Download DIVISION 6.NS.1 Solving Problems Involving

DIVISION 6.NS.1
Solving Problems Involving Division
Purpose:
To solve problems involving division of fractions and mixed numbers
Materials:
Paper and pencils
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Fractions divided by fractions
Pose the following problems and discuss solutions.
paper and
pencils
 If one lap of an elliptical track is 1/12
mile, how many laps will equal 3/4
mile? (3/4 ÷ 1/12 = 9)
 If 1/8 teaspoon of baking soda is needed for each pan of biscuits, how many
pans of biscuits can be made with ½ teaspoon of baking soda? (1/2 ÷ 1/8 = 4)
 Orman has 2/3 cup of cocoa and plans to make chocolate cookies. If each batch
of cookies uses 1/6 cup of cocoa, how many batches can he make? (2/3 ÷ 1/6 =
4)
Ask students to create a division problem for the following information.
 Suppose that ¼ cup of sugar is needed and ¾ cup is available.
Activity 2 Division involving fractions and mixed numbers
 An experiment requires 1/3 ounce of sulfide. How many experiments can be
run with 1 2/3 ounces of sulfide? (1 2/3 ÷ 1/3 = 5)
 If the recipe calls for 1 ½ cups of peeled and sliced peaches for each bowl of
Peach-Gelatin, then 6 cups of peaches will be enough for how many bowls? (4)
 Each batch of Cheese Strudel requires 1 2/3 cups of cheddar cheese. How many
batches can be made if 5 cups of cheddar cheese are available? (5 ÷ 1 2/3 = 3)
Ask students to create a division word problem involving the following information:
A satellite sent signals for 7 ½ hours, and during that time it orbited the earth every 1 ¼
hours. (Example: How many orbits did the satellite make during this time? (6 orbits)
Activity 3 Whole numbers divided by whole numbers
 If Josh can walk one mile in 15 minutes, how many miles can he walk in 48
minutes? (48 ÷ 15 = 48/15 = 3 3/15 = 3 1/5 miles)
If 40 gallons of sap can be boiled down to one gallon of maple syrup, how many
gallons of maple syrup will 100 gallons of sap produce? (100 ÷ 40 = 2 20/40 =
2 ½ gallons)
 A 20-inch ribbon needs to be cut into 3 equal pieces. What will be the length of
each piece? (20 ÷ 3 = 20/3 = 6 2/3 inches)
 If 3 pounds of sugar are divided equally into 5 piles, what is the weight of the
sugar in each pile? (3 ÷ 5 = 3/5 pound)
Activity 4 Word problems involving ratios
pencils
and paper
 If a small gear on a machine has 8 teeth
and a large gear has 40 teeth, what is the
ratio in lowest terms of the number of
teeth on the small gear to the number of
teeth on the large gear? (8 to 40 and 8/40
= 1/5)
 Out of 250 middle-school students in Lincoln School, 50 are from out of town
and 200 live in town. What is the ratio in lowest terms of the number of out-oftown student to the number of in-town students? (50 to 250 and 50/250 = 1/5)
 If the Cedar River School has 4 teachers for its 120 fifth grade students, what is
the ratio in lowest terms of teachers to students? (4 to 120 and 4/120 = 1/30)
 If a baby boy weighs 14 pounds and his older sister weighs 49 pounds, what is the
ratio of the baby's weight to his sister's weight? (14 to 49 and 14/49 = 2/7)
Activity 5 Variety of types of division
Select from the following problems. Ask students for solutions and explanations.
 If a sugar maple tree gives ¼ gallon of sap each day, how many days will it take
to obtain 4 ½ gallons of sap? (4 ½ ÷ ¼ = 9/2 ÷ ¼ = 9/2 × 4 = 36/2 = 18 days)
 The recipe for a pan of Millet Spoon Bread requires 1/3 cup of dry millet. If Dora
has 2 cups of millet, how many pans of bread can she make? (2 ÷ 1/3 = 2 × 3 = 6
pans)
 If 8 members of a committee voted for a tax increase and 20 members voted
against the increase, what is the ratio in lowest terms of the number of members
voting for the increase to the number voting against the increase? (8 to 20 and
8/20 = 2/5)
 A home-owner asked a hardware store worker to cut a 16 foot piece of plank into
5 equal lengths. What was the length of each piece? (16 ÷ 5 = 16/5 = 3 1/5 feet)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 6.NS.1 #5 and #6