Teaching Early Math Skills
A. Relationships
1. Size and Quantity (single object)
- big - little
- long-short
- large - small
- many - few
- high - low
- all - none
- heavy - light
- thick - thin
2. Position
- Under - over
- first - last
- middle
- high - low
- far - near
- bottom - top
- above - below
- in front of - behind - on top of
- beside - by - next to
- between
- around
- inside - outside
- right - left
3. Comparison of Two or More Quantities
- younger(est) - older(est)
- fewer(est)
- more(most - less(least) - referring to sets
- greater than - less than - referring to sets
- larger(est) - small(est)
- longer(est) - shorter(est)
- straight - crooked
- bigger(est) - littler(est)
- heavier(est) - lighter(est)
- taller(est) - shorter(est)
- thicker(est) - thinner(est)
4. Measurement
Capacity
- empty - full
- pair
- cupful
- spoonful
- pint
- quart
- liter
- gallon
Linear
- ruler
- yardstick
- meterstick
Temperature
- hot - cold
- thermometer
- degree
Weight
- pound
- ounces
- grams
Time
- early - late
- yesterday - tomorrow
- today
- morning - afternoon
- noon - midnight
- night - day
- evening
- minute
- hour
- week
- month
- year fast - slow
Money
- penny
- nickel
- dime
- quarter
- buy - sell
- spend - save
- pay
- cost
5. Awareness of Similarities and Differences (sorting activities according to)
- categories - animals, boys, girls, etc.
- position - first, second, third
- shape
- size
- color
- thickness
6. Geometric Figures and Shapes (sorting activities with and recognition of)
- square
- rectangle
- circle
- triangle
- cube
- sphere (globe)
- cylinder
- prism
- open and closed curve
7. 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
- extending incomplete patterns
- creating patterns
Concept Cluster Sets
Elementary Concepts of Sets
- recognizing a set as a collection of distinguishable objects
- demonstrating one-to-one correspondence between elements of two disjoint sets
- recognizing one-to-one correspondence between elements of two disjoint sets
- using one-to-one correspondence to show two sets are equivalent
- recognizing equivalent sets
- recognizing non-equivalent sets
- comparing two or more disjoint sets by visual inspection
- constructing disjoint sets which model the same cardinal number
- constructing disjoint sets which contain one element more or (less) than the given set
- matching numeral with the number of elements in a given set
- identifying the empty set
- recognizing a subset of a given set
- recognizing union of two disjoint sets
- modeling union of two disjoint sets
- recognizing set separation
- modeling set separation
More advanced concepts of Sets
- recognizing two overlapping sets
- recognizing intersection of sets
- recognizing the distinction between finite and infinite sets
- knowing the meaning of replacement set
- knowing the meaning o solution set
- describing the universal set
- interpreting Venn diagrams
- construction Venn diagrams
- recognizing the complement of sets
Concept Cluster-Counting Numbers and Whole Numbers
- rational counting by 1's to 10
-
understanding cardinality of numbers (0-9)
viewing a model of a set and verbally stating its cardinality (0-9)
modeling a set after hearing a cardinal number (0-9) - rational counting by 1's to 20, 50, 100
-
rational county by 2's
starting with two to 29
starting with one to 19
starting with any given two-place number
starting with any given many-place number - rational county by 5's
- rational counting by 10's
- rational counting by 100's
-
Identifying the number of objects in a set
by counting
by partial counting
by counting using other than ones
by using subsets - selecting a specific number of objects from a set with many objects
- relating the term "greater than" to > when comparing numbers
- relating the term "less than" with< when comparing two numbers
- relating the term "equal to" = when comparing two numbers
-
establishing the law of trichotomy
identifying equalities and inequalities
relating terminology "greater than," "equal to," and "less than" to part A
introducing symbols <,>,= -
Concept cluster number numeral (whole numbers)
associating the proper numeral with a set model (0-9)
forming a set model when given a numeral (0-9)
writing numerals 1, 2, 3
writing numerals 3,4,5
writing numerals 6,7,8,9
Associating the proper numeral with a set model (10-99)
Forming a set model when given a numeral (10-99)
Writing numerals 10-20
Writing numerals 20--99
Recognizing odd and even numbers
Associating a written word name with a numeral
Writing a word name for a number when shown a given numeral
Associating a roman numeral with a given number
Writing a roman numeral for a given number
