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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Awkwardness with an idea or skill often signals difficulty
with previous ones. It may indicate at least one earlier skill has been missed
or forgotten. When an awkwardness is felt or seen, learners should go or be
taken back to practice the missing skills, more precisely the ones just before
them to restore confidence and build skills, so that the learner can go
further.
Can your charge do or understand the following? Where not there is
room for instruction - learning takes takes and patience, yours included.
Decimals and Whole Numbers:
- Count from 1 to 10,000?
- Read aloud numbers 1 to 10,000 from or given decimal representation of
all? Test this knowledge with a sample?
- Write numbers between 1 and 10000 as decimals? Test with a sample?
- Write numbers between 1 as 10000 as words: for instance: three thousand
three hundred and eighty-four. Ask him or her to help you fill in your
checks/cheques.
- Count by 1000s to 10,000?
- Identify place or position from first to a thousandth? Talk about
position in class or a race.
- Recognize odd and even numbers, and explain why?
- Recognize when a number is a multiple of 2, 3, 5 or 10?
- Add and subtract pairs of numbers from 1 to 18 automatically?
- Add and subtract lists of 2 digit numbers all at once or by grouping and
adding partial sums to obtain the total?
- Understand and explain place value in decimal notation for numbers from 1
to 1000?
- Add and subtract two and three digit decimal numbers with and without
carries or borrows?
- Know how to check the results of a subtraction via an addition?
- Fill in the 10, 12 or 20 times table by repeated addition.
- Fill in the 12 times table from memory?
- Fractions: add and subtract decimal fractions, multiples of 0.1
and/or 0.01.
- Add and subtract small amounts of money (dollars and pennies) from 0.01 to
10000 dollars? read and write the decimal notation for amounts of
money, and also write the word-only description of these amounts.
- Add pairs of numbers in the range 1 to 10000 by decimal column
methods. Test with examples that do not and then do involve carries. Have
your charge test the result of an addition via a subtraction?
- Subtract or find the difference between pairs of numbers 1 to 10000
by decimals column methods? Test with examples that do not and
then do involve borrows? Have your charge test the result of subtraction via
an addition?
- Say which is the greater or smaller in a pair of numbers? Can you
charge use the greater and less than signs > and < to indicate when
one number is greater than or less than another? (Here greater than is used
to compared magnitude. Later on, your charge will be used to indicate the
relative location of signed numbers along the real number line.)
- Order a set of numbers in - increasing order and in decreasing
order? There are two exercises here.
- Locate whole number plus fraction distance along a ruler or
real number line.
Geometry and Multiplication
- Pick a unit length, say one inch or one centimeter. With your charge
to draw a large square with sides of length 10 units and then asked him or
her to divide the square into one hundred small, equal-size squares, each
with sides of length one unit. Next with your child to fill in the 10
times table by finding the number of small squares there are in rectangles
of dimensions 1 by 1 to 10 by 10. Your charge may see multiplication as a
form of repeated addition and as a way to count the the number of squares in
a rectangles with sides of length 1 to 10 units.
Fractions:
- Write a whole number plus a proper fraction as an improper fraction?
- Write an improper fractions as a whole number plus a proper
fraction.
- locate whole and fractional distances along a ruler or real number
line: 1, 1/2, 1/3, 2/3, 1/4, 2/4, 3/4, 4/4, 1/5, 2/5,3/5, ... and so on.
- Read fractions aloud?
- Add fractions with the same denominator using notation ( 3/7 + 2/7 = 5/7)
and verbally (three fifths plus one fifth is four fifths)
- Understand that 3/5 is 3 times 1/5th?
- With the aid of a ruler, order proper and improper fractions by size
and position.
- Order proper fractions by size with the aid of lengths representing
each fraction.
- Visualize the product (1/5)(3/4) as dividing each of the three quarters of
a unit length into five equal pieces, and taking one fifth of all. The
result is 3/20.
- Visualize the product (2/5)(3/4) as dividing each of the three quarters of
a unit length into five equal pieces, and taking two fifths of all.
The result is 3*2/20.
- Measure how many times a fractional length (say 3/4) goes into a whole
number or fractional length (say 8, 7.5 or 11).
- Take the result of the previous and multiply it by 3/4.
- Multiply pairs of numbers in the range 1 to 1000 by decimal column
methods?
- Divide pairs of numbers in the range 1 to 1000 by long division
methods, and thus find quotients and remainder. Does your child know
that the remainder plus (quotient times divisor) yields the
"original" number.
- Understand and explain place value in the decimal representation of whole
numbers, 1 to 10000? Where are the units, tens, hundreds, thousand columns?
- Draw rectangles with sides of integral length (multiples of 1) or
fractional length (multiples of 1/2) and then count how many full, half or
quarter squares are needed to cover the rectangle. In each full square
should be lightly divided into four equal quarters by dashed lines -
assuming the borders are solid. Check that the count equals width times
length - that gives a shortcut for computing the count.
Geometry
- Recognize or describe pentagons, hexagons, octagons, pyramids and
triangular prisms?
- Can you child measure lengths to the nearest fraction of a unit on a
ruler?
- Can your unit use inches, feet and miles in measurement? (USA/UK only)
- Use centimeters, meters and kilometers for measurement?
- Use units of weight: ounces, pounds, ..? (USA/UK only)
- Use units of mass: kilograms, grams.. ?
- Calculate perimeters of circles, triangles and rectangles by measurement?
- Calculate the area of rectangles by covering with unit squares?
Sides may be multiples of a unit length or multiples of one half the unit
length in the first instant. The latter will lead to areas (number of
squares required to cover) in terms of whole numbers, halves and
quarters.
- Count the volume (number of cubes) in a small rectangular box constructed
from the cubes (physical ones).
Time Intervals
- Ask your child to add intervals of time like 5 hours, 30 minutes, 15
seconds in which minutes counting more than 60 are converted into hours and
second over 60 are converted into minutes. Doing this may help your
child understand carries in decimal arithmetic.
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www.whyslopes.com
Help your Child or Teen Learn:
Area Intro
Up
1. Speaking Skills
2. Reading & Writing
3. Preparing for Science
4. Learning Takes Time and Effort
5. Math Books: kids & teens
6. Math Books: teens & adults
7. Readings for Parents
8. Patience Please
9. Who is in Charge
10. Motivation
11. Will to Learn
13. Links For Parents
14. JumpMath WorkBooks
15. Discipline in Schools
Maths for Ages 5+
Ages 5 or 6
Ages 6 or 7
Ages 7 or 8
Ages 8 to 9
Ages 10 to 13
Age 14
Where is it going
D
What to do in School & Why
E.How to Study Mathematics
To read, write and spell, your children need to
learn and memorize the alphabet. Anything less would be absurd. That being
said, learning and using mathematics demands that your children meet key
skills and concepts, and not skip any. Where local schools do not provide the
latter, you need to provide remedies.
Care and Precision: If your child can learn
to follow multi-step methods carefully and precisely in arithmetic, he or she
may do so in other subjects, as well. Get your child or teen, if you
can, to sit down and study. Suggest he or she aim for skill and concept
development and perfection for their own sake, not that of their teachers.
The will to learn is the key to success in
school. Parents do have to be educated to support or guide their
children and teens. What matters more is support for the will to learn, for
children and teens to be told to try to learn and to ask teachers, their
schools or classmates for help and more help, as needed. Teachers and parents
need to push students, help them find the will to learn, teamwork helps.
The main reason and focus for high school
mathematics is or should be preparation for calculus. That requires skill and
knowledge perfection with fractions, algebra, geometry, trig and functions.
Many high school programs do not provide this. Make sure alone or with
help that your children and teens have a good command of
fractions.
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