Water for Schools
Menu

Math problem set Grade 3 Math

Cedar Hollow's Leak Repairs: A Grade 3 Scaled Picture Graph Set

Students read a fictional town's picture graph of leaks fixed in five neighborhoods, where one drop stands for five leaks, then redraw rows at the same scale.

Objectives

  1. Students will read a picture graph in which one symbol stands for five items.
  2. Students will solve how-many-more and put-together problems from a scaled graph.
  3. Students will decide how many symbols a new graph row needs at a given scale.

Vocabulary

Key words: picture graph, scale, symbol, leak

Teacher overview

Cedar Hollow is a fictional town whose water crew keeps a running count of the leaking pipes it repairs in each neighborhood, and the town clerk posts that count as a picture graph on the library wall. Because the month's total runs past a hundred leaks, the graph uses a scale in which one drop stands for five repaired leaks, which is the scaled-graph reading grade 3 introduces. The misconception this set targets is counting symbols instead of reading the scale, so a row of seven drops gets reported as seven leaks rather than thirty-five. Problem 10 puts that error in front of students directly, and problems 7 through 9 ask them to work backward from a leak count to a number of drops.

Cedar Hollow's Leak Repairs: A Grade 3 Scaled Picture Graph Set — Grade 3 Math
Name: ____________________________ Date: ______________

Problems

Cedar Hollow fixed leaking pipes in five parts of town last month. The clerk made a picture graph. On this graph, one drop stands for 5 leaks.

Neighborhood Drops on the graph
Maple Ridge 6 drops
Center Street 4 drops
Fox Hill 7 drops
Birch Row 3 drops
Stone Mill 5 drops
  1. Maple Ridge shows 6 drops. Each drop stands for 5 leaks. How many leaks were fixed in Maple Ridge?
  2. Fox Hill shows 7 drops. How many leaks were fixed in Fox Hill?
  3. Birch Row shows 3 drops. How many leaks were fixed in Birch Row?
  4. How many more leaks were fixed in Fox Hill than in Birch Row?
  5. Center Street shows 4 drops. Stone Mill shows 5 drops. How many leaks were fixed in those two parts of town in all?
  6. How many leaks were fixed in all five parts of town?
  7. This month the crew fixed 40 leaks in Fox Hill. How many drops will the Fox Hill row need?
  8. The clerk also drew a bar graph. On the bar graph, one square stands for 5 leaks. How many squares tall is the Maple Ridge bar?
  9. The clerk wants one new row for Birch Row and Center Street together. How many drops will that row need?
  10. Marla looked at the graph and said Fox Hill had 7 leaks. How many leaks did Fox Hill really have?

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: 30 leaks. There are 6 drops, and each drop stands for 5 leaks, so 6 × 5 = 30 leaks.
  2. Answer: 35 leaks. There are 7 drops, so 7 × 5 = 35 leaks.
  3. Answer: 15 leaks. There are 3 drops, so 3 × 5 = 15 leaks.
  4. Answer: 20 leaks. Fox Hill had 35 leaks and Birch Row had 15 leaks, so 35 − 15 = 20 leaks.
  5. Answer: 45 leaks. Center Street had 4 × 5 = 20 leaks and Stone Mill had 5 × 5 = 25 leaks, so 20 + 25 = 45 leaks.
  6. Answer: 125 leaks. The five rows hold 30 + 20 + 35 + 15 + 25 leaks. Add in order: 30 + 20 = 50, 50 + 35 = 85, 85 + 15 = 100, and 100 + 25 = 125 leaks.
  7. Answer: 8 drops. Each drop stands for 5 leaks, so divide: 40 ÷ 5 = 8 drops. Check by multiplying: 8 × 5 = 40 leaks.
  8. Answer: 6 squares. Maple Ridge had 30 leaks and each square stands for 5 leaks, so 30 ÷ 5 = 6 squares. The bar is the same height as the number of drops in the picture graph row.
  9. Answer: 7 drops. Birch Row had 15 leaks and Center Street had 20 leaks, so the new row stands for 15 + 20 = 35 leaks. Then 35 ÷ 5 = 7 drops.
  10. Answer: 35 leaks. Marla counted the drops instead of using the scale. Each drop stands for 5 leaks, so the 7 drops mean 7 × 5 = 35 leaks.

Differentiation

Support

Give students a copy of the graph with a small key printed beside every row, reading "1 drop = 5 leaks," and let them write 5, 10, 15, 20 under the drops as they skip-count across a row. Have them finish problems 1 through 3 before moving on, since the later items reuse those three totals. A hundred chart supports the addition in problem 6.

Extension

Ask students to redraw the whole graph at a scale where one drop stands for 10 leaks, decide which rows can no longer be drawn with whole drops, and write two sentences explaining why the town clerk chose a scale of 5 instead. Then have them state how many drops Stone Mill would need if the crew fixed 15 more leaks there.

ELL supports

Pre-teach "leak," "row," "scale," and "stands for" with a labeled drawing of one graph row and a dripping pipe. Post the sentence frame "___ drops stand for ___ leaks." Allow students to answer problem 10 by circling the correct number on a number line marked in fives rather than writing a full sentence.

Extensions

Have students collect a real class data set with values large enough to need a scale, such as the number of minutes each group spent at the classroom sink over a week. Ask them to choose a scale of 5, draw the picture graph, and then trade graphs with another group to check that the reader gets the same totals the makers intended.