After tackling my homework for math training, grocery shopping, and spending several hours leveling my library (such a daunting task), I didn't have the energy left to process what I'd learned.
However, today I was home much earlier so I could reflect on yesterday and today's math trainings.
Days 2 & 3:
We talked about multiplication. We talked about it...a lot. Perhaps it's because I teach fifth grade and have taught inclusion, but none of the strategies mentioned were new information. I grasped the concept right away and helped my neighbor make the same mathematical discoveries.
However, I did learn a few new things over the past few days. Here are my "ah ha" moments:
The minuend is the first number in a subtraction problem and represents the amount you start with. The subtrahend is the amount that is being removed or subtracted.
This discovery raised an interesting question within our group. Why is it that other math vocabulary terms (addend, sum, factor, product, quotient, etc) are well-known but minuend and subtrahend aren't? Why can teachers (and hopefully their students) use the correct vocabulary for the other operations, but stumble on subtraction terms? I know I'll be incorporating these terms into my math instruction!
"Give One, get one, move on" strategy
The page is divided into four sections. Students solve the problem in the first quadrant, which is labeled "give". After time to process the problem, students then will stand up and find three other people to "get" strategies from. The students will work in pairs to explain their strategies to one another. Not only does this allow for movement, but students can explain their thoughts to one another. During this time, the teacher is monitoring as an informal assessment to see what students are grasping the content and which ones still need a little more practice time.
The next classroom tweak deals with these manipulatives:
Found in almost every elementary classroom, I always called these "ones", "tens", "hundreds" and so on. Most teachers do.
However, in doing so, you're limiting students' understanding of the relationship (powers of ten) between the manipulatives.
These will henceforth be referred at as units (smallest), rods (long ones), flats, and cubes.
By doing so, a teacher is able to stress the relationship between a value being ten times larger or smaller than the value next to it on a place value chart.
Referring to these as units, rods, flats, and cubes also allows for the manipulation in upper elementary. If my "one" is now the cube, I can use these manipulatives to represent a tenth (flat), a hundredth (rod), and thousandth (unit). I can also regard the unit as a thousand, then have students prove the other values. (Rod would be 10,000, flat 100,000, cube 1,000,000).
Finally, we played close to 100 (from Investigations). While this game was not new to me, I did appreciate the discussion about its importance in the classroom. In playing this math game (and others), students are provided the opportunity to practice many math skills such as estimation, reasoning, critiquing the reasoning of others, operations, and place value. These games take minutes to learn, can be a good task for students if they finish early with an activity, and can be used as homework. I know my students would much rather go home and play a math game as their homework then fill out a worksheet.
Close to 100 also reminded me of another quick math activity:
What an easy way to get their brains working during the first few moments of the day!
Stay tuned for a recap of days 4 and 5!