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Discover the Number Machine · 1
Practice and check
Worked example
Both examples use one rule: multiply, then add. Apply that rule to the last input.
(7 − 5) ÷ (5 − 3) = 1; 5 − 3 × 1 = 2; 11 × 1 + 2 = 13 → 13
- Read one problem and its conditions before starting. Work without a timer, and keep the key visible where the task requires it.
- Find one multiply-then-add rule that fits both given pairs before using the query.
- x → mx+b · Step 1: ×1+2 / ×1+3 · Step 2: ×3+0 · Step 3: ×3+6 / ×3+7
Check answers after trying
1: 13 2: 17 3: 27 4: 36 5: 51 6: 46
Both examples use one rule: multiply, then add. Apply that rule to the last input.
Why this answer
- 1. (7 − 5) ÷ (5 − 3) = 1; 5 − 3 × 1 = 2; 11 × 1 + 2 = 13 → 13
- 2. (9 − 6) ÷ (6 − 3) = 1; 6 − 3 × 1 = 3; 14 × 1 + 3 = 17 → 17
- 3. (21 − 9) ÷ (7 − 3) = 3; 9 − 3 × 3 = 0; 9 × 3 + 0 = 27 → 27
- 4. (24 − 9) ÷ (8 − 3) = 3; 9 − 3 × 3 = 0; 12 × 3 + 0 = 36 → 36
- 5. (33 − 15) ÷ (9 − 3) = 3; 15 − 3 × 3 = 6; 15 × 3 + 6 = 51 → 51
- 6. (37 − 16) ÷ (10 − 3) = 3; 16 − 3 × 3 = 7; 13 × 3 + 7 = 46 → 46
- 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 Both examples use one rule: multiply, then add. Apply that rule to the last input. x → mx+b · Step 1: ×1+2 / ×1+3 · Step 2: ×3+0 · Step 3: ×3+6 / ×3+7 Original practice activities, not a standardized test or IQ score. Steps describe the task, not an age or ability grade. Try one example Both examples use one rule: multiply, then add. Apply that rule to the last input. (7 − 5) ÷ (5 − 3) = 1; 5 − 3 × 1 = 2; 11 × 1 + 2 = 13 → 13. 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 Find one multiply-then-add rule that fits both given pairs before using the query. 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 x → mx+b · Step 1: ×1+2 / ×1+3 · Step 2: ×3+0 · Step 3: ×3+6 / ×3+7 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
Both examples use one rule: multiply, then add. Apply that rule to the last input. Find one multiply-then-add rule that fits both given pairs before using the query.
Next Step
x → mx+b · Step 1: ×1+2 / ×1+3 · Step 2: ×3+0 · Step 3: ×3+6 / ×3+7 Try the next step when the current method feels manageable. You may repeat a problem, use a paper marker, or stop and return later.