Learning Target · What & Why
I can compare time records using arithmetic so I can check whether an explanation fits the evidence.
I Know I Am Successful When…
- I multiply visits by minutes and compare the total with the log.
- I calculate the average time needed for the records to match.
- I explain what the mismatch shows without claiming it proves guilt.
Investigate a fictional school mystery using multiplication, addition, and evidence. You will compare the reported visit times with the security log, then explain what the numbers do and do not prove.
MATH MYSTERY · GRADE 7
The Missing Trophy: Check the Time Records
Big question: How can multiplication and addition help you check an explanation against evidence?
School staff are reviewing the visitor records for a missing science trophy. The access log shows 9 visits totaling 146 minutes. Three students reported how long they spent at the case. Jordan’s and Marcus’s times were independently confirmed, but Priya’s time is only an estimate. These are fictional data.
| Student | Visits | Minutes per visit | Evidence |
|---|---|---|---|
| Jordan | 4 | 12 | Confirmed |
| Priya | 3 | 24 | Estimate |
| Marcus | 2 | 22 | Confirmed |
Your turn: Two questions
- If Priya’s estimate is correct, what is the total time for all three students? Show your multiplication and addition. Does it match the 146-minute log?
- Using the confirmed records for Jordan and Marcus, what would Priya’s average minutes per visit have to be to match the log? Explain why the reported estimate needs another check.
Write 3–5 sentences after your calculations. “The reported total is ___ minutes, but the log says ___. For the log to match, Priya’s visits would need to average ___ minutes because ___.”
Optional challenge: What do the numbers NOT prove?
Does an incorrect time estimate prove that someone took the trophy? Explain why a mismatch is a reason to investigate, not proof of guilt.
Before posting: Include calculations with units and a short explanation. Use the existing comment section.
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16 Responses
The times Jordan visit the trophy case is 10 times and the times Priya visits the trophy case that week is 6 times. Priya stays at the trophy case that week is 2 h and 30 mins. As for Jordan 2 h 55 min together is 5 h 25 mins. Jordan doesn’t make sense because why look at all day 35 mins each day. As for Priya makes sense because the trophy is a science and Priya is in science club but Jordan is not. So I think that Jordan is lying.
The log shows 9 total visits. After subtracting 1 visit by Marcus, 8 visits remain. Jordan claims to have visited 2 times per day for 5 days (
visits), which exceeds the remaining 8 visits. The total recorded time is 186 minutes. Priya visited twice for 75 minutes each (150 minutes total). This leaves only 36 minutes for Jordan’s 8 visits, averaging 4.5 minutes per visit—which is noted as being unrealistic.
Jordan’s claims do not match the log, while Priya’s details fit the clues
Jordan is lying. He claims he made 10 visits (2 per day for 5 days), but the log shows only 9 total visits, and one was made by Marcus, leaving just 8 visits for everyone else. So Jordan’s 10 visits are impossible. For time, Priya’s 2 visits at 75 minutes each total 150 minutes (2 hours 30 minutes). The total recorded time is 186 minutes, leaving 36 minutes for the remaining visits. If Jordan made those 8 visits, each would take only 4.5 minutes, which is unrealistic. Therefore, Jordan’s claims don’t match the log, while Priya’s do.
Since there are only 8 visits left but Jordan visited 10 times, this is impossible.
Jordan is lying My calculations: Visits by Jordan = 2 visits per day for 5 days → 2 × 5 = 10 visits, Visits by Priay = 2 visits, Since there are only 8 visits left but Jordan visited 10 times, this is impossible. On time: Time spent by Priay = 1 hour 15 minutes per visit → 75 minutes × 2 visits = 150 minutes, 150 minutes = 2 hours 30 minutes. Total time should equal 3 hours and 6 minutes = 186 minutes 186 minutes – 150 minutes = 36 minutes remaining for the other person Since Jordan had 8 visits, then 36 ÷ 8 = 4.5 minutes per visit, which is far from being true. My reasoning: Jordan’s total number of visits and total time do not agree with what was recorded in the log.
Jordan’s Claim: 2 visits per day for 5 days = 10 visits.
Priya’s Claim: 2 visits (Tuesday and Thursday).
The Log: Shows 9 total visits.
The Calculation: 9 total visits – 1 (Marcus) = 8 visits remaining.
Conclusion: Since there are only 8 visits left for the two of them, Jordan’s claim of 10 visits is mathematically impossible.
Jordan is lying,Visits by Jordan = 2 visits per day for 5 days → 2 × 5 = 10 visits, Visits by Priay = 2 visits, Since there are only 8 visits left but Jordan visited 10 times, this is impossible. Priya’s 2 visits at 75 minutes each total 150 minutes (2 hours 30 minutes). The total recorded time is 186 minutes, leaving 36 minutes for the remaining visits. If Jordan made those 8 visits, each would take only 4.5 minutes, which is unrealistic. Therefore, Jordan’s claims don’t match the log, while Priya’s do.
Jordan is lying because, the security log says only 8, but he went 10 times.His total minutes is 175, and Priyas is 150 minutes. Jordan goes over the 3 hours and 6 minutes record.
Jordan is lying because the security log says only 8 but he went 10 times. His total minutes is 175 and Priyas is 150. fordan goes over the 3 hours and 6 minutes record.
Jordan’s Claim: 2 visits per day for 5 days = 10 visits.
Priya’s Claim: 2 visits (Tuesday and Thursday).
The Log: Shows 9 total visits.
The Calculation: 9 total visits – 1 (Marcus) = 8 visits remaining.
Conclusion: Since there are only 8 visits left for the two of them, Jordan’s claim of 10 visits is mathematically impossible.
Jordan is lying. He claims he made 10 visits (2 per day for 5 days), but the log shows only 9 total visits, and one was made by Marcus, leaving just 8 visits for everyone else. So Jordan’s 10 visits are impossible. Since there are only 8 visits left but Jordan visited 10 times, this is impossible. On time: Time spent by Priay = 1 hour 15 minutes per visit → 75 minutes × 2 visits = 150 minutes, 150 minutes = 2 hours 30 minutes. Total time should equal 3 hours and 6 minutes = 186 minutes 186 minutes – 150 minutes = 36 minutes remaining for the other person Since Jordan had 8 visits, then 36 ÷ 8 = 4.5 minutes per visit, which is far from being true.
Jordan is lying. He claims he made 10 visits (2 per day for 5 days), but the log shows only 9 total visits, and one was made by Marcus, leaving just 8 visits for everyone else. So Jordan’s 10 visits are impossible.Time spent by Priay = 1 hour 15 minutes per visit → 75 minutes × 2 visits = 150 minutes, 150 minutes = 2 hours 30 minutes. Total time should equal 3 hours and 6 minutes = 186 minutes 186 minutes – 150 minutes = 36 minutes remaining for the other person Since Jordan had 8 visits, then 36 ÷ 8 = 4.5 minutes per visit, which is far from being true.
The times Jordan visit the trophy case is 10 times and the times Priya visits the trophy case that week is 6 times. Priya stays at the trophy case that week is 2 h and 30 mins.
Jordan said he visited 2 days per day for 5 days (2 x 5) which is 10 visits. Priya said she visited 2 times, Tuesday and thursday. The log showed 9 visits, and Marcus visited once so that 8 remained (1 – 9). Priya spent 1 hour and 15 minutes, In minutes 75 minutes per visit (1 hour = 60 minutes, 60 + 15 = 75). So in 2 visits she spent 150 minutes in hours 2 and 50 minutes. Total time = 3 hours and 6 minutes. In minutes 186 (186 – 150 = 36.) Since Jordan had 8 visits (36 ÷ 8 = 4.5) 4.5 minutes per visit, which is NOT true. Jordans lying.
Jordan is lying because, the security log says only 8, but he went 10 times.
Jordan is lying. He claims he made 10 visits (2 per day for 5 days), but the log shows only 9 total visits, and one was made by Marcus, leaving just 8 visits for everyone else. So Jordan’s 10 visits are impossible.Time spent by Priay = 1 hour 15 minutes per visit → 75 minutes × 2 visits = 150 minutes, 150 minutes = 2 hours 30 minutes. Total time should equal 3 hours and 6 minutes = 186 minutes 186 minutes – 150 minutes = 36 minutes remaining for the other person Since Jordan had 8 visits, then 36 ÷ 8 = 4.5 minutes per visit, which is far from being true.