Maths practical homework 10 year old stuff

Well I tried and I am stumped.... (not that that is hard either:rolleyes:)

E brought home 2 coloured square bits of paper last night and a split pin.

Her practical homework was to create a circle in the squares, draw some lines within the circle to cut out another square again, put the two "new" squares together using the split pin in the centre, with the result that when turning each square in opposing directions, each side should still be equal and meet with the other piece.....

Well, she was in tears and I thought how hard can that be so measured off 10cm rectangle and folded it in half. I then found centre of those 2 squares however 1/4 opposing turns had one square overlapping the other....

so then I went and got another piece of paper, folded it corner to edge to ensure I had a proper square, cut it out. Did the same with another piece and joined them together with the split pin.

Same result, with opposing 1/4 turns, the edge of one square overlaps...

How can this be?

Does anyone know the trick of drawing the square within the circle so its exactly right all round when placed on top of an identically "engineered" square.....:confused::confused::confused::confused::confused::confused:

Say what??

my head hurts;)

Thank crikey its not just me then......[]

but do try cutting two equal squares and centering them on a pin and turning each square opposite to the other, it doesn't work and I want to know why when a square is equal sided......

is she allowed to use a protractor?

if not:

I tried

I started with a square of that 4" notepad loose paper that comes in boxes, so I KNOW it was a square when I started. fold corner to corner, the repeat with opposite corners. now fold side to side, each way. you should have what looks to be an 8 armed star folded into the paper as creases. where the rays touch each side of the paper, use those as a reference to draw your circle. the paper bends easily along the creases now, flex the paper so a short crease to the side lays along a long crease to a corner, fold the excess corner over the side. repeat around the 4 corners.

this gives you 8 points of reference equidistant from the centre from which to draw your circle freehand. Cut that out.

now from where every SECOND ray from the centre touches the perimeter of the circle, draw a connecting line to outline a square. cut this out

Repeat for the second piece of paper.

pin together.

Did it work?

The other way is to fold the piece of paper in half side to side, then fold in half again lengthways. that way you end up with a squareone corner has a single folded edge on one side and 4 separate edges of paper on the other, the other opposite corner has two folds on one side and 3 separate edges on the other, draw a line straight across from corner to corner, fold those corners together and crease, now from the corner with 4 spearate points of paper, fold the top down to touch the line at the centre of the crease and the line and crease the fold mark the point where the crease meets the other crease. using the two corners and the mark just made, draw a semicircular arc and cut it out. unfold the paper and you have a circle, fold again and cut the line from corner to corner, and unfold again and you have a square.

easier?

or do I have to draw pictures?

I googled "Geometry problem+ two squares" Facinating...not! Try it though as I think one of the sites was heading in that direction. King of resources fo teachers. Geometry at 10? Good grief.

Kiwi303;185669 wrote: is she allowed to use a protractor?

No.

if not:

I tried

I started with a square of that 4" notepad loose paper that comes in boxes, so I KNOW it was a square when I started. fold corner to corner, the repeat with opposite corners. now fold side to side, each way. you should have what looks to be an 8 armed star folded into the paper as creases. where the rays touch each side of the paper, use those as a reference to draw your circle. the paper bends easily along the creases now, flex the paper so a short crease to the side lays along a long crease to a corner, fold the excess corner over the side. repeat around the 4 corners.

this gives you 8 points of reference equidistant from the centre from which to draw your circle freehand. Cut that out.

now from where every SECOND ray from the centre touches the perimeter of the circle, draw a connecting line to outline a square. cut this out

Repeat for the second piece of paper.

pin together.

Did it work?

The other way is to fold the piece of paper in half side to side, then fold in half again lengthways. that way you end up with a squareone corner has a single folded edge on one side and 4 separate edges of paper on the other, the other opposite corner has two folds on one side and 3 separate edges on the other, draw a line straight across from corner to corner, fold those corners together and crease, now from the corner with 4 spearate points of paper, fold the top down to touch the line at the centre of the crease and the line and crease the fold mark the point where the crease meets the other crease. using the two corners and the mark just made, draw a semicircular arc and cut it out. unfold the paper and you have a circle, fold again and cut the line from corner to corner, and unfold again and you have a square.

easier?

or do I have to draw pictures?

Many thanks Kiwi, I will print this last bit out and see how we go.

DiDi;185673 wrote: I googled "Geometry problem+ two squares" Facinating...not! Try it though as I think one of the sites was heading in that direction. King of resources fo teachers. Geometry at 10? Good grief.

Apparently Didi its called "Rotating Symmetry"....[xx(]

Kiwi303;185669 wrote:
I started with a square of that 4" notepad loose paper that comes in boxes, so I KNOW it was a square when I started. fold corner to corner, the repeat with opposite corners. now fold side to side, each way.

I was confused on this bit, but soldiered on how I "thought".... wrong..

you should have what looks to be an 8 armed star folded into the paper as creases.

Nope. half a sandwich.....

where the rays touch each side of the paper, use those as a reference to draw your circle. the paper bends easily along the creases now, flex the paper so a short crease to the side lays along a long crease to a corner, fold the excess corner over the side. repeat around the 4 corners.

I did this when I unfolded my paper. Similar result.

this gives you 8 points of reference equidistant from the centre from which to draw your circle freehand. Cut that out.

[][][] but how far out from the centre, I assume you mean edge (side) of square to side of square....[]

now from where every SECOND ray from the centre touches the perimeter of the circle, draw a connecting line to outline a square. cut this out

I am lost.... but I did end up with a square (but not a circle in the process) so I cheated and traced the same square onto another bit of paper. It didn't work.....

Repeat for the second piece of paper.

pin together.

Did it work? See above.

?

Painful aren't I.... apparently they are re-visiting the subject in coming weeks. Perhaps I should book a chair now!

no wonder she cried i am almost in tears for her....poor kid...i hate maths and pass that subject on to hubby..although he goes right around the houses and stresses the teens out there is no A to B in our houes...you have to vist C D & E to get there....hahahaha....poor kids..i just nod...

Kiwi303;185669 wrote:
I started with a square of that 4" notepad loose paper that comes in boxes, so I KNOW it was a square when I started.

Pic 1

Kiwi303;185669 wrote: fold corner to corner, the repeat with opposite corners.

Thats pics 2 and 3, you should now have pic 4, where the light grey lines are creases.

Kiwi303;185669 wrote:

now fold side to side, each way.

Pics 5 and 6

Kiwi303;185669 wrote:
you should have what looks to be an 8 armed star folded into the paper as creases.

Pic 7, the red dot where everything crosses at a single point is the centre. the blue dots are a reference for the next step

Kiwi303;185669 wrote:
flex the paper so a short crease to the side lays along a long crease to a corner,

the blue dot one one side is on a short side crease, flex the paper so that crease lies along the long crease to the corner with the other blue dot.

Kiwi303;185669 wrote:
fold the excess corner over the side.

Pic 8, you can see how theres a long corner sticking out of the covering paper from the side when the creases line up? fold that over the short bit of paper to make a crease.

Kiwi303;185669 wrote:
repeat around the 4 corners. This gives you 8 points of reference equidistant from the centre from which to draw your circle freehand.

The green dots in pic 9

Kiwi303;185669 wrote:
Cut that out.

you can see the circle drawn in pic 10

Kiwi303;185669 wrote:
now from where every SECOND ray from the centre touches the perimeter of the circle, draw a connecting line to outline a square. cut this out

The brown lines in pic 11.

Kiwi303;185669 wrote:
Repeat for the second piece of paper.

pin together.

or do I have to draw [colour=red]MORE[/colour] pictures? [/QUOTE]

Ah Kiwi, you are a continuing legend!!!!

I will have another play over the weekend or in a moment of boredom... but I still don't understand why a "normal" square won't be the same on all sides when opposed to matching square.

Any takers?

Okay, I'm seriously impressed, and that's just with the diagrams! My jaw is still hitting the ground from the fact that the problem got solved!!!

Diane, another who was horrid at maths.

I think the Matching Squares problem is mostly a matter of how carefully you do the drawing and cutting, it sounds to me more like a problem in precision than in straight out geometry.

You could probably manage the same thing with a ruler, a slide rule and a cosine/sine table and making sure the lengths and angles on the paper matched, I find origami does the same thing if ANY of the creases are slightly off and do not cross in the same point as everything else, then you have problems.

Kiwi - I am so impressed! I count on my fingers and to realise that there are people out there who GET maths, geometry or whatever blows my socks off. My father was a Maths teacher and he used to get so frustrated with me his eyes would role back in his head! I used to just remind him of the time he smacked into the back of my head reversing the Zepher out of the garage as I was reversing the homemade trolley (neither aware fo the other) and insisted he had scrambled my brain! Maybe some of us just don't get the necessary wiring!