It was really amazing to see students teaching other students. Our teacher then handed out a test they had previously taken and encouraged the tutor students to guide them through the test - "They should be able to take the same test again and do much better!"

I actually learned how to divide a second way yesterday also! One of the tutor-students despises long division and taught me the open array to divide. The open array works best with single digit numbers, but I used the open array to divide 792 by 17.

The strategy is a multi-step process, but I compressed it into one picture. So I'll explain.

1) The array is set up with an open array with the divisor on the side. For 487 divided by 9, you have the 9 on the side.

2) Start building to the answer by making arrays with easy numbers (10s, 20s, etc). I tried to explain using estimation to help speed up the process. If you know 50 x 9 is close but not quite, it's much easier than starting off with lots of 10s.

3) Continue building until you get as close as possible with a remainder (or not).

4) While you're adding more arrays, remind your students to keep a running total at the bottom. If you track it well, you won't go over and waste valuable standardized test time.

5) Finally add up your multiplicands/multipliers at the top to get your final answer. Don't forget your remainders!

The technique works well with single digit divisors, but like I said, it will work with multiple digit division problems as well. A strong sense of estimation and close tracking of sums will greatly help your students. I enjoy this strategy because it's using partial sums to get to a final answer.

Having students teach each other is great reinforcement for what the students have already learned. If you can teach it to someone else, it means you really know what you're doing. I also used this technique at MathSTARS with some of my 9th graders who were working on physics. Not only did tutor-student reinforce her knowledge of the physics concepts, but the student being helped could understand and relate to the extra help.

I also use the student-teaching method when there are too many students who need help and it's harder to help all your students at once. For example, when all four of your students are asking questions about completely different problems. I tend to ask the student who is done already, or finished the particular problem to help his/her classmates.

.

Having students working together is great. I found these long division worksheets. Where a pair of students can work together by comparing the answers of their respective sheets.

ReplyDelete