YOU are better than YOU think. Show yourself how:
|
// _ _ \\
/\ /\
<| (o) (o) |>
\ | | /
|
Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence in
work Learn to read notes and textbooks like a lawyer, so that no nuance, no subtlety and no clause escapes your attention. |
-/[]\-
||
/ \_
||||||||||||||||||||||||||||
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;
|
// _ _ \\
/\ /\
<| (o) (o) |>
| |
| |
\
/
\ = /
|
Caution: Site advice is approximately correct, for some circumstances, not all. That leaves room for thought |
-/[]\-
||
_ / \
||||||||||||||||||||||||||||
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.
1. Taking Tests and Examinations:
On tests and examinations, start writing after you have read all problems. Then while you are doing one, your mind may have ideas for doing the others. Learning takes time and effort. No one but you can provide this for your education.
Proper notation is must. Or, improper notation means you do not how to express your ideas and solutions correctly, and so (ouch) deserve to lose marks. Avoid that if you can.
For questions in mathematics, science and technology that require written answers and you to show work, you must give (state, write) any and all formulas used in your solution and specify the values of the numbers or quantities that appear in them, you should give name of each formula (if it has one) and you should give names of any rules or physical principles used to obtain equations. Diagrams may be used by themselves or besides words to explain your shorthand notation for geometric or physical quantities. Try to to give enough information so that your answer makes sense by itself to someone who has not seen the question.
Who will get a better mark?
- Student A in answering the question what is the area of a
rectangle that is 8 cm wide by 5 cm high writes
50
(instead of 40) alone and by itself without further explanation of how this number was obtained. He gets 0.
- Student B in answering the same question writes
50 square cm = 50 cm2
He might gets 0.5 marks out of four as the proper units are included.
- Student C in answering the same question writes
40
He gets 1 mark out of four as units do not appear. If I say I am give you 10 units of something, you do not what what you will get until the unit is specified.. Answers to mathematics should be full and precise - exact.
- Student D draws the rectangle, marks the lengths of width
and height on it, write the formula, replaces letters by lengths, and then
gets the wrong answer 50 cm2. His
mark is 3 out of four even though he gave the same answer
as student B. But the work done records the reasoning fully step by
step, so the marker can observe and see evidence of what the student
understands. So credit is given.
height
H = 5 cmArea A = ?
width W = 8 cm
Area A = W H
= (8 cm)(5 cm)
= 50 cm2 // Answer.
If Students D had put 40 instead of 50, his answer would have been worth 4 out of 4 (or more).
The show work safety net: By drawing diagrams, stating the formulas that you use , giving the values used in them, showing the substitution, and then doing the arithmetic you are demonstrating know-how and giving yourself a better chance of earning marks You may get part to full marks if the formula is correct and the arithmetic is not, or if the formula is wrong, while the arithmetic is correct. And in all this, do not abuse the equal sign.
Abuse of Equal Signs: Expressions of the form a = b = c means and demands a = b and a = c. For instance in computing the average of numbers 1, 2, 3 and 4, it is wrong to write
See the webpage Proper Use of Equal Sign to learn more.1+ 2 + 3 + 4 = 10 /4 = 2.5 as 1 + 2 + 3 + 4 = 10
while 1+ 2 + 3 + 4 = 10 is not equal to 2.5
You could and should write (1 + 2 + 3 + 4)/4 = 10/4 = 2.5
ADVERTISEMENT
Algebra, Odds& Ends,
Etc, Etc
[ Up ] [ Next ]
1. Hints for Exams 2A. Exact Arithmetic 2B. Fractions Briefly 3. What is a Variable? 4.. Square Roots 5. Straight Lines 6. Problem Solving Methods 7. Trig and Complex No. 8. Complex Applet 9. History of No.s 10. ln(x) and exp(x) 13. Rename the > Sign 14. Problems: Quadratics 15. Problems: Algebra Test 16. Problems: Linear Eqns I 17. Problems: Linear Eqns II 18. Problem Solving Hints 19. Functions & Sets 20. Independent Variables 21. Why Logic 22. Why Math 23. The 15 Times Table 24. The 20 Times Table 25. Algebra Formulas 26. On Learning Maths 27. Maths in Biology 28. Navigation +Time 29 Quibble-What is Algebra 30. Logic in Maths
Odd and Ends, Essays
Constant Retirement Rate Road Safety 3 Strikes Law in California. Math HOW-TOs 9 Steps in Maths
Study With Others: twiddla.com has developed a collaborative whiteboard with audio & text chat that allows students, tutors & teachers to explore & scribble on blank pages and copies of webpages together, If scribbling is awkward with one browser, try another.
In Volume 2, Three Skills for Algebra, Chapters 8 to 14 and postscript What is a Variable point to a greater & clear use of words in algebra. Chapter 14 introduces a 4th skill for algebra, an elaboration of the third: - The direct and indirect use of formulas, numerically and algebraically, is unifying theme that should be mentioned aloud, with words, in each and every use of formula.