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Scaling Transformation - Absolute-Beginner Level: core concept mastery Scaling Transformation ABSOLUTE BEGINNER

This skill primer 🌟 worksheet focuses on Scaling Transformation - a key topic in Rule Detection. You'll solve 20 absolute-beginner-level problems (Worksheet 1 of 10). The primary focus is on core concept mastery. Master scaling transformation problems, scaling transformation reasoning questions, and scaling transformation practice through systematic practice.

📝 Worksheet 1 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Absolute Beginner level

What you'll learn in this worksheet:
Your progress through Scaling Transformation
Worksheet 1 of 10 (0% complete)

Question 1

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 35 units
- Figure 2: radius = 30 units
- Figure 3: radius = 25 units
- Figure 4: radius = 20 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 30 - 35 = -5 units
- Fig 2 → 3: 25 - 30 = -5 units
- Fig 3 → 4: 20 - 25 = -5 units

RULE HYPOTHESIS:
The circle radius decreases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: -5 units ✓

APPLICATION:
Figure 5 radius = 20 + -5 = 15 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = -5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 2

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 35 units
- Figure 2: radius = 30 units
- Figure 3: radius = 25 units
- Figure 4: radius = 20 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 30 - 35 = -5 units
- Fig 2 → 3: 25 - 30 = -5 units
- Fig 3 → 4: 20 - 25 = -5 units

RULE HYPOTHESIS:
The circle radius decreases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: -5 units ✓

APPLICATION:
Figure 5 radius = 20 + -5 = 15 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = -5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 3

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 4

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 5

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 6

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 7

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 8

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 9

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 10

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 15 units
- Figure 2: radius = 20 units
- Figure 3: radius = 25 units
- Figure 4: radius = 30 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 - 15 = 5 units
- Fig 2 → 3: 25 - 20 = 5 units
- Fig 3 → 4: 30 - 25 = 5 units

RULE HYPOTHESIS:
The circle radius increases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: 5 units ✓

APPLICATION:
Figure 5 radius = 30 + 5 = 35 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = 5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 11

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 12

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 15 units
- Figure 2: radius = 20 units
- Figure 3: radius = 25 units
- Figure 4: radius = 30 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 - 15 = 5 units
- Fig 2 → 3: 25 - 20 = 5 units
- Fig 3 → 4: 30 - 25 = 5 units

RULE HYPOTHESIS:
The circle radius increases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: 5 units ✓

APPLICATION:
Figure 5 radius = 30 + 5 = 35 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = 5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 13

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 14

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 15 units
- Figure 2: radius = 20 units
- Figure 3: radius = 25 units
- Figure 4: radius = 30 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 - 15 = 5 units
- Fig 2 → 3: 25 - 20 = 5 units
- Fig 3 → 4: 30 - 25 = 5 units

RULE HYPOTHESIS:
The circle radius increases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: 5 units ✓

APPLICATION:
Figure 5 radius = 30 + 5 = 35 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = 5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 15

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 16

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 17

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 18

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 35 units
- Figure 2: radius = 30 units
- Figure 3: radius = 25 units
- Figure 4: radius = 20 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 30 - 35 = -5 units
- Fig 2 → 3: 25 - 30 = -5 units
- Fig 3 → 4: 20 - 25 = -5 units

RULE HYPOTHESIS:
The circle radius decreases by 5 units (linear progression)

VERIFICATION:
All consecutive differences are consistent: -5 units ✓

APPLICATION:
Figure 5 radius = 20 + -5 = 15 units

SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = -5

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 19

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 10 units
- Figure 2: radius = 20 units
- Figure 3: radius = 40 units
- Figure 4: radius = 80 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 20 ÷ 10 = 2×
- Fig 2 → 3: 40 ÷ 20 = 2×
- Fig 3 → 4: 80 ÷ 40 = 2×

RULE HYPOTHESIS:
The circle radius doubles each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 2× ✓

APPLICATION:
Figure 5 radius = 80 × 2 = 160 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 2

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type

Question 20

Identify the scaling rule in this sequence: Figure 1: Figure 2: Figure 3: Figure 4: Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 80 units
- Figure 2: radius = 40 units
- Figure 3: radius = 20 units
- Figure 4: radius = 10 units

Step 2: Calculate size changes between consecutive figures
- Fig 1 → 2: 40 ÷ 80 = 0×
- Fig 2 → 3: 20 ÷ 40 = 0×
- Fig 3 → 4: 10 ÷ 20 = 0×

RULE HYPOTHESIS:
The circle radius halves each time (geometric progression)

VERIFICATION:
All consecutive ratios are consistent: 0× ✓

APPLICATION:
Figure 5 radius = 10 × 0 = 5 units

SCALING PATTERN TYPES:
- Geometric progression: constant r = 0

COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type
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