Practice and check
Worked example
Change every black cell to white and every white cell to black. Draw the result in the empty grid.
■ ↔ □ → 2, 3 → 2, 3
- Read one problem and its conditions before starting. Work without a timer, and keep the key visible where the task requires it.
- Swap every black and white cell, including initially empty positions. Keep the grid size fixed.
- ■ ↔ □ · Step 1: 2×2 · Step 2: 3×3 · Step 3: 4×4
Check answers after trying
1: 2, 3 2: 1, 2 3: 1, 3, 4, 5, 8, 9 4: 1, 2, 3, 6, 7, 8 5: 1, 2, 4, 5, 6, 7, 10, 11, 12, 13, 15, 16 6: 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14
Change every black cell to white and every white cell to black. Draw the result in the empty grid.
Why this answer
- 1. ■ ↔ □ → 2, 3 → 2, 3
- 2. ■ ↔ □ → 1, 2 → 1, 2
- 3. ■ ↔ □ → 1, 3, 4, 5, 8, 9 → 1, 3, 4, 5, 8, 9
- 4. ■ ↔ □ → 1, 2, 3, 6, 7, 8 → 1, 2, 3, 6, 7, 8
- 5. ■ ↔ □ → 1, 2, 4, 5, 6, 7, 10, 11, 12, 13, 15, 16 → 1, 2, 4, 5, 6, 7, 10, 11, 12, 13, 15, 16
- 6. ■ ↔ □ → 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14 → 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14
- 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 Change every black cell to white and every white cell to black. Draw the result in the empty grid. ■ ↔ □ · Step 1: 2×2 · Step 2: 3×3 · Step 3: 4×4 Original practice activities, not a standardized test or IQ score. Steps describe the task, not an age or ability grade. Try one example Change every black cell to white and every white cell to black. Draw the result in the empty grid. ■ ↔ □ → 2, 3 → 2, 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 Swap every black and white cell, including initially empty positions. Keep the grid size fixed. 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 ■ ↔ □ · Step 1: 2×2 · Step 2: 3×3 · Step 3: 4×4 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
Change every black cell to white and every white cell to black. Draw the result in the empty grid. Swap every black and white cell, including initially empty positions. Keep the grid size fixed.
Next Step
■ ↔ □ · Step 1: 2×2 · Step 2: 3×3 · Step 3: 4×4 Try the next step when the current method feels manageable. You may repeat a problem, use a paper marker, or stop and return later.