Using Critical Thinking to Solve Everyday Problems
A Stone Wall
Sarah wants to build a stone wall along one side of her garage. Sarah collects stones from the field behind her house. The first day, Sarah collects four small stones and five large stones. The second day, Sarah collects eight small stones and eight large stones. The third day, Sarah collects twelve small stones and eleven large stones. If this pattern continues, how many small and large stones does Sarah collect on the tenth day? Sarah realizes that she now has enough small and large stones for her stone wall. How many small and large stones does Sarah collect for the stone wall? Explain or show your mathematical thinking.
I know Sarah collected forty small stones because she started at four and each day she collected four more. So I decided to add four ten times and got an answer of forty.
Sarah collected thirty-two large stones. I know this because she started at five and added three ten times so I got my answer of thirty-two.
I got my answer when I saw that large rocks were skip counting by three and the small rocks were skip counting by 4. I knew this was true because as the days progressed the large rocks went from 5 to 8 then to 11. I know this was adding three because in my basic facts 5 Plus 3 equals eight and then eight plus three equals eleven, so if I keep adding three from 11 I will eventually reach my answer of 32.
With the small rocks I know its four because in my second column four times two is eight. then when I get to ten four times 10 is 40.
Sarah has collected 72 stones on the tenth day. It includes 40 small stones, and 32 large stones. I subtracted 4 small stones from 8 small stones because on the 1st day she collected 4 small stones, and on the 2nd day, she collected 8 small stones. I got 4 small stones as my answer, so I concluded that the rule was +4. I added 4 small stones to 12 small stones, then I kept adding on 4 small stones to the next numbers, until I added them 10 times. Then, for the large stones, I subtracted 8 large stones from 5 large stones because on the 1st day she collected 5 large stones, and on the 2nd day she collected 8 large stones. I got 3 large stones as my answer, so I said that the rule +3. I added 3 large stones to 11 large stones, and I kept adding on 3 large stones to the next numbers. On the tenth day, I got 40 small stones and 32 large stones, and I added them together to get 72 small stones and large stones.
In all, Sarah has collected 308 small stones and large stones to build her wall. For my answer, I added 8, 4, 12, 16, 20, 24, 28, 32, 36, and 40 small stones together to get 136 small stones. Next, I added 8, 5, 11, 14, 17, 20, 23, 26, 29, and 32 large stones together, to get 172 large stones. Lastly, I added 172 large stones and 136 small stones together and I got 308 as my answer. So in total, Sarah has 308 large and small stones to build her wall.3