 # Word Problems- The Reading Problem That Can Be Addresses in a Math Class

 The Strategy This is the algorithm.   * Use A TOPIC SENTENCE. * Use English words with your mathematical symbols. * This means use words in equations as many text books now do. * Employ “and,” “of,” and propositional phrases to obtain details. * Use color to highlight these details in class notes. * Solve the equation as usual.

 "Two Keys to Solving Area and Word Problems" Summarize the Problem in Code Review Of and And "Resources" Examine the NJCCCS Review Order of Operations, ## Examples 1 and 2

 1 Compute the change from a fifty dollar bill for the purchase of 3 notebooks at \$2.90 each and 2 CDs at \$14.50 each. 2 Three consecutive integers are involved. The sum of the first, triple the middle, and four times the largest is 131. Find the integers.

```	   1. Compute the change from a fifty dollar bill for
the purchase of 3 notebooks at \$2.90 each and 2 CDs
at \$14.50 each.```
 In semicode``` 50 - 3(notebooks) - 2(CDS) 50 - 3(2.90) - 2(14.50) 50 - 8.70 - 29.00 \$12.30 is the change``` In the usual way ```	   2. Three consecutive integers are involved.  The
sum of the first, triple the middle, and four times
the largest is 131.  Find the integers.

(first) + 3(second) + 4(third)	= 131
(x)     + 3(x + 1)  + 4(x + 2)	= 131
x     + 3x + 3   +   4x + 8	= 131
8x + 11	= 131
8x	= 120
x		= 15
the numbers are 15, 16, 17
```

 Summarize the Problem in Code     The semi/pseudo code looks like this and is "half symbols, half words." ``` 50 - 3(notebooks) - 2(CDS) (first) + 3(second) + 4(third) = 131 ```     Use the semi/pseudo code for the following reasons: To present a unified and complete representation of the problem. To facilitate, through this intermediate step, the transition from words to mathematical symbolic notation. To foreshadow computation on graphing or symbol manipulating calculators. Because it helps "decode" a word problem!     Here are the rules: Use words (including nicknames) and arithmetic to express an idea.Perhaps encircle the words with parentheses for clarity. Use no variable numbers. Use only constant numbers.Use order of operations.

Of and And, Very Important Signals

In math, as in English, AND is a signal that at least two ideas are involved. Very often these ideas also involve addition, but not always.

In math, as in English, OF is a signal that information about 1 item is going to be stated.

Here are expressions/equations involving of and/or and.

• five and seven: 5, 7
• the product of five and seven: (5)(7)
• the sum of five and seven: 5 + 7
• the product of two and a number: 2(x)
• The area of a rectangle is the product of length and width.
• The area of a rectangle is the product of length and width.
• The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides.

Below is a partial list, with mathematical symbols, of operations/ functions which require information provided through an of prepositional phrase.

 the opposite of: -( ) the absolute value of: | | the reciprocal of: 1/( ) half of: ( )/2 the square of: ( )2 the cube of: ( )3 the square root of: ( )

The preposition "of" also acts to nest or arrange information. See how the meaning of the phrase below are changed with the arrangement of the "of." Complete Example 3.

Write the code and the equation and compute the area.

 Compute the area. Area Problems:
Integer Problems:
Money and Percent Problems:
Other Kinds of Expression Problems:

 NJCCCS Standard 4.5 – Mathematical Processes Grades 6, 7, 8 COMMUNICATION ___ use reading, writing, discussion, listening and questioning                 to organize and clarify their mathematical thinking ___ communicate their mathematical thinking coherently and clearly                 to peers, teachers, and others, both orally and in writing ___ analyze and evaluate the mathematical thinking and strategies of others ___ use the language of mathematics to express mathematical ideas precisely REASONING ___ recognize that mathematical facts, procedures, and claims must be justified ___ use reasoning to support their mathematical conclusions and problem solutions ___ select and use various types of reasoning and methods of proof ___ rely on reasoning, rather than answer keys, teacher, or peers,                 to check the correctness of their problem solutions ___ make and investigate mathematical conjectures ___ evaluate examples of mathematical reasoning and determine whether they are valid REPRESENTATIONS ___ Create and use representations                 to organize, record, and communicate mathematical ideas                 through concrete, pictorial, symbolic and graphic representations ___ select, apply, and translate among mathematical representations to solve problems ___ use representations to model and interpret physical, social, and mathematical phenomena

 Order of Operations: Math Syntax     Order of Operations is literally the order in which operations are to be performed. The rules are understood by all who write and speak mathematics. THE ORDER OF OPERATIONS (Topmost First) Functions Parentheses or other Marks of Inclusion (Innermost First) Roots or Exponents Multiplication or Division (Leftmost First) Addition or Subtraction (Leftmost First)     Restated it's: Functions, Parentheses first, next Roots or Exponents, then Multiply or Divide (left to righ) then Add or Subtract (left to right): Finally Please, Readily Excuse, My Dear Aunt Sally.     Restated in a more complete form math syntax is "FIRE My Dear Aunt Sally!" In formal language, top priority first, Functions, Parentheses (and other marks of inclusing, innermost first), next Roots or Exponents (easier first), then Multiplication or Division (leftmost first), then Addition or Subtraction (leftmost first).     Here's a picture or gif file. Here's a 26-page tutorial on Order of Operations. Here's are two connect the dot puzzles: 1, and 2 and their answers 1 answers and 2 answers. Here's extra problems and solutions.

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