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Balanced Math K-8.ppt - mnpsmath

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					Balanced Math
    K-8 Framework
     October 2010



     Saville-Brock 2010   1
Norms

• Be prompt
    Return from breaks on time
• Be respectful
    Put cell phones on silent.
• Be a polite and positive participant
    Speak in a normal tone of voice, and listen
     attentively.
• Be a problem solver




                      Saville-Brock 2010           2
Who are these guys?



     This is who I am
     by the numbers…..
         1985, 25,
          155551


            Saville-Brock 2010   3
By the numbers…….

• A significant year in my
  life was 1985
• I’ve spent 25 wonderful
  years with MNPS.
• My favorite palindrome
  is 155551.
           Saville-Brock 2010   4
Meet your neighbor by the
numbers…
• Select 5 numbers that are meaningful to
   you that will help someone understand
   who you are.
• Then write a sentence or question for
   each number, leaving a blank line where
   the number should go.
• Share you numbers and sentences with
   your neighbor. See if he or she can
   match the correct number to the line.


                Saville-Brock 2010       5
Activity: Group and Label

• Write each of your numbers on a post it.
  One number per post it.
• Place all of your numbers from your table
  in the middle and eliminate any duplicates.
• Then group your numbers and label them
  according to some common
  characteristics. Then turn you labels over.
• Visit another table and try to figure out
  there groupings.
• Discuss how you can use this activity in
  your own classroom.
                  Saville-Brock 2010       6
Why a Balanced Approach?




            Saville-Brock 2010   7
Why a Balanced Approach?

   The National Mathematics Advisory Panel
   States…


   “The mutually reinforcing benefits of
   conceptual understanding, procedural
   fluency, and automatic, i.e. quick recall of
   facts.”




                  Saville-Brock 2010              8
            Conceptual
           Understanding




Computational                        Problem
  Fluency                            Solving


                Saville-Brock 2010             9
Why a Balanced Approach?

 Traditional Approach to Teaching
               Math
 • Large group instruction
 • All students work on the same level
 • Primarily instruction and practice from
   text book
 • Emphasis on paper and pencil work
 • One correct answer
 • Individual work
                  Saville-Brock 2010         10
Why a Balanced Approach?
 Effectiveness of the Traditional
            Approach
 • Successful for some students
 • Even less successful for struggling
   students
 • Encourages emphasis on computation
   skills
 • Little opportunity for communication
 • More emphasis on evaluation, rather
   than assessment for learning

                 Saville-Brock 2010       11
Why a Balanced Approach?
The Statistics
• Fifth graders spend more than 90
  percent of their time in their seats
  listening to the teacher or working alone
  and only about 7 percent of their time
  working in groups.

• The average fifth grader received five
  times as much instruction in basic skills
  as instruction focused on problem
  solving or reasoning. The ratio was 10:1
  in first and third grades.
                     From a study published by Robert Pianta et al.
                    The Global Achievement Gap by Tony Wagner.
                 Saville-Brock 2010                        12
Why a Balanced Approach?
 To teach math more effectively,
 teachers must…
  • reach students at all levels of
    achievement

  • provide diverse methods of learning

  • allow more opportunities for
    observation and communication by
    students

  • encourage active engagement by
    students      Saville-Brock 2010      13
  Teaching Procedures
What the Research and Experts Say
 According to the National Mathematics
  Advisory Panel, students should
    understand key concepts
    achieve automaticity as appropriate (e.g.,
     with addition facts)
    develop flexible, accurate, and automatic
     execution of standard algorithms
 Computational Proficiency is dependent on
    automatic recall of math facts
    a solid understanding of core concepts

       National Mathematics Advisory Panel. Foundations for Success: The Final
       Report of the National Mathematics Advisory Panel, U.S. Department of
       Education: Washington, DC, 2008.
                                 Saville-Brock 2010                              14
              Conceptual vs. Procedural

                  Striking the Balance

 Vocabulary                                 Four
  development                                 operations
 Manipulatives                              Standard-
                                              algorithms
 Multiple
  representations                            Step-by-step
                                              methods
 Pictures
                                             Math facts
 Real-life
  contexts                                   Release of
                                              responsibility
                                             Practice

                       Saville-Brock 2010                  15
Day            15 min                              40 minutes                         5 minutes
 1    Math         Mental    Concept Lesson                                           Closure/
      Review       Math      Problem solving, manipulatives, small groups, centers    math
                                                                                      journals
 2    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

 3    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, small groups , centers

 4    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

 5    Math Facts Practice/   Problem-based activities, centers, games, small groups
       Math Review Quiz
 6    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

 7    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

 8    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

 9    Math         Mental    Concept Lesson                                           Closure
      Review       Math      Problem solving, manipulatives, small groups, centers

10     Assessment/Math                                       Assessment
                                        Saville-Brock 2010                                  16
         Review Quiz
Saville-Brock 2010   17
Saville-Brock 2010   18
•One more/one less, before/after, a given number

•Counting by twos, fives, tens

•Doubles

•Fact families

•Measurement (time, money, calendar, feet, etc.)

•Math Vocabulary/Math Word Wall

•Addition &/ or Subtraction Facts

•Estimation

•Math Around the Room
                         Saville-Brock 2010        19
     Math Review and Mental
       Math- Rally Coach
  Partners Take turns, one solving a problem while the other coaches.
  Each pair needs one set of problems and one pencil.


           Person A                                    Person B

• Partner A solves the first • Partner B watches and
  problem. Talking out         listens, checks, coaches
  their thinking.              if necessary and praises.
• Partner A watches and      • Partner B solves the
  listens, checks, coaches     next problem. Talking
  if necessary, and praises.   out their thinking.


                                  Saville-Brock 2010                    20
Saville-Brock 2010   21
                 Balanced Math
    What is Conceptual Understanding?
 It is the underlying knowledge behind the concept
 Teaching techniques include: concrete models, vocabulary
  connections, problem solving, real-life applications, etc.
 Conceptual understanding is important for two main reasons:
    In order to apply knowledge to new situations
    Subsequent math concepts rely on students’ ability to
     understand the current concept




                           Saville-Brock 2010            22
Conceptual Understanding




            Saville-Brock 2010   23
Vocabulary Development




 Content vocabulary words are used within the subject
 matter you are teaching (e.g., fractions, decimals).
 Academic vocabulary is the higher-level language
 needed to understand the content (e.g., analyze,
 identify).
                   Saville-Brock 2010                   24
          Vocabulary Development
                           Word Wall
 Bulletin board display of
  key vocabulary or concept
  words
 Students can be involved
  in their creation
 Include illustrations,
  photos, examples
 Refer to the words often
  during instruction

                                    http://www.kealakehe.k12.hi.us/amilwordsmedia/FWWordWall/FWWordW
                                    all-Images/21.jpg

                             Saville-Brock 2010                                          25
     Vocabulary Development
    Developing Math Vocabulary to
      Make Concepts Accessible



 Identify      Decide on            Engage Your
Vocabulary      Teaching             Students!
  Words        Strategies




               Saville-Brock 2010             26
   Group and Label Activity

Purpose:
Group and Label asks students to conceptualize
  their way to deep understanding by organizing
  mathematical data into meaningful categories.
  Students analyze a collection of mathematical
  information, group the items into categories,
  and label each category in a way that explains
  why the items go together. Finally, students
  use their labeled groups to generate a set of
  hypotheses or generalizations, which they
  revisit periodically and refine in light of new
  Learning.


                  Saville-Brock 2010           27
Saville-Brock 2010   28
Problem Solving

                      A Starting Point
                    for Problem Solving

    Many children think of mathematics as a
     subject that relies on their memorizing
    facts and practicing skills. But, the true
  test of children’s success in mathematics is
   when they can’t remember a fact or have
     forgotten a skill, they are able to think,
     reason, and solve problems and make
          sense of mathematical ideas.
                                        Marilyn Burns



                   Saville-Brock 2010                   29
Thought is
STRATEGIC…
Therefore, we need a
classroom that models
instructional practices and
strategies that enhance
students’ ability to think.

        We can't solve problems by using the
        same kind of thinking we used when we
        created them.
        -- Albert Einstein
             Saville-Brock 2010                 30
Teaching through Problem
         Solving




         Saville-Brock 2010   31
How Much Does Matt Weigh?

What We Know…….
• Matt’s head weighs 15 lbs
• His torso weighs as much as
  his head and legs together
• His legs weigh as much as his
  head and half his torso

             Saville-Brock 2010   32
       Using
Manipulatives




 Saville-Brock 2010   33
Using Manipulatives

What Are Manipulatives?
Manipulatives are colorful, intriguing
materials constructed to illustrate and
model mathematical ideas and
relationships and are designed to be
used by students in all grades (Burns
and Sibley 2008).




                Saville-Brock 2010        34
Using Manipulatives

Why Use Manipulatives?

Using Manipulatives, “helps
 students understand the
 mathematical concepts and
 processes, increases thinking
 flexibility, provides tools for
 problem-solving, and can
 reduce math anxiety for some
 students. (The Education
 Alliance 2006).

             Saville-Brock 2010    35
          Using Manipulatives
    Classroom Management Tips for Manipulatives
• Organize manipulatives.   • Set expectations.




                                 • Give students time to
• Model examples.                  practice.




                    Saville-Brock 2010                     36
Laura went shopping




            Saville-Brock 2010   37
 Using Manipulatives
Phases of Instruction and Learning
             C-R-A




-Moving with Math




                    Saville-Brock 2010   38
Using Manipulatives

          Concrete
Hands-on teaching method using
manipulatives such as:
 • Algebra Tiles
 • Toothpicks
 • Counting blocks
 • Unifix Cubes
 • Cuisenaire Rods
 • Food
 • Algeblocks
 • Balance scales
 • Hands-On Equations
             Saville-Brock 2010   39
Using Manipulatives
        Representational
 Uses:
 • Pictures
 • Tally marks
 • Diagrams
 • Drawings
 • Maps
 • Graphs
 • Charts


 Relates directly to the manipulatives
                 Saville-Brock 2010      40
Using Manipulatives
          Abstract
A teaching method using written words
and symbols.
 • Graphs (meaning)
 • Matrices
 • Estimation
 • Predictions
 • Tables (ex. slope)
 • Oral explanations
 • Systems of equations

              Saville-Brock 2010        41
Differentiating to Meet Students Needs
      Mathematical Thinking Tasks
Think about the enduring understandings.
 – What do you want students to learn during the activity?
 – All students should work toward the same objective.



Objective: Students will demonstrate understanding of the
relationship between factor, product, and multiple.




                            Saville-Brock 2010               42
   Differentiating to Meet Students Needs
 • Create the activity you want your on-grade-level
   students to complete.
1) On graph paper, draw an array to represent the multiplication problem 3 x 4.
   What is the product? How do you know?
2) Make an array with a different length and width, but with the same product as
   3 x 4.
3) Write a multiplication number sentence to represent your array.
4) For both arrays, complete the sentences below by writing the number in the
   blank.

   This array has ____ rows by _____ columns.
   This array has _____groups of _____.
5) List the factors shown in both arrays.
6) The product is also called a multiple. How is the
   multiple related to its factors?
7) List some other multiples and their factors.
                               Saville-Brock 2010                         43
   Differentiating to Meet Students Needs
• Revise the activity for your English language learners.

                                                                        4
1) An array is putting objects in equal rows and
                                                           2
   columns to make a rectangle. On graph paper, draw
   an array to show the multiplication problem 3 x 4.            array
2) The product is the answer to a multiplication
   problem. What is the product of 3 x 4?
   How do you know?                                       3x4=
3) Draw an array with a different length and width. Use                     product
   the same number of squares, so the array has the
   same product as 3 x 4.
                                                               length




                                                                                  width
4) An example of a multiplication number sentence is 2
   x 4 = 8. Write a multiplication number sentence for
   your array?



                                Saville-Brock 2010                           44
   Differentiating to Meet Students Needs
    Revise the activity for your English language learners.
                                                                column
5) For both arrays, complete the sentences by writing
    the number in the blank.                              Row
   This array has ___ rows by ___ columns.
   This array has      groups of ____.
6) The factors are the number of objects in a row and a
    column of the array. Write the factors shown in the
    row of columns of both arrays.
7) The product is also called a multiple. How is the
    multiple related to its factors. You can show your
    answer with pictures.
8) Draw arrays showing other multiples and their
   factors.

                                 Saville-Brock 2010                      45
   Differentiating to Meet Students Needs
• Revise the activity for your below-grade-level students.

1) Write a number sentence with repeated addition to represent this array.
2) Write a multiplication number sentence to
   represent the array.
3) What is the product of the number sentence? How do you know?
4) For the array, complete the sentences by writing the number in the blank.
   This array has ____ rows by _____ columns.
   This array has _____groups of _____.
5) What are the factors of the product shown in this array?
6) The product is also called a multiple. How is the
    multiple related to its factors
7) Using manipulatives, make an array with a different factors,
   but with the same product as 3 x 4. Draw this array.
   Name the factors and the multiple.
                                Saville-Brock 2010                           46
   Differentiating to Meet Students Needs
• Revise the activity for your above-grade-level students.

1) On graph paper, draw an array to represent the multiplication problem 6 x 4.
   What is the product? How do you know?
2) Make at least two arrays with different factors, but with the same product as
   6 x 4.
3) Write multiplication number sentences to represent your arrays.
4) List the factors shown in all of your arrays. Does the product or multiple have
   any other factors, not shown in your arrays?
5) How is the multiple related to its factors?
6) Write a real-life scenario to represent one of your arrays. What are the
   factors, product, and multiple in your scenario?




                                 Saville-Brock 2010                           47
    Game Time!

Concept-Based Games




      Saville-Brock 2010   48
• Math Journals
• Reflect individually and with
  whole-group
• Record representation of key
  concepts
• Opportunity to use math
  vocabulary/word wall in context
• Pose questions
• Making their thinking visible!

               Saville-Brock 2010   49
Three-Way-Tie

1. Along each side of the triangle, the student
   writes a sentence that clearly relates the two
   terms.
2. Have students use their three sentences to
   develop a brief summary of the concept.
3. Allow students time to share and explain what
   they wrote on their organizers.


   PRODUCT, FACTORS,
       MULIPLES
                     Saville-Brock 2010             50
Saville-Brock 2010   51
FORMATIVE—checking on learning
 as students progress

SUMMATIVE—checking on learning
 at the end of the learning
 experience



              Saville-Brock 2010   52
       Assessment
“When the cook tastes the
 soup, that’s formative; when
 the guests taste the soup,
 that’s summative.”

                           (Stake, 2005)




              Saville-Brock 2010           53
        Bringing It
        Altogether




Saville-Brock 2010   54
Bringing It Altogether
      Mix-Freeze-Share
• What resources do you use
  to teach mathematics?
• How do you determine what
  to teach?
• What is the process you use
  to write your lesson plans?




                  Saville-Brock 2010   55
Bringing It Altogether
      Things to Consider
• Amount of instructional time for each phase
• Meeting students’ needs
• Grouping of students
• Strategies for engaging students
• Differentiation strategies to be used
• How are students’ assessed on the TCAP?




                   Saville-Brock 2010           56
Balanced Math Lesson

• In a grade level group, develop a Balanced
  Math Lesson that you could use in your class
  this year.
• We will share with the group in a gallery walk at
  the end of the day.
• On chart paper, include your math
  review/mental math, strategies and methods for
  teaching the concept, and the closure.




                    Saville-Brock 2010            57

				
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