Download DIVISION 6.NS.1 Dividing by Fractions and Mixed Numbers

DIVISION 6.NS.1
Dividing by Fractions and Mixed Numbers
Purpose:
To divide by fractions and mixed numbers and to approximate quotients by rounding
Materials:
Fraction Bars and water-base pens
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Dividing fractions whose quotient is not a whole number
Fraction
Bars
water-base
pens
1. Show students and have them find the red bar for 5/6 and the yellow bar for 1/3.
 How many times greater is the shaded amount of the 5/6
bar than the shaded amount of the 1/3 bar? (2 and ½
times greater) Illustrate by drawing lines on bars or
transparent bars with water-base pens.
5/6 ÷ 1/3 = 2 ½
pencils
and paper
 Compute 5/6 ÷ 1/3 using the invert and multiply rule and write the division
equation. (5/6 ÷ 1/3 = 5/6 × 3 = 15/6 = 2 ½) Discuss the fact that his answer
makes sense because in the illustration with the bars, the remaining shaded
amount of the red bar is ½ the size of the shaded part of the yellow bar.
2. Show students and have them find bars for 7/12 and 1/4.
 What is the whole number of times the shaded
amount of the ¼ bar "fits into" the shaded amount
of the bar for 7/12? (2 times)
7/12 ÷ 1/4 = 2 1/3
 Compute 7/12 ÷ 1/4 using invert and multiply and write the division equation.
 Explain why the bars show that this answer makes sense. (The shaded amount of
the orange bar that is left over is 1/3 the size of the shaded amount of the blue bar.)
Activity 2 Quotients less than one
1. Show students and have them find the red bar for 1/6 and the green bar for 1/2.
Fraction
Bars
pencils
and paper
 How many times will the shaded amount of the bar for 1/2
"fit into" the shaded amount of the bar for 1/6? ( 0 times)
 Compute 1/6 ÷ 1/2 and write the division equation.
1/6 ÷ 1/2 = 1/6 × 2/1 = 1/3
 Explain why the bars help to show that the answer 1/3 makes sense. (The shaded
amount of the 1/6 bar is 1/3 the size of the shaded amount of the 1/2 bar.)
2. Write the following quotients on the board or overhead
1
2
÷
1
3
1
4
÷
2
3
7
10
÷
1
3
3
4
÷
1
5
2
5
÷
7
8
 Without computing, determine whether each quotient is less than 1 or greater
than 1 and explain your reasoning. (1/2 ÷ 1/3 is greater than 1 because 1/3 is less
than 1/2; etc. Discuss with students that if a number is divided into a larger
number, the quotient will be larger than 1; and if a number is divided into a
smaller number, the quotient will be less than 1.)
Activity 3 Division involving mixed numbers and fractions
Fraction
Bars
1. Have students find the red bars for 3/6 and 5/6
and place their shaded amounts end to end.
 What is the total shaded amount? (1 2/6 bars)
water-base
pens
 Find the yellow bar for 1/3 and determine how many times its shaded amount
fits into the total shaded amount of the two red bars. (4 times) Show with lines.
 Use the invert and multiply rule to compute 1 2/6 ÷ 1/3.
1
2
6
÷
1
8
1
8
3
24
=
÷
=
×
=
= 4
3
6
3
6
1
6
2. Have students compute the following quotients by first replacing the mixed numbers
by improper fractions. Then ask them to approximate each quotient by rounding the
mixed numbers to whole numbers and dividing. (The rounded results are in brackets.)
2
7
8
÷1
1
3
=2
[3]
4
10
1
1
4
÷1
1
3
=1
[1]
10
22
4
1
2
÷2
1
13
=1
[2 ½]
3
14
Note: NCTM's Standards 2000 (page 152) notes that there is a common, but incorrect,
generalization that "division always makes things smaller." Ask students to compute
the following quotients and write a statement about what happens as a given number is
divided by smaller and smaller numbers. 1 ÷ 1/2; 1 ÷ 1/3; 1 ÷ 1/4; 1 ÷ 1/5; 1 ÷ 1/6
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 6.NS.1 #3 and #4
fractionbars.com Set 1 Equations
Game (Fractions from the bars or
cards are placed into 10 blanks to
form equations involving the four
operations. It is often challenging,
but is always possible. By clicking
GO, the computer will check the
equations that have been completed.)