Number Lines & Distance
A point starts at -2 on a horizontal number line and moves 6 units to the right. What is its final position?
What is 4?
-2+6=4
What is the sum of any integer and its additive inverse (opposite)? Give an example.
What is 0?
Ex. -7+7=0
Rewrite 4 - (-5) as an equivalent addition problem using the additive inverse rule p - q = p + (-q), then solve.
What is 4+5=9?
-3.5 + 7.8
What is 4.3?
Rewrite -5.2-10.95 as an equivalent addition problem using the additive inverse rule p - q = p + (-q), then solve.
What is -5.2+(-10.95)=-16.15?
Write an absolute value expression to find the distance between -8 and 3 on a number line, and state the distance.
What is |-8-3|=11 units (or |3-(-8)|=11)?
A temperature starts at -9 degrees Fahrenheit and rises by 2 degrees Fahrenheit. Write an addition expression and find the final temperature.
What is -9+2=-7 degrees Fahrenheit?
Rewrite -5-(-2) as an addition problem and solve.
What is -5+2=-3?
Solve 1/4 + (-3/2) and write your answer as a simplified fraction or mixed number.
What is -5/4 (or -1 1/4)?
Solve -2.4 - (-2.6) and explain how the double negative changes the operation.
What is 0.2? (Subtracting a negative becomes adding a positive: -2.4+2.6 = 0.2)
An arrow on a vertical number line starts at 5 and points down to -4. What subtraction equation and distance does this movement show?
What is 5-9=-4 (a distance of 9 units)?
Rewrite and solve -14 + 8 + 14 + (-5) using the commutative property to group opposites first.
What is -14+14+8+(-5)=0+3=3?
An arrow on a number line starts at -4 and moves LEFT 4 units. Write the subtraction equation represented by this movement.
What is -4-4=-8?
Evaluate -2 1/3+ 5 5/6
What is 3 1/2 (or 7/2 or 3.5)?
Solve -3/4 -1.25
What is -2?
Find the distance between -4.25 and 2.75 on a number line using absolute value.
What is |-4.25-2.75|=|-7|=7 units?
An arrow on a vertical number line starts at -6 and moves UP 4 units. Write the addition sentence and state the ending position.
What is -6+4=-2?
A diver is at -12 feet relative to sea level and descends another 8 feet. Write a subtraction expression and state the diver's new position.
What is -12-8=-20 feet?
Use properties of operations to solve 3/7 + (-2/5) + 4/7 efficiently.
What is 3/5?
Evaluate 5/6 - 2/3 - (-1/6) efficiently using properties of operations.
What is 1/3?
A hiker is at an elevation of -50 feet relative to sea level, and a drone is flying directly above at 350 feet. Write an expression using absolute value to find the total distance between them.
What is |350-(-50)|=400 feet?
Use properties of operations to solve -18 + 25 + (-12) efficiently without adding left-to-right.
What is -18+(-12)+25=-5?
25+(-18)+(-12)=-5
Explain why subtracting a negative integer yields the same result as adding a positive integer (e.g., why 3-(-4) = 3+4.
What is "Subtracting a negative removes a deficit, which increases the total value (or moving left by a negative distance means moving right)"?
Mariah owed her grandfather $2.25 (represented as $-2.25) and paid him back $1.50. Write an addition expression for this situation and state her remaining balance.
What is -2.25+1.50=-0.75?
She owes $0.75
A freezer's temperature dropped from 3.2 degrees Celsius to -18.5 degrees Celsius. Write a subtraction expression representing the total change in temperature, and find the change.
What is -18.5-3.2=-21.7 degrees Celsius?
A drop of 21.7 degrees Celsius