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Rational Exponents Worksheet Grade 10 - PowerPoint

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Rational Exponents Worksheet Grade 10 - PowerPoint Powered By Docstoc
					Using Instructional Strategies for
   Differentiating Instruction

      Dr. Joseph Merhaut
      Dr. Robert Snyder
      Choice Boards & Menus
• Also called Tic Tac Toe Boards or Learning
• A type of learning that provides a ―menu‖
  of activities-some that all students must do,
  and some that allow students choices.
• Ensures that each learner focuses on
  knowledge, understanding and skills
  designated as essential.
 Think-Tac-Toe Money Unit
 Complete any three boxes. The products and assignments are due by ___________.

   Complete the Sweet Treat                                               Count the money amounts in each
                                    Complete the file folder games on
 shopping cut and paste activity                                          piggy bank and record the amount
             sheet.                                                             on the recording sheet.

  There are 13 different ways to
  make 25 cents using a quarter,    Draw a picture of a toy you want.     Write an explanation to someone
dimes, nickels, and pennies. Use    Tell how much it will cost. Then      telling how you would count the
the table worksheet to record the   draw the money to show its cost.       money in the money envelope.
      ways that you can find.

                                                                           Complete the Choices, Choices
                                    Play the Shop ‘Til You Drop game.               worksheet
  Complete the Money riddles
                                    You will turn in your shopping list                 OR
                                         after you play this game.                In the Garden
                     Choice Board Activity
                                Language/Level: English 7
                          Unit/Theme: Poetry: Literary Elements

Locate at least one example of     Locate at least one example of      Locate at least one example of
each of the following: elements:   each of the following: idiom and    each of the following: simile and
alliteration and hyperbole, from   personification from the poem…      metaphor from the poem…
the poem Sarah Silvia Cynthia

Explain the literal meaning of a   Explain the literal meaning of an   Explain the literal meaning of a
hyperbole from the poem Sarah      idiom or personification from the   simile or metaphor from the
Silvia Cynthia Stout.              poem…                               poem…

Create your own example of         Create your own example of an       Create your own example of a
alliteration and hyperbole.        idiom and personification.          simile and metaphor.
                   Choice Board Ancient Egypt – Grade 6
                         ( You need to choose one topic from each row and one style from each column for your
                                                      assessments in this chapter.)
                              BUILD IT                            CREATE IT                                  WRITE IT
                   As an ancient cartographer, you     Assume you are persuading             You are a builder commissioned by
                                                                                             the pharaoh to transport stone from

                   have been ordered by the pharaoh    others to visit your ancient
                   to create a map of the Egyptian                                           the quarry to the destination site for
                                                       civilization. Design a descriptive,
                   Empire during the reign of Ramses                                         the temple. As you travel the Nile
                                                       accurate travel brochure.             River, be sure to include the
                   II. Be sure to includes elements    Include both natural and man-         geographic features you would see,
                   common to most maps and at
                                                       made elements that would              wildlife you would encounter, and any
                   least 10 notable landmarks from                                           difficulties you might encounter along
                                                       attract tourists.
                   the time period.                                                          the way.

                   You are a famous sculptor.          You are pharaoh of Egypt.             Write a journal entry from the
                   Create a 3D representation of a     Create a Photostory profiling         prospective of a tomb robber. Give a
                                                                                             detailed account of your plan to rob a
                   well-known leader, god,             your life. Include name,
                                                                                             famous pharaoh’s tomb and how your
                   goddess, or common citizen.         birth/death, family (parents,         plan came to fruition. This should
                   Include detailing who the statue    spouses, children, important          include risks taken and rewards.
                   is of and what their role and       siblings), monuments erected,         What did you see, hear, feel, and
                   accomplishments may have            important achievements.               smell as you searched the tomb.
                   Construct one of the great          Written language was essential        Write an essay detailing the

                   architectural achievements from     to Egyptians. Your task is to         importance of the art of
                   the time. This can be made          create your own written               mummification in world history.
                   from any materials of your          language to serve as a Rosetta        Thoroughly explain the process
                   choice. Include a note card         Stone. Include a translation into     for the ancient Egyptians as well
                   containing who built it, when it    modern English and place a            as its similarities to what we do
                   was built, use of it, and           message in your language and          in the United States today.
                   dimensions.                         English on an artifact to submit.
                                                Choice Board
1.   Choose a number.              1.    Get a magazine.             1.   Cut out pictures that show 1.   Glue your pictures to the
                                                                          your number.                    correct number poster.

1.   Choose a number.              1.    Look at our math word       1.   Find a card that matches   1.   Sort them into the correct
                                         cards.                           the number you chose.           basket.

         Created by Julie Dill -Math Coach, Wicomico County, 2010
        Dinner Menu Example
• Main Dish (Complete all)
• Measure the length of the objects in the
  measurement container using any of the
  nonstandard units we have used in class.
• Use the large paper clips to measure the pictures
  of the objects on the worksheet R 17.1
• Complete the ―Different Units of Measure‖
          Dinner Menu Example
• Side Dishes (Select at least 2)
• Read the book The Biggest Fish. Measure the length of
  the fish in the fishing net to the nearest inch. Then glue
  them onto a sentence strip from shortest to longest.
• Complete the ―What’s My Length?‖ activity.
• Use a ruler to draw and label lines for the following
  measurements: 10 inches, 5 inches, 3 centimeters, 15
  centimeters, 1 foot, 1 inch, 3 inches, and 10 centimeters.
• Organize the pictures of the objects in order from smallest
  to largest.
• Complete the ―How Far to the Dragon’s Lair?‖ activity
        Dinner Menu Example
• Dessert (Optional- Select 1)
• Draw a map. Label 4 locations on your map with
  a large dot. Using you ruler draw lines to connect
  these locations. Measure and label these lines on
  your map to the nearest inch. Write a story
  problem on an index card that can be solved using
  your map.
• Read How Big is a Foot? Then pick 5 objects
  from the measurement container to measure using
  a small paper clip, an eraser, and a ruler.
  Complete the worksheet for this activity.
          Cubing/Think Dots
• Cubing is an instructional strategy that asks
  students to consider a concept from a
  variety of different perspectives.
• The cubes are six-sided figures that have a
  different activity on each side of the cube.
• A student rolls the cube and does the
  activity that comes up.
              Cubing/Think Dots
• Not all students receive the same cube.
• You can differentiate cubes according to readiness,
  learning profile, or interest (see differentiated
  cubing examples included).
• Cube Side Suggestions:
  Describe it * Compare it * Associate it *Analyze it * Apply it *
  Connect it * Illustrate it* Change it * Solve it* Question it
  *Rearrange it * Satirize it * Evaluate it * Relate it to something
  else * Contrast it * Investigate it * What is the significance of
  it? * Put it in historical perspective * What are the cause/effects
  of it * Cartoon it * Tell the parts of it * Argue for/against it *
             Think Dots
       Probability and Statistics
Argue it                            Conduct a survey                     Use it
Make an argument for which          Choose a random sample of n=         Is there such a thing as a truly
graphing method is the easiest to   15 students from this class and      ―random
read: pie charts, stem-and-leaf     conduct a survey of their            Sample.
plots, bar graphs, or line          favorite sports team/food rock/
graphs. Construct a visual model    star/etc. (your choice1). Describe
to show us                          how you arrived at your random
why.                                sample, and create a data display
                                    of your results.

Define it                           Evaluate it                          Plot it
What is a random stratified         Look at today’s USA                  Plot the distribution of scores
sample? When                        newspaper’s opinion poll. What       from last year’s final exam (get
would you use it?                   type of graph is it using to         the scores from the teacher—
                                    display its results? Do you feel     sorry, all names have been
                                    that the data display is accurate    removed!)
                                    or misleading?
                         Geometry Think Dots
       Directions: At your table group, take turns rolling the dice and complete the learning task from the
 corresponding dot. It is okay if more than one person rolls the same number as each person’s response will be

TRIANGLE TOOTHPICKS                     PROTRACTOR PROS                               MAKE A MAP OF LINES
 Find all the triangles you can make    Using your protractor, measure each      Create a map of the school. Include
  using 3-12 toothpicks, and sketch      angle on your card. Be sure to label    each hallway. List the hallways that
them on a piece of paper. Label each    the angles as acute, right, obtuse, or     are parallel, perpendicular, and
        triangle with its name.                        straight.                            intersecting.

  SHAPE TASK CARDS                      COLORED SYMMETRY                         CONGRUENT SORTING
   Label each task card with its            Color the following sheet in a       Sort the shapes from your envelope.
geometric name. Be sure to tell how      symmetrical way. Be sure to make           Pair up all the shapes that are
many sides, angles, and vertices each      your picture colorful and neat.        congruent. Keep the extra shapes
             shape has.                                                           separate. List the congruent pairs
                                                                                             on your sheet.
         THINK DOTS
Describe…      Apply…      Question…

Argue for or   Satirize…   Compare and/or
against…                   contrast…
       RAFT (Role, Audience, Format,
    Role of the Writer – Students choose a role they wish to emulate. Options may
    include a soldier, a chemist, a bird, a mayor, or a sheep. Writing from a different
    perspective helps students to develop critical thinking skills as they have to consider
    what would be important to the specific role they chose.

•   Audience – Writing for a specific audience also leads to high order thinking as the
    student will need to consider what the audience needs to know. An audience could be a
    person or a group of people and might include anything from zoo patrons to the United
    States Congress. Reviewing informal and formal types of writing will be key when
    discussing how to address a specific audience.

•   Format – The writing format should correspond with the role of the writer, the
    audience, and the topic. Teachers will want to step away from regular reports and
    essays. Let students work on writing formats such as lyrics, raps, letters, speeches,
    journals, fables, flyers, or even political cartoons.

•   Topic – Topics can stem from the research students are doing within a subject, themes
    that are being studied in school, or subtopics within a unit that needs more clarification
    or enrichment. The goal is to make sure the topic is not too broad (Strayer & Strayer,
         Possible Ideas for a RAFT
             Choose ideas that advance the learning goals.

Characters         Public service Key terms       Scientists or
from a story       job                            politicians
Historical         Musical          Diseases      Geographic
figures            instruments                    formations
Vocabulary         Cartoon          Types of      Composers or
words              characters       fabric        artists
Instruments        Shapes or        Authors or    Business or
or tools           colors           inventers     industry person
Minerals or        Cities,          Brand         Technical terms
chemical           countries or     name or
elements           continents       object
          Possible RAFT Formats to Differentiate by
                     Learning Modality
Written         Visual       Oral            Kinesthetic
Diary entry     Comic        Song            Model
Bulleted list   Crossword    Monologue       Cheer
Obituary        puzzle       Radiocast       Mime
Invitation      Map          Museum          Demonstration
Recipe          Graphic        guide         Sales pitch
Movie critic    organizer    Interview        with demos
FAQs            Print ad     Puppet show     Sew, cook,
Editorial       Photograph   Political        build
Gossip          Fashion        speech        Wax museum
column          design
                             Story teller
                       Fractions RAFT

ROLE        AUDIENCE              FORMAT           TOPIC
                                                    Do You
Fraction    Whole Number           Children’s     Want a Piece
                                     Book           of Me?

Fraction         Its             Invitation and   Come to the
             Equivalents            a Mask        Masquerade
Fraction-    The Public             Wanted          This
disguised                           Poster/        dangerous
 -as-a                            Warning Ad       fraction is
decimal                                           disguised as
                                                  a decimal…

                                  Paper People      What to
Fraction    Other Students         Wardrobe       wear when
                                    Changes        you are a
                                                  decimal, and
                   Other Math RAFT Ideas
     Role               Audience                Format                    Topic

   Exponent                 Jury               Instructions         Laws of Exponents

Acute Triangle        Obtuse Triangle        Dear John Letter         Our Differences

    Percent               Student             How-To Guide        Mental ways to calculate

Prime Number          Rational Numbers     Club Membership Form    How to Join My Club

Parts of a Graph        TV Audience               Script            Which of Us Is Most

   Plus Sign         Multiplication Sign      Romantic Card        Why We Go Together
     Analyzing a RAFT Lesson
• What are the learning goals for this lesson and are
  they built into every choice?
• How is this RAFT being differentiated?
   – Does it appeal to different learning styles?
   – Is there a range of difficulty in the:
      • Roles?
      • Formats?
      • Readiness levels?
   – Do the roles, formats or topics appeal to a variety of
Structured Academic Controversy

• Controversy can fuel some great discussions and
  cultivate rich thinking and language. Structured
  academic controversies (SAC) emphasize
  communication, perspective-taking, and problem-
  solving (Johnson & Johnson, 1995).

• Unlike debates, students work together to
  collaborate on a resolution to the controversy after
  they have taken both sides of the issue. They are
  less competitive—there is no ―winner‖ or ―loser.‖
            SAC Example
• US Metric Conversion

• One position is: The metric conversion is
  necessary for the health of the US economy.

• The other position is: The need for metric
  conversion is obsolete and would actually
  harm the economy if businesses were
  mandated to change.
             SAC Example
• Science: Acid Rain
• Fact: Industries provide us with needs and
  wants that in some cases result in acid rain.
• Team 1: The needs and wants of a
  community are more important than the
  effects of acid rain.
• Team 2: The results of acid rain are more
  dangerous than limiting industries’
  production of needs and wants.
                    SAC Example
• To Drop or Not to Drop?
• This structured academic controversy lesson is designed to teach
  students both sides of the debate surrounding the use of the Atomic
  bomb at the end of World War II. The bombings of Hiroshima and
  Nagasaki were the catalysts that caused the end of World War II and
  are the only two times that a nuclear weapon has been used in war. It
  is important that students learn about the circumstances leading to their
  use and understand the controversy that surrounds those events. It is
  also important for students to understand the magnitude and significant
  destruction caused by atomic weapons so that they can be informed
  participants in today’s world. The purpose of this lesson is to present
  students with arguments from both sides of the debate so that they may
  draw their own conclusions regarding the bombing of Hiroshima and
       Curriculum Compacting
• Curriculum compacting is a three-step process
  implemented by the teacher for one or more students
  who have mastered portions of the essential
• pre-assess to determine what a student knows about
  content/skills to be taught;
• modify learning activities so that the student
  receives instruction only about what he/she does not
  already know provide alternative learning activities
  that offer acceleration of meaningful, challenging
• Tiered instruction is like a stairwell
  providing access within the large building
  called learning. The bottom story
  represents learning tasks for students
  with less readiness and fewer skills. The
  stairwell continues through enough levels
  to reach the appropriate challenge for
  advanced readiness students with very
  high skills and complex understanding.
       •   ASSIGNMENTS
       •   ACTIVITIES
       •   ASSESSMENTS
       •   MATERIALS
       •   EXPERIMENTS
       •   HOMEWORK
       What is Tiered Instruction?
                              By keeping the focus of the
Teachers use tiered           activity the same, but
activities so that all        providing routes of access at
students focus on             varying degrees of difficulty,
essential understandings      the teacher maximizes the
                              likelihood that:
and skills but at different
levels of complexity,         1) each student comes away with
abstractness, and open-          pivotal skills & understandings
                              2) each student is appropriately
   Creating Multiple Paths For
                   Key Concept

    Struggling                      Understand
    With The        Understanding      The
     Concept                         Concept

Reaching Back    READINESS LEVELS   Reaching Ahead
               IDENTIFY OUTCOMES



     GROUP 1          GROUP 2         GROUP 3
      TASK             TASK            TASK
 Guidelines for Tiered Instruction
• 1. Ensure that group membership is flexible.
  The word tiered is not a euphemism for stagnant low-middle-high
  groups that label who can learn and who is not learning. Tiered
  assignments denote all children as able to learn the same essential
  skills in different ways. The make-up of students working at each
  tier varies with the content, assignment, and quantity of tiers.
• 2. Plan the number of levels most appropriate for instruction.
  Different quantities of tiers are needed for different curricula
  areas, concepts, and skills in relation to different learners' needs.
  Sometimes, two tiers are sufficient; at other times, three to five or
  more work better to match the wide range of learners. Changing
  the number of tiers is also a way to vitalize flexible groupings and
  ensure that students are not always in the same group.
   Guidelines for Tiered Instruction
• 3. Recognize that complexity is relative.
  The complexity of a tiered assignment is relative because it is
  determined by the specific needs of the students and because learners'
  readiness levels vary in different curricula areas. In classes with below
  grade-level learners, the lowest tier would respond to those students. In
  classes in which all students are at or above grade level, the lowest tier
  would respond to grade-level or even above grade-level readiness.
• 4. Promote high-level thinking in each tier.
  Avoid always allocating simple thinking tasks for students with the
  fewest skills. All students need opportunities to analyze, synthesize,
  and evaluate information.
• 5. Provide teacher support at every tier.
  Every tier requires teacher modeling and support for the students
  working at that tier. All learners benefit from a teacher's instruction,
  interaction, guidance, and feedback--even gifted children whom some
  educators perceive as always making it on their own.
           Tiered Lesson Example
• Tier I will be made up of students who I feel will benefit best from a
  simpler form of learning, such as defining and giving the significance
  of various key terms or people and answering basic questions. Some
  of the terms they will be expected to identify will be:

• Slavery, Nat Turner, Elijah Lovejoy, William Lloyd Garrison,
  abolitionists, Henry Clay, John Calhoun, Stephan Douglas, popular
  sovereignty, Fredrick Douglass, Harriet Beecher Stowe’s Uncle Toms
  Cabin, John Brown and Harper’s Ferry, Dred Scott Case, Abraham
  Lincoln, republicans, democrats, Lincoln/Douglas debates, Kansas-
  Nebraska Act, and the Presidential Nominating Conventions of 1860,
           Tiered Lesson Example
• Tier II would be comprised of students that I felt capable of taking
  historical facts and analyzing them to show how these people/events
  led to the escalation of conflict that led to the civil war. I would give
  these students various questions that asked them to link certain events
  to the causes of the civil war. Some example questions that I may ask
  of these students are:
• 1) How did the publishing of Harriet Beecher Stowe’s Uncle Toms
  Cabin help lead to civil war?
  2) What did the Dred Scott Case decide? What did it mean for slaves
  and former slaves? Did the Supreme Court overstep its constitutional
  limits in their decision?
  3) What were the differing points of view in the Lincoln/Douglas
  4) What key figure in this time period favored popular
  sovereignty? How did other key figures react to his ideas?
  5) What were the views of the abolitionists? What were the
  differences in views held by Lovejoy, Garrison, and Douglass?
         Tiered Lesson Example
• Tier III students will be those students who I feel have a
  good grip on the ideas presented and can think critically
  and explain how these key terms/figures/events eventually
  led to the civil war. I would ask these students to present a
  3-4 page essay on how the key points of the lecture and
  readings ended up causing the civil war. These students
  will be expected to provide their own ideas on why these
  situations occurred and what the effects of these events
  were. These students will be given more freedom to
  handle the material. Their own ideas will shape their
  responses and mold the essay.
           Tiered Lesson Example
• Tier 1
• Students will illustrate the five geometric terms and create a book out
  of it.
• Materials: Paper, stapler, colored pencils.
• Procedures:
• Students learn about the five geometric terms: point, line, line segment,
  ray, and angle using the Geometry Powerpoint.
• Each student individually takes 3 sheets of paper and folds them in half
  to make a book. Secure the book by stapling the crease.
• On each page a new term is written, and an illustration of that term is
  drawn using colored pencils.
• Add a title to the book on the front.
           Tiered Lesson Example
• Tier 2
• Students will compare and contrast two of the five geometric terms.
• Materials: Paper, pencil.
• Procedures:
• Students learn about the five geometric terms: point, line, line segment,
  ray, and angle using the Geometry Powerpoint.
• Students will individually complete a Venn diagram on Inspiration
  choosing only two of the terms to compare/contrast.
           Tiered Lesson Example
• Tier 3
• Students create an argument for which of the five geometric terms is
  most important.
• Materials: Paper, pencil
• Procedures:
• Students learn about the five geometric terms: point, line, line segment,
  ray, and angle using the Geometry Powerpoint.
• Students either individually or in pairs create an argument about which
  of these five terms is the most important for the world of math.
• Students can use the paper to plan for an oral presentation of their
  argument, or use the paper to prepare a written piece which can be
  typed in Microsoft Word.
           Tiered Lesson Example
• Tier 4
• Students will go on a scavenger hunt in the room of each of the five
  geometric terms.
• Materials: Paper, pencil, classroom environment
• Procedures:
• Students learn about the five geometric terms: point, line, line segment,
  ray, and angle using the Geometry Powerpoint.
• Students get into pairs.
• Each pair is given a sheet of paper that is divided into 5 categories, one
  for each term.
• Student pairs are given 10 minutes to find as many examples of each as
  they can, and then draw a picture or write about it in the correct
  category on the paper.

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