Mixing
Garden Problem! I’m stumped… 5th grade math problem
Okay so I’ve been trying to solve this problem but I need a fresh mind. I feel totally embarrassed because this is a 5th grade problem, but I suppose I’m totally missing the point of my sons homework!
The problem -
“Garden Problem”
A family decides to create a vegetable patch on a square area (ground)
The parents use 1/4 of the ground. This is also in the shape of the square that takes up in northeast section.
The 3/4 that remains are divided identically between the four children: same area/same shape
Drawl the shape of the vegetable patch showing how you divided it correctly.”””””
Thanks so much in advance !
geometry
asked Nov 20 '18 at 19:02
Coco B
141
add a comment |
Okay so I’ve been trying to solve this problem but I need a fresh mind. I feel totally embarrassed because this is a 5th grade problem, but I suppose I’m totally missing the point of my sons homework!
The problem -
“Garden Problem”
A family decides to create a vegetable patch on a square area (ground)
The parents use 1/4 of the ground. This is also in the shape of the square that takes up in northeast section.
The 3/4 that remains are divided identically between the four children: same area/same shape
Drawl the shape of the vegetable patch showing how you divided it correctly.”””””
Thanks so much in advance !
geometry
asked Nov 20 '18 at 19:02
Coco B
141
Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28
add a comment |
Okay so I’ve been trying to solve this problem but I need a fresh mind. I feel totally embarrassed because this is a 5th grade problem, but I suppose I’m totally missing the point of my sons homework!
The problem -
“Garden Problem”
A family decides to create a vegetable patch on a square area (ground)
The parents use 1/4 of the ground. This is also in the shape of the square that takes up in northeast section.
The 3/4 that remains are divided identically between the four children: same area/same shape
Drawl the shape of the vegetable patch showing how you divided it correctly.”””””
Thanks so much in advance !
geometry
asked Nov 20 '18 at 19:02
Coco B
141
Okay so I’ve been trying to solve this problem but I need a fresh mind. I feel totally embarrassed because this is a 5th grade problem, but I suppose I’m totally missing the point of my sons homework!
The problem -
“Garden Problem”
A family decides to create a vegetable patch on a square area (ground)
The parents use 1/4 of the ground. This is also in the shape of the square that takes up in northeast section.
The 3/4 that remains are divided identically between the four children: same area/same shape
Drawl the shape of the vegetable patch showing how you divided it correctly.”””””
Thanks so much in advance !
geometry
geometry
asked Nov 20 '18 at 19:02
Coco B
141
asked Nov 20 '18 at 19:02
Coco B
141
asked Nov 20 '18 at 19:02
Coco B
141
asked Nov 20 '18 at 19:02
Coco B
141
asked Nov 20 '18 at 19:02
Coco B
141
141
Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28
add a comment |
Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28
Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28
Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28
add a comment |
3 Answers
3
active
oldest
votes
Here are the pieces: P for parents, 1-4 for children:
11PP
12PP
3224
3344
answered Nov 20 '18 at 19:06
Federico
4,709514
add a comment |
Each child gets 3 squares.
$leftarrow N -$
You want them to be contiguous and congruent. By trial and error, there are not that many ways to do it.
$leftarrow N -$
answered Nov 20 '18 at 19:21
Doug M
44k31854
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
add a comment |
Divide the square area into a 4x4 grid of 16 equal squares, labelled (1,1) to(4,4) with the north-most row, from W to E being (1,1),(1,2),(1,3),(1,4), the row just below it being (2,1),(2,2)... etc. The garden is (1,3),(1,4),(2,3),(2,4).
You need to divide the other 12 squares into 4 congruent pieces. Consider the square (4,1) diagonally opposite to the garden. By symmetry we may suppose it is part of the same piece as (3,1). Now:
(I). If (3,2) is part of that piece then the remaining 9 squares are in two disconnected parts: 5 squares (1,1)(1,2),(2,1) (2,2), (3,1) in one part and the last 4 squares in the other part, which means those 9 squares can't be divided into 3 connected pieces of 3 squares each.
(II). If (2,1) is part of that piece then there must be another connected piece made up of (1,1),(1,2), (2,2), which is a different shape.
Therefore (4,1),(3,1),(4,2) must be one piece . The pieces that include the other corner squares (1,1) and (4,4), being also of the same shape, must be (1,1),(1,2), (2,1) and (4,4),(4,3)(3,4). And what's left is the last piece (2,2),(3,2),(3,3).
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Here are the pieces: P for parents, 1-4 for children:
11PP
12PP
3224
3344
answered Nov 20 '18 at 19:06
Federico
4,709514
add a comment |
Here are the pieces: P for parents, 1-4 for children:
11PP
12PP
3224
3344
answered Nov 20 '18 at 19:06
Federico
4,709514
add a comment |
Here are the pieces: P for parents, 1-4 for children:
11PP
12PP
3224
3344
answered Nov 20 '18 at 19:06
Federico
4,709514
Here are the pieces: P for parents, 1-4 for children:
11PP
12PP
3224
3344
answered Nov 20 '18 at 19:06
Federico
4,709514
answered Nov 20 '18 at 19:06
Federico
4,709514
answered Nov 20 '18 at 19:06
Federico
4,709514
answered Nov 20 '18 at 19:06
Federico
4,709514
4,709514
add a comment |
add a comment |
Each child gets 3 squares.
$leftarrow N -$
You want them to be contiguous and congruent. By trial and error, there are not that many ways to do it.
$leftarrow N -$
answered Nov 20 '18 at 19:21
Doug M
44k31854
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
add a comment |
Each child gets 3 squares.
$leftarrow N -$
You want them to be contiguous and congruent. By trial and error, there are not that many ways to do it.
$leftarrow N -$
answered Nov 20 '18 at 19:21
Doug M
44k31854
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
add a comment |
Each child gets 3 squares.
$leftarrow N -$
You want them to be contiguous and congruent. By trial and error, there are not that many ways to do it.
$leftarrow N -$
answered Nov 20 '18 at 19:21
Doug M
44k31854
Each child gets 3 squares.
$leftarrow N -$
You want them to be contiguous and congruent. By trial and error, there are not that many ways to do it.
$leftarrow N -$
answered Nov 20 '18 at 19:21
Doug M
44k31854
edited Nov 20 '18 at 22:19
answered Nov 20 '18 at 19:21
Doug M
44k31854
answered Nov 20 '18 at 19:21
Doug M
44k31854
answered Nov 20 '18 at 19:21
Doug M
44k31854
44k31854
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
add a comment |
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
On your map the garden in the NE is at the top right, which means N is left and E is up.... :).... Medieval European cartographers sometimes put N on the right , with W at the top.
– DanielWainfleet
Nov 20 '18 at 19:55
add a comment |
Divide the square area into a 4x4 grid of 16 equal squares, labelled (1,1) to(4,4) with the north-most row, from W to E being (1,1),(1,2),(1,3),(1,4), the row just below it being (2,1),(2,2)... etc. The garden is (1,3),(1,4),(2,3),(2,4).
You need to divide the other 12 squares into 4 congruent pieces. Consider the square (4,1) diagonally opposite to the garden. By symmetry we may suppose it is part of the same piece as (3,1). Now:
(I). If (3,2) is part of that piece then the remaining 9 squares are in two disconnected parts: 5 squares (1,1)(1,2),(2,1) (2,2), (3,1) in one part and the last 4 squares in the other part, which means those 9 squares can't be divided into 3 connected pieces of 3 squares each.
(II). If (2,1) is part of that piece then there must be another connected piece made up of (1,1),(1,2), (2,2), which is a different shape.
Therefore (4,1),(3,1),(4,2) must be one piece . The pieces that include the other corner squares (1,1) and (4,4), being also of the same shape, must be (1,1),(1,2), (2,1) and (4,4),(4,3)(3,4). And what's left is the last piece (2,2),(3,2),(3,3).
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
add a comment |
Divide the square area into a 4x4 grid of 16 equal squares, labelled (1,1) to(4,4) with the north-most row, from W to E being (1,1),(1,2),(1,3),(1,4), the row just below it being (2,1),(2,2)... etc. The garden is (1,3),(1,4),(2,3),(2,4).
You need to divide the other 12 squares into 4 congruent pieces. Consider the square (4,1) diagonally opposite to the garden. By symmetry we may suppose it is part of the same piece as (3,1). Now:
(I). If (3,2) is part of that piece then the remaining 9 squares are in two disconnected parts: 5 squares (1,1)(1,2),(2,1) (2,2), (3,1) in one part and the last 4 squares in the other part, which means those 9 squares can't be divided into 3 connected pieces of 3 squares each.
(II). If (2,1) is part of that piece then there must be another connected piece made up of (1,1),(1,2), (2,2), which is a different shape.
Therefore (4,1),(3,1),(4,2) must be one piece . The pieces that include the other corner squares (1,1) and (4,4), being also of the same shape, must be (1,1),(1,2), (2,1) and (4,4),(4,3)(3,4). And what's left is the last piece (2,2),(3,2),(3,3).
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
add a comment |
Divide the square area into a 4x4 grid of 16 equal squares, labelled (1,1) to(4,4) with the north-most row, from W to E being (1,1),(1,2),(1,3),(1,4), the row just below it being (2,1),(2,2)... etc. The garden is (1,3),(1,4),(2,3),(2,4).
You need to divide the other 12 squares into 4 congruent pieces. Consider the square (4,1) diagonally opposite to the garden. By symmetry we may suppose it is part of the same piece as (3,1). Now:
(I). If (3,2) is part of that piece then the remaining 9 squares are in two disconnected parts: 5 squares (1,1)(1,2),(2,1) (2,2), (3,1) in one part and the last 4 squares in the other part, which means those 9 squares can't be divided into 3 connected pieces of 3 squares each.
(II). If (2,1) is part of that piece then there must be another connected piece made up of (1,1),(1,2), (2,2), which is a different shape.
Therefore (4,1),(3,1),(4,2) must be one piece . The pieces that include the other corner squares (1,1) and (4,4), being also of the same shape, must be (1,1),(1,2), (2,1) and (4,4),(4,3)(3,4). And what's left is the last piece (2,2),(3,2),(3,3).
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
Divide the square area into a 4x4 grid of 16 equal squares, labelled (1,1) to(4,4) with the north-most row, from W to E being (1,1),(1,2),(1,3),(1,4), the row just below it being (2,1),(2,2)... etc. The garden is (1,3),(1,4),(2,3),(2,4).
You need to divide the other 12 squares into 4 congruent pieces. Consider the square (4,1) diagonally opposite to the garden. By symmetry we may suppose it is part of the same piece as (3,1). Now:
(I). If (3,2) is part of that piece then the remaining 9 squares are in two disconnected parts: 5 squares (1,1)(1,2),(2,1) (2,2), (3,1) in one part and the last 4 squares in the other part, which means those 9 squares can't be divided into 3 connected pieces of 3 squares each.
(II). If (2,1) is part of that piece then there must be another connected piece made up of (1,1),(1,2), (2,2), which is a different shape.
Therefore (4,1),(3,1),(4,2) must be one piece . The pieces that include the other corner squares (1,1) and (4,4), being also of the same shape, must be (1,1),(1,2), (2,1) and (4,4),(4,3)(3,4). And what's left is the last piece (2,2),(3,2),(3,3).
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
answered Nov 20 '18 at 19:44
DanielWainfleet
34.2k31647
34.2k31647
add a comment |
add a comment |
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Why did anyone downvote this? It's a great question.
– littleO
Nov 20 '18 at 22:28