Choose one of three rule cards, fill in the missing value and endpoint, and check your numbers before revealing the explanation. SC1 starts 46 and adds 10 four times, giving missing 66 and endpoint 86. Its wrong-path challenge identifies 56→67 as the first violating gap, even though later local jumps return to +10.
Give the rule before asking for the missing value
Illustrative Mathematics' comparison task discusses successive base-ten additions/subtractions and number-line reasoning. Here, students apply repeated additions to an explicitly stated start and jump count. Illustrative Mathematics: Repeated Base-Ten Steps
SC1 states Start at 46. Add 10 at each jump. Make exactly four jumps.
The rule has three parts: starting value, step and jump count. A row of numbers without those parts can support many possible continuations. This activity supplies its rule explicitly rather than pretending a short pattern uniquely determines one.
Use point indexes 0–4. Index zero is the start before any jump. Index four is the destination after four jumps.
| Point index | Jumps completed | SC1 value |
|---|---|---|
| 0 | 0 | 46 |
| 1 | 1 | 56 |
| 2 | 2 | 66 |
| 3 | 3 | 76 |
| 4 | 4 | 86 |
Five points have four gaps. The endpoint is 46 + 4 × 10 = 86. Ten added five times would create a fifth jump and reach 96; ignoring the start and reporting 50 answers a different calculation.
Locate the first violating gap
Use this original proposed wrong path: 46, 56, 67, 77, 87. The stated rule is still +10, and the stated start is still 46.
| Gap number | Transition | Actual change | Local rule check |
|---|---|---|---|
| 1 | 46 → 56 | +10 | Matches |
| 2 | 56 → 67 | +11 | First violation |
| 3 | 67 → 77 | +10 | Matches locally, from an incorrect point |
| 4 | 77 → 87 | +10 | Matches locally, from an incorrect point |
Name gap two, from point index one to two. The change is 67 - 56 = 11, not ten. Later local +10 steps keep the path one above the correct values; they do not restore the intended SC1 state.
This distinguishes one first faulty transition from several resulting wrong points. Indexes two, three and four differ from the correct path, but they are not three independently wrong increment calculations.
When fixing the first violation, recompute the following points too: 66, 76, 86. Changing only 67 to 66 while leaving 77 and 87 would introduce another +11 gap. Keep the rule and downstream state together.
Change the start without keeping the old answer
SC2 keeps +10 and four jumps but starts at 60. Its points are 60, 70, 80, 90, 100. The final value is 60 + 40 = 100, not SC1's 86.
SC3 is an independent extension: start 26, add 5, four jumps. Its points are 26, 31, 36, 41, 46. Adding five does not require every value to end in zero or five when the starting point has a different remainder.
| Original rule card | Start | Step | Jumps | Final value |
|---|---|---|---|---|
| SC1 | 46 | +10 | 4 | 86 |
| SC2 | 60 | +10 | 4 | 100 |
| SC3 | 26 | +5 | 4 | 46 |
Selecting SC2 or SC3 clears the previous answers and feedback. The point at index two is 80 for SC2 or 36 for SC3. The wrong-path challenge disappears on those cards because its proposed sequence belongs only to SC1.
The missing-value and endpoint fields accept whole numbers from zero through 200. SC1's gap field accepts only 1 through 4. The three cards are fixed, so prepare a separate answer key if you introduce a different start or step.
Use Check for the fixed numeric fields and discuss the written reason separately. Rule changes clear answers and hide SC1's diagnosis for other cards. Reset clears the current card without changing its rule. Recompute downstream points after repairing a gap rather than changing only one number.
Copy a prompt for this example
Create one self-contained HTML skip-counting activity with embedded CSS and JavaScript. Use a bright number-path layout with large values, clearly labeled answer fields, generous spacing, and controls that stack on a phone.
Provide three rule cards. SC1 starts at 46 and adds 10 for exactly four jumps: 46, 56, 66, 76, 86. SC2 starts at 60 and adds 10: 60, 70, 80, 90, 100. SC3 starts at 26 and adds 5: 26, 31, 36, 41, 46. Explain that five points have four gaps. Hide the value at index two and ask for it and the endpoint. The answers are 66 and 86, 80 and 100, or 36 and 46 respectively.
For SC1 only, show the proposed wrong path 46, 56, 67, 77, 87. Ask for the first violating gap. The answer is gap 2 because 56 to 67 adds 11. Later additions of 10 carry the earlier error forward.
Include a written explanation field, Check, a separate answer-key reveal, and Reset. Require whole numbers from 0 through 200 for the missing and endpoint values, a gap number from 1 through 4 for SC1, and a nonblank explanation. Check the fixed numeric answers while leaving the explanation for teacher discussion.
Card changes clear responses and hide the old key. Hide the diagnostic challenge on SC2 and SC3. Reset clears answers for the selected card. Return only the complete HTML file.
For the next number-path discussion, NOS can display this prepared HTML activity. Ask a pair to distinguish the first faulty gap from the later wrong points, then switch to SC3 and explain why adding 5 need not produce numbers ending in 0 or 5.