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Find Odd Overlaps · 2
Practice and check
Worked example
Shade a cell when it is black in an odd number of models: one, or three. Leave other cells white.
2, 3, 4 ⊕ 2, 4 → 3 → 3
- Read one problem and its conditions before starting. Work without a timer, and keep the key visible where the task requires it.
- Count black layers at each position. Keep odd counts, not every overlap.
- 1,3→■; 0,2→□ · Step 1: 2×2 · 2 layers · Step 2: 3×3 · 2 layers · Step 3: 4×4 · 3 layers
Check answers after trying
1: 3 2: 4 3: 1, 2, 9 4: 5, 6, 7 5: 6, 7, 8, 9, 10, 12 6: 1, 11, 12, 13, 14, 15
Shade a cell when it is black in an odd number of models: one, or three. Leave other cells white.
Why this answer
- 1. 2, 3, 4 ⊕ 2, 4 → 3 → 3
- 2. 1, 3, 4 ⊕ 1, 3 → 4 → 4
- 3. 2, 3, 8, 9 ⊕ 1, 3, 8 → 1, 2, 9 → 1, 2, 9
- 4. 4, 5, 7, 8 ⊕ 4, 6, 8 → 5, 6, 7 → 5, 6, 7
- 5. 6, 7, 10, 11 ⊕ 6, 8, 11 ⊕ 6, 9, 12 → 6, 7, 8, 9, 10, 12 → 6, 7, 8, 9, 10, 12
- 6. 11, 12, 15, 16 ⊕ 11, 13, 16 ⊕ 1, 11, 14 → 1, 11, 12, 13, 14, 15 → 1, 11, 12, 13, 14, 15
- If an answer differs, return to the first step that differs and explain the choice. Change the answer after checking rather than guessing a new rule.
- Try the next step when the current method feels manageable. You may repeat a problem, use a paper marker, or stop and return later.
- Original practice activities, not a standardized test or IQ score. Steps describe the task, not an age or ability grade.
Tips for Parents
What is on the sheet Shade a cell when it is black in an odd number of models: one, or three. Leave other cells white. 1,3→■; 0,2→□ · Step 1: 2×2 · 2 layers · Step 2: 3×3 · 2 layers · Step 3: 4×4 · 3 layers Original practice activities, not a standardized test or IQ score. Steps describe the task, not an age or ability grade. Try one example Shade a cell when it is black in an odd number of models: one, or three. Leave other cells white. 2, 3, 4 ⊕ 2, 4 → 3 → 3. Read one problem and its conditions before starting. Work without a timer, and keep the key visible where the task requires it. Check a difficulty Count black layers at each position. Keep odd counts, not every overlap. If an answer differs, return to the first step that differs and explain the choice. Change the answer after checking rather than guessing a new rule. Choose the next step 1,3→■; 0,2→□ · Step 1: 2×2 · 2 layers · Step 2: 3×3 · 2 layers · Step 3: 4×4 · 3 layers Try the next step when the current method feels manageable. You may repeat a problem, use a paper marker, or stop and return later.
What This Worksheet Builds
Shade a cell when it is black in an odd number of models: one, or three. Leave other cells white. Count black layers at each position. Keep odd counts, not every overlap.
Next Step
1,3→■; 0,2→□ · Step 1: 2×2 · 2 layers · Step 2: 3×3 · 2 layers · Step 3: 4×4 · 3 layers Try the next step when the current method feels manageable. You may repeat a problem, use a paper marker, or stop and return later.