Session 2 Solutions Part C: Patterns in Context

A B C D E
Homework

Solutions for Session 2, Part C

See solutions for Problems: C1 | C2 | C3

Problem C1

Generalized arithmetic allows you to state things like the commutative property of addition: a + b = b + a. Or the property that when you add zero to a number, you get the same number: 0 + n = n. Or the property that the product of two square numbers is a square number: x² * y² = (x * y)².

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Problem C2

The answer is n = 4. One method is the patented "guess-and-check." Others include systematic testing of values of n starting with n = 1, or "undoing" the operations on the left side‹if we have to multiply n by 9, then add 4, a way to find n would be to subtract 4, then divide by 9.

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Problem C3

Some situations include the relationship between the length of a side of a square and the square's area (A = s²), the relationship between Fahrenheit and Celsius temperature (F = 1.8C + 32), and the relationship between distance, rate, and time (D = r * t). In all of these, the variables vary and represent relationships between two or more quantities.

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