Author: stephensmithcwu

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

The Path To Simple Savings HSA.REI.D.11

stephensmithcwu Common Core State Standards Mathematics, HS Algebra, HS Modeling

Image result for dollar sign

Student engagement is key when creating lessons. This lesson revolves around modeling for savings, which is a great source of engagement for students. Using the lesson plan provided, students will create models, using a graphing calculator or desmos.com, based on simple interest savings scenarios. Students can then apply these concepts to everyday life.

Click to view this lesson plan: Interest Modeling

Just How Strong is Gravity? HSF.IF.C.8.B

Quote stephensmithcwu Common Core State Standards Mathematics, HS Algebra, HS Functions, HS Modeling

Do you ever wonder just how strong gravity actually is? What is this invisible force that is holding all of us down? Does gravity affect all object equally? These questions and more can be answered with an engaging classroom activity.

For this lesson,  we will use a vernier motion detector to model the effect of gravity on various objects. Product image for Calculator-Based Ranger 2

The objects used will be dropped from a specific distance away from the probe and the data collected will be used to help estimate for the force of gravity. Students will be broken up into small groups of 3-5 students. Each group will be given three objects to model with: a book, a piece of paper, and a baseball. Groups will then drop their objects following the worksheet directions and find an estimate for gravity based on their findings.

 

 

Content standards included in the lesson:

  1. CCSS.MATH.CONTENT.HSF.IF.C.7 – Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
  2. CCSS.MATH.CONTENT.HSF.IF.C.7.A – Graph linear and quadratic functions and show intercepts, maxima, and minima.
  3. CCSS.MATH.CONTENT.HSA.CED.A.1 – Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Activity Adapted from Vernier’s Bounce Back: Acceleration Due to Gravity

Putt Putt Golf and Vectors HSN.VM.A.2

stephensmithcwu Common Core State Standards Mathematics, HS Number and Quantity, Picture Problems

It is often difficult to engage students when it comes to harder concepts in Mathematics. In particular, mathematics involving vectors is difficult to grasp and therefore students are less likely to engage during instruction. To help alleviate the tendency to disengage, teachers can use an image to pull the students into the lesson. Video games tend to be an engaging and relevant aspect to students’ lives.

For this activity we will use the picture above of a golfing game. We can see that the golfer is looking from his ball position (initial point) to the cup (terminal point). We can assign these two points on the Cartesian plane. Using those two points as reference, we can break down the distance from the ball to the cup in to their i and j components on the x and y axis. Similarly, other video games or sports that can be represented in two dimensions can be used to create the engagement with students.

This problem is aligned to :

CCSS.MATH.CONTENT.HSN.VM.A.2

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.