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Math problem set Grade 3 Engineering & Design

Lowmeadow Park Pipe Loop: A Grade 3 Design Math Set

A grade 3 problem set measuring two water pipe routes around a fictional park ball field, then choosing the plan that reaches four fountains within a limit.

Objectives

  1. Students will find the distance around a rectangular field.
  2. Students will count 10-meter pipe pieces needed for a route.
  3. Students will pick the pipe plan that meets a goal and a materials limit.

Vocabulary

Key words: perimeter, route, joint, limit

Teacher overview

Every problem here comes from one scenario, which is a water pipe being planned for the new park in the fictional town of Lowmeadow, where four drinking fountains sit one on each side of a rectangular ball field. Students measure two proposed routes, count the 10-meter pipe pieces each route needs, and then decide which plan reaches all four fountains without going past the pipe the town owns. The error this set is built to catch is adding the length and the width only once and calling that total the distance around the field, which turns 300 meters into 150 and makes the cheaper route look like the obvious winner. A second common slip is counting pipe pieces by ones instead of counting by tens, so the answer key shows both steps separately.

Lowmeadow Park Pipe Loop: A Grade 3 Design Math Set — Grade 3 Engineering & Design
Name: ____________________________ Date: ______________

Problems

The town of Lowmeadow is building a new park. The ball field is a rectangle. It is 90 meters long and 60 meters wide. Four drinking fountains sit on the field, one on each side.

Workers must lay a water pipe to reach the fountains. Pipe comes in 10-meter pieces. The town has 28 pipe pieces on the truck.

Route A follows all four sides of the field. Route B follows only three sides, which are one long side, one short side, and the other long side. Route B does not reach the fountain on the fourth side. A branch pipe 30 meters long would reach that last fountain.

  1. Route A follows all four sides of the field. What is the total length of Route A?
  2. Route B follows one long side, one short side, and the other long side. What is the total length of Route B?
  3. How much shorter is Route B than Route A?
  4. Pipe comes in 10-meter pieces. How many pieces does Route A need? Count by tens.
  5. How many 10-meter pieces does Route B need?
  6. Add the 30-meter branch pipe to Route B. What is the total length of Route B plus the branch?
  7. How many 10-meter pieces does Route B plus the branch need?
  8. The town has 28 pipe pieces on the truck. How many more pieces does the town need to build Route A?
  9. A plan is allowed only if it reaches all four fountains and uses no more than the 28 pieces on the truck. Which plan is allowed: Route A, Route B, or Route B plus the branch?
  10. Write one reason the town should not choose Route B on its own.

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: 300 meters. The field has two long sides and two short sides. The two long sides are 90 + 90 = 180 meters. The two short sides are 60 + 60 = 120 meters. All four sides together are 180 + 120 = 300 meters.
  2. Answer: 240 meters. Route B uses one long side, one short side, and the other long side, so 90 + 60 = 150 meters, and 150 + 90 = 240 meters.
  3. Answer: 60 meters. Route A is 300 meters and Route B is 240 meters, so 300 − 240 = 60 meters shorter.
  4. Answer: 30 pieces. Route A is 300 meters. Counting by tens from 10 up to 300 takes 30 counts, so Route A needs 30 pieces of 10-meter pipe.
  5. Answer: 24 pieces. Route B is 240 meters. Counting by tens from 10 up to 240 takes 24 counts, so Route B needs 24 pieces.
  6. Answer: 270 meters. Route B is 240 meters and the branch is 30 meters, so 240 + 30 = 270 meters in all.
  7. Answer: 27 pieces. Route B plus the branch is 270 meters. Counting by tens up to 270 takes 27 counts, so that plan needs 27 pieces.
  8. Answer: 2 pieces. Route A is 300 meters, which needs 30 pieces of 10-meter pipe. The truck holds 28 pieces, so 30 − 28 = 2 more pieces are needed.
  9. Answer: Route B plus the branch. That plan reaches all four fountains and needs 27 pieces, which is within the 28 on the truck. Route A reaches all four fountains but needs 30 pieces, which is 2 more than the town has. Route B on its own fits the limit at 24 pieces but leaves one fountain dry.
  10. Answer: Accept any reason naming the missed fountain. Route B stops after three sides, so the fountain on the fourth side gets no water, and a plan that leaves a fountain dry fails the goal even though it uses the least pipe.

Differentiation

Support

Give these students a labeled sketch of the rectangle with 90 and 60 already written on all four sides, so problems 1 and 2 become addition rather than recall. Provide a number line marked in tens to 300 for the piece-counting problems, and allow students to trace each route with a finger before writing.

Extension

Ask these students to find a fourth plan that reaches all four fountains using fewer than 27 pieces, for example by running a branch across the middle of the field instead of around a full side, and to state one problem their plan would cause for people using the field. Have them write the rule they used to decide which plan to recommend.

ELL supports

Pre-teach route, branch, piece, and fountain with a simple labeled map of the field and its four fountains. Provide the frames "Route ___ is ___ meters long" and "Plan ___ is allowed because ___." Allow students to mark the pipe pieces as tick marks on the sketch before writing a number.

Extensions

Give the class the outside measurements of the school building or the playground and ask them to plan a pipe route that reaches three outdoor taps. Students can count the 10-meter pieces their route needs and compare it with a classmate's route using the same two tests of reaching every tap and staying within a stated number of pieces.