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How to Enhance Children's Math Skills

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That Teachers & Parents Can Use as Guidelines For Mental Growth

Relationships

 

  1. Size and Quantity (single object)
    a.  big - little
    b.  long - short
  1. tall – short
  2. large – small
  3. many – few
  4. high – low
  5. all – none
  6. heavy – light
  7. thick – thin
Position

  1. under - over
  2. first – last
  3. middle
  4. high – low
  5. far – near
  6. bottom – top
  7. above – below
  8. in front of – behind – on top of
  9. beside – by – next to
  10. between
  11. around
  12. inside – outside
  13. right – left

Comparison of Two or More Quantities

  a.  younger(est) – older(est)
  b.  fewer(est)

  1. more(most) – less(least) – referring to sets
  2. greater than – less than – referring to sets
  3. larger(est) – shorter(est)
  4. longer(est) – shorter(est)
  5. straight – crooked
  6. bigger(est) – littler(est)
  7. heavier(est) – lighter(est)
  8. taller(est) – shorter(est)
  9. thicker(est – thinner(est)

Measurement

  a.Capacity
     1)  empty - full
     2)  pair
     3)  cupful
     4)  spoonful
     5)  pint
     6)  quart
     7)  liter
     8)  gallon
  b.  Linear
     1)  ruler
     2)  yardstick
     3)  meterstick
  c.  Temperature
     1)  hot - cold
     2)  thermometer
     3)  degree
  d.  Weight
     1)  pound
     2)  ounces
     3)  grams
  e.   Time
     1)  early - late
     2)  yesterday - tomorrow
     3)  today
     4)  morning - afternoon
     5)  noon - midnight
     6)  night - day
     7)  evening
     8)  minute
     9)  hour
   10)  week
   11)  month
   12)  year
   13)  fast - slow
  f.  Money
     1)  penny
     2)  nickel
     3)  dime
     4)  quarter
     5)  buy - sell
     6)  spend - save
     7)  pay
     8)  cost

Awareness of Similarities and Differences (sorting activities according to)

  1. categories – animals, boys, girls, etc.
  2.  position – first, second, third
  3. shape
  4. size
  5. color
  6. thickness
  7. Geometric Figures and Shapes (sorting activities with and recognition of)
    square
    rectangle
    circle
    triangle
    cube
    sphere (globe)
    cylinder
    prism
    open and closed curve
  8. Patterns
Discovering a pattern in a given arrangement of objects using the attributes of color, shape, size and thickness

  1)  one attribute

  2)  two attributes

  3)  three attributes

  1. extending incomplete patterns
  2. creating patterns

    Concept Cluster-Sets

 Elementary Concepts of Sets

  1. recognizing a set as a collection of distinguishable objects
  2. demonstrating one-to-one correspondence between elements of two disjoint sets
  3. recognizing one-to-one correspondence between elements of two disjoint sets
  4. using one-to-one correspondence to show two sets are equivalent
  5. recognizing equivalent sets
  6. recognizing non-equivalent sets
  7. comparing two or more disjoint sets by visual inspection
  8. constructing disjoint sets which model the same cardinal number
  9. constructing disjoint sets which contain one element more or (less) than the given set
  10. matching numeral with the number of elements in a given set
  11. identifying the empty set
  12. recognizing a subset of a given set
  13. recognizing union of two disjoint sets
  14. modeling union of two disjoint sets
  15. recognizing set separation
  16. modeling set separation

More Advanced Concepts of Sets

  1. recognizing two overlapping sets
  2. recognizing intersection of sets
  3. recognizing the distinction between finite and infinite sets
  4. knowing the meaning of replacement set
  5. knowing the meaning of solution set
  6. describing the universal set
  7. interpreting Venn diagrams
  8. constructing Venn diagrams
  9. recognizing the complement of sets

 

 

Concept Cluster-Counting Numbers and Whole Numbers
1.  Rational counting by 1’s to 10
2.  Understanding cardinality of numbers (0-9)

  1. viewing a model of a set and verbally stating its cardinality (0-9)

        2.  modeling a set after hearing a cardinal number (0-9).
        3.  Rational counting by 1’s to 20, b. 50… c. 100…
        4.  Rational counting by 2’s

  1. starting with two to 20
  2. starting with one to 19
  3. starting with any given two-place number
  4. starting with any given many-place number

 

        1. Rational counting by 5’s
        2.Rational counting by 10’s
        3. Rational counting by 100’s

  1. Identifying the number of objects in a set
    a.  by counting
  2. by partial counting
  3. by counting using other than ones
  4. by using sub-sets
    a. Selecting a specific number of objects from a set with many objects
  5. Relating the term “greater than” to > when comparing numbers
  6. Relating the term “less than” with < when comparing two numbers
  7. Relating the term “equal to” with = when comparing two numbers
  8. Establishing the law of trichotomy
    a.  identifying equalities and inequalities
    b.  relating terminology “greater than,” “equal to,” and “less than” to part A
  9. introducing symbols <, >, =

D.  Concept Cluster – Number/Numeral (Whole Numbers)

       1.  Associating the proper numeral with a set model (0-9)

       2.  Forming a set model when given a numeral (0-9)

       3.  Writing numerals 0,1,2

       4.  Writing numerals 3,4,5

       5.  Writing numerals 6,7,8,9

       6.  Associating the proper numeral with a set model (10-99)

       7.  Forming a set model when given a numeral (10-99)

       8.  Writing numerals 10-20

       9.  Writing numerals 20-99

     10.  Recognizing odd and even numbers

     11.  Associating a written word name with a numeral

     12.  Writing a word name for a number when shown a given numeral

  1. Associating a roman numeral with a given number
  2. Writing a roman numeral for a given number
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