Celio

=Celio's Page=

[] Common Core State Standards Initiative website

[] North Carolina Department of Public Education website as it addresses the core curriculum.

[|http://www.learnnc.org/scos/#common] Learn NC is a program maintained by the School of Education at UNC Chapel Hill.

[] provides detailed explanations of the new standards as well as sample problems.

[] provides sample problems using the common core

[] video illustrating lesson on properties of quadrilaterals using common core curriculum

[] detailed powerpoint presentation with information behind the common core

[] PDF file which explains new high school pathways with common core

[] various videos which provide information on the common core

[] website dedicated to helping teachers understand how to meet the requirements of the common core through various teaching methods

[] lesson plans based upon the common core

**__ WHAT IS SLOPE? __**




 * __ BEFORE __**__ : (40 minutes) __

Most students in Algebra I have some idea about what slope means because they have probably worked with it in earlier math classes. If asked for the definition, the usual response would be that slope is the rise over the run and on a graph, the students can usually indicate "this over that" to demonstrate what the slope is. Not as many can relate the slope of a line to slopes that they encounter everyday though. I will ask if students can come up with any objects or situations they have come in contact with where slope is an issue. There may not be many responses initially and if this is the case, I will show them pictures of the road signs indicating road grade and the pictures showing the slope of a roof. I will be looking for students to mention things such as roller coasters, ski slopes, skate board ramps, wheel chair accessible ramps, stairs, and windshields. We will then discuss why certain objects have the slope they have and the effect of the slope.


 * __ DURING __**__ : (30 minutes) __

I will refer back to the rise over run definition for slope and explain that this is actually a ratio of the change in the height of the object (from any two points on the incline/decline) as compared to the change in the length of the object (from those same two points on the incline/decline) and is usually reduced to its simplest form. This is how we get the slope using two points on a line.

__example:__ Given two points A(0,0) and B(20,20), find the slope of the line that passes through both points.

__answer:__ Using the formula for finding the slope (slope = change in y divided by the change in x) we get (20-0) divided by (20-0) which is 1.

__example__: We have a one-story house which measures 40 feet by 100 feet. If the base of a roof is 40 feet long and at its highest point, the height of the roof is 20 feet above the base, what is the slope of the roof?

__answer__: The change in the height is 20 feet and the change in the length is 20 feet (remember that the highest point of the roof is typically right in the middle of the house) so the slope is 1.

I chose these problems hoping to help students see the relationship between what they typically do with slope in the classroom and how slope is used in everyday life.

In situations where we are provided a slope, like in the case of a road sign with a percentage for a decline, can we determine what this means?

First I will ask students if they understand what percent means and if it can be displayed in other ways. I am hoping someone will say that it can be written as a fraction but if not I will tell them. I will then ask if someone can tell me what 25% means and to write it in terms of a fraction. I expect students to be able to tell me it can be written as 25/100 which can then be reduced to 1/4. I will then draw a road sign showing a 25% decline and ask if anyone can tell me what this means based upon what we have been working on. The students still may not understand the concept so I will be ready to walk them through this. I will remind them we already stated that 25% can be written as the fraction 1/4. I will then ask them to relate the information on the road sign to slope and ask if anyone has any ideas. I am hoping this will get some of the students to see what is happening. If I still cannot get a response, I will remind them that slope is the ratio of the change in the height of the object (from any two points on the incline/decline) as compared to the change in the length of the object (from those same two points on the incline/decline) and is usually reduced to its simplest form. This means that the ratio of the change in height is 1 and the ratio of the change in length is 4. So in this case, for every foot the road rises or falls, the change in either direction is 4 feet. I will draw this on the board to make sure students understand this concept and explain that although we indicate in mathematics whether a slope is positive or negative, this is not something they will see in most situations.

__example:__ If a road sign indicates a road has a grade of 10% going downhill, what is the slope for this road?

__answer:__ 10% can be written as the fraction 10/100 which can be reduced to 1/10 so the slope is 1/10.


 * __ AFTER __**__ : (15 minutes) __

This lesson will take up most of the class period because I want to make sure students can understand what slope is and how to calculate it. I also want to spend as much time as possible on the real-world situations to help make a connection for the students. we will review the formula for finding the slope as well as finding the changes in the ratio as it pertains to a given percentage. The assignment they will be given from this lesson will be to identify at least three objects which have some sort of slope identified with them. They will then measure or provide a good estimate of the dimensions and calculate the slope. They will also provide their thoughts or research on why the slope for the object is what it is or how it affects the object. I will ask students to give examples of objects they might try to measure for this assignment to make sure they are on track and to give ideas to students who may not be sure of what to look for.

CCSS for Mathematics F-IF.6