DIVISION 5.NF.3
Quotients of Whole Numbers that Equal Fractions
Purpose:
To divide whole numbers by whole numbers whose resulting quotients are fractions
Materials:
Fraction Bars, 1-inch wide strips of paper with lengths 6, 12 and 18 inches, pencils and
paper
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Quotients of whole numbers that equal fractions
Fraction
Bars
1. Each group will need decks of bars and strips of paper the width of a Fraction Bar
and lengths of 6 inches, 12 inches, and 18 inches.
strips of
paper
 Use your Fraction Bars to measure the length of each strip of paper to see how
many whole bars it represents. (The strips represent 1 bar, 2 bars, and 3 bars.)
pencils
and paper
 Label each strip as a 1-bar, 2-bar or 3-bar.
2. Ask students to take their paper 3-bar and place the other paper bars aside for now.
 How can a 3-bar be divided into 4 equal parts by paper-folding? (Fold the
entire bar in half and then fold the result in half.)
 Fold your 3-bar into 4 equal parts and then open the 3-bar and mark the crease
lines to show the 4 parts. Shade one of these parts. What Fraction Bar has the
same shaded amount as one of the 4 parts of the 3-bar? (The blue 3/4 bar.)
Students can show this by placing the 3/4 bar next to the shaded part of their
3-bar.
 Write the division equation for 3 ÷ 4. (3 ÷ 4 = 3/4)
3-bar
3÷4 =
3
4
3. Ask students to use their paper 2-bar for the next activity.
 How can a 2-bar be paper-folded into 3 equal parts? (The two ends of the strip
can be folded toward each other to overlap in 3 parts.)
 Fold your 2-bar into 3 equal parts, open the parts and mark the creases, and
shade one of the parts. What Fraction Bar has the same amount of shading as
the shaded part of your 2-bar? (2/3 bar)
 Write the division equation for 2 ÷ 3. (2 ÷ 3 = 2/3)
2-bar
2÷3 =
2
3
4. For the next activity, ask students to use their paper 1-bar.
 Fold your paper 1-bar into either 2 or 3 or 4 equal parts and shade one of the
parts. Describe the Fraction Bar with the same amount of shading. (Either a
green, yellow or blue bar with 1 part shaded.)
 Write the division equation for either 1 ÷ 2 or 1 ÷ 3 or 1 ÷ 4. (1 ÷ 2 = 1/2;
1 ÷ 3 = 1/3; and 1 ÷ 4 = 1/4)
5. Generalizing: List the equations from the preceding activities.
3÷4 =
3
4
2÷3 =
2
3
1÷2 =
1
2
1÷3 =
1
3
1÷4 =
1
4
 Look for patterns and write a statement for dividing one whole number by
another. (When one whole number is divided by another, the resulting
fraction has the first whole number as the numerator and the second
whole number as the denominator.)
pencils
and paper
Activity 2 Using the generalization to solve problems
1. Select from the following problems.
 If a piece of wood with a length of 5 feet is cut into 6 equal pieces, what is the
length of each piece? (5/6 of a foot)
 If three chicken pies are shared equally among 5 people, what fraction of a pie
will each person have? (3/5 of a pie)
 If 8 pounds of grass seed are divided equally into 5 piles, what is the weight of
one of these piles? (8/5 or 1 3/5 pounds)
2. Show students this sketch and present the following problem.
 If Mr. Green used 32 feet of fence to build a rabbit
pen and the length of the pen is twice the width,
what is the width of the pen? Explain your
reasoning. (Some students may notice that the
perimeter of the pen has 6 equal parts and compute
32 ÷ 6 = 32/6 = 5 2/6 feet.)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NF.3 #1 and #2