DIVISION 6.NS.3
DIVISION BY MIXED DECIMALS
Purpose: To divide mixed decimals by mixed decimals
Materials: Decimal Squares, Decimal Squares Grid (attached)
TEACHER MODELING/STUDENT RESPONSE
Activity 1
Decimal
Squares
Grid
Rectangular Model for Division by Mixed Decimals
1. Use your Decimal Squares Grid to mark off a 1.4
by 1.7 rectangle and compute 1.4 × 1.7. (Some
students may need help marking off the dimensions.)
What is the number of whole squares and parts of a
square contained in the rectangle? (2 whole squares
and 38 parts out of 100. Discuss student methods of
determining the number of whole squares and parts
of a square. Some students may see the whole 10 by
10 square and count the columns and rows of 10
hundredths to obtain a second whole square. Others
may compute 1.4 × 1.7 = 2.38 to obtain 2.38 whole
squares.) Note: A transparency or projection of the
grid is convenient for student/teacher demonstrations.
2. Suppose a rectangle has been formed with
one dimension of 1.8, and it contains 4 whole
squares and 14 parts out of 100, that is, 4.14
square units. What is the missing dimension
of this rectangle? (2.3. Discuss student
reasoning. Some students may use the grid to
form a rectangle that has one dimension of
1.8 and then extend the rectangle so that it
contains 4 whole squares and 14 parts out of
100. Others may obtain the missing dimension
by division, that is, 4.14 ÷ 1.8 = 2.3.)
Discuss the relationship between multiplication and division.
In the first example above, the area of a rectangle was found
by multiplying the two dimensions. In the second example,
the area of a rectangle and one dimension were given, and
the missing dimension was found by dividing the area of the
rectangle by the given dimension.
Activity 2
Long Division Algorithm
1. Show students the two diagrams at the right. The
rectangle with one missing dimension is similar to the form
shown below the rectangle that is used for long division. The
quotient in long division may be thought of as the missing
dimension of a rectangle. Notice that
suggests part of
a rectangle.
2. Consider the following statement from the previous lesson on
dividing decimals by decimals. This rule also holds for dividing a
mixed decimal by a mixed decimal: Move the decimal point in both
numbers to the right the same number of places to make the
divisor a whole number and then divide as though dividing by a
whole number. It is interesting that when using long division to divide
by decimals or mixed decimals, the decimal or mixed decimal is
always changed to a whole number by moving the decimal point.
Activity 3
Solving Word Problems Involving Division of Mixed Decimals
Decimal
Squares
Grid
The information in the following word problems can be modeled by
using the grid for help in finding a solution.
 A rectangular countertop with one dimension of 2.6 feet is tiled
with 5.46 square feet of tiles. What is the missing dimension of
this rectangle? (2.1 feet, since 5.46 ÷ 2.6 = 2.1)
 A rectangular flower garden has one dimension of 2.4 yards and
an area of 6.48 square yards. a. What is the missing dimension
of the garden? (2.7 yards) b. If a fence is placed on the four
sides of the garden, what is the length of the fence? (10.2 yards)
Activity 4
Approximating Quotients by Rounding Mixed Decimals
Approximate the following quotients by first rounding each mixed
decimal to the nearest whole number. a. 15.3 ÷ 4.8 ≈ 15 ÷ 5 = 3
b. 40.4 ÷ 9.6 ≈ 40 ÷ 10 = 4 c. 20.73 ÷ 6.27 ≈ 21 ÷ 6 = 3.5
Game: In the game APPROXIMATE QUOTIENTS, each player
in turn takes any two Decimal Squares and rolls the die twice. The
player uses the two whole numbers from the die and the two
decimals from the squares to form two mixed decimals, and then
rounds the mixed decimals to the nearest whole numbers and
computes the quotient of the larger whole number divided by the
smaller. The quotient is then rounded to the nearest whole number
for the player's score. In the example here, the player's score is
4 ÷ 3 ≈ 1. The first player to score 10 points wins the game.
INDEPENDENT PRACTICE AND ASSESSMENT
Worksheets 6.NS.3 #30, #31 and #32
decimalsquares.com Laser Beams
Mixed decimals are rounded whole to
numbers for computing quotients,
products, differences, and sums.
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