Math problem set Grade 1 Math
Thistlewick's Leak Line Slips: A Grade 1 Data Sorting Set
Ten grade 1 problems in which students sort eighteen mixed leak-report slips into three piles, total them, compare two piles, and move one slip.
Objectives
- Students will sort an unsorted list of leak reports into three categories and count each category.
- Students will find the total number of reports by adding the three category counts.
- Students will tell how many more and how many fewer reports one category holds than another.
- Students will explain why moving one report from one category to another leaves the total unchanged.
Vocabulary
Key words: slip, pile, sort, in all, how many fewer
Teacher overview
The town of Thistlewick is made up, and so is the Thistlewick Water District, which keeps a leak line that residents call when they find water running somewhere it should not be. Every call is written on a paper slip, and the slip records only where the caller saw the leak: at a sink, at a hose, or at a pipe. Eighteen slips came in over one week, and they arrive in this set as a mixed stack rather than as a finished chart, so students do the sorting themselves. The misconception this set is built to correct is treating the three category counts as three separate answers rather than as three parts of one whole, so that a student who reports 8 sinks, 6 pipes, and 5 hoses sees nothing wrong even though those three counts cannot have come from a stack of eighteen slips. Problem 4 makes that check explicit by asking the three piles to add back to the number of slips, and problems 7 through 10 approach the same idea from the other side by moving one slip between two piles and asking what changes and what does not. Cutting the table into eighteen paper slips is worth doing for any student who loses the count while reading down a list.
Problems
The town of Thistlewick has a leak line. People call when they see a leak. Each call gets a slip. The slip says sink, hose, or pipe. Here are the 18 slips.
| Slip | Leak | Slip | Leak | Slip | Leak |
|---|---|---|---|---|---|
| 1 | sink | 2 | hose | 3 | pipe |
| 4 | sink | 5 | sink | 6 | pipe |
| 7 | hose | 8 | sink | 9 | pipe |
| 10 | sink | 11 | pipe | 12 | hose |
| 13 | sink | 14 | pipe | 15 | sink |
| 16 | hose | 17 | pipe | 18 | sink |
Sort the 18 slips into three piles. Then answer.
- How many slips say sink?
- How many slips say pipe?
- How many slips say hose?
- The sink pile has 8 slips. The pipe pile has 6 slips. The hose pile has 4 slips. Add the three piles. How many slips in all?
- The sink pile has 8 slips. The hose pile has 4 slips. How many more slips are in the sink pile?
- The pipe pile has 6 slips. The hose pile has 4 slips. How many fewer slips are in the hose pile?
- A worker checks one pipe slip. The leak was really at a hose. The worker moves that slip to the hose pile. The pipe pile had 6 slips. How many slips are in the pipe pile now?
- The hose pile has 4 slips. One more slip goes in. How many slips are in the hose pile now?
- Now the piles have 8 slips, 5 slips, and 5 slips. How many slips in all?
- Before the move the piles had 8 slips, 6 slips, and 4 slips. After the move they have 8 slips, 5 slips, and 5 slips. Did the number of slips in all change? Write yes or no.
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: 8 slips. Slips 1, 4, 5, 8, 10, 13, 15, and 18 say sink, and that is 8 slips.
- Answer: 6 slips. Slips 3, 6, 9, 11, 14, and 17 say pipe, and that is 6 slips.
- Answer: 4 slips. Slips 2, 7, 12, and 16 say hose, and that is 4 slips.
- Answer: 18 slips. 8 plus 6 is 14, and 14 plus 4 is 18. The three piles add back to the 18 slips on the list, which is how a student checks that no slip was counted twice and none was skipped.
- Answer: 4 slips. 8 minus 4 equals 4, so the sink pile holds 4 more slips than the hose pile.
- Answer: 2 slips. 6 minus 4 equals 2, so the hose pile holds 2 fewer slips than the pipe pile.
- Answer: 5 slips. 6 minus 1 equals 5, because one slip left the pipe pile.
- Answer: 5 slips. 4 plus 1 equals 5, because the slip that left the pipe pile arrived here.
- Answer: 18 slips. 8 plus 5 is 13, and 13 plus 5 is 18.
- Answer: No. The piles held 8, 6, and 4 slips, which is 18, and they now hold 8, 5, and 5 slips, which is also 18. Two pile counts changed, yet no slip left the stack, so the number of slips in all stayed the same.
Differentiation
Support
Copy the slip table onto a sheet these students may cut apart, so the eighteen slips become objects they can push into three labeled piles rather than lines they must track down a column. Stop the assignment after problem 6, and count the first pile with them one slip at a time.
Extension
Ask these students to imagine a second week on the leak line in which four more slips arrive, two saying hose, one saying sink, and one saying pipe. Have them write the three new pile counts and the new total for both weeks together, then explain how they know the total rose by exactly four.
ELL supports
Post the three words sink, hose, and pipe with a photograph or simple drawing beside each, and point to the picture every time the word is read aloud. Provide the frame "The ___ pile has ___ slips" so every count is written in the same shape, and allow students to answer problem 10 by holding up two sorted stacks instead of writing a sentence.
Extensions
Run a leak line in the classroom for one week. Give students small blank slips and ask them to write one slip for every drip they find at school or at home, marking each slip sink, hose, or pipe. Sort the slips together on Friday, count the three piles, and check the three counts against the number of slips the class collected. Suppose a slip names a place none of the three words covers, such as a drinking fountain; the class then has to decide whether to open a fourth pile or to fold that slip into one it already has, which raises the question of how categories get chosen.