Subtraction with Like Fraction Worksheet by zxj15946

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									          Michigan Department of Education
        Technology-Enhanced Lesson Plan

Lesson Title: Fraction Facts taken from:
http://www.shodor.org/interactivate/lessons/multdeci.html


Adapted by: Marsha Myles and Carolyn Newkirk

Lesson Abstract: The following discussions and activities are designed to
introduce students to fractions, including operations with fractions,
converting fractions to decimals and percents. The activities provide ample
practice opportunities to reinforce the information from the discussions.

Subject Area: Mathematics
Grade Level: 6
Unit Title: Numbers and Operations


Michigan Educational Technology Standards Connection:

Technology Productivity Tools
1. apply common software features (e.g., thesaurus, formulas, charts,
graphics, sounds) to enhance communication and to support creativity
2. use a variety of technology resources, including the internet, to increase
learning and productivity
3. explore basic applications that promote creativity (e.g., graphics,
presentation, photo-editing, programming, video-editing)

Technology Communication Tools
1. use a variety of telecommunication tools (e.g., e-mail, discussion groups,
IM, chat rooms, blogs, video-conferences, web conferences) or other online
resources to collaborate interactively with peers, experts, and other
audiences




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Michigan Grade Level Content Expectations Connection:
N.MR.06.01 Understand division of fractions as the inverse of
multiplication, e.g.,
              ■, then __ x ■ = __ , so ■ = __ • __ = _ __   .
N.FL.06.02 Given an applied situation involving dividing fractions, write a
mathematical
statement to represent the situation.
N.MR.06.03 Solve for the unknown in equations such as:         ■         ■=
_ and __ = 1 • ■.
N.FL.06.04 Multiply and divide any two fractions, including mixed numbers,
fluently.
N.ME.06.05 Order rational numbers and place them on the number line.
N.ME.06.06 Represent rational numbers as fractions or terminating
decimals when possible,
and translate between these representations.
N.ME.06.07 Understand that a fraction or a negative fraction is a quotient
of two integers,
e.g., - __ is -8 divided by 3.
N.MR.06.08 Understand integer subtraction as the inverse of integer
addition; add and
subtract integers using integers from 10 to -10.
N.FL.06.09 Add, subtract, multiply, and divide integers between -10 and
10; use number line
and strip models for addition and subtraction.
N.FL.06.10 Add, subtract, multiply and divide positive rational numbers
fluently.



Estimated time required to complete lesson or unit: One 45 – 60
minute class period



Instructional resources:
http://www.shodor.org/interactivate/lessons/multdeci.html
http://www.shodor.org/interactivate/activities/sequencer/worksheet1.h
tml



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http://www.shodor.org/interactivate/activities/sequencer/worksheet2.h
tml
http://www.shodor.org/interactivate/activities/sequencer/index.html




Prior required technology skills:

        o    perform basic mouse manipulations such as point, click and
             drag
        o    use a browser such as Netscape for experimenting with the
             activities




Sequence of Activities:
Multiplying Decimals and Mixed Numbers


Abstract

This lesson is designed to reinforce skills associated with multiplying
decimals and mixed numbers and allow students to visualize the effects of
multiplying by a decimal or mixed number.

Objectives

Upon completion of this lesson, students will:

     have practiced multiplying decimals and/or mixed numbers.
     have explored the effects of multiplying decimals and mixed numbers.
     have practiced predicting the effects of multiplying a number by a
      decimal or mixed number.

Standards

The activities and discussions in this lesson address the following NCTM
Standards:




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Numbers and Operations

Understand numbers, ways of representing numbers, relationships among
numbers, and number systems

     work flexibly with fractions, decimals, and percents to solve problems

Understand meanings of operations and how they relate to one another

     understand the meaning and effects of arithmetic operations with
      fractions, decimals, and integers
     understand and use the inverse relationships of addition and
      subtraction, multiplication and division, and squaring and finding
      square roots to simplify computations and solve problems

Compute fluently and make reasonable estimates

     select appropriate methods and tools for computing with fractions and
      decimals from among mental computation, estimation, calculators or
      computers, and paper and pencil, depending on the situation, and
      apply the selected methods
     develop and analyze algorithms for computing with fractions,
      decimals, and integers and develop fluency in their use

Algebra

Analyze change in various contexts

     use graphs to analyze the nature of changes in quantities in linear
      relationships

Links to other standards.

Student Prerequisites

     Arithmetic: Students must be able to:
         o multiply whole numbers.
         o recall some knowledge regarding multiplication of mixed
            numbers and decimals.
         o It will also prove helpful if students have the skills needed to
            interpret a line graph.
     Technological Students must be able to:
         o perform basic mouse manipulations such as point, click and
            drag


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         o   use a browser such as Netscape for experimenting with the
             activities

Teacher Preparation

Students will need:

     Access to a browser
     Pencil and paper
     Access to a calculator (optional)
     Copies of supplemental materials for the activities:
        o Multiplying Decimals Worksheet
        o Multiplying Mixed Numbers Worksheet


Lesson Outline

  1. Focus and Review

      Remind students what has been learned in previous lessons that will
      be pertinent to this lesson and/or have them begin to think about the
      words and ideas of this lesson:

         oCan someone tell me what a decimal/mixed number is?
       o If I multiply the number 1 by a decimal, will the result be larger
          or smaller than 1? OR If I multiply 1 by a mixed number, will the
          result be larger or smaller than 1?
       o Entertain a discussion on decimals and mixed numbers,
          including how to multiply these types of numbers.
  2. Objectives

      Let the students know what it is they will be doing and learning today.
      Say something like this:

         Today, class, we will be talking about multiplying decimals and
         o
         mixed numbers.
       o We are going to use the computers to look at the effect of
         multiplying a number by a decimal or mixed number, but please
         do not turn your computers on or go to this page until I ask you
         to. I want to show you a little about this program first.
  3. Teacher Input




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     Explain to the students how to do the assignment. You should model
     or demonstrate it for the students, especially if they are not familiar
     with how to use the computer applets on the Project Interactivate site.

        o Open your browser to The Sequencer in order to demonstrate
          this activity to the students.
        o Show the class that there is a box where they may enter a
          starting number, in other words, the number that will be
          multiplied by a decimal or mixed number.
        o Show the class the box where they will enter the multiplier, or
          the number that our starting number will be multiplied by.
        o Explain to the class that they should enter a "0" into the add-on
          box as this lesson is about multiplying decimals, not adding
          them. Show students where to enter the zero.
  4. Guided Practice
        o After answering all questions that the students might have
          regarding the use of The Sequencer, pass out the Multiplying
          Decimals Worksheet.
        o Walk the students through the worksheet, having all of the
          students in class use the same numbers, for example: 3 for the
          whole number and 0.43 for the decimal number. For each
          question, ask two different students what they think the answer
          is. Ask the students to settle any disputes on what the answers
          are.
  5. Independent Practice
        o Allow students to work independently or in groups to complete
          the worksheet and circulate the room to offer help where
          necessary.
        o When the students are finished with the Decimal worksheet,
          pass out the Multiplyi ng Mixed Numbers Worksheet and have
          them work through it independently.
  6. Closure

     You may wish to bring the class back together for a discussion of the
     findings. Allow students to describe what steps are needed and how
     they differ when numbers are multiplied by a decimal or a mixed
     number.

Alternate Outlines

This lesson can be rearranged in several ways.




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     You may choose to allow students to work in cooperative groups to
      make predictions about the effects of multiplying two particular
      number together and then check them as a class.
     You may invent your own way of using this lesson to suit the needs of
      your students.

Suggested Follow-Ups or Extensions

This lesson can be followed by:

     Fraction Facts: A lesson which introduces students to fractions and
      explores basic mathematical operations with fractions, comparing
      fractions, and converting fractions into decimals or percents.
     Ideas that Lead To Probability: which is an introduction to concepts
      about probability.




Assessments:
   Pre-Assessment: This worksheet could be used as a pre-
    assessment activity:


                    Multiplying Decimals Worksheet


Please answer the following questions, showing your work where
appropriate. Good luck!

  1. Choose a whole number to be your starting number:
     _______________
  2. Choose a decimal to multiply the number in #1 by: _______________
  3. Will the product (multiplication) of the numbers you chose be larger or
     smaller than the starting number? _______________
  4. What is the product when the two are multiplied? _______________
     What is the difference between this product and the starting
     number?_______________
     Please show your work.
  5. What will happen if you multiply the result in #4 by the decimal you
     chose in #2? Will the result be larger or smaller than the starting



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     number? than the result in #4? Please explain and show work that
     supports your conjecture:


  6. What is the ratio of the starting number and the result in #4?
     _______________
     What is the ratio of the result in #4 and the result in #5?
     _______________
     How do the two ratios compare? Please show your work:


  7. If you continue to multiply each result by the decimal that you chose
     in #2, what will happen over time?


  8. Enter your starting number and multiplier into the computer program.
     Look at the numbers that were generated. Were your predictions
     correct? If not, what was different about the result?


  9. Try this again with another starting number. Perhaps you would like
     to try a starting number that is a decimal? What results might that
     give you? Can you come up with a starting number and a multiplier
     that give interesting or unexpected results?




   Post-Assessment:
  Using different values for the starting numbers, etc., the worksheet
  can now be utilized as a final assessment.

                  Multiplying Mixed Numbers Worksheet


Please answer the following questions, showing your work where
appropriate. Good luck!

  1. Choose a whole number to be your starting number:
     _______________



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2. Choose a mixed number to multiply the number in #1 by:
   _______________
3. Will the product (multiplication) of the numbers you chose be larger or
   smaller than the starting number? _______________
4. What is the product when the two are multiplied? _______________
   What is the difference between this product and the starting
   number?_______________
   Please show your work.


5. What will happen if you multiply the result in #4 by the mixed number
   you chose in #2? Will the result be larger or smaller than the starting
   number? than the result in #4? Please explain and show work that
   supports your conjecture:



6. What is the ratio of the starting number and the result in #4?
   _______________
   What is the ratio of the result in #4 and the result in #5?
   _______________
   How do the two ratios compare? Please show your work:



7. If you continue to multiply each result by the mixed number that you
   chose in #2, what will happen over time?



8. Enter your starting number and multiplier into the computer program.
   Look at the numbers that were generated. Were your predictions
   correct? If not, what was different about the result?


9. Try this again with another starting number. Perhaps you would like
   to try a starting number that is also a mixed number? What results
   might that give you? Can you come up with a starting number and a
   multiplier that give interesting or unexpected results?




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Technology (hardware/software):
Individual computers for each student, put students in groups of 2 to
3 to a computer, or use teacher computer to work through the activity
as a class.

Key Vocabulary:
fractions
percents decimals
mixed numbers
multiplier
inverse relationships
square a number
square root of a number
estimation


Application Beyond School:
Students will utilize these skills in both higher level mathematics and in real
world applications in their personal and professional lives.


Teacher Reflection and Notes:




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