20 by 20 Multiplication Table
During the school year, practice filling in the 10 or 12 times
table at least three times correctly without a calculator. Observe how the
numbers increase by a constant amount in each row and in each column.
| * |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| 1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| 2 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
22 |
24 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
40 |
| 3 |
3 |
6 |
9 |
12 |
15 |
18 |
21 |
24 |
27 |
30 |
33 |
36 |
39 |
42 |
45 |
48 |
51 |
54 |
57 |
60 |
| 4 |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
32 |
36 |
40 |
44 |
48 |
52 |
56 |
60 |
64 |
68 |
72 |
76 |
80 |
| 5 |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
55 |
60 |
65 |
70 |
75 |
80 |
85 |
90 |
95 |
100 |
| 6 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
66 |
72 |
78 |
84 |
90 |
96 |
102 |
108 |
114 |
120 |
| 7 |
7 |
14 |
21 |
28 |
35 |
42 |
49 |
56 |
63 |
70 |
77 |
84 |
91 |
98 |
105 |
112 |
119 |
126 |
133 |
140 |
| 8 |
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
72 |
80 |
88 |
96 |
104 |
112 |
120 |
128 |
136 |
144 |
152 |
160 |
| 9 |
9 |
18 |
27 |
36 |
45 |
54 |
63 |
72 |
81 |
90 |
99 |
108 |
117 |
126 |
135 |
144 |
153 |
162 |
171 |
180 |
| 10 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
110 |
120 |
130 |
140 |
150 |
160 |
170 |
180 |
190 |
200 |
| 11 |
11 |
22 |
33 |
44 |
55 |
66 |
77 |
88 |
99 |
110 |
121 |
132 |
143 |
154 |
165 |
176 |
187 |
198 |
209 |
220 |
| 12 |
12 |
24 |
36 |
48 |
60 |
72 |
84 |
96 |
108 |
120 |
132 |
144 |
156 |
168 |
180 |
192 |
204 |
216 |
228 |
240 |
| 13 |
13 |
26 |
39 |
52 |
65 |
78 |
91 |
104 |
117 |
130 |
143 |
156 |
169 |
182 |
195 |
208 |
221 |
234 |
247 |
260 |
| 14 |
14 |
28 |
42 |
56 |
70 |
84 |
98 |
112 |
126 |
140 |
154 |
168 |
182 |
196 |
210 |
224 |
238 |
252 |
266 |
280 |
| 15 |
15 |
30 |
45 |
60 |
75 |
90 |
105 |
120 |
135 |
150 |
165 |
180 |
195 |
210 |
225 |
240 |
255 |
270 |
285 |
300 |
| 16 |
16 |
32 |
48 |
64 |
80 |
96 |
112 |
128 |
144 |
160 |
176 |
192 |
208 |
224 |
240 |
256 |
272 |
288 |
304 |
320 |
| 17 |
17 |
34 |
51 |
68 |
85 |
102 |
119 |
136 |
153 |
170 |
187 |
204 |
221 |
238 |
255 |
272 |
289 |
306 |
323 |
340 |
| 18 |
18 |
36 |
54 |
72 |
90 |
108 |
126 |
144 |
162 |
180 |
198 |
216 |
234 |
252 |
270 |
288 |
306 |
324 |
342 |
360 |
| 19 |
19 |
38 |
57 |
76 |
95 |
114 |
133 |
152 |
171 |
190 |
209 |
228 |
247 |
266 |
285 |
304 |
323 |
342 |
361 |
380 |
| 20 |
20 |
40 |
60 |
80 |
100 |
120 |
140 |
160 |
180 |
200 |
220 |
240 |
260 |
280 |
300 |
320 |
340 |
360 |
380 |
400 |
Two message to help you build skills and confidence
Do you know about the domino effect of mistakes and errors in
arithmetic? If not, ask parents, teachers or fellow students to explain
what that might be. If yes, if you know about it, then you know about the
need to be careful in each arithmetic step you take. The domino effect
of errors appears both in and outside of arithmetic. In it, an error
in one step likely makes all following steps and any result wrong. Taking
care to avoid the domino effects is a must for building skills and
confidence in all skill based subjects at home, at work and in school.
Good luck.
Understanding exactly or precisely what is said or written will avoid
confusion when you are following instructions at home, at school and at
work. Learning to write and speak exactly or precisely will avoid confusion
of others when you explain or give instructions as well. When
you are old enough (or now), read the site math free chapter on two
logic puzzles. The chapter may help you read, write
and speak with precision. That in turn may help you avoid the domino
effects in many subjects.
Good Luck.
Some good practices for skill development in arithmetic appear in site
arithmetic and number theory steps. Where these good practices are not
best, say so.
-
Definition of Primes, Simplified : A simpler definition of
prime numbers which takes advantage of the 12 times tables to
identify small primes upto 13. In particular, a whole number is said
to be prime if it is not the product of two smaller whole numbers.
With the word smaller in the definition, the whole numbers 11 and 13
are prime because it is not given by a product inside the 10 and 11
times table. [This was the small example given above]
-
Quick Prime Factorization of Small Whole Numbers: Emphasis of
a square or square root rule to provide QUICK prime factorization
skills for whole numbers less than 169 = 132. In
particular, a whole number less 169 is prime if and only is it is not
a multiple of the primes 2, 3, 5, 7 and 11 less than 13. Simple
divisibility rules and calculators (an overkill) here may be used to
recognize multiples of 2, 3, 5 and 11. Quick prime factorization of
whole numbers is a key to exact and efficient fraction practices
employed in mathematics from algebra to calculus. There is no escape.
-
Fraction Operations Explained: A thought-based development of
addition, comparison, subtraction, multiplication and division
operations starting with simpler cases where operations are easily
explained, and continuing on to general cases where all operations
are justified by raising terms. In higher mathematics, if not
elementary mathematics, comprehension of why methods work is highly
valued, it is part of the spirt of mathematics mastery. Understanding
how and why operations are justified should move you away from
learning by rote. Reference:
fraction operations by raising terms
-
Arithmetic and Fractions With Units: Figuring with denominate
numbers, that is multiples of units of measure for physical
quantities and units of value for monetary quantities. This practical
value for calculations involving speed, rates in general and
associated proportionality constants in daily life and also in
practical and applied arts and sciences. (In algebra taught by rote,
you may see similar figuring with multiples and powers of variables
in products and quotients. The path here has more meaning and is very
practical)
-
Oral Dimension of Arithmetic: Verbal description and extension
of common practices for finding counts, totals and products by
forming and adding or multiplying subcounts, subtotals and
subproducts. Here calculation practices are introduced and described
orally instead of symbollically, the latter being harder for many to
grasp. For many, how to calculate averages and how to calculate
perimeters of polygon are best described with words, the use of
letter or symbols being to complicated to understand in the first
instance. Mastery of common practices for counting, totaling and
multiplying do not have to wait for their algebraic description.
Instead, the verbal forms can be given. [These arithmetic notes
expand on part of the big example given above.]
-
Place Value Revisited: An exposition of place value in
decimals with places before an after the decimal point in groups of
three may amuse and inform. In it, students in North America may
learn how to read aloud and write on paper the decimal
6,571,045,375,905,333,034,412.450,033,870
as 6 sextrillions, 571 quintrillons, 45 quadrillionths, 375
trillionths, 905 billionths, 333 millions, 34 thousands, 421 ones,
450 thousandths, 33 millionths and 870 billionths. In contrast,
students elsewhere may use the following "SI" (system international)
method how to read aloud and write on paper the decimal form of 6
zettaunits, 571 exaunits, 45 petaunits, 375 teraunits, 905
giga-units, 333 megaunit, 34 kilounits 421 ones, 450 milliunits, 33
microunits and 870 nanounits.
-
Addition, comparison, subtraction, multiplication and division of
decimals: The site development may covered more lightly than
presented. The development of place value methods for all but long
division is thought-based. Why methods work are both indicated. Long
division method is given without justification, but with a method to
check results. In all methods, students will meet the domino effects
of care and mistakes. Avoiding the latter provides an end, value and
tool for skill mastery, an echo of the old fashion idea that figuring
well is a sign of practical intelligence.
-
Signed Numbers: The site description of arithmetic with
integers and arithmetic with signed numbers is not bad. The site
objective so far has not been to cover everything in mathematics, but
to develop and express ideas on how mathematics should be learnt or
taught. That being done, a clearer account of arithmetic with signed
numbers is due.
-
More Steps To Elaborate - not in site material: Talk about
scientific notation, arithmetic with, and arithmetic with mixed
decimals - that is, decimals with multiple places before and after
the decimal point. Relate foregoing to fraction skills and practices.
Explain the comparison, addition and subtraction of scientific in
terms of of finding a common factor or denominator.
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For home-tutoring or -schooling, or for schools or colleges
with course content control: Secondary
Mathematics for Ages 11+, A Practical Approach.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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