Author: mutchl

High School Geometry: Conditions for Parallelograms

mutchl CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Geometry

parallelogram art

This learning progression, that can be accessed through the link below, was designed primarily for 9th grade students in an honors geometry course. The Common Core State Standards that it will be satisfying are the following: HSG.GPE.B.4 and HSG.GPE.B.5. While the math practices that we will be implementing are: MP1, MP2, and  MP3. 

The primary instructional methods will be the Socratic Method and Direct Instruction. Students will have to take this information and apply it to mathematics problems that are given to them. As they work on problems the teacher will walk around and assess their work. The students will be allowed to talk to their table partners to check answers and tutor one another. As they are doing this the teacher will insert themselves into conversations that are headed the wrong direction, coming to a lull when it is clear one of both of the students is still lost or when the students are simply getting off task. An example of the types of questions the students will be working on can be seen at the bottom of this article.

After the students complete their class work they will be given an exit task to complete before the day is over. The exit task will include Benchmark Assessments that will show whether or not the students learned what they were supposed to learn that day. Once again example problems can be seen below.

instructional pic                    exit task final pic

Instructional Task                                   Assessment Task

Learning progression for TPA

High School Geometry: Special Triangles

mutchl CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Geometry

test

 

This learning progression was designed primarily for 9th grade students in an honors geometry course. The Common Core State Standards that it will be satisfying are the following: HSG.SRT.B.4, HSG.SRT.B.5, HSG.SRT.C.6. While the math practices that we will be implementing are: MP1, MP2, and  MP8.

At the very beginning of the lesson progression the students will be guided through deriving the common ratios found in 30, 60, 90 triangles using the Socratic method. After this, by actively implementing the information they just derived, students will able to assimilate it. The students will all receive white boards and they will be told to draw a 30, 60, 90 triangle on their board. They will then be given various side lengths and asked to find the lengths of the missing sides.Next, the same possess will be used to teach the students about 45, 45, 90 triangles.

For more details, see the following link:

Learning progression

CCSS.Math.Content.HSN.Q. Work it harder, Make it better, Do it faster, Makes us stronger.

mutchl Assessment of CCSS-Math, HS Number and Quantity

Alignment to Content Standards

CCSS.MATH.CONTENT.HSN.Q.A.1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.

CCSS.MATH.CONTENT.HSN.Q.A.3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

daft punk

Tasks

Both of the guys from Daft Punk are supposed to go onstage in 20 minutes but first they need to clean their helmets. It would take one of them 50 minutes to clean both helmets by himself and it would take the other 35 minutes to clean them both by himself. Using your knowledge of algebra, ratios, and unit analysis, determine how long it will take them to clean the helmets if they work together. Will their concert be able to start on time?

See the following file for the assessment task, commentary, and solution for this problem:

IM Writing Task Template-1 (1)

Trick Photography HSG.MG.A.1. and HSG.SRT.B.5

mutchl HS Geometry, HS Modeling, Picture Problems, Technology Teaching Issues

picture

Optical tricks often intrigue us. In reality a little math can often explain exactly why they work. In the picture above the only math needed to figure out how far one must stand from the Lincoln Memorial in order to view the real life figure and the picture on the bill as the same size is triangle similarity and manipulation of proportions. One must also know how tall the real memorial is, how large the picture on the $5.00 bill is, and how far they are holding the bill from their eyes. The following is a diagram of the similar triangles that can be used to calculate how far you are from the Memorial where the bill and the memorial are Parallel:

triangle

This problem satisfies the CCSS’s HSG.MG.A.1. and HSG.SRT.B.5 which are, “Use geometric shapes, their measures, and their properties to describe objects,” and “Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures,” respectively.

 

 

Simple Harmonic Motion: HSF.TF.B.5 and HSA.CED.A.2

mutchl HS Algebra, HS Functions, HS Modeling, Technology Teaching Issues

Simple Harmonic Motion:

harmonic motion pic

The Vernier physics activity titled Simple Harmonic Motion shows students how sinusoidal functions appear in the world around them.

This activity fulfills the following Common Core State Standards:

CCSS.MATH.CONTENT.HSF.TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

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.

Students often learn trigonometry but fail to recognize how often it shows up in their lives. Since it seems like all trigonometry is, is playing with triangles and some weird graphs that never actually show up in real life, it is easily forgotten. This lab will help them understand both how applicable trigonometry is and how to manipulate trigonometric functions. This will be done by recording the position and velocity of an object at the end of an oscillating spring using Verniers motion detector in conjunction with a computer that has Logger Pro software on it. The students will experiment with their springs motion when different weights are attached to. A ready prepared lab will lead them though this experiment and help them make connections between simple harmonic motion.

The equipment needed for this activity is the following:

  • computer ring stand
  • rod
  • right-angle clamp
  • Vernier computer interface Logger Pro
  • Vernier Motion Detector spring with a spring constant of approximately 15 N/m
  • twist ties
  • 200 g and 300 g masses
  • wire basket
  • lab worksheet (attached below)

Many of these items can be borrowed from Central Washington University’s CESME department.

PWV-15-COMP-simple_harmonic_motion

 

Slice It! HSG.MG.A.3

mutchl Common Core State Standards Mathematics, HS Geometry, HS Modeling, Technology Teaching Issues

 

swipe

Using the interactive App Slice it! Students will be playing a highly addictive game that is really just a bunch of geometric modeling problems. This application gives students a geometric figure and tells them to cut it into a given number of pieces, all with equal areas, using a certain number of lines. Sometimes these pieces will be nearly congruent while other times they will look nothing alike. This lesson will prepare students to play the game using mathematics to obtain better scores and will force them to make connections between the algebra they learned in previous years and the geometry they are now working on. Because this application was made for people of all ages, the lesson itself can be altered for a different target audience with ease.

Slice It! can be found in the google play store and in the iTunes store. The lesson plan and worksheet used in this lesson can be downloaded by clicking on the link below.

slice it