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If you feel like acting, you can pretend to “discover” this trick in the course of demonstrating a 2-digit multiplication problem. For students who finish early, have them try the trick for two-digit numbers: does (10 + 10 + 10) x 37 fit in with the earlier pattern? Explanation 2: (7 + 7 + 7) x 37 = (7 x 3) x 37 = 7 x ( 3 x 37) = 7 x (111) = 777, and likewise for other digits.
Once students know that they’re trying to confirm or disprove this pattern, use that to get them double-check their work when they get an answer that doesn’t fit with the pattern. Don’t let them know that you believe this trick will always work, or students won’t be motivated to solve it for every digit. You can follow this question with the division version: if you repeat digit three times to get a 3-digit number, will it always be divisible by 37? Route 37 follows along a circuitous route beginning at the intersection of Ravenhurst Street and Dugald Road through the suburbs of Transcona and Elmwood before crossing the Red River at the Redwood Bridge and ending at the corner of Redwood Avenue and Salter Street.
Southbound view on Ravenhurst Street showing the new marker indicating the upcoming end of Route 37. Southbound view on Ravenhurst Street showing a closeup of the new marker indicating the upcoming end of Route 37.
Southbound view on Ravenhurst Street showing the last eastbound marker and the newly installed directional sign underneath. Northbound view on Ravenhurst Street at Pandora Avenue East showing the marker directing Route 37 traffic east on Pandora Avenue. Northbound view on Ravenhurst Street at Pandora Avenue East showing a closeup of the marker directing Route 37 traffic east on Pandora Avenue.

Eastbound view on Pandora Avenue East showing the new marker indicating that Route 37 follows Ravenhurst Street to the right. Westbound view on Pandora Avenue East past Ravenhurst Street showing the first westbound marker.
Westbound view on Pandora Avenue East past Ravenhurst Street showing a closeup of the first westbound marker.
Westbound view on Pandora Avenue East showing the newly installed marker featuring Clearview numbering. Westbound view on Pandora Avenue East showing a closeup of the newly installed marker featuring Clearview numbering.
Westbound view on Midwinter Avenue at Levis Street showing a new marker for Route 37 featuring Clearview numbering.
Westbound view on Midwinter Avenue at Levis Street showing a closeup of a new marker for Route 37 featuring Clearview numbering. Northbound view on Watt Street approaching the intersection of Levis Street and Chalmers Avenue.
Northbound view on Watt Street at the intersection of Levis Street and Chalmers Avenue showing a closeup of the weather-beaten marker. This problems in multiplication is designed to give students the practice they need once they understand the basic idea of multiplication, with a context to provide motivation and deeper understanding. If replace the ones by twos, that would double the answer, so you’d get 222; and so on for threes, fours, etc. Emphasize that it would be a really important result to break the pattern, so they should make doubly sure they’ve got the calculation right.

The traffic light ahead had recently become operational at the time this photograph was taken. This photograph was taken prior to the installation of the traffic light shown in the previous photograph.
Route 37 follows Pandora Avenue East ahead, yet there is no sign to indicate this little detail.
There had previously been no indication that Route 37 followed Pandora Avenue and there is still no advance signage alerting motorists to turn left to follow Route 37. Farther south, Plessis Road (Road 19E) serves as the boundary between the City of Winnipeg and the RM of Springfield.
They’ll have gotten the multiplication practice they need, and the mystery can be something to continue thinking about later. If you understand the relationship between multiplication and division, the answer is clearly yes, but most students won’t intuitively understand that connection, and will need to check that the division works too. All pictures used on this site are the property of the respective photographers and are used by permission.
No picture may be used without the consent of the respective photographer.All pictures taken by Curtis Walker unless otherwise noted.