Model the Shift Teacher Guide Model the Shift
Teacher Facilitation Guide
Grade 6 Advanced Math
Duration: 45-50 Minutes
Objective
Students will visualize percent change through bar models and calculations. By the end of this lesson, students will be able to represent an increase or decrease as a portion of the original whole and apply the percent change formula.
Materials Needed
Connecting Cubes (15 per group)
Graph Paper
Colored Pencils
"Modeling Change" Worksheet
Vocabulary
Percent Change: The relative change between an old and new value.Original (Old): The starting value; the basis for comparison.Decrease: A negative change in value.Increase: A positive change in value.
Lesson Timeline
5
The Cube Tower Hook
Instructional Steps:
Have students build a tower of 10 cubes . This represents "100%" of our starting value.
Ask them to add 5 more cubes of a different color.
Discuss: "We added 5. What portion of the original 10 is the new part?" (1/2 or 50%).Visual Point: The "change" is exactly half the size of the "original."
10
Video Viewing & Formula
Math with Mr. J - Percent of Change
Stop at 2:32 (after Example 1). Focus on the "decrease" concept.
Key Teaching Moment (1:13):
Mr. J explains why we always divide by the original . Ask: "If a store drops a price from $50 to $34, are we measuring the discount based on what we used to pay or what we pay now?"
25
Modeling Change Activity
Students transition to drawing bar models. They must visually represent the "Original" bar and the "New" bar on graph paper, then highlight the "Difference."
Visual Task:
Identify the "Old" bar. Draw the "New" bar next to it. Shade the part that changed.
Calculation Task:
Divide the "Shaded Amount" by the "Old Bar Length." Multiply by 100.
5
Extension: The 50/50 Puzzle
Challenge the class: "If you increase a number by 50% and then decrease the result by 50%, do you get back to the start?"
The Truth:
No! If you start at 100, a 50% increase takes you to 150. A 50% decrease of 150 is 75. You end up at 75 because the "original" number changed for the second calculation. This previews compound change and interest.
Watch Out For...
Denominator Confusion
Students often divide by the larger number or the new number. Remind them: Percentage change is always "of" the original. The original bar is our 100% baseline.
Ignoring the Negative
In the formula \((New - Old)\), a decrease results in a negative number. Encourage students to keep the sign as it indicates the "direction" of the change.
Discussion Anchors
Q1
"If we get a percent change of 120%, what does that look like on a bar model?" (The new bar is more than double the original).
Q2
"Why do we call the original number 'old' in the formula?" (It represents the starting state before the shift occurred).
Q3
"Could you ever have a decrease of 110%?" (No, you can't lose more than you started with in most contexts, but you can increase by any amount).
Model the Shift Slides Grade 6 Advanced Math
Model the Shift
Visualizing Percent Increase & Decrease
The Hook
Build a tower of 10 cubes.
Add 5 more of a new color.
What portion of the original 10 is the new part?
The Formula
Percent Change
Amount of Change
Original (Old) Number
×
100
"Always divide by the old or original number!"
Watch: Percent of Change with Mr. J
Embedded media
Stop after Example 1 (2:32)
Key Point: Why divide by the "Old"?
Example 1: Decrease
50 to 34
Is this an increase or decrease?
1
Difference: \(34 - 50 = -16\)
2
Divide: \(-16 \div 50 = -0.32\)
3
Result: 32% Decrease
Bar Model View
Old:
50 (100%)
New:
34
Lost 16
How to Model Change
Draw
Sketch the Original bar on graph paper. This is your 100% baseline.
Shade
Show the Difference. Is it a tail growing longer or a piece being cut away?
Compare
What fraction of the Original bar is that shaded region?
The 50/50 Puzzle
If you increase a number by 50%...
...and then decrease the result by 50%...
Do you get back to the start?
A) Yes
B) No
C) It depends
Modeling Change Worksheet Model the Shift
Visualizing Percent Change
Name
Date
The Formula
\( \% \text{ Change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100 \)
Step 1: Draw your "Old" bar. This is your 100% baseline.
Step 2: Draw your "New" bar. Shade the part that represents the change.
Step 3: Calculate what percent the shaded area is of the "Old" bar.
1. Small Sprout | 10 to 12
Increase
Draw your bar models on the grid:
Show Your Work
Final Percent Change:
2. Sales Slump | 20 to 15
Decrease
Draw your bar models on the grid:
Show Your Work
Final Percent Change:
3. Rapid Growth | 4 to 10
Mega Increase
Draw your bar models on the grid:
Show Your Work
Final Percent Change:
The 50/50 Puzzle Challenge
If you start with a tower of 100 cubes , increase it by 50%, then decrease the new total by 50%, do you end up with 100 cubes again? Explain using math or a quick sketch.
Hint: What is 50% of the NEW total after the increase?
Modeling Change Answer Key Model the Shift
Answer Key & Grading Guide
Worksheet Solutions
1. Small Sprout (10 to 12)
Expected Bar Model:
• Old bar: 10 units long.
• New bar: 12 units long.
• Shaded Region: A "tail" of 2 units added to the end.
Calculation Steps
\( \frac{12 - 10}{10} = \frac{2}{10} = 0.2 \)
20% Increase
2. Sales Slump (20 to 15)
Expected Bar Model:
• Old bar: 20 units long.
• New bar: 15 units long.
• Shaded Region: The last 5 units of the "Old" bar (showing what was lost).
Calculation Steps
\( \frac{15 - 20}{20} = \frac{-5}{20} = -0.25 \)
25% Decrease
3. Rapid Growth (4 to 10)
Expected Bar Model:
• Old bar: 4 units long.
• New bar: 10 units long.
• Shaded Region: 6 units added to the end (longer than the original!).
Calculation Steps
\( \frac{10 - 4}{4} = \frac{6}{4} = 1.5 \)
150% Increase
4. The 50/50 Puzzle Solution
Step 1: Start at 100. Increase by 50% (+50). New total = 150 .
Step 2: Decrease 150 by 50%. Since 50% of 150 is 75, we subtract 75.
Final Result: 150 - 75 = 75 .
Conclusion:
No, you do not get back to the start. You lose more in the second step because 50% of a larger number (150) is greater than 50% of the original (100).
