DIVISION 5.NBT.7
DIVISION OF DECIMALS BY DECIMALS
Purpose: To divide decimals by decimals
Materials: Decimal Squares and Blank Decimal Squares for
Dividing Decimals by Decimals (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1
Blank
Decimal
Squares
for
Dividing
Decimals
by
Decimals
Shading Blank Decimal Squares to Find Quotients
1. Use #1 on the activity sheet and shade the first square with 9 parts
and the second square with 3 parts. Determine how many times bigger
the shaded amount for .9 is than the shaded amount for .3, write the
number (quotient) in the box, and complete the equation beneath the
squares. Discuss that lines can be drawn on the .9 square to show that
.3 "fits into" .9 three times. Use #2 on the sheet to illustrate .8 ÷ .2, write
its quotient in the box, and complete the division equation.
2. Use #3 on the sheet and shade the two squares with 20 shaded
parts and 5 shaded parts. Determine how many times bigger .20 is
than .05, and write a division equation for .20 ÷ .05. (.20 ÷ .05 = 4)
Draw lines on the .20 squares to show that .05 "fits into" or can be
"subtracted from" .20 four times.
3. Use #4 on the sheet, and shade the first square for .60, and the
second square for .15. Draw lines on the first square to show how many
times .15 "fits into" .60, and write the division equation below the
squares.
4. Use the squares in #5 to illustrate .30 ÷ .02. How many times bigger
is .30 than .02? (15 times bigger) Write the division equation for this
result. (.30 ÷ .02 = 15) Discuss that this example shows that dividing by
small numbers can produce large numbers, a result that sometimes
surprises students. Look at the .30 square to see that .30 ÷ .01 = 30.
5. Shade the squares in #6 for .40 and .16 and determine how many
times bigger .40 is that .16 by marking off two groups of 16 on the
.40 square. Explain how these squares can be used to show that
.40 ÷ .16 = 2 ½ or 2.5 (.16 fits into .40 two times and the remaining 8
hundredths squares are half of 16, that is, .16 "fits into" .40 two and
one-half times.)
Activity 2
cc
Summarizing to See Patterns and Relationships
Look for patterns in the examples of dividing decimals by decimals and
write a rule for dividing one decimal by another. Students may have
noticed that these activities involved dividing whole numbers of shaded
parts by whole numbers of shaded parts. This suggests the following
rule for using long division. 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 whole numbers.
Activity 3
Approximating Quotients with Compatible Numbers
Approximate each quotient by finding convenient compatible number
replacements. Your answers will vary.
a. .61 ÷ .2 ≈ .6 ÷ .2 = 3 b. .9 ÷ .4 ≈ .8 ÷ .4 = 2 c. .77 ÷ .23 ≈ .75 ÷ .25 = 3
EXPANDING THE CONCEPTS
Decimal
Squares
In the game EXACT FITS, each player in turn takes two
red squares or two green squares (decimals with the same
number of decimal places), selects the square for the
greater decimal, divides the number of shaded parts of this
square by the number of shaded parts of the other square,
and rounds the quotient to the nearest whole number. This
number is the player's score for the turn. The player with
the greatest point total after 5 rounds win the game. In the
example shown here, the player receives 3 points.
Bonus Turn: If a player's quotient is a whole number and does not have to
be rounded, the player has an "Exact Fit" and in addition to receiving the
points for the turn, receives a bonus turn.
INDEPENDENT PRACTICE AND ASSESSMENT
Worksheets 5.NBT.7 #27, #28
and #29
decimalsquares.com (Laser Beams
In this game, mixed decimals are
rounded to whole numbers, and if
their quotient are computed in time,
the asteroids will be destroyed
before they pass out of view.)
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