Math problem set Grade 4 Math
Turnbull Meter Route: Multiplying and Dividing House Counts
A grade 4 problem set following a fictional water meter technician's route, multiplying houses per street and dividing a route total across a work week.
Objectives
- Students will multiply two two-digit numbers to find the houses on a meter route.
- Students will divide a four-digit total by a one-digit number and name the remainder.
- Students will explain why a daily work total varies even when a plan divides evenly.
Vocabulary
- Water meter
- A device that measures how much water a home or business uses so the utility can bill fairly. Reading the meter can also reveal hidden leaks.
Also: route, technician, remainder, reading
Teacher overview
Every house in the fictional town of Turnbull has a water meter that records how much water the household used, and a technician walks a route each month to read them. The town splits its streets into a north route and a south route, and the technician plans the month by figuring out how many houses fall on each working day. This problem set follows that planning from street counts to a daily target. The misconception to watch for is treating the remainder in problem 4 as a fraction of a house, when the leftover houses in problem 5 are whole houses that have to be added to one of the days.
Problems
Turnbull's north route has 8 streets. Each street has 46 houses. How many houses are on the north route?
The south route has 27 streets. Each street has 34 houses. How many houses are on the south route?
How many houses are on the north route and the south route together?
The technician plans to read all of those houses in 7 days, reading the same number of houses each day. How many houses is that each day?
Using your work from problem 4, how many houses are left over after the 7 equal days?
Reading one meter takes 3 minutes. On a day with 183 houses, how many minutes does the reading take?
A helper reads 1,464 houses in 6 days, reading the same number each day. How many houses does the helper read each day?
The route van drives 38 miles each day for 5 days. How many miles is that?
Explain why the technician might not read exactly 183 houses on every one of the 7 days.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 368 houses.
46 × 8. Splitting 46 into 40 + 6 gives 40 × 8 = 320 and 6 × 8 = 48, and 320 + 48 = 368 houses.Answer: 918 houses.
34 × 27. Splitting 27 into 20 + 7 gives 34 × 20 = 680 and 34 × 7 = 238, and 680 + 238 = 918 houses.Answer: 1,286 houses.
The two routes add to 368 + 918 = 1,286 houses.Answer: 183 houses.
1,286 ÷ 7. Seven goes into 12 hundreds 1 hundred times, using 700 and leaving 586. Seven goes into 586 eighty-three times, using 581 and leaving 5. The plan is 183 houses a day.Answer: 5 houses.
The division in problem 4 leaves a remainder of 5. Those 5 houses are whole houses, so the technician adds them to one of the days rather than splitting them.Answer: 549 minutes.
183 × 3. Splitting 183 into 180 + 3 gives 180 × 3 = 540 and 3 × 3 = 9, and 540 + 9 = 549 minutes.Answer: 244 houses.
1,464 ÷ 6. Six goes into 14 hundreds 2 hundreds times, using 1,200 and leaving 264. Six goes into 264 forty-four times with nothing left, so the helper reads 244 houses a day.Answer: 190 miles.
38 × 5. Splitting 38 into 30 + 8 gives 30 × 5 = 150 and 8 × 5 = 40, and 150 + 40 = 190 miles.Answer: Some days include the 5 leftover houses, and a meter that is hard to reach or a house with a locked gate slows the route down.
Accept any answer that names the remainder from problem 5 or a real interruption such as weather, a blocked meter, or a customer question.
Differentiation
Support
Give students an area model grid for problems 1 and 2 with the tens and ones already separated, so each multiplication becomes two smaller products and one sum. For problem 4, supply the multiples of 7 up to 7 × 9 on a reference strip.
Extension
Ask students to build a 6-day plan for the same 1,286 houses, compare the daily number with the 7-day plan, and write one sentence about which schedule they would choose and why.
ELL supports
Pre-teach "route," "meter," "technician," and "left over" using a simple street map with houses drawn in rows. Provide the sentence frame: The route has ___ streets with ___ houses on each street, so it has ___ houses in all.
Extensions
Have students count the doors along one hallway of the school, estimate how long it would take to check each one at 3 minutes apiece, and compare their estimate with a timed trial of five doors.