Distance Difference Worksheet Distance Difference Worksheet
Name:
Date:
Exploring distance through depths, heights, and changes.
1. Warm-up
A bird is flying at an elevation of +50 feet . A fish is swimming at a depth of -40 feet .
How far apart are they? Use the space below to draw or calculate.
Total Distance:
feet
2. Expedition Observations
Scenario 1: Ocean Depth
Why did the narrator use absolute value to find which animal was closest to sea level?
Definition Check:
Absolute Value is the ___________ from ___________.
Scenario 2: The Iditarod
When looking for the "biggest weight change," does it matter if the number is positive or negative? Why?
3. Main Activity: Distance Formula
The Golden Formula: \(|a - b|\)
To find the distance between any two points (\(a\) and \(b\)) on a number line, we find the absolute value of their difference.
Task: Ocean Expedition Deep Dive
From the video, we know the locations of these two points:
Coral Reef: -68 feetClownfish: -45 feet
Calculate the distance between the Coral Reef and the Clownfish:
Show your work steps:
|
- (
) |
Final Distance:
feet
4. Independent Practice
1
The temperature in Fairbanks, Alaska was -12°F in the morning and +8°F in the afternoon. What was the total range in temperature?
2
A diver is at -32 feet . They swim up to -10 feet . What distance did they travel?
Exit Ticket: The "Why"
Why do we use absolute value when finding the distance between two points, even if one or both of the points are negative?
Absolute Distance Slides The Absolute Distance
Using absolute value to measure the gap between two worlds.
7th Grade Mathematics
Warm-up
A bird is flying at +50 feet.
A fish is swimming at -40 feet.
How far apart are they?
Intuitive Check
Don't use a formula yet! Just look at the numbers. What is the total distance between them?
Draw a mental number line...
Expedition: Real World
Embedded media
Pause at 0:48: Predict the closest animal!
Pause at 2:03: Why did -45 become 45?
Ocean Depths Recap
|-45| = 45 feet
|-68| = 68 feet
|50| = 50 feet
The Big Question
"What does the absolute value represent in this real-life scenario?"
DISTANCE
from sea level (zero)
The Distance Formula
To find the distance between Point A and Point B:
| a - b |
The Absolute Value of the Difference
Example: Sea Level Depth
The Problem:
How far apart is the Clownfish (-45) and the Coral Reef (-68)?
On your worksheet, set up the formula...
1
| -45 - (-68) |
2
| -45 + 68 |
3
| 23 | = 23 feet
Scenario 2: The Iditarod
Embedded media
Pause at 3:04: What does negative weight mean?
Pause at 4:15: Biggest number vs Biggest Change?
Independent Practice
Complete the problems on your Distance Difference worksheet.
10 Minutes
Exit Ticket
Before you pack up, answer the final question on your sheet:
"Why do we use absolute value when finding the distance between two points, even if one or both are negative?"
Hint: Think about what "negative distance" would mean in the real world.
Calculator Quick Guide Calculator Quick Guide
Mastering Absolute Value on your device.
1. Scientific Calculators
The "abs" Button
Most scientific calculators have a dedicated button for absolute value. It is often labeled as:
abs |x|
Tip: If you don't see it, check the 2nd or Shift functions above the ( or hyp buttons.
How to Type:
1 Press the abs button.
2 Enter your expression (e.g., 5 - 12).
3 Close the parentheses ) if needed.
2. TI-84 Plus / Graphing
Method: Math Menu Standard for TI-Series
MATH
Step 1
NUM (Right Arrow)
Step 2
1: abs(
Step 3
Test Your Skills
Try typing these into your calculator exactly as shown to see if you get the right answer!
Challenge A
| 5 - 12 |
Answer
7
Challenge B
| -45 - (-68) |
Answer
23
Remember: Absolute value always results in a positive number or zero!
Facilitation Guide Facilitation Guide
The Absolute Distance Expedition
Total Time: 45 Minutes
Lesson Timeline
5 Min
Warm-up
Bird & Fish Scenario
10 Min
Video Viewing
Scenario 1 & 2
15 Min
Main Activity
|a - b| Formula
10 Min
Practice
Independent Work
5 Min
Closure
Exit Ticket
Video Pause Points
0:48
Prediction Moment
"Without doing math yet, just looking at the picture, which animal looks closest to the water line?"
2:03
Distance Conceptualization
Ask: "Why did the -45 become positive 45? What does that positive number represent in real life?" (Key Answer: Distance is always positive).
3:04
Real-World Interpretation
"What does a negative weight change mean for Loki or Yeti? What does a positive change mean?"
4:15
Magnitude vs. Direction
Discuss the difference between "biggest number" and "biggest change." Emphasize that "change" looks at the magnitude, not the direction.
Common Misconceptions
Negative Distance: Students may calculate a negative result and assume it's correct. Remind them that distance measures "how far," which is always a magnitude (positive).Subtracting Negatives: In the formula |a - b|, if \(b\) is negative, students often forget the double negative: \(| -45 - (-68) |\).
Pro-Tips
Physicality: Use a physical meter stick or number line tape on the floor to demonstrate that walking from -2 to +3 is 5 steps, regardless of direction.Ordering: Emphasize that \(|a - b|\) gives the same result as \(|b - a|\). Distance is symmetric.
Learning Objective
Students will use absolute value to find the distance between two points on a number line.
Distance Difference Answer Key Answer Key
Distance Difference Worksheet
1. Warm-up
Total Distance Answer:
90 feet
Reasoning: 50 feet up to zero + 40 feet down from zero = 90 total feet.
2. Expedition Observations
Scenario 1
Distance is always positive. Absolute value converts negative positions (depths) into positive magnitudes (distances from zero).
Definition Check:
Absolute Value is the distance from zero.
Scenario 2
No. Change refers to the magnitude of the weight loss or gain. A 5lb gain and 5lb loss both represent the same amount of "change."
3. Main Activity
Formula Setup:
| -45 - (-68) | = | -45 + 68 | = | 23 |
Final Distance: 23 feet
4. Independent Practice
1. Fairbanks Temperature:
| 8 - (-12) | = | 8 + 12 | = 20°F
2. Diver Travel:
| -10 - (-32) | = | -10 + 32 | = 22 feet
Exit Ticket Key
Distance represents a physical gap or magnitude. It cannot be negative because distance measures space traversed regardless of direction. Absolute value ensures we focus on that positive magnitude.
