Download Carpet Fraction Cover Up KEY

Fraction Carpet Cover Up KEY
Keisha is going to create several models to show customers how portions of room would look
carpeted. For each given situation:
1.
2.
3.
4.
5.
6.
7.
Give an estimate and how you determined your estimate.
Use fraction squares to model the situation. The one whole square represents 1 room.
Draw a diagram of the problem and label all parts correctly.
Shade the area of the room that will be carpeted.
Find a solution that states what fraction of the room will be carpeted. Justify your response.
Review your estimate and solution.
Write a number sentence to show the relationship between the numbers in the problem and
the diagram.
Problem 1
Two-thirds of the room is designated workspace. Four-fifths of the workspace will
be carpeted.
Estimate: The area of a rectangle may be calculated by doing length times width. The
length and width are both close to 1, but less than 1, so the solution must be less than 1
square unit because 1 unit x 1 unit = 1 square unit. Two-thirds is the size of the group we
begin with (portion of the room designated as workspace) which means we begin with less
than 1 whole unit. We want less than one complete group of two-thirds (four fifths), which
means we will carpet less than two thirds of the room. We will carpet a little less than twothirds because five-fifths would be all of the two thirds and since we will carpet four-fifths,
(not quite a complete group of two thirds), the solution is somewhere between one-half and
two-thirds.
Diagram:
2
3
workspace
4
5
carpet
Four-fifths of two-thirds is eight-fifteenths
Number Sentence:
4
carpet
5
x
2
workspace
3
=
8
of the room is carpet
15
Review estimate and solution: The solution is between the estimate which was between
1
2
and . Write equivalent fractions for each estimate and the product to further compare
2
3
the fractions.
Why Does This Work:
4x2
4 rows with 2 in each row
number of equal size parts in double shaded region
=
=
5x3
5 rows with 3 in each row
number of equal size parts in the whole square
2
4
= 0.8 and
 0.67
5
3
0.8 x 0.67 is calculated by doing 67 x 8 = 536
Where do you place a decimal point for the product to be reasonable? 0.536
How does 0.536 relate to
8
?
15
8 ÷ 15 = 0.533… which is reasonably close to 0.536.
1
2
2
3
0.533… is between 0.5 ( ) and 0.666… ( )
Fraction Carpet Cover Up KEY
Keisha is going to create several models to show customers how portions of room would look
carpeted. For each given situation:
1.
2.
3.
4.
5.
6.
7.
Give an estimate and how you determined your estimate.
Use fraction squares to model the situation. The one whole square represents 1 room.
Draw a diagram of the problem and label all parts correctly.
Shade the area of the room that will be carpeted.
Find a solution that states what fraction of the room will be carpeted. Justify your response.
Review your estimate and solution.
Write a multiplication number sentence to show the relationship between the numbers in the
problem and the diagram.
Problem 2
One-half of the room is designated workspace. One-half of the workspace will be
carpeted.
Estimate: The area of a rectangle may be calculated by doing length times width. The
length and width are both less than 1, so the solution must be less than 1 square unit
because 1 unit x 1 unit = 1 square unit. Since half, of one-half is one-fourth, my estimate is
one-fourth.
Diagram:
1
workspace
2
1
2
carpet
One-half of one-half is one-fourth
Number Sentence:
1
carpet
2
x
1
workspace
2
=
1
of the room is carpet
4
Review estimate and solution: The solution and the estimate are the same.
Why Does This Work:
1x1
1 row with 1 in each row
number of equal size parts in double shaded region
=
=
2x2
2 rows with 2 in each row
number of equal size parts in the whole square
1
1
= 0.5 and = 0.5
2
2
0.5 x 0.5 is calculated by doing 5 x 5 = 25
Where do you place a decimal point for the product to be reasonable? 0.25
How does 0.25 relate to
1
?
4
1 ÷ 4 = 0.25 which is equivalent to
1
4
Fraction Carpet Cover Up KEY
Keisha is going to create several models to show customers how portions of room would look
carpeted. For each given situation:
1.
2.
3.
4.
5.
6.
7.
Give an estimate and how you determined your estimate.
Use fraction squares to model the situation. The one whole square represents 1 room.
Draw a diagram of the problem and label all parts correctly.
Shade the area of the room that will be carpeted.
Find a solution that states what fraction of the room will be carpeted. Justify your response.
Review your estimate and solution.
Write a multiplication number sentence to show the relationship between the numbers in the
problem and the diagram.
Problem 3
Three-fourths of the room is designated workspace. One-third of the workspace
will be carpeted.
Estimate: The area of a rectangle may be calculated by doing length times width. The
length and width are both less than 1, so the solution must be less than 1 square unit
because 1 unit x 1 unit = 1 square unit. One-third of three-fourths is one-fourth, because
there are three one-fourth pieces in three-fourths. My estimate is one-fourth.
Diagram:
3
workspace
4
1
3
carpet
One third of three-fourths is three twelfths
1
3
carpet
x
workspace =
3
4
simplify at this point so students may see the pattern.
Number Sentence:
3
of the room is carpet. Do not
12
Review estimate and solution: The solution and the estimate are the same. By using the
3  3
1
GCF for 3 and 12 to simplify:
, the equivalent fraction is .
12  3
4
Why Does This Work:
1x3
1 rows with 3 in each row
number of equal size parts in double shaded region
=
=
3x4
3 rows with 4 in each row
number of equal size parts in the whole square
1
3
 0.33 and = 0.75
3
4
0.33 x 0.75 is calculated by doing 33 x 75 = 2475
Where do you place a decimal point for the product to be reasonable? 0.2475
How does 0.2475 relate to
3
?
12
3 ÷ 12 = 0.25 which is reasonably close to 0.2475
0.25 is equivalent to
1
4
Fraction Carpet Cover Up KEY
Keisha is going to create several models to show customers how portions of room would look
carpeted. For each given situation:
1.
2.
3.
4.
5.
6.
7.
Give an estimate and how you determined your estimate.
Use fraction squares to model the situation. The one whole square represents 1 room.
Draw a diagram of the problem and label all parts correctly.
Shade the area of the room that will be carpeted.
Find a solution that states what fraction of the room will be carpeted. Justify your response.
Review your estimate and solution.
Write a multiplication number sentence to show the relationship between the numbers in the
problem and the diagram.
Problem 4
Two-thirds of the room is designated workspace. One-half of the workspace will be
carpeted.
Estimate: The area of a rectangle may be calculated by doing length times width. The
length and width are both less than 1, so the solution must be less than 1 square unit
because 1 unit x 1 unit = 1 square unit. Since half of two-thirds is one-third (there are two
one-thirds in two-thirds), my estimate is one-third.
Diagram:
2
workspace
3
1
2
carpet
One half of two thirds is two sixth
1
2
2
x
=
2
3
6
(Note: do not simplify at this point so students may see the pattern.)
Number Sentence:
Review estimate and solution: The solution and the estimate are the same. By using the
2  2
1
GCF for 2 and 6 to simplify:
, the equivalent fraction is .
6  2
3
Why Does This Work:
1x2
1 row with 2 in each row
number of equal size parts in double shaded region
=
=
2x3
2 rows with 3 in each row
number of equal size parts in the whole square
2
1
 0.67
= 0.5 and
2
3
0.5 x 0.67 is calculated by doing 67 x 5 = 335
Where do you place a decimal point for the product to be reasonable? 0.335
How does 0.335 relate to
2
?
6
2 ÷ 6 = 0.333… which is reasonably close to 0.335
0.333… is equivalent to
1
3