Download + + ADDITION 5.NF.1 Adding Mixed Numbers

ADDITION 5.NF.1
Adding Mixed Numbers - Unequal Denominators
Purpose:
To add mixed numbers having unequal denominators and to approximate sums
involving fractions and mixed numbers.
Materials:
Fraction Bars
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Mixed numbers with the same denominator
Fraction
Bars
1. Use bars to represent the mixed numbers 2 1/6 and 1 3/6 by using the backs of red
bars to represent each value of the unit.
+
2
pencils
and paper
1
6
+
1
3
6
 How can this sum be computed? (Compute the sum of the whole numbers and
fractions separately.)
 Write the addition equation for this sum in both the horizontal and vertical
forms.
Horizontal form:
2
1
3
4
+1 =3
6
6
6
2. Find bars to represent 3 5/12 and 2 11/12 and compute the sum of these mixed numbers.
3
Fraction
Bars
5
11
16
4
+2
= 5
= 6
12
12
12
12
 Why can the improper fraction in 5 16/12 be replaced by the mixed number 6
4/12. (The denominator in 16/12 indicates a whole bar with 12 equal parts and
there are 16 parts in all. So 16/12 represents one whole bar and 4 parts out of
12. That is, 16/12 = 1 4/12.)
Activity 2 Mixed numbers with different denominators
1. Use bars to represent the mixed numbers 2 1/3 and 1 1/4 by using the backs of yellow
bars and a blue bar to represent each value of the unit.
pencils
and paper
+
2
1
3
+
1
1
4
 How can this sum be computed? (Replace the 1/3 and 1/4 bars by 4/12 and
3/12 bars. That is, find common denominators for the fractions and compute
the sums of the whole numbers and fractions separately.)
 Write the addition equations for this sum.
2
1
1
4
3
7
+1
= 2
+1
= 3
3
4
12
12
12
2. Write the following sums, one at a time, for students to compute. Ask volunteers to
show their work and discuss questions that arise.
a. 3
pencils
and paper
1
2
+2
8
3
(a. 3
b. 1
1
1
+3
4
2
c. 5
1
2
3
16
19
+2 =3
+2
=5
8
3
24
24
24
b. 1
1
3
+2
2
5
d. 4
3
1
+2
10
5
1
1
1
2
3
+ 3 = 1 + 3 = 4 ; etc.)
4
2
4
4
4
Some students may have used a common denominator of 8 in example b and a common
denominator of 50 in example d. Point out that the smaller denominators of 4 and 10 are
more convenient for these examples and review multiplying the numerator and
denominator by the same number to obtain equal fractions.
Activity 3 Approximating sums of fractions and mixed numbers
Write the following sums, one at a time, and ask students to approximate the sums by
first rounding the fractions and mixed numbers to the nearest whole number.
a. 3
pencils
and paper
2
1
+2
3
4
(a. 3
b. 5
1
3
+2
2
5
2
1
+2 ≈4+2=6
3
4
c.
b.
5
7
1
+ 4
10
3
d.
7 12
+
8 13
e. 6
1
2
+ 3
4
5
1
3
+ 2 ≈ 6 + 3 = 9; etc.)
2
5
Discuss the convenience of rounding off numbers when only an approximate answer is
needed. For example, if 10 pounds of potatoes are needed and 4 2/3 pounds and 3 3/4
pounds are available, rounding these mixed numbers to 5 + 4 would show that the sum
of these weights is less than 10 pounds.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NF.2 #5 and #6
fractionbars.com Set 1 Fraction Bars
Blackjack (The player competes
against the computer and tries to
obtain a sum that is less than or equal
to 2. The player is dealt two cards on
each round and can click "Hit me" for
more cards. The first player to win
three rounds (three points) wins the
game. For the round shown here, both
the player and the computer received
one point because their sums were
equal.)