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Solving Linear
Equations
(Feb 14, 2005)
with & then without stick diagrams plus
solving word problems; and solving systems: - essentially one
unknown, essentially triangular & general
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Read them in order
(i) x + 20 = 29 WS
(ii) 2x + 6 = 24 WS
(iii) 3x + 10 = 32 WS
(iv) 5a + 16 = 3a+ 24 WS
(v) (½)x + 8 = 24½ WS
(vi) (¾)a + 16 = (¼)a+ 24 WS
(vii) (¾)q + 17 = 32 WS
(viii) 13 =[2/3]x +7 twice WS
(5/6)q + 8+(5/6) = 14 + (2/3) WS
Proper Use of Equal Sign
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Three Ways to Do the Same Problem
(two animated gifs and one text-based solution)
| Example: |
2
3 |
x |
+7 |
= 13 |
First Solution - Times 3
first,½ second.(animated gif) |
| Example: |
2
3 |
x |
+ 7 |
= |
13 (animated gif) Second Solution-Times ½ first,
3 second. |
Same Example, Third Time with a single multiplication instead of 2.
|
2
3 |
x |
+ 7 |
= |
|
13 . |
|
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2
3 |
x |
= |
|
6 |
3
2 |
* |
2
3 |
x |
= |
3
2 |
*6 = 3* 3 |
| Therefore |
|
|
x |
= |
|
9 |
| |
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Math How-TOs
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Volumes (orders)
1, Elements of
Reason. 1996
1A. Pattern
Based Reason 1995
1B. Math
Curriculum Notes 1996
2. Three
Skills for Algebra 1995
3 .Why.Slopes.&.More.Math.1995
Skill
& Concept
Review or Development
1. Decimal
Arith - Video Based ]
2 Fractions
3. Fractions
with Units
3. Solving
Linear Equations -
making alg easier
4. Formulas
forwards & Backwards - unifying theme for Algebra
5. Proportionality,
Back- & For-wards - theme at work.
6. Logic
- Math Free, good for precision in work & studies
7. Euclidean-Geometry
(leanly)
8. Slopes
and Lines
9. Why
Study Slopes - a context
10. Quadratics
11 Polynomials
12 Factored
Polys - a context
13 Functions
- For-& Back -wards
14 Number
Theory, Richly
15. Exponents,
Radicals & logs.
16 Calculus
- Examples & Advice
17. Real
Analysis
18
Electric
Circuits Etc (So So)
19 Maps,
Similarity & Trig, (alt view)
20 Complex
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21
Logic with Symbols+truth tables
22 Consistent
Story Telling
23. Even
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