EQUALITY 5.NF.5
Obtaining and Recognizing Equal Fractions
Purpose:
To introduce rules for obtaining and recognizing equal fractions
Materials:
Fraction Bars, water-base pens and Fraction Playing Cards (optional)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Obtaining equal fractions by splitting parts of bars
1. Show students the bar for 3/4.
Fraction
Bars
 How many parts does this bars have and how many are shaded? (4 parts and 3
shaded)
 What is the fraction for this bar? (3/4)
water-base
pens
With a water-base pen, draw lines on the 3/4 bar
to split each part in half as shown.
3
4
=
6
8
 How many parts does this bar have now and how many are shaded? (8 parts
and 6 shaded) Has the shaded amount of the bar increased? (No)
 What does this show about the fractions 3/4 and 6/8? (They are equal.)
2. Repeat this process of splitting the parts of bars into two equal parts for the following
bars. This activity can be done by students coming to the overhead, if transparent bars are
available, or by having students draw lines on their bars with water-based pens. These
marks can be wiped off the transparent bars or plastic Fraction Bars with a moist paper
towel. Keep the examples of these bars and equations for later generalizations.
1
2
=
2
4
1
4
=
2
8
2
3
=
4
6
3. Have students find the 1/2 bar and draw lines to split each part into 3 equal parts.
 What is the effect on the fraction 1/2 of splitting each part of its bar into 3
equal parts? (The numerator and denominator both get multiplied by 3.)
4. Using the following bars, split the parts of a 1/4 bar into 3 equal parts, the parts of a 2/3
bar into 4 equal parts, and the parts of a 1/2 bar into 5 equal parts. With the help of the
students write the equations for the fractions before and after the splitting of the bars.
1
4
=
3
12
2
3
=
8
12
1
2
=
5
10
 What is the effect on a fraction of splitting all the parts of its bar into 3, 4, or 5
equal parts? (Its numerator and denominator are both multiplied by 3, 4, or 5,
respectively.)
5. Pose the following question to guide students into generalizing the above results.
 If you multiply both the numerator and denominator of a fraction by any nonzero number, will an equal fraction be obtained? (Yes. For any fraction, an
equal fraction can be obtained by multiplying the numerator and
denominator by the same nonzero number. This can be shown by the
following equations. Since n/n is the fraction for a bar with n out of n parts,
n/n = 1 and we can write 1 × a/b = n/n × a/b = na/nb.)
Activity 2 Finding patterns to determine equal fractions
pencils
and
paper
Write the following equalities and ask students to look for patterns to tell when two
fractions are equal.
1
4
=
3
12
3
4
=
6
8
1
2
=
3
6
1
3
=
5
15
4
5
=
8
10
2
6
=
3
9
Possible patterns: (1) If the numerator and denominator of one fraction can be
multiplied by the same number to obtain a second fraction, the fractions are equal;
and (2) If the products of the numerators and denominators as indicated by the
arrows in this diagram are equal, then the two fractions are equal.
Fraction
Playing
Cards
(optional)
2
6
3
9
Activity 3 Equal fractions from Fraction Playing Cards (optional)
1. Each group will need a deck of Fraction Playing Cards, or if not available, write
the 32 fractions for the Fraction Bars on slips of paper.
 Select any card and multiply the numerator and denominator of its fraction
by the same number. Write an equation for the fraction equality.
2. Play the game Match in which three cards are
turned face up to form the Board. Each player in turn
takes the top card in the Deck to determine if its
fraction is equal to one from the Board. If so, the
player wins both cards. If not, the selected card is
placed on the Board. If there are less than 3 cards on
the Board, move more cards from the Deck to the
Board. Play continues until the stack has been used.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NF.5 #2 and #3