# 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

# 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

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

# Fun in the sun with converting Percents, Decimals, and Fractions CCSS.MATH.CONTENT.4.NF.C.5

My learning progression is on converting percents, decimals, and fractions. It will lead to comparing ratios and using fractions and percents for ratio lengths. I will cover how to convert from percent to decimal to fraction and vise versa. I will start off with a hinge question then go in with my lesson. I plan to have the students in groups of four and they will be handed a worksheet of conversion.

learning progression percents edtpa-12sg8wn

# How to Introduce Complex Numbers N.CN.A

High School:  Algebra 2

Complex Numbers

This learning progression will be taught to a class that consists of sophomores and juniors in high school who are currently taking Algebra 2.  The Common Core State Standards that will be addressed come from two different domains.  The first domain is from High School:  Algebra-Arithmetic with Polynomials and Rational Expressions.  The CCSS Math cluster that will be addressed is “Understand the relationship between zeros and factors of polynomials.”  The second domain is High School: Number and Quantity-The Complex Number System.  The CCSS Math clusters that will be addressed are “Perform arithmetic operations with complex numbers,” “Represent complex numbers and their operations on the complex plane,” and “Use complex numbers in polynomial identities and equations.”  The third domain is from High School: Number and Quantity-The Real Number System.  The cluster that will be addressed is “Extend the properties of exponents to rational exponents.”  Students will also meet Mathematical Practices 1, 2, 3, 7, and 8.

The textbook that I will use as a resource is Glencoe’s Algebra 2:  Integration, Applications, and Connections.  The lesson will be taught from sections eight through ten of chapter five of this book.  These sections transition students from simplifying expressions including radicals and rational exponents to simplifying expressions containing numbers that are a part of the complex plane.

The central focus of this learning progression is an introduction to complex numbers and the complex plane.    The progression begins with the strategies that are used in simplifying expressions involving radicals.  These strategies will help student s understand how to use complex numbers and how to simplify expressions that contain complex numbers.   Students will be first introduced to what a complex number is and will then learn how to graph them in the complex plane.  The purpose of this learning progression is for students to gain a better conceptual understanding of the complex plane and will lead into solving quadratic equations that do not have real solutions.  This progression is set up so that the entry tasks from each section review a concept or ask students to think critically about a problem that will help them understand the new information that will be taught during the lesson.  How students do on this introductory information will influence where each lesson begins.  This will then influence how far we get in the planned lesson and so the next day’s lesson will also be affected.  Each lesson has been set up to be flexible and to run off of the previous lesson.  Beginning the class with questions that lead students to recall information that they have previously learned and to explore a new way of thinking will help students be more successful during the remainder of the class period and will help students become more interested in what they are learning.  Kubiszyn and Borich state in the book Educational Testing and Measurement that by imbedding a formative assessment into each lesson, “well-constructed performance test can serve as a reaching activity as well as an assessment.  This type of assessment provides immediate feedback on how learners are performing, reinforces hands-on teaching and learning…it moves the instruction toward higher order behavior.”

Common Core State Standards

Extend the properties of exponents to rational exponents.

CCSS.MATH.CONTENT.HSN.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Perform arithmetic operations with complex numbers.

CCSS.MATH.CONTENT.HSN.CN.A.1
Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.

CCSS.MATH.CONTENT.HSN.CN.A.2
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CCSS.MATH.CONTENT.HSN.CN.A.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Mathematical Practices

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8  Look for and express regularity in repeated reasoning.

Learning Progression

Learning Progression-Complex Numbers-164vuer

# Fun with Multiplying Binomials CCSS.MATH.CONTENT.HSA.SSE.A.1

This learning progression is made to take place in a high school Algebra classroom of 25 students. This class consists of freshman and sophomores. The desks in the classroom are arranged in groups of four. The lesson is based off the Algebra I textbook. The students have prior knowledge of binomials and what they look like and prior knowledge on the GCF.
learning progression-tt6ir7

# Learning Progression for: Reason quantitatively and use units to solve problems.

This learning progression was designed primarily for a 9th grade algebra course. The three Common Core State Standards that this learning progression will be satisfying are from the cluster titled “Reason quantitatively and use units to solve problems,” these are HSN-Q.A.1, HSN-Q.A.2 and HSN-Q.A.3. In this course, students are focusing on mastering the Common Core State standards for Algebra. Throughout this learning progression, students will focus on three mathematical practices which are MP2, MP4, and MP6.

There are three instructional tasks/activities included in this learning progression. Each one was provided by Illustrative Mathematics.

The following is an excerpt from the learning progression regarding the task “Fuel Efficiency”

Learning Target:

I can use unit conversions and proportions to determine fuel efficiency.

Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are comparing how fuel efficient the two cars are. Sadie tells Nanette that her family’s car is getting 42 miles per gallon. Nanette has no idea how that compares to her family’s car because in Germany mileage is measured differently. She tells Sadie that her family’s car uses 6 liters per 100 km. Which car is more fuel efficient?

Guiding questions:

Are the two mileages given in the same form? (no, our task says they aren’t)

When we say 42 miles per gallon this is an example of a (rate)?

How should we set up the problem? (use proportions)

____________________________________________________

At the end of the unit the students will do a project for the summative assessment. The students will be told to look through newspapers and magazines and collect 2 examples of situations to be expressed algebraically.  They are then supposed to come up with the algebraic expression that accompanies each. They must also write up what each variable represents, what quantities are involved and what units are being used.

Combined Learning Progression and Formative Assessment

# Systems of Inequalities Assessment A.REI.D

System of inequalities (CCSS.Math.Content.HSA.REI.D.12)

Alignment to Content Standards

Alignment: CCSS.Math.Content.HSA.REI.D.12

Alignment: CCSS.Math.Content.HSA.REI.D.10

Find the system of inequalities for the graph below. Write the inequalities in slope-intercept form.

Then, determine if the following points are in the solution set of the system of inequalities:

(0,0), (1,1), (-1,1).

Commentary

The purpose of this assignment is to assess whether the students understand systems of linear inequalities and the solution set. In this task, the students will be working with two major skills. They will be creating equations for two inequalities in two variables for a system of equations from a graph. The students will also be determining if a point satisfies the solution set from the system of inequalities. The students will have to have a full understanding of the concept to be able to complete this assessment since the students are given the solution and must work backward to find the system that satisfies the solution.

Solution

The first step to completing this assignment, the students must first create inequality equations for each line. Since the assignment says the equations must be in slope-intercept form, the student can use the plotted points to calculate the slope and find the y-intercept for each then create the formula for the equation. They must then choose a point in the solution set, that is the shaded region, and plug that into their equations and choose the correct inequality symbol to create a true statement.

For the purple line, the slope is -3 and the y-intercept is 1; therefore, the equation for the line is y=-3x+1. Then by putting a point into the equation that is in the solution region and simplifying, we can find the correct inequality symbol. For this one I put in the origin point, (0,0) and simplified.

0 ? -3*0 + 1

0 ? 1, 0 ≤ 1

Therefore, the inequality should read y ≤ -3x + 1. The inequality has the equal to part since the line is a solid line and not a dashed line. If it was dashed then the symbol would only be less then, <.

For the blue line, the slope is 2 and the y-intercept is 4; hence, the equation for the line is y=2x+4. Similarly to the purple line, by putting in the origin, (0,0), which is a point in the solution shaded region, we can find which inequality symbol to use.

0 ? 2*0 + 4

0 ? 4, 0 ≤ 4

Thus, inequality is y ≤ 2x + 4. Again, since this line is solid the symbol contains the equal to part as well as the less then, <.

Finally, the student need to determine if the three points are in the systems solution set or not. The students can do this in two different ways. They can either look on the graph and see if the point is in the shaded region then it is in the solution set. Or the students can put the point into both equations and see if the statement is true for both inequalities. If the point creates a true statement for both, then the point is in the systems solution set. Therefore, (0,0) and (-1,1) are in the systems solution set and (1,1) is not.