A focused Grade 6 learning session for Opposites and Absolute Value using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving opposites and absolute value.
Opposites and Absolute Value means choosing a model, naming what each number means, and explaining the strategy.
Question: The opposite of the opposite of \(-5\) is:
Why it works: The opposite of \(-5\) is \(5\). The opposite of \(5\) is \(-5\). So the opposite of the opposite returns to the original number.
Answer: \(-5\)
Question: On a number line, which number is farthest from zero?
Answer: \(|5|\)
Question: A submarine is \(650\) feet below sea level. Which expression represents this depth using absolute value?
Answer: \(|-650|\)
Question: A stock price decreased by \($18\). How much did it decrease in absolute value?
Why it works: A decrease of \($18\) is represented as \(-18\). The absolute value \(|-18|=18\) dollars represents the magnitude of the change.
Answer: \(18\) dollars
Opposites and Absolute Value becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the value of \(|-12|\)?
Answer A: \(12\)
The absolute value of a number is its distance from zero on a number line, always non-negative. \(|-12|=12\).
Which number is the opposite of \(7\)?
Answer A: \(-7\)
The opposite of a positive number is its negative. The opposite of \(7\) is \(-7\), equidistant from zero on the other side.
What is \(|-8|\)?
Answer B: \(8\)
Absolute value measures distance from zero. Distance is always positive or zero, so \(|-8|=8\).
The opposite of the opposite of \(-5\) is:
Answer D: \(-5\)
The opposite of \(-5\) is \(5\). The opposite of \(5\) is \(-5\). So the opposite of the opposite returns to the original number.
Which pair of numbers are opposites?
Answer B: \(-4\) and \(4\)
Opposites are numbers equidistant from zero on opposite sides of the number line. \(-4\) and \(4\) are opposites.
What is the opposite of \(-15\)?
Answer A: \(15\)
The opposite of a negative number is its positive version. The opposite of \(-15\) is \(15\).
On a number line, which number is farthest from zero?
Answer B: \(|5|\)
We compare absolute values: \(|-3|=3\), \(|5|=5\), \(|-2|=2\), \(|1|=1\). The largest is \(5\).
Find \(|0|\).
Answer A: \(0\)
The absolute value of zero is zero. Zero is its own distance from zero on the number line.
Which expression with a negative number equals \(10\)?
Answer A: \(|-10|\)
\(|-10|=10\) because absolute value is distance from zero.
A submarine is \(650\) feet below sea level. Which expression represents this depth using absolute value?
Answer A: \(|-650|\)
Below sea level is represented by a negative number: \(-650\). The absolute value \(|-650|=650\) represents the magnitude of the depth.
Which list shows the absolute values in order from least to greatest?
Answer A: \(|-2|, |-5|, |6|, |-9|\)
Computing: \(|-2|=2\), \(|-5|=5\), \(|6|=6\), \(|-9|=9\). In order: \(2 < 5 < 6 < 9\).
