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- From: CRS Collaboration
- Contributed By: Joe Schlessinger
In this Math I/Math I Support course, students will explore specific aspects of the six Family of Functions and be able to graph and identify each by key characteristics.
Group Size: Any
Learning Objectives:
A. Identify functions by graph and equation
B. Identify critical points and slope
C. Identify characteristics: Domain and range, zeros and intercepts, max and min, end behavior, and increase and decrease
C. Graph equation
D. Write equations from graph
E. Identify parent graphs.
Guiding Question:
How do we identify and graph each of the family of functions?
Materials: Presentation materials: PowerPoint & Promethean flipscharts from Valdosta High School Math I Team, graph paper, colored pencils, construction paper for graphic organizer,
Additional materials. Textbook: Georgia High School Mathematics 1. McDougal Littell, 2008.Workbook: Math 1: Georgia Notetaking Guide. McDougal Littell, 2008.Test Prep: Georgia Mathematics 1: Test Preparation and Practice. McDougal Littell, 2008.Coach: Georgia GPS Edition Standards Based Instruction. Triumph Learning. 2009. Procedures:
What do students need to learn to be able to answer the Essential Question? Answer Assessment Prompts: Assessment Prompt #1: White Board: Identify family of function equations: x1, x2, │x│, x3, √x, 1/x (Math I Concept 2 Promethean Flipchart page 12.)Assessment Prompt #2: White Board/Promethean: Identify parent graphs (Math I Concept 2 Promethean Flipchart page 80.)Assessment Prompt #3: Graph the parent graphs by completing a graphic organizer. Assessment: Quiz: Math I Concept 2 PowerPoint or Promethean Flipchart Day One Ticket out the Door: Georgia Mathematics 1: Test Prep and Practice (McDougal Littell, 2007. ISBN-13: 9780-618-92023-5). Day Two 3-2-1 Draw 3 linear graphs, Draw 2 quadratic graphs, Draw 1 Absolute Value graph Day Three (if necessary): Find the critical points on samples of each type of graph
Answer Key or Rubric:
Answer Key: Included within Promethean charts, text and resource materialsAP #1: Math I Concept 2 Promethean Flipchart page 14AP # 2: Math I Concept 2 Promethean Flipchart page 80 Benchmark or Standards: Georgia Performance Standards for Math I/Math I Support MM1A1.a: How do we represent functions using function notation?
MM1A1.b: How do we graph and write equations for each of the Family of Functions? MM1A1.c: How do we graph transformations of functions?
MM1A1.d: What are the characteristics of a function and how do you use them?
MM1A1.e: How do we use graphs and tables to investigate behavior of functions? MM1A1.f: How do we recognize sequences as functions with domains that are whole numbers?
MM1A1.g: How do constant rates of change compare to variable rates of change within the Family of Functions?
MM1A1.h: How do we determine graphically and algebraically whether a function has symmetry and whether it is odd, even, or neither?
MM1A1.i: How do we interpret an equation in x, and its solutions as f(x) = g(x) and show where they intersect?
Attached Files:
A 50 minute lesson that focus on the FOIL method and how it's used in real world applications.
"Algebra Pinball" is a fun, online, math competition. Students (and friends and family!) can compete to get the best times on algebra and pre-algebra exercises, ranging from arithmetic with signed numbers to solving linear equations and factoring trinomials. Follow the link to see how it works at Miss Hall's School (Pittsfield, Massachusetts). Then, follow the instructions to get "Algebra Pinball" up-and-running in your own school! (Internet Explorer required)
Navigate to This External Web Link:
This is a revised and modified task or class activity from the "Task Wonderland to Functionland" from the state in Unit 1, Lesson 9. This activity (task) will extend the introduction of conditional statements.
Before the lesson: You will need to make a hypsometer for each of the groups in your class. Follow the instructions on the “Making a Hypsometer” word document provided in order to make a homemade hypsometer. Also, familiarize yourself with how a hypsometer works and what types of things can you measure with it. You will then select at least two objects (tree, light pole, building etc.) for each group to determine the height of. In the case of poor weather, objects within the class room (intercom speaker, wall mounted TV, etc.) can be used as replacements.
Group Size: Small groups
Learning Objectives:
MM2G2c: Students will define and apply sine, cosine, and tangent ratios to right triangles. c. Solve application problems using the trigonometric ratios.
Essential Question:
How can trigonometry be used to help you solve real world problems?
Materials:
1. Hypsometer (for measuring the angle of elevation) 2. Measure Tape/Yard Stick 3. TI-84 Graphing Calculator 4. OK RESA Web Link - The Mathematics I and II unit development was a collaborative project between Okefenokee RESA, Coastal Plains RESA, and Southwest Georgia RESA to provide a resource for lessons to assist teachers as they implement Mathematics I and II. The units were written by high school mathematics teachers. OK RESA URL: http://www.ciclt.net/sn/adm/editpage.aspx?Code=okresa&FileName=Services_Mathematics Changes were made to Lesson#11: These are very large files. Please be patient. You will need Adobe Reader to view the Unit files. If you do not have Adobe Reader, go to www.adobe.com to download the newest version. 5. “Making a Hypsometer” doc - Collins, William, et al. Algebra 1. New York: Glencoe, 1998. 6. Making a Hypsometer Sheet- image: © 2009 Colorado School of Mines - inside.mines.edu (internet image) http://inside.mines.edu/~khellman/cde/clinometer_activity.pdf 7. When a Ruler Isn’t Enough-By: Bob Tower @ Education.ti.com - © Copyright 1995-2009 Texas Instruments Incorporated. All rights reserved.
Procedures:
Before the lesson: You will need to make a hypsometer for each of the groups in your class. Follow the instructions on the sheet provided in order to make a homemade hypsometer. Also, familiarize yourself with how a hypsometer works and what types of things can you measure with it. You will then select various objects (tree, light pole, building etc.) for each group to determine the height of. In the case of poor weather, objects within the class room (intercom speaker, wall mounted TV, etc.) can be used as replacements.
Mini – Lesson: The students will be paired up for the activity using the "Find Your Complement" cards provided in Reproducible Materials section. Use this time to remind to of the types of angle pairs that form complements. This activity will provide students with the necessary background knowledge needed when using a hypsometer.
Opening: The teacher will walk through a sample problem with the students on the board or overhead. Students will use a scientific calculator to work the sample problem with the teacher. A sample problem with Teacher dialog is provided in Reproducible Materials section. After the opening, students will then be put in groups of 3 to 4. Work Session: Step1) Each group of students is given a hypsometer, tape measure and yarn. Step 2) Each student is given a Student Handout provided in Reproducible Materials documents. Step 3) The class moves to the teacher selected object(ex. Tree) and begins the activity. (The procedures are listed in steps on the Student Handout.) Steps: 4a) A volunteer, within the group, stands in a location within around 15 to 30 feet of the object. Note: This volunteer doesn’t move until step 4 is complete. b) A second group member measures distance from ground to volunteer member’s eye level: ___________. c) Another group member measures the distance from the volunteer to the object. (write in Table A as distance 1) d) The volunteer from step 1 reports the hypsometer reading. As a group find the angle of elevation to top of the tree (write in Table A as angle 1). **Remember that the angle of elevation is the complement of the hypsometer reading.** e) Now, move to the next object. Repeat the same procedure as you did with the 1st object. Step 6) The students return to the classroom to complete the diagrams. The students will use the scientific calculator to find the height of the objects (Table B). After heights are determined, the students answer the writing portion of the Student Handout. Step 7) Each group returns the hypsometer and tape measure to the specified location. Step 8) Have a group share answers to discussion questions on Student Handout. Closing: Discuss with the class the good things or bad thing you found in the activity. Did this activity help you to understand how trig is used in the real world. Give another example of how trig can be used in the real world.
Assessment:
TI – Navigator Learning Check ( used in conjunction with TI-84 Plus calc. and TI- Navigator Classroom System) Website Link for Learning Check Assessment: “WhenARulerIsntEnough” URL- http://education.ti.com/educationportal/activityexchange/download_file.jsp?cid=US&fileurl=Math/Geometry/2281/WhenARulerIsntEnough.edc
Answer Key or Rubric:
How High Is It Anyway? – Scoring Rubric – word doc
Benchmark or Standards:
(insert)
Attached Files:
CSR Lesson Plan - Trig Ratios 5 Question Mixed Review
| FindyourComplementsCards.doc |
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| HOWHIGHISITANYWAY-scoringrubric.doc |
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| MakingaHypsometer.doc |
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| SampleProblem-TeacherDialogue.doc |
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| HOWHIGHISITANYWAY-studentdoc.doc |
“Optimization Saga” will take you (a cub reporter for The Washington Post) on an adventure to several places in Washington, DC. You will be solving the following types of optimization problems: Norman window, boat & taxi, stick around a corner and cylinder in a sphere. All the places and items in the adventure are authentic (except for some artistic license).
Navigate to This External Web Link:
http://www.dlt.ncssm.edu/DeConti/AdventuresInTrigWorkshop.htm
Lesson with built in graphic organizer, practice and assessment
Lesson on using the Counting Principle with practice, graphic organizer, and assessments built in
This lesson compares mean absolute deviation and introduces standard deviation through hands on activity.
This plan utilizes the GPS Math I Logo Symmetry Task as the focus of the lesson. This lesson is designed for a 9th grade Math I class.
This is a very fun Geometry and STEM wiki; I teach everything with arts and sciences and humanities. It is projects based learning and discovery learning; it is a work-in-progress and encourages collaborations across all subjects and worldwide...
Navigate to This External Web Link:
Play Video
Some problems involving basic geometric constructions.
Some problems involving congruent triangles.
Lesson 1
Lesson 2
Lesson 3
