Hi, I am looking for some math projects or ideas to my students in the elementary level: Grades 4 and 5. they're using the harcourt text book. But i want some nice, new and maybe weird ideas such that they can do it with me or by their own. I need to put these math projects in the school's exhibition, and their parents will see their work. (It could be a math project using the thick boards (cork or foam boards). Any ideas or cool websites PLEASE!!! thanks, maths
Some ideas (they're common ones though) 1. geometric properties of figures demonstrated using models 2. geometry in real life...figures, structures, constructions 3. properties of numbers 4. somethings with geoboards, etc... You could google this... Cheers vivek
I remember seeing a book at the library full of math projects, can't remember what it's called though sorry. Take a look at your library though you might find something. The fibonacci sequence is always interesting, the golden ratio. or maybe looking at the Fleet Scheduling Programme ? (Set partitioning, matrix representation, combinatorial optimisation). Prime numbers? (Sieve of eratosthenes?) Non-euclidian geometry? What age are people in grades 4 and 5 ? (please forgive me I'm an ignorant kiwi ). Good luck! I wish my maths teachers gave out more projects/assignments :( no fun anymore!
I hope this is not too simple but I used to be fascinated with calculating areas as a kid. I had a necklace, and I remember putting it onto my desk and rearranging it into different shapes - a triangle, square, rectangle, and finally a circle, playing with the calculations as to what would give me the maximum area.
You could ask how many regular tilings of the plane there are, lots of experimenting to piece things together with cutouts. Or how many platonic solids are there. There should be lots of visual problems to play around with in graph theory, bridges of Konigsberg, colouring problems (4-colours in a plane and variants). You should be able to do some fun work with [tex]\pi[/tex]. Have them approximate it using buffon's needle problem, or maybe by approximating the area of a circles using rectangles. The needle problem might be fun, getting your entire class gather data would be interesting. Explaining to the parents that their kids are throwing sticks in the air during math class would be an experience too.
Count all the floor tiles in the school. :) Kidding. Golden Ratio is a good one, along with the Fibonnaci Sequence. Although prime numbers, might be hard to understand if they don't know anything about dividing. If they do, well then that's good. If they started solving variables using two or three equations, show them the basic properties of matrices. It's the exact same thing. Finding your own pi value. Using the method Archmedes used.
I remember an extra credit assignment we once had to explain Bhaskara's proof of the Pythagorean theorem. It was similar to what is posted on this web site: http://www.math.ntnu.no/~hanche/pythagoras/ I thought that was kinda neat-o!
Explanation : thathaasthu (which is Sanskrit for "behold", or more commonly "so shall it be"). Well, that's all the explanation that bhaskara gave ! <shrug>
Some suggestions : 1 . Showing why circles, ellipses, parabolas are called "conic sections" - by actually making cones and cutting them in different ways 2. Demonstrate, by making right triangles out of square pieces, that (3,4,5), (5,12,13), etc are Pythgorean triples. 3. Use a length of string to measure the circumference of different circular discs, and divide these lengths by the measured radii of the discs. 4. Demonstrate, using examples, that the k'th differences are equal, for a sequence where t(n) = an^k 5. Demonstrate that the definition of an ellipse as being the locus of a point whose sum of distances from two fixed points in constant - using a board with a sheet of paper, two push-pins, a length of string, and a pencil. 6. Do one of the many puzzles where an object drawn on paper with squares is cut up and rearranged to give a new object of seemingly different area. Show where the "cheating" happens in this - using large shapes and a good ruler. 7. Demonstrate the short cut for squaring a number ending in 5. 8. Demonstrate the divisibility tests (especially nice for 9 and 11) 9. Demonstrate the 4-color problem, and show by allowing attempts, how 3 colors fail. 10. Show by allowing attempts, that there's no solution on the plane to the Bridges of Konigsberg problem. Show that a solution exists on a torus. 11. Show the quick way to determine whether a point is inside or outside a many-sided convex polygon - by counting the number of intersections of a curve drawn from the point to the ouside. 12. Magic squares - demonstrate that the common short cut for filling these works. Many of these may seem like hard problems, and rigorous proofs would indeed be beyond the scope of Grade 4/5, but simply working with examples or doing demos are fun, and easily learnt
this is crazy. these kids are in grade ! golden ratio, Pi, matrices! I didn't learn what Pi was until grade 7. and until last week in my grade 12 geometry class I though a matrix was just a really cool movie. I think a lot of these examples are just pointless to someone who doesn't have a thorough enough background in different math concepts. I thinks finding areas of simple shapes is about as far as I got in grade 5. ON a ligher note. I remember a trick to learning the 9x table from way back. You hold out both your hands and what even number you want to multiply 9 by you put down that finger and count on both sides. eg lllll lllll these are my two hands 9x6 is... lllll xllll 5 4 there are 5 fingers on the left and 4 on the right. and gokul, what is the short cut for squaring #'s that end in a 5?
Simple optimization (linear programming) is accessible to 4th and 5th graders and has obvious applications. Think, for example, a bakery with two products. Indirect measurements of heigts and distances using proportions is pretty good - for example putting mirrors on the ground and then measuring distance from mirror to object and mirror to eye to get the height of the target. This makes for nice diagrams. Measuring distances precisely using vernier scales. This one is a bit tricky and involves fractions, but is also quite neat. Since this is an election year - why it's impossible to have a fair election. Pick's theorem. Fractals - not sure if you can even get to fractal dimension, but they make for some nifty drawings. Probability distributions - try to find examples of flat, curve, and other probability distributions. Scattering diagrams (crystalography) - find the shape of hidden shapes by bouncing things off of them.
(N5)^2 = XY25 where XY = N(N+1) Ex : 35^2 = 1225 since 34 = 12, 85^2 = 7225, 125^2 = 15625 Proof : (10N + 5)^2 = (10N)^2 + (2*10N*5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25
how about that problem with the 2 jugs, where one can hold, say, 9 litres & the other can hold 4, and you've got to get 6 litres somehow by pouring water from one jug to the other. there's a lot more stuff in coxeter/ball's "mathematical recreations and essays", check it out
what about - Russian Multiplication (Halving and doubling) - Gelosia Multiplication - What is infinity - Modular Arithmetic (ISBN numbers, Leap years, Time) - History of numbers - Guessing stuff... probabilities. tree diagrams - Counting square -> estimating area? - economy in wrapping (aluminimum & chocolate squares? mMmMmm) - density - brachistochrone? u can show with ping pong balls that the curve of a brachistochrone - a cycloid-shaped path - is the fatest route from one point down a slope to a lower one, even though the curve is longer than a straight path to teh same point. - planning pathways/building mazes with marbles. show corresponding logical "machine" flow chart diagram. - fractals/chaos theory/snowflakes etc..
:yuck: :yuck: ok look huys... i've read what u've written, and i would like to copy down what "physics is phun" wrote: (( I thinks finding areas of simple shapes is about as far as I got in grade 5. )) This is true.. my students in grades four and five are learning about addition, subtraction, graphs (line graphs, bar graphs, stem and leaf plots, line plots, and circle graphs), estimtion, multiplication, division, areas, volume, surface area, fractions, decimals, ratios, addition properties, multiplication properties, LCM, prime and composite numbers, odd and even numbers, GCD, perimeter, metric and customary units, triangles, percent, temperature, time, congruent and similar figures, solids, shapes, quadrilaterals, angles and polygons, lines and angles, and few topics from probability and integers (just introduction). ---------- This is what they learn about in grades 4 and 5... I was so surprised when u told me about the Pythagorean theorem, powers, other theorems and prooves and optimization!! Hey guys, I will put them in the scool's exhibition like boards or solid figures and i wil not explain anything to the parents.. just people will pass by and look at them. I have done a math exhibition last year, and i've made the shapes of houses to show how mathematical shapes are used in daily life, for example: square windows, rectangular doors, square floors, triangular ships... and so on...... those were some ideas.. i have made a balance for students to measure the weights. (it does not work for real, but it has the (look) of a balance)....... I have used matches to show areas on a board. Now, I am out of ideas.. (some) of you did actually give me very nice ideas.. But I want some more ideas PLEASE. Thanks, maths
Euler characteristic on a sphere-It's an easy enough concept to understand with lots of hand's on examples using a baloon+marker. Then what happens if you try the same on a torus (doughnut) or something flat. Lots of experimenting. Straightedge+compass constructions-basic things like an equilateral triangle, squares, and so on should be feasible. Let them loose and see what angles and objects they can build. Perfect, amicable, abundant, and deficient numbers should all be accessbile for experimentation if they're working on division. Even/odd can be thought of as classifying numbers according to their remainder upon division by 2. This could be extended to clasifying numbers by their remainder when divided by 3 or 4 or whatever (modular arithmetic). There's only one prime that's even, the rest leave remainder 1 when divided by 2. How about when we divide by 3? Are there many primes that leave remainder 1 or 2? A Sieve of Erathosthenes up to 100 or so to get some insight on this. Some simple cryptography might be nice-there's a substitution cipher type of puzzle in my local newspaper every week.