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MULTIPLICATION 4.NF.4
Whole Numbers Times Fractions
Purpose:
To multiply whole numbers times fractions
Materials:
Fraction Bars and "Whole Numbers Times Fractions on Number Lines" (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Whole numbers times fractions
Fraction
Bars
pencils and
paper
1. Find the Fraction Bar for the fraction 2/3.
 How many shaded parts would there be if there were three of these bars? (3 × 2 = 6)
How many whole bars would this equal? (2, because there are 3 shaded parts in one
of these whole bars.)
 How can this be indicated by an addition equation? (2/3 + 2/3 + 2/3 = 6/3 = 2)
 How can this be indicated by a multiplication equation? (3 × 2/3 = 6/3 = 2. Discuss
that 3 × 2 represents three times the number of shaded parts in a 2/3 bar.)
2. Find the Fraction Bar for the fraction 5/6.
 How many shaded parts would there be if there were four of these bars? (4 × 5 = 20)
How many whole bars would this equal? (3 and 2/6, because there are 6 shaded parts
in one of these whole bars.)
 Write both the addition equation and the multiplication equation for four of the 5/6 bars.
5
6
+
5
6
+
5
5
20
2
+
=
=3
6
6
6
6
and 4 ×
5
4!5
20
=
=
6
6
6
Discuss the convenience of using multiplication, and that (4 × 5) in the numerator of
the multiplication equation represents four times the number of shaded parts in a 5/6 bar.
This provides a connection between multiplication involving whole numbers and fractions.
3. Find any whole Fraction Bar and write the
multiplication equation for 5 times the fraction for the bar.
(Look at some examples. Point out that the fraction for a
whole bar can be replaced by 1, that is, 5 × 4/4 = 5 × 1 = 5.
4. Find any zero Fraction Bar and write the
multiplication equation for 5 times the fraction for the
bar. (Point out that the fraction for a zero bar can be
replaced by 0, that is, 5 × 0/4 = 5 × 0 = 0.
5. List a few examples from above. State a rule for multiplying a whole number times a fraction.
(Multiply the whole number times the numerator and keep the denominator.)
6. Discuss the similarity between multiplying a whole number times a whole number and
multiplying a whole number times a fraction, and illustrate with examples. In both of the
following products, the number "5" indicates how many times the whole number 7 will occur
and how many times the fraction 1/3 will occur.
5 × 7 = 7 + 7 + 7 + 7 + 7 and
5×
1
3
=
1
3
+
1
3
+
1
3
+
1
3
+
1
3
That is, multiplication by a whole number can be computed as repeated addition whether a
whole number is multiplied times a whole number, or a whole number is multiplied times a
fraction. This will help students make sense of products when multiplying a whole number
times a fraction.
activity
sheets,
pencils
and
paper
Activity 2 Products of fractions on number lines
1. Distribute the activity sheet "Whole Numbers Times Fractions on Number Lines" to
students. The first two examples of number lines from his activity sheet are completed here.
Once the activity sheet is completed, discuss how jumps on the number line illustrate repeated
addition of fractions, and repeated addition can be written as a whole number times a fraction.
 For 6 jumps of size 3/10, the distance on the number line is
3
3
3
3
3
3
18
+
+
+
+
+
=
10
10
10
10
10
10
10
Also discuss that any number of jumps of the same size can be represented as a whole number
times the numerator of the fraction to obtain the total distance on the number line. Cite examples.
 For 6 jumps of size 3/10, the total distance on the number line is
6×
Fraction
Bars and
Die
3
6!3
18
8
=
=
=1
10
10
10
10
Game: Each player in turn selects a Fraction Bar and rolls a die. The
player's score is the number from the die times the fraction from the
bar rounded to the nearest whole number. For the roll of the die and the
bar shown here, the player scores 4 points: 5 × ¾ = 15/4 = 3 ¾ which
rounds to 4. The first player to score 11 points wins the game.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 4.NF.4 #4 and #5
4.NF.4
Name:
Date
.
Whole Numbers Times Fractions on Number Lines
1. This number line shows 6 jumps of size
3
, starting at the 0 point.
10
a. Write the mixed number under the line for the point after 6 jumps.
b. Write the improper fraction and mixed number to complete the following equations:
3
3
3
3
3
3
+ + + + +
= ____ =
10 10 10 10 10 10
____ ,
and 6 ×
3
= ____ =
10
2. Starting at the 0 point on the following number line draw 7 jumps of size
____
3
.
12
a. Write the mixed number under the line for the point after 7 jumps.
b. Write improper fraction and mixed number to complete the following equations:
3
3
3
3
3
3
3
+ + + + + +
= ____ =
12 12 12 12 12 12 12
____ ,
and 7 ×
3. Starting at the 0 point on the following number line draw 3 jumps of size
3
= ____ =
12
____
3
.
6
a. Write the mixed number under the line for the point after 3 jumps.
b. Write the improper fraction and mixed number:
3 3 3
+ + = ____ =
6 6 6
____ , and 3 ×
4. Starting at the 0 point on the following number line draw 3 jumps of size
3
= ____ =
6
____
3
= ____ =
5
____
3
.
5
a. Write the mixed number under the line for the point after 3 jumps.
b. Write the improper fraction and mixed number:
3 3 3
+ + = ____ =
5 5 5
____ , and 3 ×