A focused Grade 6 learning session for Understanding Positive and Negative Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving understanding positive and negative numbers.
Understanding Positive and Negative Numbers means using place value, operations, and equations to reason accurately with numbers.
Understanding Positive and Negative Numbers means using place value, operations, and equations to reason accurately with numbers.
Question: Which number line correctly shows the position of \(-5\)? What is the correct location of \(-5\) on the number line above?
Why it works: On a number line, negative numbers are to the left of zero. \(-5\) is located five units to the left of zero.
Answer: At the fifth tick mark to the left of zero
Question: Which number line correctly shows three points: \(-3\), \(0\), and \(2\)? Based on the number line, which statement is true?
Answer: \(-3 < 0 < 2\)
Question: On a number line, which two integers are exactly \(8\) units apart?
Answer: \(-4\) and \(4\)
Question: A mountain peak is at an elevation of \(3500\) feet above sea level. A valley floor is at an elevation of \(-800\) feet. What is the difference in elevation?
Why it works: The difference in elevation is found by subtracting: \(3500 - (-800) = 3500 + 800 = 4300\) feet.
Answer: \(4300\) feet
Understanding Positive and Negative Numbers 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.
Which situation is best represented by the integer \(-8\)?
Answer C: A debt of \($8\)
Negative integers represent values less than zero. A debt of \($8\) means owing money, which is represented by \(-8\).
A thermometer shows the temperature is -12°C. Which sentence best describes this situation?
Answer D: The temperature is 12°C below zero
A negative number means the value is below zero. Since the temperature is -12°C, it is \(12\) degrees below zero.
Which number line correctly shows the position of \(-5\)? What is the correct location of \(-5\) on the number line above?
Answer C: At the fifth tick mark to the left of zero
On a number line, negative numbers are to the left of zero. \(-5\) is located five units to the left of zero.
A scuba diver descends \(25\) meters below sea level. Which integer represents this situation?
Answer B: \(-25\)
Below sea level is represented by a negative integer. A depth of \(25\) meters below sea level is \(-25\) meters.
The opposite of \(7\) is \(-7\). Which pair of integers are opposites?
Answer A: \(3\) and \(-3\)
Opposites are two numbers that are the same distance from zero but on opposite sides of zero. \(3\) is \(3\) units right of zero, and \(-3\) is \(3\) units left of zero.
A football team loses \(15\) yards on a play. How should this be represented as an integer?
Answer B: \(-15\)
A loss is a negative change. Losing \(15\) yards means the team moved \(15\) yards backward, represented by the integer \(-15\).
Which statement correctly compares the two integers \(-6\) and \(-3\)?
Answer C: \(-6 < -3\)
On a number line, \(-6\) is to the left of \(-3\), so \(-6\) is less than \(-3\). The farther left a number is, the smaller it is.
A bank account shows a balance of \(-$42\). What does this mean?
Answer D: The account is overdrawn by \($42\)
A negative balance means the account owes money. An account balance of \(-$42\) means the account is overdrawn (or in debt) by \($42\).
Which list of integers is in order from least to greatest?
Answer A: \(-4, -1, 0, 2\)
To order integers from least to greatest, place the most negative number first, then move toward zero and positive numbers. The order is \(-4 < -1 < 0 < 2\).
An elevator is at floor \(0\). It goes up \(6\) floors, then down \(10\) floors. At which floor is the elevator now?
Answer B: Floor \(-4\)
Starting at floor \(0\): up \(6\) brings us to floor \(6\). Down \(10\) from floor \(6\) brings us to floor \(6 - 10 = -4\) (four floors below ground level).
A thermometer reads -5°F in the morning. By afternoon, the temperature has risen by 8°F. What is the new temperature?
Answer B: 3°F
A temperature rise of 8°F means we add \(8\) to the starting temperature: \(-5 + 8 = 3°\)F.
