Beth Hopta
Name: Beth Hopta
Date: July 12, 2011
Title: It’s a pitch.
Subject/Grade Level: Math- 11th grade Concepts of Mathematics
Investigative Question:
“When will I ever use slope in real life?” – The question that plagues the
classroom!
PA Academic Standards:
2.5.11.A: Develop a plan to analyze a problem, identify the information
needed to solve the problem, carry out the plan, check whether an answer
makes sense, and explain how the problem was solved in grade
appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation,
mathematical rules, graphing and other types of mathematical
representations to communicate observations, predictions, concepts,
procedures, generalizations, ideas and results.
M11.D.2.1.2: Identify or graph functions, linear equations or linear
inequalities on a coordinate plane.
M11.D.2.1.3: Write, solve and/or apply a linear equation (including problem
situations).
M11.D.3.2.1: Apply the formula for the slope of a line to solve problems
(formula given on reference sheet).
M11.D.3.2.2: Given the graph of the line, 2 points on the line, or the slope
and a point on a line, write or identify the linear equation in point-slope,
standard and/or slope-intercept form.
Reading in History from Common Core Standards:
1. Cite specific textual evidence to support analysis of primary and
secondary sources, connecting insights gained from specific details to an
understanding of the text as a whole.
Source: PA Department of Education- Standards- Aligned Systems
website- http://www.pdesas.org/standard/views/
Beth Hopta
Learning Objectives:
1. The students will calculate slopes based off of a coordinate plane.
2. The students will draw a house with a 7/12 roof pitch on a coordinate
plane.
3. Te student will look at roof pitches around the United States.
4. The student will note differences from around the country. What are
some noted differences? Why are they different?
5. The student will create a blueprint of a house you may have found in
around the United States, and then justify why they made their roof
the pitch they created it to be.
Duration:
This lesson will take 4 days. There will be two days allotted to introduce
and work on slope (change in y/change in x). Followed by two days left for
students to look over roof pitches as well as design their roof pitch for a
house of their choice around the United States.
Materials & Citation of resources:
Library of Congress: Penasco, Taos County, New Mexico. Winters are
severe and many of the homes have pitched roofs to shed the long rains
and snows. Library of Congress Prints and Photographs Division
Washington, D.C. 20540, 1945 http://hdl.loc.gov/loc.pnp/fsa.8d13925
Beth Hopta
Library of Congress: Library of Congress Prints and Photographs Division
Washington, D.C. 20540 Between 1933 and 1945
http://www.loc.gov/pictures/item/owi2001045620/PP/
Roof Pitch Chart
http://www.carpentry-pro-framer.com/images/roof-pitch-chart.gif
Beth Hopta
Roof Pitch Picture
http://marauder.millersville.edu/~cjsander/graphics/Roof%20Pitch/roofpitch
1.png
Roof Pitch pictures
http://novagutters.com/roof%20pitch%20examples.gif
Roof Calculator Software and webpage:
http://roofgenius.com/roofpitch.htm
Inquiry-Based Instruction:
I will use an Inquiry-Based Instruction Model with the following
components:
Questioning: I will ask the students to first explore slope for students on a
coordinate plane. After they have a better understanding of that, I will ask
that students discuss roof pitches and look at the different pictures that are
shown above. And begin asking why there are different pitches to houses
around the country.
Research: Students will investigate housing pitches after first looking at a
few pictures. They will try to find out why a house may have a different
pitch to it.
Discussing: I will ask students what they found out about the different
slopes/pitches? Ask them how a roof pitch is made as well as related to
the slope we just finished.
Creating: The Students will create their own blueprint drawing of a house
that they may find in one particular part of the United States.
Beth Hopta
Reflecting: I will begin by asking why a house in Erie Pennsylvania may
have a different roof pitch then a house in Washington Pennsylvania? I will
ask them to tell me if they can better understand slope on a coordinate
plane. What factors will a builder have to take into effect when designing a
house roof?
Assessment: Students will create a blueprint design of a house. This
house must include a roof pitch that they may create, then state where you
may find this house. They must be able to back up their pitch design with
why they made it as steep or as flat as they did.
Description of procedures:
This activity is to help put a halt to the age old question of, “When am I
going to use this in real life?” Students are bombarded with the PSSAs
and other standardized tests so much that they forget that they are really
learning to help become successful members of society. Students are
going to be introduced with the topic of slope or change in y over (divided)
by change over x. This is traditionally known to be done specifically on a
coordinate plane with two or more points on the line. However, students
are unable to link slope and coordinate planes to when they may actually
use this in real life. I have a hard time finding a lot of examples to throw
back at them, one I have found is a roof pitch. A pitch to a house uses the
rise over run idea to establish the slope of the roof. If a roof has a 7/12
pitch, this means that the roof will have a slope that goes up 7 inches then
over 12 inches. If you were to plot these points on graph paper, then will
be the exact slope of your houses roof. If you go to areas where they have
harsher winters, the pitch to their house may have a steeper slope, such as
up 10 inches, over 7 inches. This will help to make the snow slide off the
roof in the winter.
Beth Hopta
I will begin this section by introducing slope on a coordinate plane. I will
have a line drawn on the coordinate plane and have students help me
choose two points that fall on the line, making sure that it hits the cross
hairs exactly. Once we have the two points chosen, students will be told to
label their x’s and label their y’s. Making sure they follow the format of how
a coordinate is put together, (x,y), domain first then range. Then students
will be asked to pick their 1’s and pick their 2’s, (x1, y1)(x2, y2). After
completing this, students will have to plug their numbers into the formula
and solve.
Formula for slope: y2-y1
x2-x1
Example coordinates to use. (2, 3) (4, 6)
Label X & Label Y: x= 2 y = 3, x = 4 y = 6
Pick your 1’s and pick your 2’s: x 1 = 2 y 1 = 3, x 2 = 4 y 2 = 6
Plug it into the equation: 6 – 3
4–2
Slope = 3/2 or rise 3, run (over to the right) 2
Students will complete two of their own problems on slope then the
following day students will draw a line on a graph paper when they are
given a coordinate to start from and the slope to follow. Students will
graph the line on graph paper and practice on this.
After students have a good understanding of slope, I will then introduce its
relationship to a roof pitch by showing pictures and asking them questions
about it. They will need to describe what they see and how it will relate to
Beth Hopta
class and what we were just doing. Once they start to see the relationship,
students will need to strap on their tool belts and get to carpentry class.
Here is our real world link: Roof pitch is SLOPE! When you are designing
your house you will have to determine what roof pitch you will need. I will
work through some pitch problems by drawing houses on graph paper and
determining what the pitch will be. After students are able to determine the
roof pitch, they will have to do a little bit of research to find out why a roofs
pitch may be as steep or as level as it may be. What factors determine it?
What weather conditions determine it? What were roofs made of in the
1800’s?
Once students feel comfortable finding roof pitch, they will be turned loose
on creating their blueprint of their house, fully equipped with a roof pitch.
Students will then have to explain how they came up with their roof pitch
and explain why they decided to make it the slope that it is.
This activity helps to get rid of the eluding question of when students will
use this. Students are always a little more willing to learning about
something they will have to know about forever.
Beth Hopta
Name: Beth Hopta
Date: July 12, 2011
Title: It’s a pitch.
Subject/Grade Level: Math- 11th grade Concepts of Mathematics
Investigative Question:
“When will I ever use slope in real life?” – The question that plagues the
classroom!
PA Academic Standards:
2.5.11.A: Develop a plan to analyze a problem, identify the information
needed to solve the problem, carry out the plan, check whether an answer
makes sense, and explain how the problem was solved in grade
appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation,
mathematical rules, graphing and other types of mathematical
representations to communicate observations, predictions, concepts,
procedures, generalizations, ideas and results.
M11.D.2.1.2: Identify or graph functions, linear equations or linear
inequalities on a coordinate plane.
M11.D.2.1.3: Write, solve and/or apply a linear equation (including problem
situations).
M11.D.3.2.1: Apply the formula for the slope of a line to solve problems
(formula given on reference sheet).
M11.D.3.2.2: Given the graph of the line, 2 points on the line, or the slope
and a point on a line, write or identify the linear equation in point-slope,
standard and/or slope-intercept form.
Reading in History from Common Core Standards:
1. Cite specific textual evidence to support analysis of primary and
secondary sources, connecting insights gained from specific details to an
understanding of the text as a whole.
Source: PA Department of Education- Standards- Aligned Systems
website- http://www.pdesas.org/standard/views/
Beth Hopta
Learning Objectives:
1. The students will calculate slopes based off of a coordinate plane.
2. The students will draw a house with a 7/12 roof pitch on a coordinate
plane.
3. Te student will look at roof pitches around the United States.
4. The student will note differences from around the country. What are
some noted differences? Why are they different?
5. The student will create a blueprint of a house you may have found in
around the United States, and then justify why they made their roof
the pitch they created it to be.
Duration:
This lesson will take 4 days. There will be two days allotted to introduce
and work on slope (change in y/change in x). Followed by two days left for
students to look over roof pitches as well as design their roof pitch for a
house of their choice around the United States.
Materials & Citation of resources:
Library of Congress: Penasco, Taos County, New Mexico. Winters are
severe and many of the homes have pitched roofs to shed the long rains
and snows. Library of Congress Prints and Photographs Division
Washington, D.C. 20540, 1945 http://hdl.loc.gov/loc.pnp/fsa.8d13925
Beth Hopta
Library of Congress: Library of Congress Prints and Photographs Division
Washington, D.C. 20540 Between 1933 and 1945
http://www.loc.gov/pictures/item/owi2001045620/PP/
Roof Pitch Chart
http://www.carpentry-pro-framer.com/images/roof-pitch-chart.gif
Beth Hopta
Roof Pitch Picture
http://marauder.millersville.edu/~cjsander/graphics/Roof%20Pitch/roofpitch
1.png
Roof Pitch pictures
http://novagutters.com/roof%20pitch%20examples.gif
Roof Calculator Software and webpage:
http://roofgenius.com/roofpitch.htm
Inquiry-Based Instruction:
I will use an Inquiry-Based Instruction Model with the following
components:
Questioning: I will ask the students to first explore slope for students on a
coordinate plane. After they have a better understanding of that, I will ask
that students discuss roof pitches and look at the different pictures that are
shown above. And begin asking why there are different pitches to houses
around the country.
Research: Students will investigate housing pitches after first looking at a
few pictures. They will try to find out why a house may have a different
pitch to it.
Discussing: I will ask students what they found out about the different
slopes/pitches? Ask them how a roof pitch is made as well as related to
the slope we just finished.
Creating: The Students will create their own blueprint drawing of a house
that they may find in one particular part of the United States.
Beth Hopta
Reflecting: I will begin by asking why a house in Erie Pennsylvania may
have a different roof pitch then a house in Washington Pennsylvania? I will
ask them to tell me if they can better understand slope on a coordinate
plane. What factors will a builder have to take into effect when designing a
house roof?
Assessment: Students will create a blueprint design of a house. This
house must include a roof pitch that they may create, then state where you
may find this house. They must be able to back up their pitch design with
why they made it as steep or as flat as they did.
Description of procedures:
This activity is to help put a halt to the age old question of, “When am I
going to use this in real life?” Students are bombarded with the PSSAs
and other standardized tests so much that they forget that they are really
learning to help become successful members of society. Students are
going to be introduced with the topic of slope or change in y over (divided)
by change over x. This is traditionally known to be done specifically on a
coordinate plane with two or more points on the line. However, students
are unable to link slope and coordinate planes to when they may actually
use this in real life. I have a hard time finding a lot of examples to throw
back at them, one I have found is a roof pitch. A pitch to a house uses the
rise over run idea to establish the slope of the roof. If a roof has a 7/12
pitch, this means that the roof will have a slope that goes up 7 inches then
over 12 inches. If you were to plot these points on graph paper, then will
be the exact slope of your houses roof. If you go to areas where they have
harsher winters, the pitch to their house may have a steeper slope, such as
up 10 inches, over 7 inches. This will help to make the snow slide off the
roof in the winter.
Beth Hopta
I will begin this section by introducing slope on a coordinate plane. I will
have a line drawn on the coordinate plane and have students help me
choose two points that fall on the line, making sure that it hits the cross
hairs exactly. Once we have the two points chosen, students will be told to
label their x’s and label their y’s. Making sure they follow the format of how
a coordinate is put together, (x,y), domain first then range. Then students
will be asked to pick their 1’s and pick their 2’s, (x1, y1)(x2, y2). After
completing this, students will have to plug their numbers into the formula
and solve.
Formula for slope: y2-y1
x2-x1
Example coordinates to use. (2, 3) (4, 6)
Label X & Label Y: x= 2 y = 3, x = 4 y = 6
Pick your 1’s and pick your 2’s: x 1 = 2 y 1 = 3, x 2 = 4 y 2 = 6
Plug it into the equation: 6 – 3
4–2
Slope = 3/2 or rise 3, run (over to the right) 2
Students will complete two of their own problems on slope then the
following day students will draw a line on a graph paper when they are
given a coordinate to start from and the slope to follow. Students will
graph the line on graph paper and practice on this.
After students have a good understanding of slope, I will then introduce its
relationship to a roof pitch by showing pictures and asking them questions
about it. They will need to describe what they see and how it will relate to
Beth Hopta
class and what we were just doing. Once they start to see the relationship,
students will need to strap on their tool belts and get to carpentry class.
Here is our real world link: Roof pitch is SLOPE! When you are designing
your house you will have to determine what roof pitch you will need. I will
work through some pitch problems by drawing houses on graph paper and
determining what the pitch will be. After students are able to determine the
roof pitch, they will have to do a little bit of research to find out why a roofs
pitch may be as steep or as level as it may be. What factors determine it?
What weather conditions determine it? What were roofs made of in the
1800’s?
Once students feel comfortable finding roof pitch, they will be turned loose
on creating their blueprint of their house, fully equipped with a roof pitch.
Students will then have to explain how they came up with their roof pitch
and explain why they decided to make it the slope that it is.
This activity helps to get rid of the eluding question of when students will
use this. Students are always a little more willing to learning about
something they will have to know about forever.