We’ve spent this last week covering decimal multiplication. The biggest issue my students have had is trying to line up the decimal points to do the multiplication. Students (and even I) find it confusing that, in addition and subtraction, you line up the decimal points to perform the operation, but multiplication and division are more based in whole number operations.
After we had covered solving decimal multiplication with both the standard algorithm and by using fractions, I provided students with 6 practice problems and allowed them to choose the method that worked best for them. The majority chose the standard algorithm, but many were still having problems with the multiplication because of the decimal point. One student called me over for help and said “I just don’t know what to do, I don’t know how to multiply these.” I rewrote the problem without the decimal points, he looked at me and told me “oh I can do this!”
I’m hoping that giving students a skills sheet that has multiple problems to practice with will help them. It’ll be interesting to see how many will still try and line up the decimal points to solve the problem.
At the beginning of the decimal unit, we included a variety of addition and subtraction problems on the warm-up for practice.
One day we had an addition problem, one that we were using to ensure that students knew how to “carry” when the sum in one column was a double digit number. The standard way to solve decimal addition is to line up the decimals, then to add from right to left. “Riley” chose to solve the addition problem a different way. He split each number into it’s whole number and fraction parts. He added up the fraction parts first, then added up the whole parts. Then he added the two results together to get his final answer.
If the problem was 12.37+4.86, he first added together 0.37 and 0.86 to get 1.23. Then he added together 12+4 to get 16. Finally he added 16+1.23 to get his final answer of 17.23.
It was a unique way to solve the problem. It isn’t the most efficient way to solve the problem and it opens up more opportunities for error, but it was fascinating to see how he view the problem and how to solve it.
During the ratio and rates unit, we provided a variety of warm-up problems that allowed students to practice the math. One of the unit rate problems was to find the price for one apple if 5 apples cost $8.35.
At the beginning of class during the warm-up, we paused the time and had students line up in the hallway. As we were walking out, “Michael” asked me what the problem was. I told him the problem, he thanked me, and we went out in the hall. After a few minutes, we returned to the classroom and everyone resumed working.
As I went around to check on students’ progress, “Michael” stopped me. He asked me to check his answer to the apple unit rate problem. As I looked over it, he told me that he did all the math in his head as we were standing out in the hallway.
It was impressive to me that he could do that kind of mental math. Most of my 6th grade students need to write out all of their division problems and that he could do the division without needing to see it in front of him was really interesting to me.