Introduction
Draw a conclusion or make a statement about something that is more general than is justified by the available evidence.
Overgeneralizing
#1
State the rule that teachers share with students.
This rule is taught when students are learning to multiply a whole number times ten.
Rule #1 When you multiply a number by ten, just add zero to the end of the number.
borrowing or carrying
Regrouping
thinking 0.273 is larger than 0.6 debunks this myth.
Rule #11 The longer the number, the larger the number.
Waitress or Waiter rely on these + magician =
Tips and Tricks
#2
Explain the rule.
-5 - (-8) = 3
Rule #5 Subtraction and division make numbers smaller.
Say this, instead of saying 1 out of 7 for a fraction
1/7th
Two quantities should be the same amount but you see me as just the answer.
Rule #13 The equal sign means Find the answer or Write the answer.
a symbol indicating a relationship between two quantities (or amounts).
Equal sign =
#3
Discuss how students inappropriately over-generalize it.
This rule doesn't always hold true for addition and subtraction of integers.
Rule #7 Two negatives make a positive.
Please don't call me the top number in a fraction. Call me this....
Numerator
Multiplication doesn't necessarily come before division.
Rule #12 Please Excuse My Dear Aunt Sally
Its purpose is to advocate for students to become problem solvers who can reason, apply, justify, and effectively use mathematics vocabulary to demonstrate their understanding of mathematics concepts.
The Common Core State Standards (CCSS)
#4
Provide counterexamples,noting when the rule is not true.
Encourages students to strip numbers from the problem and use them to perform a computation outside of the problem context.
Rule #2 Use keywords to solve word problems
Reducing Fractions
Simplifying
Order of Operations
Rule #8 Multiply everything inside the parenthesis by the number outside the parenthesis.
Not being exact. Especially when defining something.
Imprecise vocabulary.
#5
State the "expiration" date.
Addition with zero does create a sum larger than either addend.
Rule #4 Addition and Multiplication make numbers bigger.
I'm not a separate number. I'm just below the numerator.
Denominator
3 dozen is more than 8 eggs and truly breaks this rule.
Rule #10 The number you say first in counting is always less than the number that comes next.