He was seeing doubles.
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He couldn't keep his eye on the ball.
The answer to page 13.10 in the Punchline Algebra book is typically a math problem or exercise that requires solving equations or manipulating algebraic expressions. As for where the tree invited all its friends on Friday night, this is likely a joke or riddle included in the book to add humor and engage students in the learning process. The answer to the joke would be a playful or imaginative location, not a literal event.
Answering the question in general terms: 1. Since we are taught the property at an early age (initially without identifying it formally as a property) , our use of it generally goes unnoticed (for example, when it occurs in a multiplication problem involving the digit 1). 2. When solving algebra or arithmetic problems or proofs, if we can reduce a factor to 1, then by the property we can eliminate this complicating factor. 3. Having identified this property, we can create new mathematical systems within which we can then decide whether or not to include that property.
You memorize the rules that are considered standard.
An Independent variable is what you control; you decide the focus of your experiment and what you control on the independent variable. Dependent variable is what you want to look at or find results for; you decide what you want to see from manipulating your independent variable.