For nine to ten year olds
skills to check or develop
More on Counting and Decimals
Place Value and Counting from 1 to 100,000
-
Place Value Comprehension: Read aloud numbers 1 to 100 000
from or given their decimal representation
In English, a long way to read 87,563 aloud
is to say eight
times ten thousands, 7 thousands, 5 hundred, six tens and three ones.
A shorter way is to say eighty-seven thousand, 5 hundred and
sixty-three. Either way points to mastery of place value.
-
Dictation Exercise: Write numbers between 1 and 100 000 as
decimals when described in words.
-
Writing Exercise: Given numbers between 1 as 100 000 in
written or oral form, produce their decimal representation..
-
Skip Counting Continued: Add Counting by 1000, 5000 and 10000
to and from 100,000 to the skip counting skill list of previous
levels.
More on Addition and Subtraction of Decimals
-
Add two and five digit decimal numbers with and without carries or
borrows?
-
Subtract or find the difference between pairs of numbers 1 to 100
000 by decimals column methods? Test with examples that do not and
then do involve single and multiple conversions, especially in the
case of subtraction. See explanations in previous level and in the
site folder with
Decimal Comparing and Subtracting Methods of J-concept and
notation for conversions needed in comparison and subtraction.
-
Show How to check the result of subtraction via an addition.
Emphasize again that when a check fails, the mistakes or mistakes are
between the the start of the solution and the end of the check, and
may occur in one or both.
-
Subtraction Shortcut: Given the sum of a first and second
number equals a third, observe that the first gives the value of the
third minus the second, and that the second gives the value of the
third minus the first.
-
Show how to add, compare and subtract decimals that have one or two
decimal places in the one tenth and one hundred place values.
Addition and subtraction with amounts of money involve pennies and
full units of currency [dollars, Euros, pounds] provides a context
for this. Include here shopkeeper method for adding change to the
cost of an item to find or give the correct amount of change due when
someone pay for an item with a full number of units. Include in class
buying and selling stories, activites or scenarios where decimal
amounts of money need to be added, compared, subtracted [and after
the introduction of multiplication methods] below multiplied.
The Manipulative Division of Whole Numbers
Decks of cards and collections of pennies and others may be divided
almost evenly among a group by dealing or sharing the items in question,
one at a time, one after another. That provides a physical way of
answering the question: How many whole times does a small number, say 4,
go into in a larger number, like 30, and what is the remainder.
Comparison Review and Extension
-
Review: Say which is the most or least in a pair of numbers?
Review or explain again the use of the more and less than signs >
and < to indicate when one number is more than or less than
another. Show how to use conversions to compare numbers and to
calculate by how much one is more than or less than the other.
-
Extension: Explain again the use of the composite signs
> and < to indicate when one number is more than
or equal, or less than or equal another.
Multiplication
Preparation for multiplication by more that one digit multipliers
Multiplication by 10 Example . Let illustrate this with the
example of adding 345 to itself nine times. The result is 10 addends all
equal to 345. The repeated addition is written out in full.
|
1
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
2
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
3
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
4
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
5
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
6
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
7
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
8
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
9
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
|
10
|
345
|
= 3 hundreds + 4 tens + 5 ones
|
Now we obtain the result by grouping. Details follow. The details suggest
a rule, namely to muliply by ten, shift all digits to the left by one
place and put a zero in ones place. The details explain or try explain
why the foregoing works. However, the rule by itself will likely be
sufficient for most students - those who presently want to learn without
being overwhelmed by the details. Course material needs to provide
include the details as reference for the minority who won't do or learn
if explanation is not given.
Explanation of why - optional
Add the hundreds: There three hundreds, ten times.
|
1
|
one hundred
|
one hundred
|
one hundred
|
|
2
|
one hundred
|
one hundred
|
one hundred
|
|
3
|
one hundred
|
one hundred
|
one hundred
|
|
4
|
one hundred
|
one hundred
|
one hundred
|
|
5
|
one hundred
|
one hundred
|
one hundred
|
|
6
|
one hundred
|
one hundred
|
one hundred
|
|
7
|
one hundred
|
one hundred
|
one hundred
|
|
8
|
one hundred
|
one hundred
|
one hundred
|
|
9
|
one hundred
|
one hundred
|
one hundred
|
|
10
|
one hundred
|
one hundred
|
one hundred
|
|
Sum
|
one thousand
|
one thousand
|
one thousand
|
Now ten hundreds is a thousand. So three hundreds, ten times, is
three thousand.
Add the tens: There four tens, ten times.
|
1
|
ten
|
ten
|
ten
|
ten
|
|
2
|
ten
|
ten
|
ten
|
ten
|
|
3
|
ten
|
ten
|
ten
|
ten
|
|
4
|
ten
|
ten
|
ten
|
ten
|
|
5
|
ten
|
ten
|
ten
|
ten
|
|
6
|
ten
|
ten
|
ten
|
ten
|
|
7
|
ten
|
ten
|
ten
|
ten
|
|
8
|
ten
|
ten
|
ten
|
ten
|
|
9
|
ten
|
ten
|
ten
|
ten
|
|
10
|
ten
|
ten
|
ten
|
ten
|
|
Sum
|
one hundred
|
one hundred
|
one hundred
|
one hundred
|
Now ten tens is a hundred. So four tens, ten times, is four
hundred.
Add the ones; There are five ones, ten times.
|
1
|
one
|
one
|
one
|
one
|
one
|
|
2
|
one
|
one
|
one
|
one
|
one
|
|
3
|
one
|
one
|
one
|
one
|
one
|
|
4
|
one
|
one
|
one
|
one
|
one
|
|
5
|
one
|
one
|
one
|
one
|
one
|
|
6
|
one
|
one
|
one
|
one
|
one
|
|
7
|
one
|
one
|
one
|
one
|
one
|
|
8
|
one
|
one
|
one
|
one
|
one
|
|
9
|
one
|
one
|
one
|
one
|
one
|
|
10
|
one
|
one
|
one
|
one
|
one
|
|
Sum
|
ten
|
ten
|
ten
|
ten
|
ten
|
There are ten of each of those ones in ten times five ones. By
grouping all the ones together, we get five tens.
The net results is the sum of the hundreds, tens and ones: That
gives nine thousand, 4 hundreds and 5 tens = 3450 for the value
of 10 × 345
Tell students to assume a similar pattern multidigit numbers
multiplied by 10.
|
Mechanical Rule for Multiplication by 10: Insert a zero in the one
place and shift the other digits to the left.
Examples:
10 × 345 = 3450
10 × 23 = 230
10 × 8 = 8
10 × 10 = 100
10 × 100 = 1000.
10 × 7865 = 78650
Multiplication by a single digit multiple of 10: The following
shows the results of a column method for multiplying 632 by 4
632
× 4
2528
Now 40 times 632 means
[10 times 4] times 632
which in turn has the same value as 10 times [4 times 632] In other
words, 40 sets of 632 elements is the same as 10 groups of 4 sets of 632
elements. We may count the elements in sets of 632 in groups of 4, and
then multiply by 10 to find the total count. That gives 40 × 632 is the
same as 10 × [4 × 632] = 10 × 2528 = 25280. The latter can be obtained
by applying the above column method, but with an extra zeroes:
632
×40
25280
The foregoing explanation of how to multiply by the single digit
multiples 10, 20, 30, 40, 50, 60, 70, 80 and 90 of 10 may be not be the
liking of all students. Students may be taught the how first with the
explanation left to second.
Multiplication by Two Digit Whole Numbers: The addition of 23
like terms 414 [that is multiplication by 23] may be computed by summing
the first three and the last twenty in two independent steps, and then
in a last step adding the results of the first two. That is done
next
|
Step 1
|
Step 2
|
Step 3
|
414
×3
1242
|
414
×20
8280
|
1242
8280 +
9460
|
That gives a justification for the following classical form of decimal
column method for multiplication
Drill and Practice with multiplication of 2 to 5 digit numbers by two
digit numbers is now required.
Note: Multiplication by one digit numbers was introduced in the
previous level.
Money Calculations: Show how to multiply amounts of money from
0.01 units to 10000 units by whole numbers. Drill and practice
Required.
The Base for Multiplication by 3 and 4 digit whole numbers:
Review the rule for multiplication by 10 first.
Multiplication by a 100 = 10 × 10. This multiplication is the
same as multiplying by 10 twice
100 × 345 = 34500
100 × 23 = 2300
100 × 8 = 80
100 × 10 = 1000
100 × 100 = 10000
100 × 7865 = 786500
Multiplication by a single digit multiple of 100: The following
shows the results of a column method for multiplying 632 by 4
632
× 4
2528
Now 400 times 632 means
[100 times 4] times 632
which in turn has the same value as 100 times [4 times 632] In other
words, 400 sets of 632 elements is the same as 100 groups of 4 sets of
632 elements. We may count the elements in sets of 632 in groups of 4,
and then multiply by 100 to find the total count. That gives 400 × 632 is
the same as 100 × [4 × 632] = 100 × 2528 = 252800. The latter can be
obtained by applying the above column method, but with an extra zeroes:
632
×400
252800
The foregoing explanation of how to multiply by the single digit
multiples 100, 200, 300, 400, 500, 600, 700, 800 and 900 of 100 may be
not be the liking of all students. Students may be taught the how first
with the explanation left to second.
Multiplication by a 1000 =10 × 100 = 10 × 10 × 10. This
multiplication is the same as multiplying by 10 three times:
1000 × 345 = 345000
1000 × 23 = 23000
1000 × 8 = 800
1000 × 10 = 10000
1000× 100 = 100,000
1000 × 7865 = 7865000
Multiplication by a single digit multiple of 1000: The following
shows the results of a column method for multiplying 632 by 4
632
× 4
2528
Now 4000 times 632 means
[1000 times 4] times 632
which in turn has the same value as 1000 times [4 times 632] In other
words, 4000 sets of 632 elements is the same as 1000 groups of 4 sets of
632 elements. We may count the elements in sets of 632 in groups of 4,
and then multiply by 1000 to find the total count. That gives 4000 × 632
is the same as 1000 × [4 × 632] = 1000 × 2528 = 2528000. The latter can
be obtained by applying the above column method, but with an extra
zeroes:
632
×4000
2528000
The foregoing explanation of how to multiply by the single digit
multiples 100, 200, 300, 400, 500, 600, 700, 800 and 900 of 100 may be
not be the liking of all students. Students may be taught the how first
with the explanation left to second.
Multiplication by Three Digit Whole Numbers: The addition of
223 like terms 414 [414 times 223] may be computed by summing the first
three and the last twenty in three independent steps, and then in a
last step adding the results of the first two. That is done
next
|
Step 1
|
Step 2
|
Step 3
|
Step 4
|
414
×3
1242
|
414
×20
8280
|
414
×200
82800
|
1242 ;
8280
+82800
92320
|
That gives a justification for the following classical form of decimal
column method for multiplication by three and longer decimals.
414
×223
1242
8280
+82800
92320
|
Multiplication of In the presence of Decimal Points
Last example answers the implies 223 times 414 pennies is 92320 pennies
or 933.20 dollars. That suggests the following extension of decimal
arithmetic
414
×223
1242
8280
+82800
92320
|
4.14
×223
12.42
82.80
+828.00
923.20
|
in which one factor has two decimal places.
Arithmetic With Fractions and Mixed Numbers
Arithmetic and Comparison Questions with Like Denominators
The following examples describe with words operations and indicate
their geometric illustration.
Show how improper fractions are possible
proper fractions result from the division of a
single object into pieces of equal value: halves, thirds, quarters and
so on. With such divisions it is possible to have upto two halves,
three thirds, four quarters and so on. But in measuring lengths and
areas with units of measure, we have 3 × &\frac12; units is 1 &
½ units. So improper fractions may appear in counting how many
half units, third units, quarters units there are in a length or
measure which is more than one unit.
|
Addition:
3 times a quarter + 2 times a quarter = [3+2] times a quarter =
5 quarters
In fraction the foregoing quarters counting argument becomes \[
\frac34 + \frac24 = \frac{3+2}4 = \frac54 \]
Geometric Model: Declare the length of a
line segment (measured or not) to be a unit length. Illustrate
the foregoing by drawing three quarters of this length and two
quarters side by side and show by counting quarter lengths, the
result is 5 quarters long.
In Fraction Notation:
Subtraction:
7 times a third - 5 times a third = [7-5] times a third = 2
thirds
In fraction the foregoing thirds subtraction argument becomes \[
\frac73 - \frac53 = \frac{7-3}3 = \frac23 \]
Geometric Model: Declare the length of a
line segment (measured or not) to be a unit length. Illustrate
the foregoing by drawing 7 thirds and subtracting 5 thirds.
show by counting quarter lengths, the result is 2 thirds
long.
Multiplication by a whole number:
3 times [4 fifths] = [3 times 4] fifths = 12 fifths.
In fraction the foregoing counting argument becomes \[ 3 \times
\frac45 = \frac{3 \times 4}5 = \frac{12}5 \]
The right hand side is just $\frac45+\frac45+\frac45$
Geometric Model: Declare the length of a
line segment (measured or not) to be a unit length. Illustrate
the foregoing by drawing 4 fiths, three times side-by-side.
Counting, repeated addition or multiplication gives 12
fifths.
Comparison:
10 sevenths is more than 4 sevenths by 6 sevenths.
since 10 its = 4 its + 6 its for any kind of its.
Reading the symbol $\gt$ as more than we may write
\[ \frac{10}7 \gt \frac 47 \quad \mbox{ by } \quad 67 \] since \[
\frac{10}7 = \frac 47 + \quad 67 \]
Geometric Model: Declare the length of a
line segment (measured or not) to be a unit length. Illustrate
the foregoing by drawing 4 fiths, three times side-by-side.
Counting, repeated addition or multiplication gives 12
fifths.
Multiplication by a Unitary Fraction: What is a quarter of
36 tenths?
The question is like asking what is a quarter of 36 ones or 36 its.
Their answers are 9 ones or 9 its because 36 = 4 × 9.
Answer: 36 tenths = 4 times 9 tenths. So a quarter
of 36 tenths is 9 tenths.
Note again The calculation is possible and easy as the
numerator 36 is a multiple of 4.
In fraction notation \[ \frac14 \times \frac{36}{10} =\frac9{10}
\]
Geometric Model: Declare the length of a
line segment (measured or not) to be a unit length. Illustrate
the foregoing by drawing 36 tenths of it. Then show that grouping the tenths into 9 at a time divides
the 36 tenths long line segment into four equal parts.
Multiplication by a Simple Fraction: What is 5 eighths of
24 sevenths?
Here an eigth of 24 ones or its is 3 ones or its. In consequence,
five eigths of 24 ones or its will be five times as many ones or
its. That gives 15 ones or its.
Answer: 24 sevenths = 8 times 3 sixteenths. So an
eighth of 24 sevenths is 3 sevenths, and hence 5 eighths of
24 sevenths would be 5 × 3 sevenths = 15 sevenths.
Note again:" The calculation is possible as the numerator
24 is a multiple of 8.
In fraction notation, we may record the foregoing reasoning as
follows. \begin{eqnarray*} \quad \\ \frac58 \times \frac {24}7
&=& 5 \times \left[\frac18 \times \frac {24}7 \right] \\
&=& 5 \times \frac37 \\ &=& \frac{15}7\\
&=& 2 +\frac17 \\ \quad \end{eqnarray*} Geometric Model: Declare the length of a line segment
[measured or not] to be a unit length. Illustrate the foregoing
by drawing 24 seventhss of it. Then show
that grouping the sevenths into threes at a time divides the 24
sevenths long line segment into 8 equal parts - eighths of it.
Now five of those eighths would 5 x 3 sevenths = 15
sevenths.
Division
Leading Questions and Examples:
What fraction of 2 is 1? Answer one-half or $\frac12$
What fraction of 3 is 1? Answer one-third or $\frac13$
What fraction of 4 is 1? Answer one-quarter or $\frac15$
What fraction of 5 is 1? Answer one-fifth or $\frac15$
What fraction of 3 is 2? Answer two-third or $\frac23$
What fraction of 3 is 3? Answer three-third or $\frac33$ or 1.
What fraction of 4 is 2? Answer two-quarter or $\frac24$ or $\frac12$ - a half
What fraction of 8 is 5? Answer five eighths or $\frac58$
More Leading Questions and Examples:
How many whole times does 4 go into 12 and what is the remainder? Here the number 4
is the divisor, and the number 12
is the dividend.
Answer: 3 whole numbers exactly - exactly because the remainder is zero.
How many whole times does 5 go into 14 and what is the remainder?
Answer: 2 whole numbers with a remainder of 3 as $14 = 2 \times 5 + 4$
Observe the remainder 4 is 4-fifths of 5.
How many whole times does 3 go into 25 and what is the remainder?
Answer: 8 whole numbers with a remainder of 1 as $24 = 8 \times 3 + 1$
Observe the remainder 1 is one-third of 3.
How many whole times does 5 go into 33 and what is the remainder?
Answer: 6 whole numbers with a remainder of 3 as $33 = 6 \times 5 + 3$
Observe the remainder 3 is 3-fifths of 5.
Still More Leading Questions and Examples:
How many times does 5 go into 20? Here the number 5 is the divisor, and the number 20
is the dividend.
Answer: Exactly 4 times since $4 \times 5 = 20$
How many times does 4 go into 26?
Solution: $26 = 6\times 4 + 2$
where 2 is 2-quarters of 4. Thus the answer is $4 +\frac24 = 4+\frac12$ times exactly.
How many times does 10 go into 46?
Solution: $46= 4\times 10 + 6$
where 6 is 6-tenths of 10 or in 3-fifths of 10 since one-fifth of 10 is 2.
Thus the answer is $4 +\frac6{10} =4 +\frac35$ times exactly.
How many times does 7 go into 18?
Solution: $18 = 2\times 7 + 4$
where 4 is 4 sevenths of 4. Thus the answer is $2 +\frac47$ times exactly.
All answers but the first are mixed numbers. We may rewrite all as
improper fractions.
Rewriting the answers as improper fractions
How many times does 5 go into 20?
Answer: Exactly 4 times since $4 \times 5 = 20$
Raising terms gives $4 =\frac41 =\frac{4 \times 5}5 = \frac {20}5$
Thus the answer is equivalent to an improper fraction - the dividend 20 over the divisor 5.
Lowering terms in the latter fraction gives the mixed number answer.
How many times does 4 go into 26?
Solution: $26 = 6\times 4 + 2$
where 2 is 2-quarters of 4. Thus the answer is $6 +\frac24 = 4+\frac12$ times exactly.
Observe the number
\begin{eqnarray*}
6 +\frac24 & = &\frac {6\times 4}4+ \frac24 \\ &=& \frac{6\times 4 + 2}4 \\ &=& \frac{26}4
\end{eqnarray*}
Thus the answer is equivalent to an improper fraction given by the dividend 26 over divisor 4.
Lowering terms in the latter fraction would give and would have given the mixed number answer.
How many times does 10 go into 46?
Solution: $46= 4\times 10 + 6$
where 6 is 6-tenths of 10 or in 3-fifths of 10 since one-fifth of 10 is 2.
Thus the answer is $4 +\frac6{10} =4 +\frac35$ times exactly.
Observe the number
\begin{eqnarray*}
4 +\frac4{10} & = &\frac {4\times 10}{10}+ \frac6{10} \\ &=& \frac{4\times 10 + 6}{10}
\\ &=& \frac{46}{10}
\end{eqnarray*}
Thus the answer is equivalent to an improper fraction given by the dividend 46 over divisor 10.
Lowering terms in the latter fraction would give and would have given the mixed number answer.
How many times does 7 go into 18?
Solution: $18 = 2\times 7 + 4$
where 4 is 4 sevenths of 4. Thus the answer is $2 +\frac47$ times exactly.
Observe the number
\begin{eqnarray*}
2 +\frac4{7} & = &\frac {2\times 7}{7}+ \frac4{7} \\ &=& \frac{2\times 7 + 4}{7}
\\ &=& \frac{18}{7}
\end{eqnarray*}
Thus the answer is equivalent to an improper fraction given by the dividend 18 over divisor 7.
Lowering terms in the latter fraction would give and would have given the mixed number answer.
|
Time and Date Matters
-
-
Extend column methods for addition and subtraction of decimals to the
column methods for addition and subtraction of intervals of time when
time intervals are expressed as multiplies of a single unit of time,
for example 75 minutes, and when time intervals are expressed in
mixed units of time, for example 2 weeks, 4 days, 3 hours and 15
minutes. Complications may follow if a difference is made between
the number of hours in a single day, and the number of regular
working hours in a day. So the working day will be shorter than the
calendar day.
Reference: The
Adding with Mixed Units of Measure
-
Number of Days in Consecutive Months of a Single Year
If the ideas are too complex this year, cover them later.
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
January
|
31
|
|
|
|
|
|
|
|
|
|
|
|
|
February
|
59
|
28
|
|
|
|
|
|
|
|
|
|
|
|
March
|
90
|
59
|
31
|
|
|
|
|
|
|
|
|
|
|
April
|
120
|
89
|
61
|
30
|
|
|
|
|
|
|
|
|
|
May
|
151
|
120
|
92
|
61
|
31
|
|
|
|
|
|
|
|
|
June
|
181
|
150
|
120
|
91
|
61
|
30
|
|
|
|
|
|
|
|
July
|
212
|
181
|
151
|
122
|
92
|
61
|
31
|
|
|
|
|
|
|
August
|
243
|
212
|
182
|
153
|
123
|
92
|
62
|
31
|
|
|
|
|
|
September
|
273
|
242
|
210
|
240
|
153
|
122
|
92
|
61
|
30
|
|
|
|
|
October
|
304
|
273
|
241
|
271
|
184
|
153
|
123
|
92
|
61
|
31
|
|
|
|
November
|
334
|
303
|
271
|
301
|
214
|
183
|
153
|
122
|
91
|
61
|
30
|
|
|
December
|
365
|
334
|
302
|
332
|
345
|
214
|
184
|
153
|
122
|
92
|
61
|
31
|
The diagonal entries give the number of days in each month of a
non-leap year. Simple addition yields the remaining non-blank
entries.
In the case of leap years, add 1 to all the bold face entries.
The April column, July row entry is 122 indicates there are
four months and 122 days in total from the first day of April to the
last day of July, first and last included. The approximation of 30
days per month would give 4 × 30 = 120 days.
Optional: Show students how to use the above chart to count
the number of days from the first day of a month in one year to the
last day of a month in the following year.
Optional: Show students how to use the above chart
to count the number of days from one mid-month date to another
mid-month date.
Note: The ideas for the above chart stems from tables for the
distance between cities charts at rest stops along long motor-routes
or highways.
Note: The above table and its applications could appear in the
next level.
|
|
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simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
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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