tag:blogger.com,1999:blog-1907702537884089718.post6015821533378783197..comments2019-03-10T11:22:42.385-07:00Comments on Exit 10A: Dot CrazyJoe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-1907702537884089718.post-69286049128073757212016-05-03T13:48:25.352-07:002016-05-03T13:48:25.352-07:00Thanks for your insight. How important is it for ...Thanks for your insight. How important is it for the students to be their own designers, to visually mark the arrays to highlight parts themselves, in ways that make sense to them? Maybe they need to see an example, such as the one you suggest, first? My instinct is to let them make sense of it on their own. Thanks also for pointing me towards the Context for Learning unit.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-6147753812233007402016-05-02T17:45:39.515-07:002016-05-02T17:45:39.515-07:00Dot images are a great way to develop early multip...Dot images are a great way to develop early multiplication strategies and build connections between addition and multiplication. When used in specific ways, they can also be used to develop big ideas in multiplication (e.g., the distributive, associative and commutative properties). The images shown in this blog, however, could be improved by having dot arrangements that could be more easily subitized. To use the “Amanda Bean’s Amazing Dream" image as an example, the center 5 x 6 array could be visually marked by the designer in a way that highlights the parts (e.g., if the there were a slight separation or a line marking to indicate the first two rows and the first 3 columns). This would mean that visually the image would vertically cut in half and each half would clearly be subdivided into a (2 x 3) + (3 x 3) array. Building in these potentially realized suggestions would support the use of the distributive property, that, 5 x 3 = (2 x 3) + (3 x 3), which is a big idea in multiplication. Other big ideas (equivalence and the associative property of multiplication) might also arise as students explore how a 6 x 5 = (2 x 3) x 5 = 2 x (3 x 5). For a beautiful example of how this might be done, see the Context for Learning unit, “Groceries, Stamps, and Measuring Strips, created by Frans Van Galen and Cathy Fosnot.Toni Cameronhttp://www.metamorphosistlc.comnoreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-25579473802234674602016-04-24T16:02:10.617-07:002016-04-24T16:02:10.617-07:00Thanks for the comment Justin. I am also amazed b...Thanks for the comment Justin. I am also amazed by the fact that it's often the simple, low- or no-tech activities that have the greatest benefits. I was also surprised here that even the students that made mistakes had such positive things to say about the task. There's a lesson in there somewhere. Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-42236678236908327662016-04-24T15:55:41.519-07:002016-04-24T15:55:41.519-07:00Great connection Sharon, and one that would've...Great connection Sharon, and one that would've never crossed my mind. Thanks for sharing!Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-85756652767902995322016-04-23T18:09:14.337-07:002016-04-23T18:09:14.337-07:00I did a very similar activity in my Education clas...I did a very similar activity in my Education class in college and it was indeed very enlightening to see how different students approached this problem. Afterward, we were shown footage of how grade school students tried to solve the problem. The first student comment in the pictures accurately reflect the reactions of the students in the footage after learning where they went wrong. Solutions to simple activities like this one never cease to amaze me.Justinnoreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-38378193383515808402016-04-23T08:16:54.026-07:002016-04-23T08:16:54.026-07:00Such a great activity which extends wonderfully to...Such a great activity which extends wonderfully to what we do at the high school level with Fawn Nguyen's Visual Patterns! Sharonhttps://www.blogger.com/profile/11879289619551243845noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-86710774014106562542016-04-22T11:38:05.600-07:002016-04-22T11:38:05.600-07:00You're welcome, and thanks for taking the time...You're welcome, and thanks for taking the time to comment. One of the (many) great things about this activity is that it has such an open middle. Many pathways to a solution, and many opportunities for kids to learn from one another. Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-2012519999935005272016-04-22T11:36:12.928-07:002016-04-22T11:36:12.928-07:00Some teachers have begun to implement the dot imag...Some teachers have begun to implement the dot image routine, not to the extent that you have, but we've made a start. Your students should have no trouble transitioning to the more complex image. Steve made me 12 x 12 cut slides to play with, and that's how I'm generating new images. They're actually kind of fun to make!Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-18168812732706301992016-04-22T10:52:39.569-07:002016-04-22T10:52:39.569-07:00I also did the dot activity with two struggling le...I also did the dot activity with two struggling learners from a third grade class. It was a great to see how each of them "broke up" the dots in different ways based on their abilities. One students immediately started to say "I can make groups of __ " and the other student wanted to show how she broke it up by using repeated addition. In the end they learned from one another and that is priceless. Thank you for bringing this activity to my attention. I will definitely be using it in the future. NJTeacherhttps://www.blogger.com/profile/13087505648355950608noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-23317888923750800902016-04-22T06:29:55.035-07:002016-04-22T06:29:55.035-07:00I always use the dot images for the ten-minute sta...I always use the dot images for the ten-minute start of the lesson, but I really like the idea of finding a more complex image and asking individual children to take time to explain how they see it - one or multiple ways. I might lift that image directly from you, Joe...!Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.com