Math problem set Grade 3 Science
Was Halverstone's Summer Unusual? A Grade 3 Rain-Record Set
Nine grade 3 problems on four years of rainy-day counts from a fictional town, where students add and compare to judge whether one dry summer was unusual.
Objectives
- Students will total and compare four years of seasonal rain records held in one table.
- Students will draw a scaled bar for a summer count using a scale of two days per square.
- Students will decide which of two explanations for a low reservoir the four-year record supports.
Vocabulary
- Reservoir
- A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
Also: season, typical, record, rainy day, scale
Teacher overview
A weather record answers a question that no single season can answer on its own, which is what counts as normal in one place. The town of Halverstone used here is fictional, and so are its rain records, yet the reasoning students do with them is the reasoning a water utility does every year before it decides whether a low reservoir calls for a new well or for nothing at all. Halverstone keeps a plain log at its town yard: the crew marks each day on which any rain falls and totals the marks at the end of every season. Last summer the reservoir dropped far enough that the crew asked residents to water their gardens less often, and two explanations were put forward. The first is that summer in Halverstone is normally a dry season, so a low reservoir in late summer is what a typical year brings. The second is that last summer was an odd one and that summers there are usually about as wet as springs. Those two explanations lead to different decisions, because only one of them means the town should expect the same shortage again next year.
The misconception this set is built to correct is the treatment of one memorable season as a description of what that season is normally like. A single long dry stretch is easy to remember and easy to mistake for the rule, while a season that behaved as usual leaves nothing to remember at all. Deciding what is typical takes several years of measurements laid out where they can be compared, which is why the problems below total, subtract, and graph the same table instead of asking about one number. Answering problem 9 from last summer alone, without using the totals from problems 3, 6, and 8, is the error this set is meant to surface.
Problems
The town of Halverstone is fictional. Its crew counts rainy days at the town yard. A rainy day is a day when any rain falls. The table holds four years of counts. Year 4 is last year.
| Year | Rainy days in spring | Rainy days in summer |
|---|---|---|
| Year 1 | 31 | 12 |
| Year 2 | 28 | 14 |
| Year 3 | 33 | 11 |
| Year 4 | 30 | 13 |
Last summer the town reservoir got low. The crew asked people to water gardens less. Two explanations were given for the low water.
Explanation 1 says that summer here is normally a dry season.
Explanation 2 says that last summer was odd, and that summers here are normally as wet as springs.
- The four spring counts are 31, 28, 33, and 30 rainy days. Add them. How many rainy days in all?
- The four summer counts are 12, 14, 11, and 13 rainy days. Add them. How many rainy days in all?
- The four springs had 122 rainy days in all. The four summers had 50 rainy days in all. How many more rainy days did the springs have?
- Look at Year 3 by itself. Its spring had 33 rainy days. Its summer had 11 rainy days. How many more rainy days did that spring have?
- The four summer counts are 12, 14, 11, and 13 rainy days. Which count is the largest? Give the number of days.
- The largest summer count is 14 rainy days. The smallest summer count is 11 rainy days. How far apart are they?
- Draw a bar for the Year 2 summer count on grid paper. That count is 14 rainy days. Let each square stand for 2 rainy days. How many squares tall is the bar?
- Explanation 2 says summers here are as wet as springs. The Year 4 spring had 30 rainy days. So Explanation 2 would expect about 30 rainy days in the Year 4 summer. The record shows 13. How many more days would Explanation 2 expect?
- In all four years, spring had many more rainy days than summer, and the four summer counts stay close to each other. Which explanation does the record support, Explanation 1 or Explanation 2?
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: 122 days.
Add the spring counts in order. 31 plus 28 is 59. Then 59 plus 33 is 92. Then 92 plus 30 is 122. - Answer: 50 days.
Pair the counts to keep the numbers small. 12 plus 14 is 26, and 11 plus 13 is 24. Then 26 plus 24 is 50. - Answer: 72 days.
Subtract the summer total from the spring total. 122 minus 50 is 72. Over these four years the springs carried more than twice the rainy days the summers did. - Answer: 22 days.
Subtract within the one year. 33 minus 11 is 22. The gap shows up inside a single year, not only in the four-year totals, which matters for problem 9. - Answer: 14 days.
That count belongs to the Year 2 summer. The other three summers had 12, 11, and 13 rainy days. - Answer: 3 days.
Subtract the smallest from the largest. 14 minus 11 is 3. The four summers sit within 3 rainy days of one another, so no summer in the record stands apart from the others. - Answer: 7 squares.
Each square stands for 2 rainy days, so count by twos up to 14 and keep track of how many counts that takes. Counting by twos gives 2, 4, 6, 8, 10, 12, 14, which is 7 counts, so the bar is 7 squares tall. - Answer: 17 days.
Subtract the recorded count from the expected count. 30 minus 13 is 17. Explanation 2 would expect 17 more rainy days that summer than the crew actually marked. - Answer: Explanation 1.
The springs had 72 more rainy days than the summers across the four years, and every single year shows the same pattern, as problem 4 shows for Year 3. The four summers also differ by only 3 rainy days, so last summer was not far from the other three. A dry summer in this town is ordinary rather than odd, which is what Explanation 1 claims. In our scenario the crew holds only four years of counts, so the claim covers those four years and does not settle what every future summer will do.
Differentiation
Support
Give these students the table recopied as two separate lists, one for spring and one for summer, so the two seasons do not have to be tracked across a row. Let them cross off each count as it is added. Suppose a student loses the running total partway through problem 1; adding the tens first and then the ones, or using a number line marked in tens, keeps the four addends in order. Assign problems 1 through 6 and problem 9.
Extension
Ask students to invent a fifth year for this fictional record whose two counts would make Explanation 2 the better-supported claim, then to write one sentence saying what those counts would have to look like and one sentence saying whether a single such year would be enough to change the answer to problem 9. Students who finish can state how many years of records they would want before calling a season typical, and why.
ELL supports
Pre-teach "season," "typical," and "record" using a two-column chart on the board labeled spring and summer, filled in together from the table one row at a time. Post the frames "Spring had ___ rainy days and summer had ___ rainy days" and "The record supports Explanation ___ because ___." Have partners read each table row aloud before any adding begins, so the numbers are attached to a season and a year before they are used.
Extensions
Have the class keep its own rainy-day count for the current season, marking one tally for each school day on which any rain falls, and compare the term total with the fictional Halverstone counts. One term will not settle what is typical anywhere, and that limit is the part worth drawing out: ask students what they would need before saying anything about a normal season in their own town, and how many years the log would have to run before a crew could plan a reservoir around it.