CCSS-Math Learning Progressions

Transformation in the Plane HSG.CO.A

stephensmithcwu CCSS-Math Learning Progressions, HS Geometry

This learning progression will be taught in a sophomore level Geometry course at Ellensburg High School. The Common Core State Standard (CCSS) domain and cluster for this learning progression is: CCSS.MATH.CONTENT.HSG.CO.A. There are two standards that the students will be learning: HSG.CO.A.1 and HSG.CO.A.2, and HSG.CO.A.4. The math practices (MP) that will be used by students during this progression will be MP1, MP3, and MP5.

This learning progression will be broken into three separate lessons. The first lesson will cover HSG.CO.A.1 and HSG.CO.A.2. The second lesson will cover HSG.CO.A.4, but it will specifically address rotations and translations. The third lesson will also cover HSG.CO.A.4, but it will focus on reflections.

CCSS.MATH.CONTENT.HSG.CO.A

Experiment with transformations in the plane

HSG.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

HSG.CO.A.2

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

HSG.CO.A.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Link to the full learning progression: Transformation Learning Progression

Similarity Transformations using Dilation HSG.SRT.A

stephensmithcwu CCSS-Math Learning Progressions, HS Geometry

This learning progression is for a High School Geometry class. The Common Core State Standard (CCSS) domain and cluster for this learning progression is: CCSS.MATH.CONTENT.HSG.SRT.A. There are two standards that the students will be learning: HSG.SRT.A.1 and HSG.SRT.A.2. The math practices (MP) that will be used by students during this progression will be MP1, MP3, and MP5.

The textbook used in the class is McDougall Littell’s Geometry 10th edition. In teaching this learning progressions, we assume that students have a strong grasp of previous concepts required for learning similarity transformations. These concepts are HSG.CO.A.1, HSG.CO.A.2, HSG.CO.A.5, HSG.CO.B.6, and HSG.CO.C.9.

CCSS.MATH.CONTENT.HSG.SRT.A

Understand similarity in terms of similarity transformations

HSG.SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor:

HSG.SRT.A.1.A

A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

HSG.SRT.A.1.B

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

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.

Read the whole learning progression here: Dilation Learning Progression

HSF.TFA.A.1,2,&3 The Unit Circle

oaksjessica CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Functions

Image result for unit circle

Ideally this learning progression would take place in an Algebra II class. This learning progression focuses on exploring the Unit circle and understanding what a radian is. Throughout the progression the students will start by discovering what a radian is by creating a radian using paper and different circular objects. The students will then move into solving the unit circle using their new understanding of radians and their prior understanding of degree measurements. After the unit circle is complete the students will be able to use the unit circle to solve special triangles using trigonometric functions.

The Common Core State Standards aligned with the learning progression are:

HSF.TFA.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

HSF.TFA.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

HSF.TFA.A.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for p/3, p/4 and p/6, and use the unit circle to express the values of sine, cosine, and tangent for x, p+x, and 2p-x in terms of their values for x, where x is any real number.

The learning progression works towards these CCSS Mathematical Practices:

MP5: Use appropriate tools strategically.

MP6: Attend to precision.

MP7: Look for and make use of structure.

The learning Progression is attached here:

Learning Progression Unit Circle

Graphing Linear Equations A.REI

rodrigyur CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Algebra, HS Functions, HS Modeling, HS Number and Quantity

This learning progression is for a high school algebra class. In this unit, students will learn important concepts about graphing linear equations. In the first lesson,  students will learn about the different properties of a graph. For the second lesson, it will be broken down to two days. Students will check whether the set of ordered pairs are  solutions to both the equation and the graph. The next day,  students will be introduced to writing the equation as a function form. For the third lesson, students will  learn how to find the x-intercept and y-intercept  both algebraically and graphically.

The following Common Core State Standards will be satisfied in this unit:

The following Mathematical Practice will be satisfied:

Learning Progression is attached:

learning progression for edtpa

 

Experiment with transformations in the plane G.CO.A

camachoo Assessment of CCSS-Math, CCSS-Math Learning Progressions, HS Geometry

This learning progression is designed for a 10th grade Geometry Class. In this unit students learn about transformations in the plane such as translation, reflection, rotation and glade reflections. The CCSS are

CCSS.MATH.CONTENT.HSG.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CCSS.MATH.CONTENT.HSG.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. CCSS.MATH.CONTENT.HSG.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CCSS.MATH.CONTENT.HSG.CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another

To teach this material I use different teaching methods as well as different activities to elicit students learning. For example, I use modeling to work detail examples and give students a visual aid in the board. At the beginning of the lesson, I use a short warm up that helps students review the material learned in the previous lesson. During and after instruction, students also have the opportunity to work with others and ask questions.  To assess students learning, I use their responses to class discussions, questions, and answers to problems in different activities For summative assessment, in this learning progression students will show their knowledge by preforming the different transformations to a shape they select and writing explanations of the changes applied to the figure.

Complete learning progression here High School Geometry

Race Graph: 8.F.A.3, SSE.A.1.A, and SSE.B.3

soton CCSS-Math Learning Progressions, HS Algebra, Uncategorized

This learning progression was designed primarily for a bilingual slower pace 9th -12th-grade Algebra 1 course. This class consists of twenty students of who ten do not speak any English and need assistance in Spanish. Throughout this unit, the lessons were provided in 50% Spanish and 50% English as well as all handouts having written directions in both languages. Aside from this class being slow paced because of the language barrier for some students there is also students who struggle in understanding. Overall, this course consists of about 50% not being able to graduate on time as the class is made up of eleven ninth-graders, four tenth-graders, three eleventh-graders and two twelfth-graders. About 50% of the students in this course are anticipated not to graduate on time as their lack of understanding affects more than this course.
The Common Core State Standards that will be satisfied are from three different domains. The first one comes from the cluster titles, “Define, evaluate, and compare functions” and is 8. S.A.3. The second one is SSE.A.1. A and comes from cluster “Interpret the structure of expressions.” The third standard is SSE.B.3 coming from cluster “Write expressions in equivalent forms to solve problems.” In this course, students focus on mastering 8th grade standards as they slowly incorporate high school content standards. Throughout this learning progression, students will focus on four mathematical practices which are MP1, MP4, MP5, and MP6.

The central focus of this learning segment is for students to be able to analyze how the equation and the graph of a line are related. Students will represent a linear relationship as points on a coordinate plane and as an equation representing a line. Students will work towards this by learning how to solve a linear equation for y leading to them discovering slope-intercept form. In this form students, will identify the slope and y-intercept of a linear equation as well as on a graph. Once being able to identify the two pieces of information be able to quickly graph lines. As well as deepen their understanding of slope of a line by being able to explain how changes in the slope affect the steepness and direction of a line. The purpose of students being able to master these skills
is to deepen their understanding of graphing linear equations by providing a quicker method to graphing. Students will understand that making a T-chart or finding x and y-intercept can be time-consuming while using the slope-intercept form is more efficient. All this building their mathematical reasoning for the second unit which is the second half of the chapter which will focus on students exploring data to determine whether a linear relationship exists. They will be able to determine functions and work with modeling direct variation and find the slope and rate of change.

Full learning progression: edtpa Learning Progression

Lesson Plan: Algebra 1 EDTPA lesson plan

HSG.CO.A.5 Transformations

sargentca CCSS-Math Learning Progressions, Common Core State Standards Mathematics, Geometry Curriculum Aligned with CCSS-Math, HS Geometry

This learning progression focuses on the first half of a unit on Transformations in a high school Geometry class, consisting of mostly 9th and 10th graders. The first lesson will cover 7.1 Rigid Motion in a Plane, which will just briefly introduce the concepts of transformations and what each transformation means. The second lesson will cover 7.2 Reflections, and will give students a more in depth understanding of reflections, and how to use them to find coordinates in a plane. The third lesson covers 7.3 Rotations more in depth, and then for the final lesson in the learning progression, students will have a review to make sure they understand these concepts before moving on to the second half of the chapter.

 

CCSS Content Standards:

CCSS.MATH.CONTENT.HSG.CO.A.5

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g. graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

 

CCSS Mathematical Practice Standards:

CCSS.MATH.PRACTICE.MP1

Make sense of problems and perservere in solving them.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

 

Throughout this learning progression, students will be getting new notes in the first three lessons, while also working on practice problems and homework assignments in every lesson. I will be implementing a lot of group work during this learning progression, because it is helpful for students to compare their answers with peers so that they can work together to figure out the correct answers. For the last lesson, they will do an activity for the review, where they are put in groups, and rotating through different stations that will be focusing on the main ideas from each concept. I will be giving them entry tasks daily as their formative assessments in this learning progression to check their understanding, along with checking their homework assignments, and going over the most missed problems so that they can see common errors.

The full learning progression is attached here: edTPA Learning Progression

Solving Linear Systems of Equations: HSA.REI.C.5 and HSA.REI.C.6

berserc CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Algebra

This learning progression was created for a 9th grade Algebra 1 class. It is supported by the textbook, “Algebra 1: Applications, Equations, Graphs,” by Larson, Boswell, Kanold, and Stiff. The progression follows chapter 7, sections 1-3 in the text. The main focus of this progression is to teach students how to solve systems of linear equations by graphing, substitution, and combination.

Common Core State Standard:

CCSS.MATH.CONTENT.HSA.REI.C.5: 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.

CCSS.MATH.CONTENT.HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Common Core Mathematical Practices:

MP1: Make sense of problems and persevere in solving them

MP2: Reason abstractly and quantitatively

MP6: Practice attention to precision

 

Learning Progression Systems

Rational Expressions A.APR.D and A.REI.A

schloemerj CCSS-Math Learning Progressions, HS Algebra

This learning progression is for an Algebra II class. The vast majority of the students are juniors but there are students of all grade levels. The lessons most generally use worksheets from Kuta Software to help facilitate the learning of the students; however, the class does have the Holt McDougal, Common Core Edition from 2012 that they use every now and again as the math department usually collaborates and creates their lesson plans with math tasks and activities to help engage the students. For this learning progression the students will be learning how to simplify rational expressions, multiply and divide rational expression, add and subtract rational expressions, solve rational equations, and solve radical equations. The standards that are applied to this unit plan are:

  • MATH.CONTENT.HSA.APR.D.6

Rewrite simple rational expressions in different forms

  • MATH.CONTENT.HSA.REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

The Mathematical Practice Standards that are applied to this unit are as follows:

  • MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them
  • MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
  • MATH.PRACTICE.MP6: Attend to precision.
  • MATH.PRACTICE.MP7: Look for and make use of structure.

A teaching strategy that will be used during this learning progression is group work and collaboration. Students will be able to work in groups in order to work in groups of three or four. In a classroom set up such as this, the teacher will be able to facilitate to more students throughout the class period and guide the lesson rather than use direct instruction. The teacher will continuously monitor the students and listen in on the group conversations to hear where the students tend to be struggling and to answer questions that the students might have. The only thing that the students will be doing separately will be the five-minute exit slip at the end of class; these will not be used every class period as students might be doing an engaging activity or they may be having a lot of group conversation which I will be able to listen in on an gauge the students’ understanding.

To view the full edTPA Learning Progression please view it here.

HSA.REI.B.4.A&B Solving Quadratic Equations

sargentca CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Algebra

This learning progression focuses on Solving Quadratic Equations using multiple methods including by inspection, taking square roots, completing the square, the quadratic formula, and factoring. This learning progression would be taught in a high school Algebra I class, consisting of mostly freshmen. In the first lesson students will be learning these methods and when to use each one of the methods, and thought the next two lessons they will be reviewing all of these methods and getting more practice on them during the activities planned for each of the following two lessons.

CCSS Content Standards:

CCSS.MATH.CONTENT.HSA.REI.B.4.A

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

CCSS.MATH.CONTENT.HSA.REI.B.4.B

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

CCSS Mathematical Practice Standards:

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP8

Look for and express regularity in repeated reasoning.

 

The learning progression is attached here:

sargent_learningprogression