Rational Numbers 6th grade unit by ashrafp

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									Decision One:                           Topic: Different forms of Rational Numbers                                                Grade: 6
Content Map of Unit
                                                                                                                                   Optional
Key Learning(s):                                        Unit Essential Question(s):                                          Instructional Tools:
 Students will understand that: there is                   Why do we need different forms of                             Pre-requisites:
 a need for numbers beyond whole                           numbers?                                                           Comparing fractions;
 numbers; the meaning of ratio,                                                                                               terminating and repeating
 proportion, percent, fraction, and                                                                                             decimals;
 decimal and their relationship to each                                                                                       solving simple equations
                                                                                                                                (mult. Div.)
 other.
Concept:                               Concept:                             Concept:                           Concept:
 Meaning                               Strategies                            Constructing Support            Real Life Applications

 Lesson Essential Questions:           Lesson Essential Questions:           Lesson Essential Question       Lesson Essential Questions:


 How can the same quantity be               How do I change from one form         How do I use Constructing Support to    How do I know which form of a
 represented in different ways?             of a number to another form?          provide support or proof of             number to use?
 How are ratios and proportions used                                              statements?                             How do I use different forms of
 to show relationships?                                                           What is the best way to change from     numbers to show how an F can
                                                                                  fractions to decimals?                  affect my grades?
Vocabulary and skills                       Vocabulary and skills                 Vocabulary and skills                   Vocabulary and skills

    fraction, decimal, percent,                     Factor, proportion,                       Constructing                      Problem Solving
    denominator, numerator,                         ratio, cross product                       Support                           Culminating Activity
    equivalent, Vinculum                                                                      Multiple ways to                  Everyday Use
                                                           Common Forms                       solve problems
           Models and                                     Setting up and
            Representations                                 solving
           Relationships                                   proportions
           Equivalency
Decision Two: The performance or product project                                                                     Note: Decision One is the
                                                                                                                           Content Map
              that will be the culminating activity of the unit

    Students’ Assignment Page for the Culminating Activity


    Essential Question of the Culminating Activity:
      How do I use what I have learned about different forms of numbers to show how an F can affect my grade?




     Paragraph Description of Culminating Activity:
      Students will use data from a quiz situation to determine what effect an F has on a final grade. This activity requires students to
      write ratios as fractions and then change fractions to decimals and percents using the methods (including setting up and solving
      proportions) learned in the unit. Determining how F’s can affect a grade is a real-world situation that students can relate to in order
      to use the skills and concepts that they have learned.




     Steps or Task Analysis of Culminating Activity (include Graphic Organizers):
     Students will work in groups of 4 to determine what effect an F has on a final grade.
     1. The groups will designate assigned roles of facilitator, encourager, checker, and recorder to the members.
     2. Everyone in the group will work together on each of the 4 given situations. The facilitator oversees that the work gets done while
     the encourager pulls everyone into the work. The checker verifies the solution of the group and the recorder writes the solution on
     paper. The recorder calls the teacher over to explain the solution.
     3. Once the group has arrived at the correct solution, members must rotate roles within the group.
     4. Groups are to complete the worksheet section for each situation and then graph the results, using a different color for each
     situation.
     5. Students answer the questions at the bottom of the assignment page.
     6. The rubric will be provided to students prior to the activity. Students should use the rubric to assess themselves during the activity.
Playing Catch Up 3
Complete each student chart as we did the other day. Then graph the result of each student on the back. Use different colors to distinguish between
the different students.

               Andy                                  Brenda                                Carlos                               Denise

Andy usually scores 96% on his         Brenda usually scores 100% on her      Carlos usually scores 89% on his    Denise usually scores 90% on her
homework. His first assignment is      homework. Her first assignment is      homework. He turns in his first     homework. She turns her first
a zero. How many assignments           a zero. How many assignments           assignment for half credit (50%).   assignment in late and receives half
will it take for Andy to get an A-     will it take for Brenda to get an A-   How many assignments will it take   credit (50%). How many
(90%)?                                 (90%)?                                 him to get a B- (80%)?              assignments will it take her to get
                                                                                                                  an A- (90%)?



               Andy                                Brenda                               Carlos                             Denise
       #      Fraction       Percent        #      Fraction        Percent       #      Fraction      Percent       #      Fraction       Percent
     1                                     1                                     1                                 1
     2                                     2                                     2                                 2
     3                                     3                                     3                                 3
     4                                     4                                     4                                 4
     5                                     5                                     5                                 5
     6                                     6                                     6                                 6
     7                                     7                                     7                                 7
     8                                     8                                     8                                 8
     9                                     9                                     9                                 9
     10                                    10                                   10                                10
     Andy        Brenda        Carlos        Denise
11          11            11            11
12          12            12            12
13          13            13            13
14          14            14            14
15          15            15            15
16          16            16            16
17          17            17            17
18          18            18            18
19          19            19            19
20          20            20            20
1. Which students achieved his or her goal the soonest?



2. Why? Give the best mathematical reason you can.



3. Which student will never reach his or her goal?



4. Why? Give the best mathematical reason you can.



5. How does an F that is a 50% differ from an F that is a ZERO?



6. How does this assignment apply to your grades? What did you learn from this exploration?
   Decision 3: Culminating Activity/Project Rubric



Scale
                                    4                           3                          2                         1
     Criteria


Work was successfully      All 4 problems were       At least 3 problems were   At least 2 problems were   At least 1 problem was
completed in the time    completed successfully.     completed successfully.    completed successfully.    completed successfully.
allowed.




                           Roles were assigned,
Team members worked      followed and rotated with   At least 3 members were    At least 2 members were    At least 1 member was
cooperatively in         all 4 members on task at       on task at all times.      on task at all times.     on task at all times.
assigned roles.                  all times.




                           All 4 problems were       At least 3 problems were   At least 2 problems were    At least 1 problem was
                         solved and graphed in a     solved and graphed in a    solved and graphed in a    solved and graphed in a
Recorded work was
                         neat and understandable     neat and understandable    neat and understandable    neat and understandable
neat and readable.
                                  format.                      format.                    format.                    format.




Total: _______________        Students in this group: ______________________________________________________________
Decision 4: Student Assessments

Plan for how students will indicate learning and understanding of the
concepts in the unit. How will you assess learning?

    •   Short answer tests or quizzes
    •   Student portfolios
    •   Informal Assessment – See Summarizer Lesson 2 for sample questions to be used for informal assessment.
    •   Formal student observations or interviews
    •   Oral or written explanations of daily work
    •   Culminating Activity
Decision 5: Launch Activities
Develops student interest and links prior knowledge. Provides the content
map and key vocabulary to students.

Literature Link: The Math Curse by Jon Scieszka and Lane Smith

1) Read this book to the students. This book is about a girl who wakes up one day to find that everything is a
math problem. In pairs, students will name as many different forms of numbers as they remember from the
story along with the situation in which they were used. They will have 2-3 minutes to do this in pairs. Each
member of the pair records the answers on his/her own paper. Then, they will “Give One, Get One” for 2
minutes. They will go back to their pairs and form a cumulative list. Discuss these as a class and reward the
pair with the most answers.

2) Use the Content Map to give students the big picture of what they will learn in the unit and to
preview the vocabulary.
 Decision 7: Extending Thinking Activities

 Have extending activities or lessons for most important concepts/skills


Cause/Effect       Compare/Contrast      Constructing Support
Justification      Induction        Deduction
Error Analysis     Abstracting      Analyzing Perspectives
Classifying        Example to Idea Idea to Example
Evaluation         Writing Prompts

Lesson 1 – Justification – decimal grid activity
Lesson 2 – Classifying, Compare/Contrast – ratio and proportion
Lesson 3 – Constructing Support – See Lesson 3 Extending and Refining Activity
Lesson 3 – Error Analysis – Summarizer
Lesson 4 – Extending Thinking Lesson
Culminating Activity - Analysis
 Decision 8: Differentiating the Unit
What accommodations will you make in order to meet the varied interests, learning
styles, and ability levels of all students?


 An acceleration lesson is included for those students considered to be at risk. Performance tasks and word problems included
 are from a variety of fields of interest. Students will be provided with choices from which they will select real world problems to
 work. Actually, some of the tasks will be chosen from the list produced by the students during the Launch activity and the first
 lesson. This unit contains auditory, visual, and kinesthetic activities to meet all learning styles. Scaffolding should be used
 where appropriate.




  Decision 9: Lesson/Activity Sequence and Timeline
 What is the most viable sequence for the experiences, activities, and lessons in
 order to help students learn to the best of their abilities? Put the Lesson
 Essential Questions, activities, and experiences in order.
 The lessons and activities in this unit are in Microsoft Word format and are numbered sequentially at the beginning of the
 filename. Headers at the top of each page identify the lesson in which the page or activity is included. Also, the Content Map
 gives an overall picture of the flow of the Unit. Since this is a new unit that has never been taught in 6 th grade there is no time
 period listed on the lessons. This school year will be used to help gauge the pace of the new Georgia curriculum and
 approximate timelines will be added at a later date.
 Decision 10: Review and Revise
How will you review this unit in order to improve it prior to using it again or sharing it?
What criteria will you use to determine the need to make improvements?
List when you will conduct distributed reflection.

 This unit will be used with hundreds of students during the 2005-2006 school year by 6th grade teachers as the new Georgia
 Performance Standards are implemented. Teachers will give feedback during reflection meetings and during consortium
 meetings at RESA.
 The main criteria used to make improvements will be results from on-going formative assessment. Summarizers should provide
 teachers with an indication of student understanding in order to review and revise this unit.
 Distributed reflection will be conducted at the reflection meetings and during consortium meetings. I will ask that teachers keep a
 portfolio of notes during this lesson to help make any adjustments needed. Also, samples of student work will be used to make
 improvements in the unit.




Decision 11: Resources and Materials for Learning Unit
 Daily newspapers with current stock quotes or internet access.
 Bubble Gum – one piece per student
 Chart Paper
 Markers
 Colored Pencils
 Construction Paper
 Scissors
 Glue
 Individual whiteboards or chalkboards
 Envelopes
 Spray Adhesive
           Acquisition Lesson Planning Form
       Plan for the Concept, Topic, or Skill --- Not for the Day


   Essential Question:           How can the same quantity be represented in different ways?


                                 See Launch Activity
   Activating Strategies:
  (Learners Mentally Active)


                                 Review terms: fraction, decimal, percent, denominator, numerator, by using the vocabulary game
Acceleration/Previewing: “Hit or Miss” prior to the unit.
           (Key Vocabulary) During the unit the term equivalent will be taught using a word map. Vinculum will be taught using
                            the Frayer Diagram.
    Teaching Strategies: Use numbered heads to create pairs. Give each pair bags with 10 decimal squares in tenths and
         (Collaborative Pairs;   10 in hundredths. Ones will work with tenths and 2’s will work with hundredths. Students will need
           Distributed Guided    colored pencils, scissors, construction paper, and glue. Ask 1’s to tell partner how many parts their
                     Practice;   grid is divided into. (10). Have 2’s do the same (100). Have 1’s shade in 2 parts of their grid. Have
   Distributed Summarizing;      2’s shade in 20 parts of their grid. Ask pairs to tell each other how this quantity would be written as
         Graphic Organizers)     a fraction not in simplest form but just as they see it (2/10), (20/100). Write these two fractions on
                                 the board. Students will then cut the shaded part of their grids out and compare the quantity by
                                 placing one on top of the other. Use the Word Map to define the term equivalent. Go back to the
                                 fractions on the board and have them read their fractions aloud to each other while the other one
                                 writes the number in words. Add this to the Word Map. Then have pairs brainstorm how the words
                                 they have written would look if the amounts were written as decimals. Check understanding and
                                 add this to the Word Map. Pairs glue their grids on the construction paper and label them in
                                 fraction and decimal form.
                                      This is a good time to present the following analogy: I have students to describe how I am
                                         dressed for school. I ask them to imagine what I would look like if I were working in my yard,
                                         attending a baseball game, going to church, and attending an opera. After pairs discuss, we
                                         list responses in columns on the board. Pose the following question: Have I changed who I
                                         am or am I still “Miss Laurian?” I am still the same person; I have only changed how I look to
                                         fit the situation. This is what we do with numbers.
                                 Have pairs discuss how the fractions and decimals they have created are like dressing for various
                                 occasions. Students work together to create 4 more equivalent amounts and write them in fraction
                                 form and in decimal form. (Tenths should always go first for this activity.) They will trade
                                 “denominators” and create 5 more and record as before. Use pairs squared to have one pair check
                                 another pair’s work.
                                 This is a good time to introduce percent. Ask them to take a look at one of the 100 decimal square
                                 grids. Pose the following questions to pairs: If you were to place one penny in each of the squares,
                                 how many pennies would you have? How many cents would that be? What if you only placed
                                 pennies on 80 of the squares? How many pennies? How many cents? Have pairs write 80 cents
                                 as a decimal the way we usually see it and then using what they have learned, write it as a fraction.
                                 Introduce the idea that the vinculum (vin” cu’ lum) is a fancy name for the fraction bar. Students will
                                 use the Frayer Diagram to learn this new word. There are several different ways to read the
                                 vinculum, such as “out of” “divided by” “for every” or “per.” They think of a word and a picture that
                                 reminds them of vinculum and record on the Frayer. (My example is “Van Column” and I imagine a
                                 van carrying a column for a house on top of it. The column is lying down horizontally on the roof of
                                 the van.) Go back to the fraction formed from 80 cents. Remind them that this fraction represents
                                 80 out of 100 squares covered. Have pairs read the fraction to each other in three different ways.
                                 If we read it as “80 per hundred” or “80 per hundred cents” then it makes “sense” that “per hundred”
                                 means “per cent.” Record this on the Word Map in RED because it is very important that they
                                 remember this fact. So, 80/100 is also the same as 80%. Students divide up their sheets with
                                 decimal grids and go back and write the % to go with the decimals and the fractions. They trade
                                 sheets and check each other’s work.


Summarizing Strategies: 3-2-1: Ones pick a fraction with a denominator of 10. Both students write:
        Learners Summarize &     3 ways to write the quantity;
     Answer Essential Question
                                 2 pictures to show the quantity is the same written in different ways; and
                                 1 statement explaining why the same quantity can be written in different ways.
                                 Write an additional page for the “Math Curse”.
             Homework:
                     What is it?
                                                             What is it like?



Important stuff to
remember:




                                   Equivalent



                                   What are some examples?
              5

              4

              3

              2

              1
                          A                   B                   C                   D                   E

Hit or Miss Directions:
Mary Kunzman and Mary Higham adapted this strategy from The Mailbox (1998) to promote knowledge of
content vocabulary. Select 10-12 vocabulary words for the game. Students copy the words from the word list
in random order somewhere on the gameboard as if placing ships on a Battleship game. Using numbered heads,
ones call out a set of coordinates. If twos have a word in that box, they say “HIT” and call out the word. Ones
then define the word, give an example of the word or use the word in a sentence according to the teacher’s
directions. If they are correct, the box gets crossed off, ones get a point, and it is twos’ turn. If incorrect or if
there is no word in the box, twos say “MISS” and then twos take a turn. The first person to get all of the points
wins – the loser will have all of his/her words crossed off.
Make copies of the grid to send home as homework so that parents can play with their children. Make extra
copies available for students to use when they complete their work or when more vocabulary practice is needed.
Ones: Pick a fraction with a denominator of 10. Tell your partner.
Each person must hand in a response:

            Different ways to write the quantity:




            Pictures to show that two of the above are the
            same:




            Statement explaining why the same quantity can be
            written different ways.




Chat Box:
              Frayer Diagram 1

What is it?           What does it sound like?




                 Vinculum




What does it mean?    Picture
Acquisition Lesson Planning Form
Plan for the Concept, Topic, or Skill – Not for the Day

          Essential Question: How are ratio & proportion used to show relationships?
        Activating Strategies: 3 Corners: Adaptation of 4 corners: See LFS Math 6-12 Activating Tab
      (Learners Mentally Active) Place signs in 3 corners of the room. Each sign has one of the following terms on it: percent, decimal,
                                 fraction. Each student draws a card from the hat with a number on it and writes the equivalent forms on
                                 post-its and posts them on the corresponding sign. Have one student share responses from the signs with
                                 the class.
                                 Blowing Bubbles – LFS Math 6-12 Numbers and Operations page 10
                                 Materials: One piece of bubble gum per student, recording sheet
                                 Have students chew gum until they are able to blow a bubble with it. Students will work in partners and
                                 collect data on the number of bubbles each student can blow in 30 seconds.

    Acceleration/Previewing: Factor, proportion, ratio, cross product – taught in context during the lesson.
               (Key Vocabulary)

         Teaching Strategies: This lesson uses an adaptation of the graphic organizer from LFS Math 6-12 to record understandings
            (Collaborative Pairs;   during the lesson. Discuss the meaning of ratio, ways to draw, write, and say it. Use counters to model it.
    Distributed Guided Practice;    Have students model sample ratios with counters in pairs. Relate ratios to fractions, equivalent fractions,
      Distributed Summarizing;      and percents with the graphic organizer from Lesson 1.
            Graphic Organizers)     Brainstorm where ratios are used in everyday life along with examples. Record on G.O. Give students
                                    real-life examples such as batting averages, miles per gallon, miles per hour, recipes, calories per serving,
                                    etc. Record these on G.O. and stress that the order that the ratio is written is important. This goes in the
                                    “The Scoop” graphic.
                                    Using Baseball Stats 1 handout students will write ratios that represent batting averages. They may bring
                                    up the fact that batting averages are read as decimals. If so, tell them that they will convert the fractions to
                                    decimals, but a ratio must be formed first. Refer to the essential question and stress that in this lesson we
                                    are looking at the meaning of ratio and proportion and how they are used to show relationships.
                                    Students should note that on this sheet, there is a column for decimals and percents. We already learned
                                    that every number can be represented as a fraction, a decimal, and a percent. This does not change the
                                    quantity that is represented – only what it looks like. (Ask them to tell their partners the metaphor used to
                                    remember this – how we dress doesn’t change who we are, only what we look like.)
                                    Notice that the handout uses simple batting statistics such as 5/10, 3/10, and 23/100 to relate writing these
                                    as a decimal and percent the way they did in Lesson 1. Have 1’s write a matchbox summary of what the
                                    ratios stand for and 2’s write a matchbox summary of why they can be written in different ways. Pairs have
                                    two minutes to share their responses and check their partner’s accuracy.
                                    Pairs get together with another pair (pairs squared) and discuss the following: How do you find the
                                    unknown percent when given a ratio in fraction form with a denominator of 5, 10, 20, 25, 50, or 100? What
                                    methods do you use? Are they all the same? Is one way any better than another? Come to some consensus
                                    to prove your method works and record it to explain to the class. They have 5-7 min. (Before they begin
                                    they must designate a timekeeper, a recorder, a mediator, and a speaker. Have speakers share with the
                                    whole class (use overhead if needed). They go back to their pairs and discuss the following: What happens
                                    when you are given a ratio such as 4/7 or 9/17. Give them about 5-10 min. to struggle with this. Suggest
                                    that they go to their math notebooks and refer to their graphic organizer from a previous unit on comparing
                                    fractions. Ask: How do you know if two fractions are equal? (cross products are equal) Given 12/18 and
                                    2/3 show how you know by writing all of the steps. So if we were missing one of the numbers, say 2, then
                                    we would have 12*3=n*18. Since we have solved simple equations before, how would you find out what n
                                    is equal to? When you write two equivalent ratios, this means that you know that their cross products are
                                    equal. Let’s go back to our word map from lesson 1 and review what equivalent means. So, if we write the
                                    steps below the ratios, using a variable for the unknown, then all we need to do is to solve for the variable.
                                    When two ratios are equivalent, this is called a proportion. If we have to find out what one of the numbers
                                    in the proportion is equal to, we are “solving proportions.” How would you check your work?
                                    Let’s record what we know about proportions on our G.O. for this lesson. Give some numerical and word
                                    problem proportions and have students solve them and share with their partner. Samples are included.
                                    After they have done a few through guided practice, take out whiteboards. Using whiteboards 1’s will write
                                    the equation and 2’s will solve for 5 problems. Then switch roles for 5 problems. (These are numerical).
                                    Then do the same for 10 word problems where they write the ratios and set up proportions and solve. Given
                                    the proportion 3/7=n/22, what does this mean. Record on G.O.

                                    Massed Practice: Bubble Gum recording sheets. Use pairs checking.

Distributed Guided Practice/ All questioning above is done in pairs. Summarizing is explained above, also.
     Summarizing Prompts:
    (Prompts Designed to Initiate
            Periodic Practice or
                  Summarizing)
    Summarizing Strategies: The Envelope Please Puzzle Questions – Directions found in both LFS Math books.
       (Learners Summarize &
     Answer Essential Question)
Sample problems:                 Answers:
    3   x             3 9
      
1) 12 28           8) 7  a         1) 7
                                   2)45
    6   x              8   x
      
2) 10 75                 
                   9) 10 15         3)15
                                    4)9
    8 12                x   15
3) 10  n                 
                   10) 100 20       5)15
                                    6)18
   a 3
4) 21  7                           7)16
                                    8)21
    85   c
       
5) 100 20                           9)12
                                   10)15
    7   x
      
6) 14 36

   4 6
7) x  24
1. The weight of the brain is about 2.5% of the total body weight. How much would the brain of
   a 120 pound person weigh?

2. Starting at age 35, humans lose approximately 7,000 brain cells a day that are never replaced.
   How many is this in a week? A month? A year?

3. In one day, humans shed about 10 billion skin flakes. How many billion would they shed in
   the year 2005?

4. Six people out of 40 are left-handed. What percent of the population is this?

5. On your first test you got 40 out of 45 correct. On your second test you got 25 out of 30
   problems correct. Which test had the better percentage?

6. TRUE FACT: In making peanut butter and jelly sandwiches, 96% of the people put on the
   peanut butter first. Out of 12,000 people making sandwiches, how many people would spread
   the peanut butter first?

7. In a bizarre turn of events, 2 people in a certain family stubbed their toe, developed gangrene,
   and died. If there were 16 people in the whole family (including aunts and uncles), what
   percent stubbed their toe?
  8. “Arachibutyrophobia” (pronounced I-RA-KID-BU-TI-RO-PHO-BI-A) is the fear of peanut
     butter getting stuck to the roof of your mouth. What percent of the letters in that word is an
     “a”?

  9. After an extended advertising campaign, the “Don’t Kick Your Poodle” Organization hopes
     to reduce poodle abuse by 15%. If last year there were 548 incidents, how many would there
     be this year?

  10.Yesterday, out of 50 students who were tardy, 80% had lame excuses. How many people is
     this?


Sources: www.pleasanton.k12.ca.us , www.funnyfact.com
 1   3     7    47    8
 2   4    10   100   50

0.45 0.32 0.05 0.7 0.4

97% 14% 56% 78% 6%

 9    55  7     2    3
10   100 100   10    5
22% 37% 8% 40% 60%

0.21 0.26 0.9 0.11 0.3
The Swamp Gravy Mathletes have had a great baseball year! Their stats are shown below. Use the batting
information for the Mathletes to find the information needed to fill in the table.

Player                  Hits At           Fraction      Decimal       Percent
                             Bats

Jackson Wilson            5       10

Jesse Erwin               7       10

Josh Phillips            10       20

Eli Wilson               12       20

Cody Phillips            15       20

Michael Boyd             20       25

Adam Phillips            25       50

Colt Calhoun             45       50

Billy Grimsley           46       50

Kameron Whitaker         72      100
                        Ratio                                  What is it?



                                                                        Say It
Draw It                              Write It



                                                                                  “THE
                                                                                 SCOOP”


Examples
                                          Uses in the Real World




           Proportion                                     What is it?




                    Solve It                                              Your Turn



                                Step 1:
          m 1
           
          4 2
  2  m  1 4                  Step 2:



     2m  4                     Step 3:

          m2
      Acquisition Lesson Planning Form
Plan for the Concept, Topic, or Skill – Not for the Day

          Essential Question: How do I change from one form of a number to another form?
        Activating Strategies: Today’s Number: p. 19 in LFS 6-12 Activating
      (Learners Mentally Active)
    Acceleration/Previewing: Review division when you need to add a decimal and annex zeros; repeating decimals 3-4 days prior to the
               (Key Vocabulary) lesson.
         Teaching Strategies: Make a 3 flap foldable. This is the G.O. to record key understandings and memory aids as the lesson is
            (Collaborative Pairs; taught.
    Distributed Guided Practice; Show decimal to % and % to decimal by moving the decimal point. This is the easiest. May use Tootsie
      Distributed Summarizing; Roll PowerPoint found at www.sw-georgia.resa.k12.ga.us on the math page. Will need to adapt it to fit this
            Graphic Organizers) lesson. Remember that the words and the motions do not coincide. This would defeat the purpose of
                                  practicing with problems if all they did was move the direction that the song states. They must look at the
                                  problem to decide which way to move the decimal point.
                                  Show fraction to % and % to fraction using proportions. Include repeating and terminating decimal answers
                                  and explain that the remainder should be written as a fraction.
                                  Show fraction to decimal by reading the vinculum as “divided by.” Show decimal to fraction for both
                                  terminating and repeating. Use the equation method to explain repeating decimals and the shortcut. See
                                  attached. Show that fraction to decimal can be done by using a proportion to change to % and then moving
                                  the decimal point to change to decimal.
Distributed Guided Practice/ Students should be encouraged to learn the most common equivalent forms such as ½=0.5=50%. Play
     Summarizing Prompts: “Concentration”, “MATHO”, or “I Have – Who Has” to help them memorize these.
    (Prompts Designed to Initiate
            Periodic Practice or
                  Summarizing)
    Summarizing Strategies: Stick-It-Up:
        (Learners Summarize & Use spray adhesive on a three column grid. Columns read fraction, decimal, and percent. One of the three
      Answer Essential Question) is given in each row. Students draw cards from the hat and show their work on a sheet of paper to change
                                 the number on the card to the other two forms. They “stick” their card in the appropriate place on the grid
                                 as they leave. They hand in the paper to be checked. The teacher can then give individual feedback the
                                 next day and there is very little paperwork to be done.
                                 Extending and Refining: Error Analysis – Switch some of the correct answers on the grid and as an
                                 activator the next day they must figure out which ones are in the wrong place and tell where they should be
                                 and why.
I have 50%.                                       I have
                                                         1
                                                         2
                                                           .
Who has this as a fraction?     (Beginning Card)   Who has this as a decimal?

I have 0.5.                                              1
Who has the fraction for 25%?                      I have  .
                                                         4
                                                   Who has this as a decimal?

I have 0.25.                                       I have 0.75.
Who has this plus 0.5?                             Who has this as a percent?


I have 75%.                                                 3
Who has this as a fraction?                        I have     .
                                                            4
                                                                       1
                                                   Who has this plus     written as a percent?
                                                                       4

I have 100%.                                       I have 1.0.
Who has this as a decimal?                                               9
                                                   Who has this minus      ?
                                                                        10

      1                                            I have 10%.
I have   .                                         Who has this as a decimal?
     10
Who has this as a percent?

I have 0.1.                                        I have 0.7.
Who has this plus 0.6?                             Who has this as a fraction?

      7                                            I have 70%.
I have   .                                         Who has this plus 20%?
     10
Who has this as a percent?

I have 90%.                                        I have 0.9%.
Who has this as a decimal?                         Who has this as a fraction?

          9                                             1
I have      .                                      I have .
         10                                             3
                     17                            Who has this as a percent ?
Who has this minus      ?
                     30

         1                                         I have 0.3 .
I have 33 % .
         3                                         Who has this plus 0.3 ?
Who has this as a decimal?
I have 0.6 .                        2
                              I have  .
Who has this as a fraction?         3
                              Who has this as a percent?

         2                    I have 30%.
I have 33 % .                 Who has this as a decimal?
         3
                     2
Who has this minus 36 % ?
                     3

I have 0.3.                         3
Who has this as a fraction?   I have  .
                                   10
                                      1
                              Who has as a percent?
                                      2
 1   3    7
 2   4 10
0.5 0.75 0.7
50% 75% 70%
 9   1
     4
          1
10
90% 25%  100%

0.9 0.25 1.0
1     2       1
3     3      10
        1
0.6   33 %
        3 0.3
 3    10% 30%
10
0.1 0.3
Put the following numbers on the board:

 1      3     1       2      1             1     9
 2      4     3       3      4     1      10    10
  7     3
 10    10   50%     75%    33 1 % 66 2 % 25% 100%
                              3      3

10%    90% 70%      30%     0.5    0.3    0.6   0.25
 1.0    0.1 0.9     0.7      0.3

 M A               T        H          O
Decimal    Decimal    Decimal    Decimal    Decimal
for        for        for        for        for
1          3          1           9         1
2          4          4          10         3

Decimal    Decimal    Decimal    Decimal    Decimal
for        for        for        for        for
  2
66 %
  3
           100%       10%        70%        30%

Fraction   Fraction   Fraction   Fraction   Fraction
for        for        for        for        for
                        1          2
50%        75%        33 %
                        3
                                 66 %
                                   3
                                            25%

Fraction   Fraction   Fraction   Fraction   Fraction
for        for        for        for        for
1.0        0.1        0.9        0.7        0.3
Percent    Percent    Percent    Percent    Percent
for        for        for        for        for
 3          7         2          1          3
10         10         3          3          4

Percent    Percent    Percent    Percent    Percent
for        for        for        for        for
1           1          9                    1
4          10         10
                                 1          2
 1   3    7    47
 2   4   10   100

0.5 0.75 0.7 0.47
50% 75% 70% 47%
 1    55    7    2
 3    72    8    25
  1     7   1    8%
33 % 76 % 87 %
  3    18   2

0.3 0.7638 0.875 0.08
 3    8
15   50
20% 0.16
0.2 16%
      Acquisition Lesson Planning Form
Plan for the Concept, Topic, or Skill – Not for the Day

          Essential Question: How do I use Constructing Support to provide support or proof of statements?
        Activating Strategies: Situation:
     (Learners Mentally Active) The school is considering a new dress code. Our class has been asked to give input for the new dress code.
                                  Brainstorm ideas in pairs (3-5 min.). Choose one of your ideas to submit to the committee for approval.
    Acceleration/Previewing: Constructing Support
               (Key Vocabulary)
         Teaching Strategies: The teacher models the steps in Constructing Support. These steps should be posted.
            (Collaborative Pairs;    1. Write a position statement.
    Distributed Guided Practice;     2. Decide if it is fact or opinion. (If fact, you will provide proof. If opinion, you will provide support.)
      Distributed Summarizing;       3. Determine if the situation warrants support. (If so, give reasons.)
            Graphic Organizers)      4. Use facts, evidence, examples, or appeals to support your argument.

                                     Use the graphic organizer from the LFS strategies book or the Extending and Refining flipchart to record
                                     information as you model the steps.


Distributed Guided Practice/ Prompts: Why is this skill important? Where might it be used in jobs? In school? At home? In other real
     Summarizing Prompts: life situations?
    (Prompts Designed to Initiate
            Periodic Practice or
                  Summarizing)
    Summarizing Strategies: The Important Thing about Constructing Support is …
       (Learners Summarize &
     Answer Essential Question)
Constructing Support



    Position Statement
Extending Thinking Lesson Planning Form
  Essential Question: What is the best way to change fractions to decimals?

         Mini-Lesson: Situation:
                          You have been asked to tutor 5th graders on how to change fractions to decimals. You must decide if you
                          think it is best to teach them to set up the fraction as a division problem where you place the decimal point,
                          annex zeros, and divide or to set up a proportion and solve.




                  Task: Groups of four:
                          Using a graphic organizer for Constructing Support, prepare a presentation on why you think that 5th
                          graders should be taught to use the method of your choice. This presentation will help you get the job to
                          tutor 5th graders. Remember to include all of the steps in Constructing Support. A rubric is attached that
                          will be used to grade your presentation.
                          Note to teacher: These steps should be posted.
                              5. Write a position statement.
                              6. Decide if it is fact or opinion. (If fact, you will provide proof. If opinion, you will provide support.)
                              7. Determine if the situation warrants support. (If so, give reasons.)
                              8. Use facts, evidence, examples, or appeals to support your argument.


 Summarize/Sharing: Students will present their method to the entire class.



          Assignment: Batting Stats 2 : A worksheet with statistics from the Atlanta Braves’ 2004 season is included. A blank
                          worksheet is included if you would like to have students search the internet to find their favorite baseball
                          payers’ statistics. If this is not possible, go to http://mlb.mlb.com/NASApp/mlb/mlb/stats/index.jsp and
                          select a team and print out stats. Be sure to elimate or cover up the column that gives the batting average.
                          They should complete the discussion athe the bottom of the sheet analyzing the stats and explaining their
                          thinking. (Mathenese is what we call “Math Talk.”) Use pairs checking.
                                      Need On-
                You’ve Got                               Go Back to
                                       the-Job
                 the Job                                  School
                                      Training
                                     Believable but
                  Logical and        not related to
                                                        What reasons and
Position       directly related to    some of the
                                                             facts?
Statement      reasons and facts       facts and
                                       reasons.

               Variety of devices
                 such as facts,
                                      Some devices
                    evidence,                           No devices used to
Support or                           used to support
                 examples, and                         support the argument
Proof                                 the argument
                appeals support
                  the argument
                                        Clear and
                   Clear and                                 Unclear or
                                     accurate, close
                accurate, within                        inaccurate, no time
                                      to time frame,
                the time frame,                          frame, and visual
                                           visual
Presentation       and visual                           absent or does not
                                        somewhat
                 enhances the                                add to the
                                      enhances the
                  presentation                              presentation
                                       presentation
From the information given, choose 10 baseball players and find their batting averages as
 fractions, decimals, and percents.

 Player                   Hits At            Fraction       Decimal         Percent
                               Bats




  Pick one player and analyze his stats. Explain what each statistic means in detail.
 Use “Mathenese” words to explain your thinking.
                                     Batter Up!

 Player                   Hits At            Fraction        Decimal        Percent
                               Bats

 A. Jones                  119      570

 R. Furcal                 157      563

 J. Drew                   158      518

 C. Jones                  117      472

 J. Estrada                145      462

 M. Giles                  118      379

 A. LaRoche                 90      324

 J. Franco                  99      320

 M. DeRosa                  74      309

 Pick one player and analyze his stats. Explain what each statistic means in detail.
Use “Mathenese” words to explain your thinking.
    Extending Thinking Lesson Planning Form
 Essential Question: How do I know which form of a number to use?
      Mini-Lesson: Carousel Chairs: Instead of moving around the perimeter of the room, students will be in groups of 4 and will change
                   seats after working one problem on each sheet. This can also be done by students staying in the same seat and passing
                   the sheets around in a circle. See attached for what should be on each sheet. Be sure to include questions as well as
                   problems.
                   Check student understanding by comparing answers from each group.
            Task: Problem solving lesson: Use ROPES and the flipchart to have students solve problems involving various forms of
                   numbers. There should be an emphasis on the “P” – Plan. This is where students should look for clues in the problem
                   that tell them which form of the number is best to use and which form the final answer should be in. Students must be
                   able to explain why they worked the problem the way that they did and why they chose the form that they chose.
                   They will be working in small groups on this task.
Summarize/Sharing: Students will share their solutions and reasons with the whole class. This is a great time to point out that all of them
                   did not work the problem the same way. They should, however, be able to explain their thinking and why they chose
                   to use the form of the numbers that they chose. The answer must be in the correct form.
      Assignment: Massed Practice:
                   Each group is given authentic problems dealing with situations of choice. Students will work individually and then get
                   together to check their work. Problems can be found at:
                   http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Proportions/Proportions_Index.html

                          Each student will work the following two problems:
                          http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Percents/PlayingCatchUp1and2/PlayingCatchUp1.html
                          http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Percents/PlayingCatchUp1and2/PlayingCatchUp2.html
Are the following ratios equivalent?   Solve each proportion.
Prove your answer.

       8 12                                    8 x
         ,                                      
1)    12 8                             1)     12 8


       1 3
        ,                                     9 6
2)     2 4                                     
                                       2)     n 18


        4 6                                   x   7
         ,                                      
3)     14 21                           3)     5 100


       16 17                                   4 6
         ,                                      
4)     32 33
                                       4)     14 x
Set up the proportion and solve.        Answer the questions.
  1) Franco uses 2 teaspoons of         1) How do you remember what
     fertilizer for each gallon of         equivalent means?
     water. How many gallons can
     he make with 15 teaspoons of
     fertilizer?




  2) Furcal has an ERA of 0.381.        2) How do your remember what
     How many hits did he get if he        the vinculum is?
     went to bat 21 times?




                                        3) What does it mean when we
  3) Goodwin of the Chicago Cubs           say that two ratios are
     had 21 hits out of 105 at bats.       equivalent?
     What is his hitting percentage?




  4) A recipe for muffins calls for 2
                             1          4) How are fractions, decimals
     cups of flour for each 1 cups         and percents alike and how are
                              2
     of sugar. How much sugar is           they different? (in just a few
     needed if 8 cups of flour are         words)
     used?
Snapshot of Webpage for massed practice problems.
Ratios, Proportions, and Percents
                                            Ratios and Proportions
Statue of Liberty                                         Tree Problem

Can be used as an introductory activity or a pre-         An activity that actually utilizes (in an authentic way)
assessment.                                               ratios.
Pulling Cubes                                             Swimming Pool Problem

After pulling cubes from a can and recording the          Students use proportions to create a table to be used by
results, students use proportions to "predict" the        swimmers for their work-out.
number of cubes of each color that are in the can.
Nautical and Statutes                                     Water, Juice, and Punch

Similar to the Swimming Pool Problem, students use        Can be used as an assessment activity.
proportions to create a conversion table between
nautical and statute miles.
Giant Hand

Another cool activity that can be used as an
assessment. It is very similar to the Statue of Liberty
problem, so makes for a great "before/after"
comparison.
                                                     Percents
Playing Catch Up 1           Playing Catch Up 2           Playing Catch Up 3           FDP Organizer

How bad does it after your   Further investigation of   Another extension.             A visual method for
grade to get a ZERO on a     how your grade is affected                                memorizing common
homework assignment?         by ZEROS rather than                                      fraction, decimal, and
This cool activity answers   "half credits".                                           percent equivalencies.
that question.
Growing Pyramids             Coke Pie Chart               Percents with Pattern        Cuisenaire Percents
                                                          Blocks
Converting between        Take actual Coca-Cola                                        Using Cuisenaire Rods to
fractions and percents.   data and convert it into a      Each block gets a chance     investigate what percent
Cool patterns.            pie chart. Converting           to be 100%.                  one rod is of another rod.
                          fracitons, decimals, and
                          percents.
Cuisenaire Back and Forth Percent Painter                 Dividing The Dollars         Human Percentages

Using Cuisenaire Rods to Using multi-link cubes to        Divinding up a certain       What percent of your body
investigate what percent convert fractions into           amount of money              is your head? Lots of other
one rod is of another rod. percents. Lots of cool         according to percentages.    cool questions.
Backwards and forwards.   patterns.
Business Percents          Science Fair               Anita's Cake                Percent Practice 1

Which payment plan is     Students convert between A problem involving            Word problems.
best for you?             fractions, decimals, and      fractions and percents.
                          percents to solve a real-life
                          problem.
Percent Practice 2        Percent Practice 3            Percent Practice Review   Percent Increase and
                                                                                  Decrease
Word problems.            Lots of word problems.      Lots and lots of word
                                                      problems.                   Calculating percent
                                                                                  increase and decrease of
                                                                                  real-life problems.
Bigger and Smaller         Percent Review
                          1999/2000
Problems taken from
actual product labels!    Just like it says.
Playing Catch Up 1
Playing Catch Up 2

								
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