Grid Model
Jason had
4
5
of a pan of lasagna to eat for dinner this week. According to the box, a
1
serving size is of a pan. If Jason ate one serving of
3
lasagna, how much lasagna is left for another meal? Use the space provided to show how
to use an area (grid) model to determine the solution. Explain how you know your answer
is reasonable.
In order to solve the problem, I need
to determine what 1/3 of the pan is. I
split the original pan in three equal
parts (thirds) horizontally since it was
split in fifths vertically. If I ignore the
vertical lines, I can see three larger
equal parts. I can see that there are
now 15 equal parts in the whole and
that there are 5/15 in 1/3. If Jason ate
one serving, that means he ate 1/3 of
the pan, which is 5/15.
To determine how much lasagna Jason has left for another meal, I need
to subtract 1/3 of the pan (5/15) from the amount he had left 4/5. I can
see that 4/5 is equivalent 12/15 from the second grid I created. I then
crossed 5/15 out from the 12/15 I had and now I see that Jason has 7/15
left for another meal.
12/15 – 5/-15 = 7/15
I know this answer is reasonable since 4/5 is close to, but a little less
than 1 whole, and 1/3 is close to, but a little less than 1/2. When if I
subtract an amount that is a close to, but a little less than 1/2, from an
amount that is close to, but a little less than 1 whole, the difference
should be close to, but a little less than 1/2. 7/15 is a little less than 1/2
– since 7/14 is exactly one half, 7/15 is a little less than 1/2.
Area Model Grid Scenarios
Scenario 1
Scenario 2
Students in Mr. Gauge’s class set The boys running club had a relay
up a weather station at the
race during last Wednesday’s
beginning of the year. The first
practice. Two boys participated
on each relay team and the total
day it rained, they recorded 34
inches of rain at their station. The distance covered was 78 of a mile.
second rainfall of the year brought If the first boy in one group ran 12
another 16 inches. How much total of a mile, what fraction of a mile
rain had they collected in their
did his partner run?
weather station after the second
rainfall of the school year?
Scenario 3
Scenario 4
Mrs. Nomic was gathering the
Jan found the recipe her 4th grade
supplies she needs for her 5th
teacher gave her for making mock
grade economy unit. She found
rocks at home. According to the
the container of beads she used
recipe, Jan needs 45 cups of sand to
last year and gave away 16 of the
mix with the other ingredients.
container of beads to her
Jan measured the sand she had
teammate. She still had 23 of the
and realized she had 107 cups of
container left to use with her
sand. Does she have enough sand
class. How much of the container
to make the mock rocks?
of beads did Mrs. Nomic begin
with?
Area Model Grid Scenarios – Answer Key
Scenario 1
Scenario 2
Students in Mr. Gauge’s class set up a
The boys running club had a relay race
weather station at the beginning of the during last Wednesday’s practice. Two
year. The first day it rained, they
boys participated on each relay team and
3
recorded 4 inches of rain at their station.
the total distance covered was 78 of a
The second rainfall of the year brought mile. If the first boy in one group ran 12
another 16 inches. How much total rain of a mile, what fraction of a mile did his
partner run?
had they collected in their weather
station after the second rainfall of the
school year?
Grids created by groups will vary.
Grids created by groups will vary.
7/8 – 1/2 = 7/8 – 4/8 = 3/8
3/4 + 1/6 = 9/12 + 2/12 = 11/12
His partner ran 3/8 of a mile.
11/12 inches of rain were collected after
the second rainfall of the year
Scenario 3
Scenario 4
Mrs. Nomic was gathering the supplies
Jan found the recipe her 4th grade
she needs for her 5th grade economy
teacher gave her for making mock rocks
unit. She found the container of beads
at home. According to the recipe, Jan
1
she used last year and gave away 6 of the
needs 45 cups of sand to mix with the
container of beads to her teammate. She
other ingredients. Jan measured the
2
7
still had 3 of the container left to use
sand she had and realized she had 10
cups of sand. Does she have enough
with her class. How much of the
sand to make the mock rocks?
container of beads did Mrs. Nomic
begin with?
Grids created by groups will vary.
Grids created by groups will vary.
4/5 – 7/10 = 8/10 – 7/10 = 1/10.
1/6 + 2/3 = 1/6 +4/6 = 5/6
Jan does not have enough sand to make
Mrs. Nomic started with 5/6 of the
the mock rocks; she needs 8/10 cups and
container of beads.
she only has 7/10 of a cup. She needs
1/10 cups more.