Gifting Your Child:
Math and Literacy from Infancy
Table of Contents
Introduction
A synopsis of what Grandson was taught by the age of 5
My hope in writing this book is to inspire prospective parents, young parents...
Level 1
Starting off with music and number-words (age of 1 week)
The alphabet and numbers (age around 3 months)
Teaching the alphabet (and numbers) to an infant
The Alphabet (and numbers) continued: Spatial visualization
Time to start with "writing" (age around 7 months)
Level 2
Pushing new material into Grandson (age around 10 months)
1 Progression to small words and the numbers 10-99
1-A-Progression to small words
-The "AT" series
-Other word series
-Progression to 4-letter uppercase words
1-B-Progression to numbers 10 - 99
2 Progression to lower-case letters
3 Reading simple children's books to Grandson, with finger-tracing
( ..... Grandson learns to talk ..... )
4 Increase in Grandson's words-vocabulary
5 Increase in Grandson's numbers-vocabulary
Level 3
6 Skip-counting
7 Reverse counting
8 The limiting factor of "60" in clocks
9 Reading an analog timepiece
10 Counting a clock down in reverse
11 Understanding a directional compass
Level 4
12 Numbers 100 to 999
13 Units, tens, hundreds, and the place value of a digit
14 Verbalizing hundreds, thousands, millions, billions, trillions.....
15 Writing out hundreds, thousands, millions, billions, trillions.....
Level 5
16 Defining "point", "line", "straight-line"
17 The all-important "number-axis"; the true meaning of Numbers
18 The concept of "positive" and "negative" numbers
19 The concept of "smaller" and "larger" numbers
20 Some logical thinking with numbers
Level 6
21 Addition
22 Addition involving negative numbers
23 Addition for the real world
24 Basic "addition" word-problems
25 Subtraction
26 Subtraction involving negative numbers
27 Subtraction for the real world
28 Subtraction leading to a negative answer
29 Direct subtraction leading to a negative answer
30 Basic "subtraction" word-problems
Level 7
31 The connection between (a-b) and (b-a)
32 The concept of "Absolute Value"
33 Multiplication
34 Multiplication for the real world
34-A-Multiplication by 10
35 Fast multiplication involving "half" (1/2)
36 Multiplication involving negative numbers
37 Basic "multiplication" word-problems
Level 8
38 Multiples and factors
39 The concept of a "matrix"
40 Squares, cubes, etc., and roots
41 Division
42 Division for the real world
43 Division involving negative numbers
44 Divisibility rules
45 Basic "division" word-problems
Level 9
46 Distributing items based on a ratio
47 Even, odd, prime
48 Fractions - proper
49 Fractions - improper
50 Fractions - negative
51 Fractions - reducing
52 Fractions - adding
53 Fractions - subtracting
54 Fractions - comparing
55 Fractions - multiplying
56 Fractions - dividing
57 Fractions - verbalizing
58 Fractions - improper, and mixed numbers
59 Fractions - and ratios
Level 10
60 Ratio and proportion, and the equivalency of ratios
61 Mathematical expressions
62 Reducing expressions
Level 11
63 Decimals
63-A-Other number systems
63-B-The decimal point
64 Math operations on decimal numbers
64-A-Addition
64-B-Subtraction
64-C-Multiplication
64-D-Division
65 Dividing decimal numbers by 10, 100, 1000, etc.164
66 Writing out hundreds, thousands, ....., etc., for decimal numbers
Level 12
67 Decimals to fractions
68 Fractions to decimals
69 Percentage
70 Fast percentage calculations
71 Percentage to fraction
72 Percentage to decimal
73 Fractions to percentage
74 Decimals to percentage
75 Summary - fractions, decimals, percentages
76 Increase, increase-fraction, increase-percentage
77 Decrease, decrease-fraction, decrease-percentage
78 The classification of numbers
Level 13
79 Rounding
80 Scientific notation
81 Permutations and combinations
81-A-Permutations
81-B-Combinations
Level 14
82 The "BALANCE" concept in Math - crucial!
82-A-The basics of the "Balance" concept
82-B-"Balances" as fractions - very useful !
83 Word problems - every student's nemesis
(but not yours - you know the "Balance" concept in math)
Level 15
84 Unit and dimension analysis and conversion
85 Areas and Volumes
85-A-Areas
85-B-Converting areas from one unit to another
85-C-Volumes
85-D-Converting volumes from one unit to another
Level 16
86 Some interesting mental math
86-A-Squares and products of larger numbers
86-B-Fast multiplication with 11
Level 17
87 Basic Algebra
87-A-Rules for writing numbers and symbols in Algebra
87-B-Some basic practice problems in Algebra
87-C-Equations
87-D-Cross-multiplication review
87-E-Expanded view of cross-multiplication
87-F-Some more practice problems in Algebra
Level 18
88 Basic Geometry
88-A-Basic definitions
88-B-5 different types of angles can form when 2 lines meet
88-C-Angles all around a point
88-D-2 straight lines crossing each other
88-E-Parallel lines crossing 2 or more other parallel lines
88-F-How to mark figures and angles
88-G-Polygon (types of)
88-H-Theorem 1
88-I-Theorem 2
88-J-Theorem 3
88-K-Theorem 4
88-L-Theorem 5
88-M-Theorem 6
88-N-Some practice problems in "congruence of triangles"
88-O-The Circle
88-P-Pi ("pie"), the universal constant
88-Q-Formulas for a circle
88-R-Some circle practice problems
88-S-Summary of some interesting circle facts
Level 19
89 Basic coordinate Geometry
89-A-Convention for navigating the coordinate axes
89-B-Practice naming the quadrants
89-C-Generic signs of the coordinates in the quadrants
89-D-Reading the coordinates of points
89-E-Points that lie on the X- and Y-axes
89-F-Coordinate Geometry, and Algebra
-line from an equation / equation of a line
89-G -Independent and dependent variables
89-H-Equations and graphs are connected
89-I-Plotting some specific equations as graphs
89-J-Negative slope
89-K-Intercept of a line on the Y-axis
89-L-Slope of a curve
89-M-Generic equation of a straight line
89-N-Finding the slope and intercept of a straight line
89-O-Equations and slopes of the X- and Y-axes
89-P-Parallel lines and their slopes
89-Q-Perpendicular lines and their slopes
Level 20
90 Basic important concepts in general science
90-A-Law of conservation of mass and energy
90-B-Einstein's Equation
90-C-Difference between "mass" and "weight"
90-D-Difference between "heat" and "temperature"
90-E-Electromagnetic induction
90-F-Composition and resolution of forces
-the single resultant of 2 or more forces on a body
-the "parallelogram of forces"
90-G-Composition and resolution of velocities
90-H-What is color?
-What is "Light" ?
-Why do objects appear colored ?
90-I-What is a flame?
90-J-Density
90-K-Anomalous expansion of Water
Appendices
Appendix A:Random ready-recall addition
Appendix B:Random ready-recall subtraction
Appendix C:Multiplication tables through 20 x 20