Math problem set Grade 4 Science
Rain Gauge Records at Larkspur Elementary: A Fraction Problem Set
A grade 4 problem set where students read a week of rain gauge data in eighths of an inch, add and subtract the fractions, and connect the total to groundwater recharge.
Objectives
- Students will read a frequency table of rainfall amounts measured in eighths of an inch.
- Students will add and subtract fractions with a common denominator to find totals and differences in rainfall.
- Students will explain how a week of recorded rainfall relates to groundwater recharge.
Vocabulary
Key words: eighth, mixed number, groundwater recharge
Teacher overview
A fourth-grade class at the fictional Larkspur Elementary School keeps a rain gauge on the playground and records each day's rainfall to the nearest eighth of an inch. This problem set uses one week of the class's own readings, organized as a frequency table instead of a written-out line plot, so students can practice adding and subtracting eighths in a real measurement context. A common misconception in this set is treating equivalent fractions that look different, such as 2/8 and 1/4, as unrelated amounts instead of recognizing 2/8 and 1/4 as the same value; problems 2 and 5 are built to surface that misconception directly.
Problems
Use this table of Larkspur Elementary's rainfall readings for the week. Each measurement is recorded in eighths of an inch.
| Rainfall (inches) | Number of days with this reading |
|---|---|
| 0 | 2 |
| 1/8 | 2 |
| 2/8 | 1 |
| 5/8 | 1 |
| 6/8 | 1 |
The seven days recorded were: Monday 0, Tuesday 2/8, Wednesday 5/8, Thursday 1/8, Friday 0, Saturday 6/8, Sunday 1/8.
How many of the seven days had measurable rain? Measurable rain means more than 0 inches.
Which single day had the most rain? How much did it measure? Write that amount two ways: as eighths, and as a simpler fraction.
Add all seven daily amounts together to find the total rainfall for the week. Write your answer as a mixed number.
What is the difference between the wettest day (Saturday) and Tuesday's reading?
Thursday and Sunday each measured 1/8 inch. Combine those two days' rainfall into one amount. What is the total?
The class has a 2-inch rain jar. Was the week's total rainfall (from problem 3) enough to fill it? If not, by how much did it fall short?
Why does keeping a weekly record like this help scientists understand groundwater? Write one or two sentences.
Challenge. Suppose the next week had exactly double this week's total rainfall. How many inches would that be? Write your answer as a mixed number.
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: 5 days.
Seven days total, minus the two days (Monday and Friday) with a reading of 0, leaves 5 days with measurable rain.Answer: Saturday, 6/8 in (= 3/4 in).
Saturday's reading of 6/8 inch is greater than every other day's reading; 6/8 simplifies to 3/4 because 6 and 8 share a common factor of 2.Answer: 1 7/8 in.
Adding all seven numerators over the shared denominator of 8: 0 + 2 + 5 + 1 + 0 + 6 + 1 = 15, so the total is 15/8 inch. Since 8/8 = 1 whole, 15/8 = 1 whole and 7/8, written as 1 7/8 inches.Answer: 4/8 in (= 1/2 in).
Saturday's 6/8 inch minus Tuesday's 2/8 inch equals 6/8 − 2/8 = 4/8 inch, which simplifies to 1/2 inch.Answer: 2/8 in (= 1/4 in).
Thursday's 1/8 inch plus Sunday's 1/8 inch equals 1/8 + 1/8 = 2/8 inch, which simplifies to 1/4 inch.Answer: No, short by 1/8 in.
2 inches written in eighths is 16/8. The week's total was 15/8 inches (1 7/8 from problem 3), so 16/8 − 15/8 = 1/8 inch short of 2 inches.Answer: Answers will vary.
A strong answer explains that rain soaking into the ground over many days and weeks is what refills, or recharges, the water stored underground, so tracking each week's total over a longer period shows whether enough rain is falling to keep the groundwater supply steady.Answer: 3 3/4 in.
Double the week's total: 15/8 × 2 = 30/8. Since 24/8 = 3 wholes, 30/8 = 3 wholes and 6/8, or 3 6/8 inches, which simplifies to 3 3/4 inches.
Differentiation
Support (below grade level)
Provide a printed number line from 0 to 1, marked in eighths, so students can plot each day's reading before comparing or adding, and complete problem 1 together as a class before students work independently on the rest.
Extension (above grade level)
Ask students to find how many eighths of an inch would need to fall on an eighth day to bring the week's total up to exactly 3 full inches, showing the subtraction that leads to their answer.
ELL supports
Pre-teach eighth, mixed number, and groundwater recharge using a labeled measuring cup or ruler divided into eighths alongside a simple sketch of rain soaking into the ground toward a water table. Allow problem 7 to be answered as a short spoken explanation recorded by a partner instead of written independently.