- Quickstart: p.32 #5 - 8 [no calculator]
- Review
(1-4) Adding Real Numbers
Vocabulary - absolute value, addend, integers, opposite
Rules for Adding Numbers - With the same sign - Add the absolute value (numerical part), keep the sign
- With different signs - Subtract the absolute value (numerical part), sign of the sum si the sign of the addend with the greater absolute value (numerical part)
- Lesson
(1-5) Subtracting Real Numbers - Using a number line
Students created subtraction expressions and then acted them out on a number line on the floor of the classroom.
Example: -2 - 4
-2 tells us to start on the number line at -2
(-) tells us the direction to move, left
4 tells us how many units to move
So, 4 units to the left of -2, the result is -6
After students acted out some problems, students completed six on their paper
(As makeup, complete Check Understanding #1, p.32) - Using a rule
We discovered that when you subtract a negative, you always end up moving to the right, the same as if you were adding. So, we have a rule
To subtract a number, add its opposite. - Absolute Value
Absolute value is the distance a number is from zero on a number line.
Students demonstrated this on the number line in the classroom.
Absolute value acts as a grouping symbol. We treat the absolute value symbol the same as parentheses and simplify everything inside the absolute value symbol first.
Example: Simplify |-13 - (-21)|
Solution: |-13 - (-21)|
= |-13 + (+21)| [add the opposite of -21]
= |8| [adding two numbers with different signs so subtract numerical part 21 - 13, keep the sign of the larger number part, 21 is positive]
= 8 [8 is 8 units from zero on a number line]
Check Understanding #4 (p.33)
Notice that the solutions from part a, b are the same but the order of the subtraction is different. The same is true for parts c, d - Evaluating Expression
When you substitute a variable for a number it is important to place the number inside parentheses to prevent mistakes (like forgeting a negative sign or forgetting to multiply)
Example: Evaluate x - (-y) for x = -3 and y = -6
Solution:
x - (-y)
= (-3) - (-(-6)) [substitute using parentheses]
= (-3) - (+6) ["-(-6)" is the same as "negative, negative 6" is the same as "the opposite of negative 6" is the same as "+6"]
= (-3) + (-6) [to subtract a number, add its opposite]
= -9 [to add two numbers with the same sign, add their absolute value and keep the sign]
Check Understanding #5 (p.34)
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