Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking. Student #1
Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking.
n
ri a
2 t
$150
ngl
es
$
6
an
tri
1 tr
ia n
gle
$5
0
50
x 2
100
0
$ 10
300
2
$ 50.00
24| 1200.00
120
0
s
50
x 3
150
gle
a
t ri
es
ngl
$3
00
s
e
0
gl
$ 1 0 ri a n
1t
50
$
50
x 6
300
150
150
300
300
100
50
+ 50
1200
I will draw a diagram
I have to find out how much each field is
worth. So find how many triangles and divide into
$1200.00 to get the answer.
Page 1 of 1
3 triangles
6
a
t ri
gle
$150
3 triangles
I put it in triangles
hexagon
rhombus
trapezoid
triangle
Answer:
Field EF $150.00
Field AB $300.00
Field CD $100.00
Field GH $50.00
Student #2
Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking. I need to find out how much and what fraction each
field is worth. I will use a chart for both problems.
Page 1 of 2
Each field is worth and fraction answers
One connection I will like to make is that you can
convert the fractions in the problem. For exm: 1/2 can
be 4/8 and still be the same value. Another
connection I will like to do is that A and B is a
hexagon. And I know that C and D are rhombi and that
E, F are trapizoids and G, H are triangles. The 8 fields
use 4 hexagon shapes. You can’t do this problem if
you don’t know how the shapes fit together. Or like
6/6 = 1 or 1/2 + 1/2 = 1. I started with the triangle and
added up by 100. It didn’t work so I used 50 and it
worked. I added and multiplied in my head. It wasn’t
very hard because of the zeros.
Page 2 of 2
Student #3
Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking. $200
200
$500
$400
200
00
$2
$200
I have to find out
what fraction of the
total value is each
field and how much is
each field
page 1 0f 1
$200
$200
$4.00
$5.00
$200
$200
$1500
Student #4
Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking. I have to find out how the fraction and the total
value of each field is.
I will use a diagram to see how many
there are.
page 1 of 2
hexagons
hexagon
A
D
1
s
F
u rho /3 E 1/2
C
b
m
m
o
bu trapezoid trapezoid
rh
s
e
gl
hexagon
B
My thinking
n
ia
Tr G 6
1/
300
4| 1200
12 .
00
0
0
100
3| 300
H ia ngle
tr
150
2| 300
2
10
10
0
0
0
50
6| 300
30
0
0
0
1/3 + 1/3 + 1/3 = 3/3 = 1 whole
1/2 + 1/2 = 2/2 = 1 whole
1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 1 whole
Answer 1: Field A = 1 whole
Field C = 1/3
Field B = 1 whole
Field D = 1/3
Field E = 1/2 Field F = 1/2
Field G = 1/6 Field H = 1/6
Answer 2: Field A = $300
page 2 of 2
Field B = $300
Field C = $100
Field D = $100
Field E = $150
Field G = $50
Field F = $150
Field H = $50
Student #5
Name_______________________ A Farmer’s Fields
A farmer’s fields are worth $1,200 total. The fields are formed with the geometric figures shown below, which are composed of triangles of the same size and with all sides the same length. Each field’s value is based on its size. What fraction of the total value is each field worth? How much is each field worth? Show and explain all of your mathematical thinking. 1 /3
$100.00
1 /2
$300
$300
1 /2
$150.00
1 whole
1 whole
$ 50.00
1 /3
1/6
$100.00
$50.00
1/6
$50.00
I have to figure out what the fields are worth and the fraction of the
fields. You can’t solve this problem if you don’t know the fractions. I will
make a table and write the answers on it.
Every thing has to be
Two trapazoids make
Two triangles make a
So the diagram really
300
4 | 1200
1200
0
equivalent
one hexagon
rhombus
has 4 hexagons
The 3, 6, 2 are the
denominators
So $300
now you can do all the shapes
150 + 150 = 300 100 + 100 + 100 = 300
50 + 50 + 50 + 50 + 50 + 50 = 300
3
|
100
300
6
|
50
300
2
|
150
300
page 1 of 2
Farmer’s Fields
Answers
Field Fractions
This is how it works
Answers
Field
values
A
1 whole
6/6
$300
B
1 whole
$300
6/6
C
1/3
$100
D
1/3
$100
E
1/2
$150
F
1/2
$150
G
1/6
$50
H
1/6
#50
My connections
list
– (I thought of 7)
1. The diagram has 1 line of symmetry I put in.
2. Shape names are hexagon
trapezoid
rhombus
triangle
3. I know some percents –
4. I know some decimals –
100%
1.00
50%
.5 or .50
5. There are really 24 triangles in the diagram or 24 sixths
50
So 24/6 = 4 hexagons, or 24| 1200
1200
This way you multiply 2, 6, 3 to get the trapezoid, hexagon,
and rhombus values. I am correct.
6. 2 trapezoids have the same area as one hexagon
7. You can’t have a square field – no equivalent area
page 2 of 2
2 x 50 = 100
3 x 50 = 150
6 x 50 = 300