IC16: Math Made Real: It's Not Just For Preschool anymore!

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IC16: Math Made Real: It's Not Just For Preschool anymore!
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Playing with blocks, putting together a puzzle, ordering and rearranging... our youngest students are natural math investigators. But why relegate the fun of physical play and exploration to grade school? Why not continue to captivate students with a math lab kit that gets kids working together and exploring mathematical phenomena with engaging manipulatives? The National Museum of Mathematics is piloting Math Made Real, a series of six activities designed to capture the interest – and the minds – of students right at that critical age when many start to walk away from math. Designed to be distributed in classrooms around the world, Math Made Real will provide teachers with a way to get students excited, and keep them engaged, with the richness of mathematics.
Mathematics Computer programming Mathematics Real number
Addition Differenz <Mathematik> Divisor Block (periodic table) Phase transition Projective plane Maxima and minima Student's t-test Object (grammar)
Geometry Point (geometry) Mathematics Cross section (physics) Scaling (geometry) Ring (mathematics) Well-formed formula Different (Kate Ryan album) Multiplication sign Solid geometry Algebra
Cylinder (geometry) Cube Dodekaeder Student's t-test Mereology Extension (kinesiology)
Moment (mathematics) Triangle Object (grammar) Student's t-test Musical ensemble Extension (kinesiology) Set theory Extension (kinesiology)
Cross section (physics) Ring (mathematics) Different (Kate Ryan album) Cuboid Social class Musical ensemble String theory Power (physics)
Cone penetration test Cylinder (geometry) Moment (mathematics) Student's t-test String theory Power (physics) Diameter
12 (number) Trail Length Multiplication sign Gradient Mathematical analysis Water vapor Student's t-test Power (physics) Power (physics) Diameter Goodness of fit Circle Figurate number
Cross section (physics) Process (computing) Film editing Different (Kate Ryan album) Cube Energy level Social class Cubic graph Student's t-test Position operator Curve fitting Diameter
Cross section (physics) Addition Cube Sheaf (mathematics) Triangle Mereology Numerical analysis Triangle Wallis, John
Different (Kate Ryan album) Well-formed formula Triangle Square number Energy level Social class Summierbarkeit Student's t-test Numerical analysis Social class
Braid Pythagorean triple 1 (number) String theory Braid Pythagorean theorem Proof theory Arithmetic mean Film editing Well-formed formula Triangle Square number Theorem Diagram Square number Set theory Social class
Greatest element Standard deviation Group action Process (computing) Braid Multiplication sign Gradient Student's t-test Braid Mereology Theory Mathematics Many-sorted logic Ring (mathematics) Order (biology) Normal (geometry) Energy level Resultant Social class
Inclusion map Mathematics Different (Kate Ryan album) Gradient Energy level Student's t-test Figurate number Imaginary number
who hold the material and the and and and so most of you know the museum of mathematics in New York City and of course we have lots of the interactive exhibits at the museum but we also do lots of outreach and we have a traveling exhibit that is the sort of like a replica of some of the pieces that are in the museum but also some other things and another outreach program that we're experimenting with and and in fact in the
trial phase now something called map made real it's sponsored by Oppenheimer fires and it it's a project to bring Mac Lad type activities into the schools so we
have a kid of which consists of 6 different activities of the intention is that of little kids when they learn about Max playing with blocks and learn about the shapes of objects and learn how to build things together and even do initial addition and subtraction by building up rows of blocks and particularly in the US the new Common Core Curriculum focuses a lot on those visual aspects of in fact that's how they learned to add multiplied divide our very visually but student center then moving
on towards taking algebra geometry in high school at that point in time there's this 0 god I hate Matisse anyway I can get out of it what can I do and the idea of this Matlab kit is to provide resources for teachers to make math fun to give some motivation and instead of just learning formulas and how to calculate different things that they actually have some hands-on work for were hopeful that we will get the funding that this will then be something that really can be of produced on a much wider scale and use worldwide
of the kids come of show you the individual activities but I also want to point out that I'm with each activity there's a very detailed lesson plans so that teachers who were not familiar with the material beforehand can really follow along and understand even have in some cases a script that helps them to teach in this somewhat for for many teachers unconventional way the so the 1st activity is similar to the ring of fire while fire that we have at the museum on but it's portable and I'll give a little demo the the on so we have this little laser being off by and through different of solids on made out of Plexiglas and the idea is to say what different cross sections can I find so the the kid comes actually with 5 only
brought 3 with me because they're very bulky to pack so the cylinder the cube and detector he's in my custody he drain and I believe also a a dodecahedron and then there's also a colon and so on in this part of it
is but we can grow it OK so up to some this is of course quite with this is of course quite 1 there however if you have a a lot of students in the
classroom it's not so easy that um everyone gets a turn at the moment but there's only 1 set of each of the various objects for a particular classroom and so we also look at ways for students to and I guess 1 could have more laser pointers but we look at ways for students to also work with these objects the the the so there's lots that you can do here to show different get a triangle and whatever all the different cross
sections but on the extension activities include also very simple things like taking a rubber band and have students wrapper rubber band for
example around the cube see if they can figure out some of the cross sections by getting the rubber band to lie flat and really getting a much better feeling than just by chance of having the laser beam shyness on another activity that's included is actually using string and have not tax and Cape and to make a cubic in the corner of a classroom with string and then actually mark of different kinds of cross sections of the so the next activity
is co 0 I let me just go back to this the 2nd 1 going the wrong way mn box I but I should not not to neglect to mention that the ring of fire which is 1 of our traveling exhibits is also available for purchase so if any of you are building a traveling exhibit or are interested in
I'm having something like that in your installations I you should contact of singular at Lorinser Lawrence and moment dot org or mn to go and moment dot org OK so the next
activity is called the power of high and this is a very simple 1 that you really don't need much at all but we provide a court the those 2 in accord the string and then I'll various-sized Our cylinders and ask students to try and get in advance whether the diameter is going to be larger or smaller than the height of the particular container that they're looking at so we quite trivially
we could take this the but it around here somebody holds their finger and we say is this going to be smaller This length smaller or larger anybody the to and lo and behold it's larger it's a lot larger but that's very astonishing to most 80's up to 12th grade students to see something like that same thing so you can simply take a bottle of water a bottle of juice peel off the label analysis students is the label going to be bigger or smaller and in nearly every case students cannot see that it's going to be larger and that's really quite a nice way to introduce the power of pi am another way to do this in the classroom is to have a student a mark out a circle and say I'm gonna walk around walk around you choose the size of the circle you walk around the circle and I is the length of the circle going to be taller than you or shorter than you and of course the only time the most circles that someone's chooses if you think of a reasonable size search circle or again the same phenomena of then have another another
nice example you can see in the picture here is a can of tennis balls because that gives you a very nice way but to show the height and in fact if you do this with the can of tennis balls you'll get to read plus a little bit so you'll see that the the the length of the diameter will actually be just this much more than the height of the yeah care so it's good it's quite likely a clever idea yeah end of another thing that you want to do is to say I have students try and figure out what so that we can what what kinds of cancer might have circumferences that are not going to be smaller and I'm usually it's quite difficult for them to find them on 1 of the that the that the examples that most students don't think of but which is really for then then very clever is for example a
simple drinking Strock to think about that because that has a very small diameter but it's it's long too but something so that's a way to teach about pi the
other thing is looking at the circumference of the wheel of a bike and most kids spikes the circumference of the wheel is again going to be taller than the height of the bike of you can then take that to the next level look at the circumference of the wheel of a car and then a tractor trailer to get an idea of the differences in size OK next activity of this 1 I didn't bring with me because it's big and bulky and hard to carry around in my suitcase but but there are 2 huge oops I when they're pushed together but you can see that the cube on the left has had some cut made into it and that the activity is to say how can a large corpora cubic fit through a smaller cube and this I activity is supplemented with a fairly nicely supplement I think also with these worksheets that students can 1st play around with this a little bit on the piece of paper and try and see if they can come up with the correct kind of course course cross sections so that that might actually work and then the teacher pulls out these 2 cubes chosen looked at the same size takes the cross-section that which is smaller than the Red cube and is able to if you a position it correctly you can pass 1 through the of the red through the red cube through the blue 1 I the so as I said we you can explore 1st with cut out and making holes and of we also provide a template for doing this out of paper paper doesn't really work out well because ripsaw it's it's much job or something like that of and this is a nice tie into the activity out of the shapes with in on because you can show the hexagonal cross-section that you need Our by taking the cube and positioning it
exactly correctly to get that cross section of this Of particular cross section was the the problem like I understand was called Prince Rupert skew because he was the 1st person to cited and John Wallace was the 1st person to come up with or you 1st person to query whether that could be done and John Wallace was the 1st person to find the section and then Peter nor land was the 1 who found the largest cross
section the next 1 is a whole bunch of acrylic pieces of to show you the triangular numbers I'll just show you quickly what the the 1 part of the set so here there's a 5
and a 6 and you can do and beta the numbers go up I believe to 17 lots of different sizes of them and you can do various
activities 1st to say what are the 1st 10 triangular numbers show how 2 of them can be combined to form a square how the sum of consecutive pairs of triangle numbers yield the square numbers and then actually our work on deriving the formula for computing the nth triangle a number so depending on the level and the sophistication of the class we provide different activities on for enrichment thought that the teacher can then all use as it works out for them so the next 1 is called the pythagorean puzzler and you can see this piece of paper here every student in middle school and high school learns a square equals C. squared equals a squared plus
b squared yeah but that's just a formula that they learned they see a right triangle OK I know a and B I can calculate see but really what does that mean and we have 2 different ways to show it again we have these acrylic pieces in 1 case in the red ones there is a square and that is actually the square that is a squared and then we found have for other pieces that I are not that easy to put together to get the square that is the the the squared 1 and then the challenge OK now I take these 5 pieces and I wanna make the square with the side of Lake City and that is an activity actually this activity is the 1 that was rated highest by the other classes that try this out we then have another set of pieces where you have to there again 5 pieces but they're 5 different cuts of the square and you have to put 1st the a square of side of latent 8 5 8 together then the 1 of side the and then figure out how do I take these 2 and make them a square of side c so it's a on visual way of proving the Pythagorean theorem and of course
but the teacher can do as much as is possible with the younger kids it's more of a puzzle of trying to figure out how to these things that together with older kids you can go further and do do many more diagrams of showing the proof of the Pythagorean theorem who the last activity ties in nicely with the genius talked this morning about braids and instead of just making a break but we have a challenge to make a braid when both ends of the string already tied so it starts off the piece of felt very simple looks like this you can also do it with 3 strings and click them
somewhere at the top of and the bottom and the activity consists of getting these sort of getting this piece to look like this and of course most certainly is all the girls and that's a good thing the girls get the girls interested in math I know how to make parades but they've never really thought about making a parade with both hands closed and I I have no way to do it and let's you why would you right so and in fact this is really not that easy and of it but maybe a little bit frustrating as well but we then have them on paraded In order to think about what is the algorithm what do I need to do how can I of plan something and have a process in doing it and it's use much more in that regard a rather than really talking about the mathematical theory of braids but and I guess 1 could do more but really it's it's beyond the normal high school or middle school curriculum so we had this type a
pilot program end of have act we asked the teachers who worked it out to get back to us we had a a questionnaire and then some freeform questions and arm and here's pretty much the summary of the pilot program on all the teachers said that the students were engaged that they thought they were easy to implement I think they felt the 1 that was the hardest implement was the braid up mostly because they probably had difficulties also In doing it for the 1st time I did it and I didn't unbraided because they wanted to have 1 braided here it takes a while to figure out what the steps actually got even if you follow the instructions on the topics but were not all consistent with what is normally taught at those grade levels and as a result particularly in the US where they're following Common Core standards it was sometimes difficult to figure out if this could be part of the regular classroom or if it should be a math club or after school activities are obviously the most exciting part was to have hands-on tools to be able to do something of the as I said earlier some teachers divided their classes into smaller groups because it was too hard to demonstrate in front of the classroom and have the students still engage the same
idea of an interactive exhibit where you actually touch things and try and figure things out yourself of and the main suggestion for improvement was to have more detailed worksheets for the students to follow along in a more step-by-step way although if we look at the worksheet that we have I actually think they are pretty step by step but maybe at different grade levels they have to be done In our a simpler way so and that's the end
of this however you have a