphing calculator, so you can plug in the formula and press the graph button to see what the graph looks like. 

3. Identify the number one goal/ topic 

My goal for today's lesson is to help everyone understand and learn the slope definition and how to find the slope of the line and graph the slope without using a graphing calculator. 

4. Go into and teach each slide

Essential Questions:

• How can a ratio be used to describe the steepness of a line?

• Why does the slope of a line remain constant?

• How can right triangles show that the slope is constant?

Skill Focus: 

Write a ratio for the slope of a line. Use similar triangles to show the slope as constant.

Vocabulary Focus: slope, change in y, change in x, rise, run, similar triangles, constant

Ways to Gain/Maintain Attention (Primacy):  treasure map, connection to skiing, predicting, note taking, cooperative activity, music, and movement, game.

Lesson Segment 1: 

How would you describe the ordered pairs graph for a relationship where the change ratio is constant? 

Have a student come to the overhead to place a point where each point in the starter should be. The team gets a little treat if a student correctly places the points. 


Q. Think-Team-share Q. How would you describe a line containing each point? 

Have the students sketch a line using their rulers through the points on their treasure map and plot several other points on that line. Have them write the directions for finding the next

point as a ratio comparing the number of spaces they moved up to the number they moved

across. Explain that the change or distance from one point to another moving up and moving across can be written as a ratio, ½. 

Q: Think-Team-Share. What makes the line straight rather than curvy? Remind students that

moving vertically is moving parallel to the y-axis, and moving horizontally is moving parallel to the x-axis. So, rather than simply using the words, we could use the words; change in y over change in x." Refer to the vocabulary on the board.

Lesson Segment 2: 

How can a ratio describe the "steepness" of a line? Why does the slope remain constant? 

Explain that the change in y compared to the change in x is called the slope. The slope refers to the steepness of the line. When a slope is a small number, the line is less steep. When the slope is a larger number, the line is steeper. Show students the Skiing graphic (attached). Have them predict whether the slope of each line will be a smaller or a larger number or a number close to 0.

Overlay each line of the skiing transparency on a graph paper transparency and demonstrate

Identify two points and then count the slope from one point to another, emphasizing how Y changes and X changes from one end to the other.


Slopes from graphs: 

We write the steepness of a line as a ratio telling how the rise of the line compares to the run of the line. Hand out the; Slopes From Graphs" worksheet. Help students identify four points where the line intersects two gridlines and have them count the change in Y and the change in x and write the difference as a ratio for each. Next, have students compare the ratio for change in y/change in x, with each point asking whether or not the ratios are equivalent. Remind students that they decided if the ratios were not equivalent, the line would not be straight.

Discuss lines with a positive, negative, 0, or no slope. A mnemonic for this is the skiing

scenario. 

When you are moving upward from right to left, this is a POSITIVE slope. 

When you are moving downward from right to left, this is a NEGATIVE slope. 

When you are skiing horizontally, this is cross country skiing with 0 slopes. 

When you are falling off a cliff (vertical line), this is NO SLOPE AT ALL

Dance: Slope Dance;- Students stand and face the front of the room. You stand behind them.

Put on music and have them use their arms to show a positive, negative, 0, or no slope line as you call each out.

Journal: Fold and cut the Finding the three Ways To Find Slope foldable. Fill in the example for finding the slope from a graph of a line.

Lesson Segment 3: 

How can ordered pairs for a linear relation show that the slope of a line is constant?

The slope from a table  Using The Table Ask Feature On the Graphing Calculator to Investigate SlopeTo find patterns leading to the concept of slope, type an equation in the Y=. In Table Set, set the Independent and Dependent to; Press the Table key and type values in the X list. Press the Enter key to put a few intermittent values in the Y list. Leave some of the values out of the Y list. Have students determine what the missing values are. Ask, How did you decide that? Some students will remember this activity from the last lesson for writing an equation. Others will reply that they saw the pattern in the change in the Y values rather than in relating Y to X. Tell them for slope, they will be using the change from Y2 to Y1 and from X2 to X1. Have them copy the tables on an assignment paper and write the change in Y to the change in X as a ratio. Do several equations in this manner. Some possible equations you may wish to try are y = x, y =

-x , y = 2x, y = -3x, y = ½ x, y = 1/3x, y = 5, y = x, y = -x

Connect the; change in Y over the change in X" from the table to count that change when looking at the graph. Discuss that just as the ratio of rise to run on the graph was always the same, the ratio of change in Y to change in X in the table must be equivalent. On their assignment paper, ask them to begin with X being 0 and y being any number they choose and construct tables of values that have the following slope:

1. ¾ 

2. 1/3 

3. ½ 

4. 2/3 

5. 0 

Game: Truth or Dare

Give each team one of the tables from the Tables and Slope Transparencies. The team works together to determine if the tables show a linear relationship by checking for a constant ratio for change in y to change in x. A team member is then selected to bring transparency to the overhead and ask the class members to determine if the table shows a linear relationship or not and how they chose their answer. Class members are given 30 seconds to check with their team to reduce risk. The student at the overhead then selects a person from the class to either tell the truth or take a dare. If the selected student can tell the truth and explain their reasoning, they take the dare. If not, the challenging team gives a dare such as Jumping up and down while barking like a dog.; All dares must be respectful, and the teacher can veto a dare if it is inappropriate. Students should copy all tables on an assignment paper and write the slope of the line IF the table indicates a linear relation. Journal: Fill in the example for finding the slope from a table on the foldable. A slope from ordered pairs. 

Have the students look again at their Slopes From Graphs; paper. On the back of that paper, have them write the ordered pair for the points they identified in each graph. Next, help them determine how y and x have changed by looking at the difference in two ordered pairs. Next, help them write a math expression to compute the change (use slope formula and place ordered pairs vertically as if in a table and subtracting). Then have them compare their computed slope value to the counted slope value from the front of the page.

Four-Corners practice: Use the ordered pairs on the 10 cards (attached). Ask person # 1 from a team to come to draw out any two ordered pairs. Then, have person #2 from another team come to do the same, person # 3 from a team, and person # 4 from another team. Next, do Four Corners, where they go to a corner, then to another corner, then the third corner, and then to the fourth corner of the room. In the corner, they look at the two ordered pairs drawn. Together, they find the slope of the line that would contain those two points. Finally, have the students return to their desks and teach their teams how to find the slopes. These four problems should also be recorded on the back of the Slopes from Graphs worksheet. Journal: Fill in the example for finding slope using two ordered pairs.

Lesson Segment 4: 

How can right triangles be used to show that the slope is constant?

Manipulative activity  Give each pair of students a few centimeter cubes. Each student should be given the Slope and Similar Triangles worksheet to record the work. Students will build a slope with Centimeter Cubes, Sketch a line along the lower vertices of the cubes, and trace the right triangles formed by the cubes. Students will then compare sides from several right triangles for a line from their sketches to determine if the triangles are similar or not. Remind students that similar triangles must have corresponding sides in proportion. If the ratios of rising to run are equivalent, the slope must be constant for the line.


4. Provide instructions on how to ask questions


Thank you, everyone, for your time. I hope everyone has a better understanding of finding the slope and graphing the slope of the line. Please, if you have any questions, feel free to email me at @gfaustin@stu.edu


References:

Houghton Mifflin Harcourt. (2014). Ratios and Finding the Slope of a Line In Florida explorations

in Core math: Algebra 1 (pp. 195-201).


McLogan, Brian. (2010, September 14). How to find the slope between two points. YouTube.

Retrieved July 17, 2022, from https://www.youtube.com/watch?v=wvzBH46D6ho


Roberts, D. R. A. F. (n.d.). Hitting the Slopes - MathBitsNotebook(A1 - CCSS Math).

MathBits.Com (MathBitsNotebook.Com) - Fred and Donna Roberts.

https://mathbitsnotebook.com/Algebra1/LinearEquations/LEHittingSlope.html

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