I'm not happy with my students understanding of integers so I've created the following document. It will involve some direct instruction and I want to get as much student participation and choral response as possible.
If you can't view it, the link is here. A fellow teacher on twitter suggest I only introduce one strategy in a day, and I took his advice and only discussed plus and minus tiles. Next week I'll review how to use a number line to visualize adding and subtracting integers.
Hearing students report out what they knew about integers was a bit uneventful. I did like that some students related it to how the x and y axes are labeled on a graph before you graph points. One student thought that decimals and fractions were not integers. I asked if you could have -2.3? They said yes. One student mentioned a tic taco to with a single diagonal of plus tiles and the rest minuses. A teacher had taught them this was the rule for multiplying integers. In the next period, a student brought it up, and said, "I was taught these are the rules for adding. A negative plus a negative is a positive." A student raised their hand and interjected "that's not true" and gave an example.@martinsean @mpershan I would be concerned about using 2 methods within one class. Tiles and # lines is a lot for one class period— Kent Haines (@MrAKHaines) October 27, 2015
It basically backed up the need for the PDF file that I've read, and that all teachers should read: Nix the Tricks. It's created by teachers for teachers, parents, and students. It's great. Of course I also heard the dreaded same change change which they said is the reason when you minus a negative it's a positive. I once again said that that rule could easily be confused with multiplying integers. A student also said a teacher had taught them when they see 3 - (-2) that the 2 minuses and the left hand parentheses look like a plus so make it a plus by connecting it. Some students also said that integers go on forever.
When I asked what questions they wrote down that they had about integers, I didn't hear many courageous or honest responses besides one student in 2nd period who said "I want to know what you're allowed to do when adding, subtracting, multiplying, and dividing!" Other students did not want have questions to share or did not feel like sharing them.
We discussed adding integers chorally. I also said what is 4 + (-10) sort of the same as? Luckily a few students said that it's like 10 minus 4, and then make it negative. This gave me the opportunity to show them when adding different signed integers you are subtracting the absolute values. The difference takes the sign of the integer with the greater absolute value. Students also liked learning the words addend, minuend, subtrahend, and difference.
After that, students wrote down 4 example integer problems. One that was a negative plus a negative. One that was adding integers with different signs. One with a smaller number minus a bigger number, and finally one where you were minusing a negative. Then they exchanged post it notes and solved someone else's. Then they checked their partners work and talked to them if they got it wrong.
The last 15 minutes were spent on the Math Shell formative assessment lesson pre assessment called Building and Solving Equations. We will begin this lesson Thursday and finish it on Monday.
In accelerated we got to do a lesson we skipped in Course 3 yesterday and one of my favorite lessons (9.2.1): using side lengths of squares to discover patterns about acute, obtuse, and right angles. Students were quick to say that it was the pythagorean theorem. They also were reminded and proved again what must be true for 3 sides to be a triangle. Aquiles, our ASB president, and new student to the school and the class was able to report out to the class that the sum of the 2 smaller sides must be greater than the longer side. He did not learn that at his last school. That was a great moment.