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Math problem set Grade 4 Engineering & Design

Vinefield Orchard's Water Haul: Tank Trips and Tree Blocks

Ten grade 4 problems on hauling water to a fictional orchard during a pipe repair, ending with a choice between a trailer plan and a truck plan on time and cost.

Objectives

  1. Students will multiply and divide multi-digit numbers to size a water haul.
  2. Students will interpret a division remainder as one more tank trip.
  3. Students will choose between two hauling plans using a time rule and a token limit.

Vocabulary

Key words: haul, round trip, tank, supply token, block

Teacher overview

Every problem in this set draws on one situation: a broken pipe at a fictional orchard, three blocks of trees that still need water this week, and two ways to haul it. The arithmetic is grade 4 multiplication, division, and a single time conversion, and the last problem turns those numbers into an actual choice between the two plans. The error to watch for is dropping the remainder in problems 4 and 8. Students divide 840 by 300, see 2 with 240 left over, and write 2 trips, which leaves 240 gallons sitting in the yard; a leftover in a hauling problem always means one more trip, and the answer key walks that reasoning through rather than just stating the number.

Vinefield Orchard's Water Haul: Tank Trips and Tree Blocks — Grade 4 Engineering & Design
Name: ____________________________ Date: ______________

Problems

Vinefield Orchard is a made-up orchard used for these problems. A pipe broke this week, so the drip lines are off. The crew must haul water to the trees by tank until the pipe is fixed.

The orchard has three blocks of apple trees. Block 1 has 60 trees. Block 2 has 45 trees. Block 3 sits up a steep track and has 35 trees.

The crew has two ways to haul water.

  • Plan A, the trailer. The trailer tank holds 300 gallons. It can reach all three blocks, including Block 3. One round trip takes 40 minutes and costs 4 supply tokens.
  • Plan B, the truck. The truck tank holds 500 gallons. It cannot climb the steep track to Block 3, so the trailer must make that one trip. One truck round trip takes 25 minutes and costs 9 supply tokens.

The crew wrote two rules. Every tree must get its 6 gallons. The whole watering must be done in 3 hours or less.

  1. The crew has 3 hours to finish the watering. How many minutes is 3 hours?
  2. Block 1 has 60 trees. Block 2 has 45 trees. Block 3 has 35 trees. How many trees does the orchard have in all?
  3. The orchard has 140 trees. Each tree needs 6 gallons in one watering. How many gallons does one watering take?
  4. The trailer tank holds 300 gallons. The crew must haul 840 gallons. How many trailer trips does that take?
  5. One trailer round trip takes 40 minutes. How many minutes do 3 trailer trips take?
  6. Each trailer round trip costs 4 supply tokens. How many supply tokens do 3 trailer trips cost?
  7. Block 1 has 60 trees and Block 2 has 45 trees. Each tree needs 6 gallons. How many gallons do Blocks 1 and 2 need together?
  8. The truck tank holds 500 gallons. The truck must haul 630 gallons to Blocks 1 and 2. How many truck trips does that take?
  9. In Plan B the truck makes 2 round trips of 25 minutes each. The trailer makes 1 round trip to Block 3 that takes 40 minutes. How many minutes does Plan B take in all?
  10. Plan A uses 3 trailer trips at 4 supply tokens each. Plan B uses 2 truck trips at 9 supply tokens each plus 1 trailer trip at 4 supply tokens. Both plans finish inside the 3-hour rule. The orchard's rule is to pick the plan that finishes in time and spends the fewest supply tokens. Which plan should the crew choose?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 180 minutes.
    1 hour = 60 minutes, so 3 hours = 3 × 60 = 180 minutes.
  2. Answer: 140 trees.
    60 + 45 = 105 trees, and 105 + 35 = 140 trees.
  3. Answer: 840 gallons.
    140 trees × 6 gallons per tree = 840 gallons. Break it apart if it helps: 100 × 6 = 600 and 40 × 6 = 240, and 600 + 240 = 840.
  4. Answer: 3 trips.
    840 ÷ 300 = 2 with 240 gallons left over. Two full trips carry 600 gallons, which leaves 240 gallons still in the yard, and those 240 gallons need a third trip. The third trip is not full, yet it still has to happen.
  5. Answer: 120 minutes.
    3 trips × 40 minutes per trip = 120 minutes. That is under the 180-minute rule from problem 1.
  6. Answer: 12 supply tokens.
    3 trips × 4 supply tokens per trip = 12 supply tokens.
  7. Answer: 630 gallons.
    60 + 45 = 105 trees in Blocks 1 and 2. Then 105 × 6 = 630 gallons. Break it apart if it helps: 100 × 6 = 600 and 5 × 6 = 30, and 600 + 30 = 630.
  8. Answer: 2 trips.
    630 ÷ 500 = 1 with 130 gallons left over. One full trip carries 500 gallons, and the leftover 130 gallons needs a second trip.
  9. Answer: 90 minutes.
    2 truck trips × 25 minutes = 50 minutes. Add the one trailer trip of 40 minutes: 50 + 40 = 90 minutes. Plan B is faster than Plan A's 120 minutes.
  10. Answer: Plan A.
    Plan A costs 3 × 4 = 12 supply tokens. Plan B costs 2 × 9 = 18 supply tokens for the truck plus 4 supply tokens for the trailer, which is 18 + 4 = 22 supply tokens. Both plans finish inside 180 minutes, so the time rule does not separate them. Plan A spends 10 fewer supply tokens, so the crew picks Plan A. Plan B is worth remembering, because it saves 30 minutes, and on a day when the heat arrives early that saving could matter more than the tokens.

Differentiation

Support

Give these students a labeled picture of the orchard showing the three blocks, the two tanks, and the steep track, so the words in each problem attach to a place. Provide a division frame for problems 4 and 8 with three boxes labeled full trips, gallons left over, and total trips, so the remainder cannot be dropped by accident. Allow a multiplication chart for problems 3 and 7.

Extension

Ask these students to find the smallest tank size that would let the trailer finish the whole watering in exactly 2 trips, and to explain why a tank that is larger than half of 840 gallons still cannot do it in one. Then have them recalculate Plan B if the steep track is repaired so the truck can reach Block 3, and say whether that repair changes the answer to problem 10.

ELL supports

Pre-teach haul, tank, round trip, block, and left over with sketches and a hand motion for going and coming back. Provide a two-column glossary card matching each term to a picture. For problem 10, offer the sentence frame "The crew should pick Plan ____ because it costs ____ supply tokens and Plan ____ costs ____."

Extensions

Ask students what other costs a real orchard would count that these problems leave out, such as the driver's time, the fuel, and the risk of a heavy trailer on a wet slope, and where each of those would push the decision. Then have them write a third plan that mixes the two tanks differently, state its trips, minutes, and tokens, and say what would have to be true for their plan to beat Plan A.