tag:blogger.com,1999:blog-1907702537884089718.post7909324374837867470..comments2018-01-14T06:04:43.269-08:00Comments on Exit 10A: Unknown UnknownsJoe Schwartznoreply@blogger.comBlogger17125tag:blogger.com,1999:blog-1907702537884089718.post-8663764556721400992016-12-29T11:23:04.327-08:002016-12-29T11:23:04.327-08:00Hi again Joe! I've just nominated this post fo...Hi again Joe! I've just nominated this post for #bestofmtbos2016.<br /><br />Part of it is to post this:<br /><br />Hello! This post was recommended for The Best of the Math Teacher Blogs 2016: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts at the end of the year and use the money raised toward a scholarship for TMC. Please let us know by responding via http://goo.gl/forms/LLURZ4GOsQ whether or not you grant us permission to include your post. Thank you, Tina and Lani.Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-91545085103867782512016-11-09T05:20:57.134-08:002016-11-09T05:20:57.134-08:00Thanks Joshua. I suppose that, without the marked...Thanks Joshua. I suppose that, without the marked lengths, students could have measured the dimensions. And now that I think of it, saying that it looks like a cube doesn't necessarily mean that it is a cube! <br />When they pass their cards around, I see them selecting particular observations, not just copying. Not sure what you mean about the semi-colons though.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-28114120350020255632016-11-07T19:02:18.661-08:002016-11-07T19:02:18.661-08:00Very interesting.
There is something to the stude...Very interesting.<br /><br />There is something to the students comments "it is a cube:" as drawn, it is hard to tell whether it is a cube or not. Other than the marked lengths, is there a way for them to decide?<br /><br />One thing I wonder about is passing the students' cards around. Do they think about what the other kids wrote or just copy? What about passing misconceptions? Like that use of semi-colons....<br /><br />I was struck by what the kids noticed about 253831. The various rounded values was probably the deepest thinking. I wonder what they would have wondered about it? For me, the immediate question: is it prime/what is the prime factorization? To dispel the suspense: 253831 = 41 x 41 x 151.<br />Joshua Greenehttps://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-48243411192935197262016-10-16T09:34:22.924-07:002016-10-16T09:34:22.924-07:00Really like that, Joe!Really like that, Joe!Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-30037826632540037812016-10-13T15:27:15.450-07:002016-10-13T15:27:15.450-07:00I don't know either! What's wonderful is ...I don't know either! What's wonderful is that this all came from a student's observation. And I'll return your gift of Talmud with another, from R. Hanina: "I have learned much from my teachers, more from my colleagues than from my teachers, but from my students I have learned the most of all." Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-29351717242080323962016-10-13T07:57:34.109-07:002016-10-13T07:57:34.109-07:00Or a regular cuboid. I don't know.
It seems t...Or a regular cuboid. I don't know.<br /><br />It seems to be their name in the UK. For instance the English National Curriculum says for Year 1 (5 and 6-year-olds):<br /><br />Pupils should be taught to:<br /> recognise and name common 2-D and 3-D shapes, including:<br /> 2-D shapes [for example, rectangles (including squares), circles and triangles]<br /> 3-D shapes [for example, cuboids (including cubes), pyramids and spheres]. Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-3376268081880347462016-10-13T07:54:07.697-07:002016-10-13T07:54:07.697-07:00I don't know if this is right, but with a soli...I don't know if this is right, but with a solid shape, we're not limited to the edges are we? So imagine you had a carpenter's square at a corner, one part of it could go along an edge and the other diagonally across the face? Or you could put the set square at some point along an edge at right angles to it...<br /><br />As you're saying Joe, these uncertain territories are the interesting and revealing places to be. "Teach the tongue to say'I don't know'", as it says in the Talmud.Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-22769301925229966632016-10-13T06:35:58.427-07:002016-10-13T06:35:58.427-07:00Excellent connection Joe. As an IL I am covering m...Excellent connection Joe. As an IL I am covering math and literacy but so often end up supporting Math I sometimes lose focus on Reading. I am going to think more on that and speak to some of my teachers.Mark Stamphttps://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-4096668083046320822016-10-13T02:40:53.348-07:002016-10-13T02:40:53.348-07:00Just did some googling on cuboid. And a cube woul...Just did some googling on cuboid. And a cube would be called a square cuboid? Maybe we should just go with "cube-ish."Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-51405257719056691942016-10-13T02:37:16.615-07:002016-10-13T02:37:16.615-07:00Thanks Linda for your kind words and encouragement...Thanks Linda for your kind words and encouragement.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-84252965008726956712016-10-13T02:36:19.144-07:002016-10-13T02:36:19.144-07:00Thanks Simon. Tunnel vision is a good way to desc...Thanks Simon. Tunnel vision is a good way to describe it; in my mind I also think of it as teaching with blinders on. I was wondering about the right angles as well. I see 3 at every corner for a total of 24, but are there interior and exterior ones? Another unknown unknown just uncovered! Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-4488241274224774012016-10-13T02:30:48.874-07:002016-10-13T02:30:48.874-07:00Thanks Mark. And I agree with everything you'...Thanks Mark. And I agree with everything you've said. Maybe a follow-up could be to show a rectangular prism with length and width and total volume but missing height and see if anyone would come up with the height from a "tell me everything you can..." prompt. And as I type this response it occurs to me that there is a nice connection between this "missing part"problem and the skill of making inferences that our counterparts in the reading world emphasize.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-31555688158579687262016-10-11T13:11:23.035-07:002016-10-11T13:11:23.035-07:00As usual, really interesting, Joe!
It's that...As usual, really interesting, Joe! <br /><br />It's that first half of What do you notice? What do you wonder?<br /><br />Without it, we're just encouraging a kind of tunnel vision. "That is only about this." And the this is just our this, or some curriculum this that's not even ours.<br /><br />I wonder about wondering too, would that uncover any unknowns...?<br /><br />(Are there really only 12 right angles? I haven't heard anyone talk about this, but it seems to me you could measure right angles all over this solid shape. Even at the vertices by twisting round... Just wondering...)Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-14070143123354086172016-10-11T13:00:52.344-07:002016-10-11T13:00:52.344-07:00Yes, I still call them cuboids!Yes, I <a href="https://twitter.com/search?f=tweets&vertical=default&q=simon_gregg%20cuboid&src=typd" rel="nofollow">still call them cuboids!</a>Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-59099003784045627352016-10-11T07:44:50.244-07:002016-10-11T07:44:50.244-07:00Joe,
This also makes me think of using the differe...Joe,<br />This also makes me think of using the different problem types in operations. A question like this appeared on our EQAO test (our standardized test) in Ontario last spring. It had a rectangular prism which only had the length and width plus the total volume listed but was missing the height. It asked them to find the height. it changes from a basic procedure question to more of a thinking based question. Its the direct connection to the problem types from primary that sometimes holds them up. If they have never been introduced or are use to finding missing part operation questions it can seriously limit their ability to answer more thinking based problems. I use the term thinking here because in Ontario the questions on the EQAO test are categorized using 3 categories: Knowledge and Understanding, Application and Thinking. The questions are either multiple choice or open response. This question was a multiple choice question. I love these types of questions like you have shown here which help us to gather so much more info about our students. It just made me think of that missing part problem which would link in well with what you have shown us. Thanks for sharing again. Always informative.Mark Stamphttps://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-15738655477083846942016-10-11T06:08:35.973-07:002016-10-11T06:08:35.973-07:00Joe, I always appreciate your thoughtful posts - t...Joe, I always appreciate your thoughtful posts - thank you!Linda Daceyhttps://www.blogger.com/profile/16808825408890384096noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-44060215079368869822016-10-11T04:03:34.934-07:002016-10-11T04:03:34.934-07:00Once upon a time the rectangular prism was called ...Once upon a time the rectangular prism was called a cuboid - shorter if nothing else.<br /><br />I like the general questions - what a variety of responses! Particularly the possible lack of appreciation of place value.Howard Phillipshttps://www.blogger.com/profile/18297158336334346872noreply@blogger.com