Author: robinsonalex

HSG.CO.A.3, HSG.CO.A.4, HSG.CO.A.5 – Translations, Reflections, and Rotation Learning Progression

robinsonalex Uncategorized

This learning progression will be taught in a high school sophomore geometry classroom.  Prior to this learning progression, students will have been introduced to basic geometric shapes.  Students will be familiar with much of the vocabulary surrounding this lesson.  They will know the definitions of each of the following terms: line, line segment, ray, quadrant, angle, etc.  This particular learning segment will introduce students to rigid transformations within the plane.  This learning progression will begin be students learning the concepts and procedures necessary to complete each of the rigid transformations: translations, reflections, and rotations.  Following each of these lessons, students will learn how to combine transformations and whether or not the order of transformations matters.  The final lesson of the progression will assess whether or not students can perform compositional transformations on a figure.  The order of the progression will allow students to build on their knowledge of geometric vocabulary and previous lessons. This progression will provide students with new conceptual understanding and will prepare them for future learning segments.

learning progression image

This learning segment will adhere to the following common core cluster:

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.
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

edTPA Learning Progression

Learning Segment for Systems of Equations

robinsonalex Uncategorized

This learning progression will be taught in a high school sophomore algebra classroom.  The common core standards that this learning progression aligns with are HSA.REI.C.5, HSA.REI.C.6, and HSA.REI.C.7.  This progressiLearning Prog Picon also makes use of the following three mathematical practices: MP1: Make sense of problems and persevere in solving them, MP3: Construct viable arguments and critique the reasoning of others, and MP4: Model with mathematics.  The lessons in this progression will take students from a basic understanding of linear equations, to a complete understanding of systems of equations and how to solve them. Students will learn to solve systems of equations using three methods: graphing, substitution, and combination.

Complete Learning Progression

Ice Cream Volume-HSG.GMD.A.3

robinsonalex HS Geometry, Picture Problems

Whenever I eat ice cream there’s always one thing that’s on my mind: MATH.  I mean, who doesn’t think about math when they eat ice cream.  While of course ice cream Picture Problemcones are a great snack on a summer day, they also pose some great potential problems for a high school geometry class.  Teachers might use a picture like this to have students solve several problems.  Students could find exactly how much ice cream can actually fit in a cone by finding the volume.  This problem provides a great opportunity for students to do this practically in class too, and enjoy a snack while they do it.  Students might also find compound volumes of cones and sphere’s by putting more ice cream on top of the cone.

 

Walk Like a Model!-A Modeling Activity Using Vernier Technology (HSA.CED.A.2)

robinsonalex HS Algebra, Technology Teaching Issues

It’s no secret that students learn better when they have the opportunity to move around and interact with each other.  So why not create an activity that take advantage of this? In Walk Like a Model! students will work in groups and they’ll get to walk around the room.  This activity also uses Vernier software to connect their movement to graphical representations.

Students willCBR begin this activity by creating directions for a model as if they were the director of a fashion show.  They’ll work in groups of four to create the directions, and then they’ll each draw a graph of their model’s movement.  This will develop students conceptual understanding of distance versus time graphs and what each of the variables really mean in real life.

After “guessing” what a graph of their model’s motion will look like, now it’s time to check their work.  Students will use the Vernier CBR 2 motion detectors and a TI-83 or TI-84 calculator to create a graph that follows their own directions.  One student from each group will be the “model,” one will watch the graph being created to help direct the “model,” and the other two will use the directions to help guide the “model.”

Finally, students will reflect upon how their guesses differ from the graphs created by the teimage002chnology.  They will answer questions about why they’re different and how well the activity went.

Walk Like a Model! is a great activity to get students out of their seats and creating their own problems.  This activity addresses the following Common Core math standards:

CCSS.MATH.CONTENT.HSA.CED.A.2

CCSS.MATH.CONTENT.HSF.LE.A.1.B

Also, here is the link to the Walk Like a Model! worksheet:

Walking Like a Model

 

Racing Through Equations! HSA.SSE.A.1

robinsonalex HS Algebra, Technology Teaching Issues

Let’s face it. Whether or not we love technology, our students sure do.  They’ve grown up in a world that’s taught them that easier is better, and that the next cool gadget is all that matters.  As future educators we can disregard this truth or we can embrace it.  Racing Through Equations is an innovative and fun lesson to teach linear equations to high school freshmen in a way that they might actually understand.

In this activity students will be provided a problem about a bike race between two boys.  After deriving equations for each of the boys’ movement, we can finally get to the fun stuff.  Students will use the FluidMath App to model the race.  FluidMath is an awesome free app that allows students to draw cars, assign equations to those cars, and then watch the cars that they drew race to the finish line.  The number one benefit of FluidMath is it will provide the students with a visual.  They no longer have to imagine a fictional race between two boys in their head, but they can watch the race unfold in front of them! Being able to watch the race will allow them to connect the equations they’ve derived to a visual aid.  On FluidMath they’ll also be able to manipulate their equations to see how the race will change.  FluidMath will allow students to create their own race, with their own variables, and then watch it happen.

IMG_0763

Studies show that students crave interaction and participation in their learning, and FluidMath provides a great opportunity for that.  Racing Through Equations is a lesson that uses FluidMath to reinforce linear equation concepts and addresses the following Common Core Math Standards:

CCSS.MATH.CONTENT.HSA.SSE.A.1   Interpret expressions that represent a quantity in terms of its context.

 

CCSS.MATH.CONTENT.HSA.CED.A.2  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

RTE Worksheet

RTE Lesson Plan