writing expressions, equations, statements using code

What's Code?

      Code's a blend of words and mathematical symbols that takes the author from words to symbols in order to write or solve symbolic statements.

      Just below, the middle three lines are code, as the author has moved from the top line in words, to the bottom line in symbols.
A bank contains $2.45 in nickels, dimes and quarters ...
(nickels) + (dimes) + (quarters) = (total)
5(nickels) + 10(dimes) + 25(quarters) = 245
5((dimes) - 2) + 10(4(quarters)) + 25(x) = 245
5(4x - 2) + 10(4x) + 25(x) = 245
Make a Choice

      The reader has a choice. The student version of how to use code writing to make translation of words to mathematical symbols is presented on this page. The teacher version of how to do the same thing, with justification and comments from the author, is linked at The Languages of the Math Classroom, page 7. Of course, the reader is welcome to do both.

Before Writing Code

      The reader should

Here's The Rules:
  • Use words (including nicknames) and arithmetic to express an idea.
  • Use parenthises to encircle every words for clarity and to indicate multiplication.
  • DO NOT use variables. Use only constant numbers.
  • Use order of operations.
Here's An Example.

      As with any "word problem" it may be necessary to read the problem 4 or 5 times.

Directions:      Write the code, then the equation, then
                  algebraically solve the problem.

      A bank contains $2.45 in nickels, dimes and quarters. There are fewest quarters. There are four times as many dimes as quarters. There are 2 fewer nickels than dimes. How many of each coin are in the bank?

1st: Code the entire problem in 1 statement without using numbers.
(nickels) + (dimes) + (quarters) = (total)
2nd: Insert constants but no variables
5(nickels) + 10(dimes) + 25(quarters) = 245
3rd: Code with variables as needed.
5(nickels) + 10(dimes) + 25(x) = 245
4th: Code with variables as needed.
5((dimes) - 2) + 10(4(quarters)) + 25(x) = 245
5th: Refine as needed.
5(nickels) + 10(4x) + 25(x) = 245
6th: Refine as needed.
5(4x - 2) + 10(4x) + 25(x) = 245
7th: Solve.
5(4x - 2) + 10(4x) + 25(x) = 245
20x - 10 + 40x + 25x = 245
85x - 10 = 245
       + 10 = + 10
85x = 255
85x/85 = 255/85
x = 3
8th: Answer the original question.
5(nickels) + 10(dimes) + 25(quarters) = 245
5(10) + 10(12) + 25(3) = 245
3 quarters, 12 dimes, 10 nickels
      Use code to write the expression/equation then check the answer. More than one answer of code may be correct. Your browser may print the answers with spaces that are not ment to be there.
1.) The sum of three numbers is five.
2.) The sum of three consecutive integers is two less than 35.
3.) the opposite of the difference between a number and six
4.) six less than half of a number
5.) the product of a number increased by four and the same number doubled
6.) When a number is doubled the result is five less than the product of 3 and five less than the number.
7.) A number is less than the product of 3 and two more than the number.

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