Worry Problems

Word-story problems cause more grief to students--and teachers--than almost any other type. The problem with word problems is that they're written in words! Words can have multiple meanings and be quite vague compared to exact math symbols. But once you learn their secrets, solving word problems can be as fun as solving any puzzle. And in a practical sense, solving real-life problems is what math is all about!

Topic Text Video
Worry Problems Slides
Translate words to math, convert units of measure, solve 2 equations with 2 unknowns, and discover cool techniques to solve percent and rate problems. These Slides are suitable for short lessons and classroom projection.

8 pages


Word Problems from Algebra Antics Book
Variety of Freeform, Geometric, Travel, Financial, Work, Mixture, and Conversion problems. Worked-out examples and solution strategies. Problems to solve. Answer Key. Extracted from Algebra Antics (p.61-78)

19 pages

Solution Strategies
* Identify, Draw, Equate, Acquire, Solve
  to take the worry out of word-story problems!
* Organize IDEAS into a solution structure.
* Test for Reasonableness: TRash check your answers.

3 pages

Words to Math
English and Math are like foreign languages. To create freeform equations, you must translate often imprecise words into precise math symbols.

5 pages

Unit Analysis
Set up problems so they'll yield the requested unit of measure.
* What am I solving for?
* Which unit of measure goes in the Numerator?
* Which unit of measure goes in the Denominator?

3 pages

Problem Analysis
Determine if you've been given enough information to solve a problem.
Analyze proportional relationships between variables.

* Equations and Unknowns (1EqUnk, 2Eq2Unk...)
* Direct vs. Inverse Proportionality

3 pages

Problem Types
* Freeform: You create equations from the words in the problem.
* Standard: You use predefined equations for Proportion, Conversion,
                  Rate, Percent, & Blended-Unit problems.
(Solutions for sample problems will appear in the following lessons.)

6 pages

Freeform Problems
Create equations by converting words to math.
* Generic Freeform Problems
* Age Problems: Find relative ages of people.
Numerical Problems: Find numbers, digits, digit-values.
Proportion Problems: Q/K = q/k [kwik-kwik]
Compare ratios of related items.

 Q   =   q                  Quantity  =  quantity
    k                  Kwantity      kwantity
* Q/K=q/k is the parent of Conversion, Q=RK, and Q=PK problems.
* Use Q/K = q/k [kwik-kwik] for 2 items.
* Use Q/K = q/uac/k [kwik-kwak] for 3 or more items.

5 pages

Conversion Problems
Convert one unit of measure to a related unit of measure.
* Q/K=q/k Conversion
* Conversion Twin Magic Hat Trick
* Conversion Twin Stack Attack
* Conversion Twin Chain

3 pages

Rate Problems: Q=RK [kyu-raak]
Compare items whose ratio forms a third item.
* Distance = Rate ● Time  [D=RT  dirt]
* Average Rate; Catch Up; Meet in Between; Move Apart.
* Distance = Mileage ● Volume [D=MV]
* Work = Rate ● Time  [W=RT  wort]
* Work1 + Work2
= Worktotal
* Wage = Rate ● Time
* Cost = Price/unit ● Number  [C=PN  coupon]
* Cost1
+ Cost2 = Costmix
Percent Problems: Q=PK [kyu-pik]
Compare items where one is part of another.
Problems where one quantity is a percent of another. [Q=PK kyu-pik]
* What is 20% of 400?; 80 is what percent of 400?; 80 is 20% of what?
Problems where percent is greater than 100. [Q=K+PK kwik-pik]
* What is 120% of 400?; 480 is what percent of 400?; 480 is 120% of what?

5 pages

* Interest = Rate ● Principal ● time  [I=RPt  I reaped]
* Volume = Amount ● Total  [V=AT  vat]
* Volume1 + Volume2 = Volumemix
Markup / Discount / Change
New = Old + Markup ● Old  [N=O+MO  noh-moh]
* New = Old Discount ● Old  [N=O-DO  noh-doh]
* Percent Change = (New Old) / Old  [P=(N-O)/O  pih-noh-kee-oh]
Blended-Unit Problems: Q=Kk [kyu-kik]
Compare items whose product forms a third item.
* Quantity = Kwantity ● kwantity
* QUNIT-unit = KUNIT ● kunit
* Examples: worker-time, person-time, kilowatt-hours, foot-pounds

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