Depth · one concept from first principles · step 2 of 4
The table shows the number of tourists who visited a town each month. The number of tourists in August was more than the average number of tourists over the other months. Find the average number of tourists per month over the months.
| Month | June | July | August | September |
|---|---|---|---|---|
| Tourists | 258 | 316 | 167 |
The three filled months add to 741, and 741 divided by 3 = 247 is the anchor.
A 6th grader knows an average is the total shared equally, so adding the three values and splitting into 3 equal parts gives the typical month for those three.
6.SP.A.3Identify SubproblemsThe three months that are filled in have an average of 247 tourists.
An average hands a total out in equal shares, so adding the three counts and splitting that sum into three equal parts gives it.
The three months have to be added together first, because the average describes them as one group and not one at a time.
August is 168 more than that partial average of 247, so add 168 to 247.
The phrase 'more than the average' is a direct add-on, so I reconstruct the missing data point by starting from the average it is compared to.
6.SP.B.5Work BackwardsNow that August is known, add all four monthly counts to get the grand total for the 4 months.
I already had the sum of the three known months (741), so I just add August on top instead of re-adding everything.
4.OA.A.3Identify SubproblemsDivide the 4-month total by 4 to get the average number of tourists per month.
An average over 4 months means splitting the whole total into 4 equal months, so I divide by 4.
6.SP.A.3Guess And CheckFind the missing piece from the average first, then average everything together.
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