# Slopes of Parallel and Perpendicular Lines HSG.GPE.B.5

This learning progression is based on the students being able find the slopes of lines and determine if two lines are parallel or perpendicular based on their slopes. It a compilation of three math tasks that will help students understand how to find the slope of a line, classify lines as parallel or perpendicular, and writing equations in slope intercept and point slope forms.

Students will use the slope formula to find the slope a line that is graphed as well as find the slope of a line when two points for a line are given.

• MATH.CONTENT.HSG.GPE.B.5– Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Students will be using the slopes of two different lines to determine if they are parallel or perpendicular. They will recognize that parallel lines have the same slope and slopes for perpendicular lines are opposite reciprocals.

• MATH.CONTENT.HSG.CO.C.9– Prove theorems about lines and angles.

Students will learn to write equations in point slope form and slope intercept form. They will use the information from these equations, as well as knowledge from the previous tasks to graph lines.

• MATH.CONTENT.HSS.ID.C.7– Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Formative assessment in the form of observation and discussion will be the primary procedure to support student learning. I will observe how they are finding solutions and ask them questions about their understanding of the learning targets.  At the end of each task students will be given a handout, which will also show how well they are able to meet the learning targets.

Slopes of Parallel and Perpendicular Lines Learning Progression

# Proportion and Similarity HSG.SRT.A.2

This learning progression is provided to support student’s understanding of ratios and proportionality in relation to similar figures. There is a series of three consecutive math tasks that will be completed by students to help guide them through using ratios and proportions to prove figures are similar.

Students will use their knowledge of algebra to express proper ratios and simplify them correctly. They will also be using the cross product of ratios to solve the proportions.

• MATH.CONTENT.HSA.SSE.B.3-Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Students will identify congruent angles and corresponding sides of a polygon so they can find the similarity ratio. Once they do this, they will be able to recognize the sides and angles that are proportional and determine if polygons are similar.

• MATH.CONTENT.HSG.SRT.A.2-Given two figures, use the definition of
similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Students will use triangle similarity theorems to show how congruent angles and corresponding sides that are proportional determine if triangles are similar.

• MATH.CONTENT.HSG.SRT.A.3-Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Formative assessment in the form of observation and discussion will be the primary procedure to support student learning. I will observe how they are finding solutions and ask them questions about their understanding of the learning targets.  At the end of each task students will be given a handout, which will also show how well they are able to meet the learning targets.

Proportion and Similarity Learning Progression

# Trigonometry Ratios G.SRT

This learning progression will take place at a 9th grade Algebra 1 classroom. The class is consisted of 32 students where the students have an individual sitting arrangements. This allows the students to work on their own and makes it easy to work with a partner as well. The book use for this class is “Geometry: Integration, Applications, and Connections” by Glencoe and McGraw-Hill. The lesson will cover chapter 8: Applying Right Triangles and Trigonometry but will focus on using sine, cosine, and tangent ratios in order to solve/find the sides and angles of a right triangle.

CCSS.Math:

1.) CCSS.Math.G-SRT.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

2.) CCSS.Math.G-SRT 7

Explain and use the relationship between the sine and cosine of complementary angles.

3.) CCSS.Math.G-SRT.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Learning Progression Trigonometry Ratios-1fej0wt

# Exponential Decay Functions F.LE

The learning progression will be based upon Exponential Decay Functions where the students will be able to understand the properties and used it to solve real-life problems. At this point, the students have prior knowledge of solving Exponential Growth Functions and will be able to build upon that knowledge and use it to understand how Exponential Decay Functions work. The CCSS.Math standards that are align with the learning progression are:

1. Math.HSF-LE.A.1: Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.
2. Math.HSF-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

3. Math.HSF-LE.B.2: Interpret the parameters in a linear or exponential function in terms of a context.

Learning Progression for Practice edTPA-1lavusr

# Statistical Reasoning – S

This learning progression will be taught to a class that consists of juniors and seniors in high school who are currently taking a college course that is taught at their high school, Math 102: Mathematical Decision Making.  The Common Core State Standards (CCSS) that will be addressed come from one domain, High School: Statistics and Probability. The CCSS clusters that will be addressed are “Make inferences and justify conclusion from sample surveys, experiments, and observational studies” and “Use probability to evaluate outcomes of decisions.”  Students will also meet Mathematical Practices 3, 5, and 7.

The central focus of this learning progression is on an introduction to statistical reasoning and the aspects of a study that may produce biased results.  The progression begins with an overview of what statistical studies are and the process that someone must go through to create one.  These foundational concepts will give the background knowledge that they will need to use throughout the remainder of the learning progression.  The students will then learn about some different types of studies and how to avoid bias while creating a study.  In the third task of this progression, the students will use all of these ideas to find their own methods of testing the validity of a study’s results.  At the end of the progression, the students will be asked to design their own study and will work on conducting this study as a project that will be added on to over time.  After completing this learning progression the students will learn how to analyze data and how to represent it graphically to be able to use the results of a study to make decisions with.  The beginning steps of this project will be the students’ assessment.

Learning Progression-Statistical Reasoning-23fwc65

# Exponential Growth and Decay Models F.LE.A

Learning Progression edTPA
High School: Algebra with Trigonometry
EXPONENTIAL GROWTH AND DECAY
The class I will be teaching is an algebra class with
trigonometry. The textbook used will be Algebra 2:
Equations, Graphs, applications by Ron Larson, Laurie
Boswell, Timothy D. Kanold, and Lee Stiff, published 2004
by McDougal Littell. This learning progression will follow
the student through meeting the Common Core State
Standards about exponential growth and decay. These
Common Core State Standards will be covered in chapter
8 of the textbook, sections 1 and 2. These sections cover
exponential growth and decay models. That is, to be able
to create an equation, graph it, and solve problems with
exponential models. The standards for these lessons will
cover the cluster involving exponential functions,
including HSF.LE.A.1.C, HSF.LE.A.3, and HSF. LE.B.5. The
math practices that are going to be used throughout the
learning progression are as follows: MP2, MP3 and MP4.
These lessons will span three days. The exponential
growth model lessons will take the first two days and the
exponential decay model lesson will take the third day.
On the fourth day, the students will have a worksheet
with practice problems covering 8.1 and 8.2. This gives
the students a chance to show me how well they are
understanding the material because I will collect the
worksheet at the end of class and will use it to see how
the students are doing. I can assess what they
understand and what I need to cover again.

CCSS.Math.Content.HSF.LE.A.1.C:
which is about modeling exponential
functions and interpreting situations that
need to be solved with an exponential model.
CCSS.Math.Content.HSF.LE.A.3:
Observe using graphs and tables that a
quantity increasing exponentially eventually
exceeds a quantity increasing linearly,
quadratically, or (more generally) as a
polynomial function.
CCSS.Math.Content.HSF.LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a context.
COMMON CORE STATE STANDARDS
MATHEMATICAL PRACTICES
CCSS.Math.Practice.MP2:
Reason abstractly and quantitatively
CCSS.Math.Practice.MP3:
Construct viable arguments and critique the
reasoning of others.
CCSS.Math.Practice.MP4:
Model with mathematics.

Lesson 8.1 Exponential Growth Day 1
This lesson is the first day of a two-day lesson on
exponential growth model. Day-one is an introductory
lesson to the concept. I will start the lesson off by asking the
students what they remember from the prior year about
exponential growth. The students would have been
introduced to the concept in their algebra 1 course with a
very basic overview of the concept. I will then give the
students the equation for exponential growth for them to
get in their notes. The equation is y=bx where b>1 to create
a growth equation. I will tell the students that if the b is less
than 1 this is a decay function which we will get to later in
the chapter. I will also define an asymptote as it relates to
the graph, that is a horizontal asymptote on the x-axis or
y=0. I will then give the students four example problems in
which we will go through graphing together. Once I will as
though the students understand how to graph exponential
growth, I will show them a more complex equation which
includes transformations. They will now have the equation
y=abx-h+k where a represents stretching and shrinking, h is
the shift left or right and k is the shift up and down. I will
then give the students one equation to graph on their own
using transformations.
After we have completed the notes for this section, I will
move to a class activity. I will post graph paper sticky notes
on the front board with exponential equations on the top of
each paper. The students will come to the front of the class
and pick a sticky note and graph it individually, which is
modeling or MP4. They will put their names on the back and
post them back on the board when they are finished. They
will then look over other answers that have been posted. If
the students have and questions or comments, they can
look at the name on the back and find the person to discuss
the answer. The students will then have to explain their
answer and their thinking which will create great
conversations about the concepts, thus using MP3 in this
activity.

Learning Targets:
I know about the exponential growth
model.
I can graph exponential growth
equations
Common Core State Standard:
CCSS.Math.Content.HSF.LE.A.1.C:
which is about modeling exponential
functions and interpreting situations
that need to be solved with an
exponential model.
CCSS.Math.Content.HSF.LE.A.3:
Observe using graphs and tables that a
quantity increasing exponentially
eventually exceeds a quantity increasing
linearly, quadratically, or (more
generally) as a polynomial function.
CCSS.Math.Practice.MP3:
Construct viable arguments and critique
the reasoning of others.
CCSS.Math.Practice.MP4:
Model with mathematics.

Lesson 8.1 Exponential Growth Models Day 2
This lesson is the second day of exponential growth model.
On day two, we will be working with applying the growth
model to word problems. I will be giving the students a new
formula they can use for application problems to create a
function as it relates to each word problem. The new growth
model is y=a(1+r)t where a is the initial amount, r is the
growth percentage as a decimal, t is the time, and y is the
end amount. I will also explain to the students that the
quantity (1+r) is known as the growth factor. After discussing
these notes, we will move to example problems to apply the
concepts. I will give the students a word problem and have
them tell me what information goes where in the formula.
Then once we have created a function, I will have them
graph it and have them solve for an end amount after a
given time. We will do this again with another problem to
practice. I will then ask the students how they are feeling
about the material by giving me a thumbs-up, thumbs-down,
or thumbs-sideways depending on how they feel. If the
students still seem to struggle with the concept, we will go
over another problem. If the students are understanding the
concepts then we will move to an activity.
For the activity for this lesson, I will write five different
exponential growth model functions on the board. The students
will choose one then graph the function and create a real-world
problem from the equation. The students will need to come up
with a scenario that will match the function. This will use MP4 for
the graphing and modeling and MP2 for reasoning abstractly and
creating a scenario from the equation. Once the students have
their scenario, they will share their word problem with their
neighbor and the neighbor must guess which function matches
the scenario. For example, student 1 and student 2 are paired up.
The students swap scenarios with the function covered or hidden.
Student 1 must guess which function student 2 choose and
explain their thinking, then they will repeat this with student 1’s
scenario. If either of them gets it wrong, they must guess again.
This gives the students a chance to show their understanding or
where they struggle. The students can help each other verify if
their answers are right and create great mathematic
conversations about exponential growth models.

Learning Targets:
I know about the exponential growth
model.
I can use the model to solve application
problems.
Common Core State Standard:
CCSS.Math.Content.HSF.LE.A.1.C:
which is about modeling exponential
functions and interpreting situations
that need to be solved with an
exponential model.
CCSS.Math.Content.HSF.LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a
context.
CCSS.Math.Practice.MP2:
Reason abstractly and quantitatively
CCSS.Math.Practice.MP4:
Model with mathematics.

Lesson 8.2 Exponential Decay
For the final lesson in this learning progression, we will be
covering exponential decay. I will remind the students about
when I briefly mentioned how decay relates to growth on
the first day. I will ask the students to remind me of the
exponential function we used on the first day with the
transformations, which is y=ab(x-h)+k. I will then ask the
students to define each term in their own words. This gives
me a chance to assess whether or not the students were
taking notes and understanding the material. By having
them put it in their own words, it forces the students to
show an understanding of the concept rather than just
reading from their notes. I will also remind them that for the
function to be a decay model rather than a growth model,
the b value must be between 0 and 1. If the b value is above
1, we will have an exponential growth model. I will also
discuss the long term for the graph, as the t value gets large,
then the end amount or y value will get closer and closer to
zero but will never be zero, therefore having an asymptote
at y=0 or the x-axis. As long as the students do not have any
questions about this equation, we will move onto doing
some practice problems of graphing three different
functions with the same b value of ½ but each has different
transformations.
Once we are done graphing each example, I will ask the
students to remind me of the exponential growth model
they had learned the day before, which was y=a(1+r)t. For
decay the equation is nearly the same except the growth
factor is now a decay factor and is 1-r instead of 1+r,
therefore making the quantity less than 1. All the terms are
the same as in the growth model, however the r value is
now a decay rate as a decimal instead of a growth rate.
Thus, the decay model being y=a(1-r)t.
After comparing the growth model to the decay model, I will
give the students a class activity. I will give the students a
word problem to apply the decay model to. This will be a
three-part problem where they will write the decay model
based on the problem, then graph the model, and finally solve for the end value after 3 years.
Students will work on this individually then discuss it with their neighbor once most people are
done. Once everybody seems to be done discussing the problem, I will give them the answer to
the end value after three years to check their work. If they got this correct then their decay
model should be correct and they should be able to find this point on their graph is they look at
what the value of y is when x is 3. This allows the students to check their work without me
going over each part and giving them all the answers.

Learning Targets:
I can graph the exponential decay
function.
I can solve problems using the
exponential decay functions.
Common Core State Standard:
CCSS.Math.Content.HSF.LE.A.1.C:
which is about modeling exponential
functions and interpreting situations
that need to be solved with an
exponential model.
CCSS.Math.Content.HSF.LE.A.3:
Observe using graphs and tables that a
quantity increasing exponentially
eventually exceeds a quantity increasing
linearly, quadratically, or (more
generally) as a polynomial function.
CCSS.Math.Content.HSF.LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a
context.
CCSS.Math.Practice.MP3:
Construct viable arguments and critique
the reasoning of others.
CCSS.Math.Practice.MP4:
Model with mathematics.

# Triangle Similarity G.SRT.B

High School: Geometry
SIMILARITY WITH TRIANGLES
The class I will be teaching will be a 9th grade high school
Geometry class. The textbook used will be Geometry:
Integration, Application, Connection by Glencoe and McGraw-
Hill Companies published in 2001. This learning progression
will follow the student through meeting the Common Core
State Standards about proving theorems involving similarities
with triangles. These Common Core State Standards will be
covered in chapter 7 of the textbook, sections 3, 4, and 5. The
Standards for this learning progression will be the cluster
involving proving theorems involving similarity, which are
CCSS.Math.Content.HSG.SRT.B.4 and
CCSS.Math.Content.HSG.SRT.B.5. The math practices that are
going to be used throughout the learning progression are as
follows: MP3, MP4 and MP5.
CCSS.Math.Content.HSG.SRT.B.4:
Prove theorems about triangles. Theorems
include: a line parallel to one side of a
triangle divides the other two proportionally,
and conversely.
CCSS.Math.Content.HSG.SRT.B.5:
Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures.
COMMON CORE STATE STANDARDS
MATHEMATICAL PRACTICES
CCSS.Math.Practice.MP3:
Construct viable arguments and critique the
reasoning of others.
CCSS.Math.Practice.MP4:
Model with mathematics.
CCSS.Math.Practice.MP5:
Use appropriate tools strategically.

Lesson 7-3 Identifying Similar Triangles
For this lesson I will start out by putting a picture under the
document camera of the pyramids in Egypt and explain how
Greek mathematician Thales used geometry for the first
time to solve for the height of the Great Pyramids. I will
write the hinge question on the white board on the side for
the students to consider throughout the lesson. The
students should be able to answer the hinge question by the
end of the lesson. The CCSS covered in this lesson is the first
part of the math standard HSG.SRT.B.5 about solving
problems for triangles with similarity and congruence.
I will follow the introduction with notes for the class in
which I will go through some example of the concepts under
the document camera for the student to copy down. I will
go through three similarities and examples for each to show
the students how they can use the similarity to solve
problems. The similarities are angle-angle (AA), side-sideside
(SSS), and side-angle-side (SAS). While going through
examples, I will be very student involved and ask students
questions as often as possible to have them solving the
problems with me. Once we have finished that, I will ask the
student if they have any questions on anything we have
done so far.
Next, we will do a hand on activity. The students will need a
ruler and protractor. Since the students will be using the
tools and drawing the triangles they will be using MP4 and
MP5. The students will draw a triangle and measure all the
sides of the triangle. They will then draw another triangle
with a scale factor of ½ of 2. They measure the angles of the
triangles to compare. They will answer the questions: Are
these triangles similar? Why? Which triangle similarity is
this? Answer: Since the sides are proportionate the triangles
are similar and this is the SSS similarity. The students
checked their answer by measuring the angles which could
be AA similarity. The students will be assigned homework in
which some problems will be basic problems directly using
the formulas while some of the problems will be real world
problems where the students will have to apply the material
and make connections to solve the problem. Therefore,
being able to answer the hinge question.
Hinge Question:
How can you use similar triangles to
solve problems?
Common Core State Standard:
CCSS.Math.Content.HSG.SRT.B.5:
Use congruence and similarity criteria
for triangles to solve problems and to
prove relationships in geometric
figures.
Angle-Angle (AA) Similarity:
If two angles of one triangle are
congruent to two angles of another
triangle, then the triangles are similar.
Side-Side-Side (SSS) Similarity:
If the measures of the corresponding
sides of two triangles are proportional,
then the triangles are similar.
Side-Angle-Side (SAS) Similarity:
If the measures of two sides of a
triangle are proportional to the
measures of two corresponding sides of
another triangle and the included
angles are congruent, then the triangles
are similar.
CCSS.Math.Practice.MP4:
Model with mathematics.
CCSS.Math.Practice.MP5:
Use appropriate tools strategically.

Lesson 7-4 Parallel Lines and Proportional Parts
I will start this activity with a warm-up related to the last
activity. I will give the students two triangles with two sides
labeled and the angle between the sides labeled as well. The
students will have to show these are similar triangles using
SAS similarity. This will be used as a way to review the
material from the day before.
I will then move onto the new material. The students will
have to prove the two theorems, 7-4 and 7-5. Similar to the
last lesson, I will walk the students through the proofs for
the theorems under the document camera. I will ask
questions to get the students involved in the proofs and
have them assisting me to solve the proof. Once the proofs
are done, I will make sure the students understand the
material and see if anybody has any questions.
I will use the rest of the class to give the students an activity.
Prior to class, I will print out an assortment of triangles with
lines through them, some parallel and some not. The
students will use rulers and protractors to make
measurements based on the theorems to determine if the
line is parallel or not. The students will put their name on
the back and tape it to the board. Once everybody has done
one problem and taped it to the front, then the students will
look at other students’ answers and discuss each other’s
answers and critique their answers and give reasons, which
is using the practice MP3.
Again, the students will be given practice problems for
homework in which some of them will be simple while
others are more challenging and will cause the students to
need to make connections and apply the concepts.
Hinge Question:
Are these lines parallel?
Common Core State Standard:
CCSS.Math.Content.HSG.SRT.B.4:
Prove theorems about triangles.
Theorems include: a line parallel to one
side of a triangle divides the other two
proportionally, and conversely.
Theorem 7-4:
If a line is parallel to one side of a
triangle and intersects the other two
sides in two distinct points, then it
separates these sides into segments of
proportional lengths.
Theorem 7-5:
If a line intersects two sides of a triangle
and separates the sides into
corresponding segments of
proportional lengths, then the line is
parallel to the third side.
CCSS.Math.Practice.MP3:
Construct viable arguments and critique
the reasoning of others.

Lesson 7-5
This lesson, I will start with a warm-up from the first lesson. I
will give the students two triangles with different sides and
angles labeled as it relates to each similarity. The warm up
will have three problems each about one of the following
similarities: AA, SSS, SAS. I will then have a follow up
question to solve for the other side using proportions. The
CCSS covered by this lesson is the second part of
HSG.SRT.B.5 about proving relationships in triangles from
similarity.
I will use the warm up to move into the new concepts. In
this lesson, the students will learn about four theorems
which come from triangle similarity. Like the other lessons, I
will use the document camera to guide the students through
examples for each theorem. We will go through the
theorems 7-7, 7-8, 7-9, and 7-10 as listed on the right. I will
go over one example for each theorem and when I am
finished I will see if the students have any questions about
any of the material covered.
We will then move to an activity where the students will
have a chance to model the concepts in a problem. The
students will use a ruler to make a diagram for the problem
45 on page 376 of the book. Two similar triangular jogging
paths are laid out in a park with one path inside the other.
The dimensions of the inner path are 300, 350, and 550
meters. The shortest side of the outer path is 600 meters.
Will a jogger on the inner path run half as far as the one on
the outer path? Explain. The students will be allowed to
work with their neighbor on this problem but they are not
allowed to move around the room. This give the students
the chance to use math practices MP4 and MP5 by using a
ruler to move the problem. The students will turn this in at
the end of class.
For the students’ homework this time they will be given a
take home quiz. There will be three matching problems to
start for the similarities AA, SSS, and SAS with three pairs of triangles and different sides or angles labeled. The next section will have theorems 7-4 and 7-5
and the students will need to show an example for each like we did in class. The final section
will have two triangles and the students will need to explain two of the theorems from today’s
lesson, that is theorems 7-7,7-8,7-9, and 7-10. This should be an easy take home quiz if the
students took notes. They will not be allowed to use the same examples as in class so they will
be showing they understand the notes.
Hinge Question:
What can similar triangles tell us about
other characteristics of the triangle?
Common Core State Standard:
CCSS.Math.Content.HSG.SRT.B.5:
Use congruence and similarity criteria
for triangles to solve problems and to
prove relationships in geometric figures.
Theorem 7-7
If two triangles are similar, then the
perimeters are proportional to the
measures of corresponding sides.
Theorem 7-8
If two triangles are similar, then the
measures of corresponding altitude are
proportional to the measures of the
corresponding sides.
Theorem 7-9
If two triangles are similar, then the
measures of corresponding angle
bisectors of the triangles are
proportional to the measures of the
corresponding sides.
Theorem 7-10
If two triangles are similar, then the
measures of corresponding medians are
proportional to the measures of the
corresponding sides.
CCSS.Math.Practice.MP4:
Model with mathematics.
CCSS.Math.Practice.MP5:
Use appropriate tools strategically.

# Solving Systems of Equations HSA.REI.C

This learning progression will be taught in a high school algebra I class. It is about solving for systems of equations and then being able to interpret the answer that you can get out. The Common Core State Standards (CCSS) domain and cluster for this learning progression is CCSS.MATH.CONTENT.HSA.REI.C.  The main standard that the students are learning is HSA.REI.C.6.

This is based on the McDougall Litell Algebra I book. And while teaching this lesson, we assume the students have worked with general graphs and equations before. They also will have looked at systems and used the graph to find the intersection.

edTPA Learning Progression-1tb37qc

# Solving for Areas 7.G.A

This learning progression is based on the concepts of area. There are three math tasks the students will need to perform: an entry task related to a real world problem, a walk around activity, and an exit task related to the entry task. The walk around activity involves the entire class getting up and moving around the room to solve problems posted on the walls. This is one way to get the students to stretch their legs while also keeping them actively engaged in the lesson. There will be twelve problems posted on the walls around the room and the students will choose eight to solve. The idea of having the students choose which problems to do gives them the sense of freedom within their own education. The CCSS-Math that align with this learning progression are as follows:

7.G.A.1 Geometry: Draw, construct, and describe geometrical figures and describe the relationship between them.

• The students will be finding areas and demonstrating their knowledge of the different shapes used throughout the unit.

HSG-GPE.B.7 Expressing Geometric Properties with Equations: Use coordinates to prove simple geometric theorems algebraically.

• During lesson 6.7, there will be a couple problems where the students need to use the distance formula to algebraically solve for one side of a shape in the coordinate plane.

HSG-SRT.B.4 Similarity, Right Triangles, & Trigonometry: Prove theorems involving similarity.

During the lesson about areas, 6.7, the students will need to use the Pythagorean Theorem to solve for the height of triangles.

Learning Progression

# Choose your own Adventure! Solving Systems of Linear Equations. A.REI.C

This learning progression is an approach to teaching how to solve systems of linear equations by graphing, combination, and substitution in a student-lead learning environment.

Standards: The Common Core State Standards that will be satisfied are from the High School Algebra: Reasoning with Equations and Inequalities cluster. We will cover CCSS.MATH.CONTENT.HSA.REI.C.6 solving systems of linear equations exactly and approximately. We will also prove that given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions with standard CCSS.MATH.CONTENT.HSA.REI.C.5. In this course, students focus on mastering basic algebra knowledge that is required by the state, while integrating in common core standards and mathematical practices. In this learning progression the students will use four mathematical practices including: MP4, MP5, and MP7.

Algebra I learning progression-1egtu8b

Learning Progression Winter 2018-1ozkjgh