Mathematics Grade 6
Strand: THE NUMBER SYSTEM (6.NS) Standard 6.NS.1
This lesson will help students understand what the division of fractions truly means.
- fraction pies
- pencil and paper
When dividing fractions, students will have a better understanding if they think of how many times the divisor will "fit" into the dividend. The reason we use reciprocals when dividing fractions is to make the divisor one.
Represent mathematical situations.
Invitation to Learn:
Ask the question, "What does it mean to divide 8 by 4?" Have students draw a representation of what it means. Encourage the students to share their representation. Ask students to then draw a model to show what 3/4 divided by 1/4 means.
The students will typically look at the above division problem as dividing 8 into 4 parts. Help them to see that you can look at the problem in another way; how many fours are in 8. This works the same for 3/4 divided by 1/4. How many 1/4's are in 3/4?
The shortcut is to multiply the dividend by the reciprocal of the divisor. Have the students record in their journal the meaning and methods of fraction division.
The following are several real world situations in which division of decimals is used. Have the students explain to one another how they would solve these situations. Then have them write equations for their procedures.
You need $69.99 to purchase a new video game. You decided to sell boxes of chocolates to kids at your school to earn the money. You buy 15 1/2 lbs of chocolate for $ 35.00. The clerk suggested that you package the chocolates in either 1/4, 1/3, 1/2 or 3/4 lb boxes. Determine how many boxes of chocolates you could fill for each of the fractions. Select which size you think would sell the best. How much would you charge for each box of chocolates? Be sure that you make enough to pay for the chocolate and your game. Do you think students would buy the chocolates for the price you are asking?
You decide to make sock bags for your friends for Christmas. You find in the closet 5 1/4 yards of cloth. You need 3/4 of a yard to make one bag. How many bags could you make?
You get a job installing tires on cars in an assembly line. You get paid $5.00 for each set of tires you install. It takes you 1/4 of an hour to put on a set of tires. If you work for 8 1/2 hours, how much would you expect to make?
Homework & Family Connections:
Have the students use manipulatives to explain to their parents or siblings what division of fractions means.
Assign students to measure the amount of food in a box (cereal, rice, noodles etc.). Have them determine how many batches they could make if a recipe calls for 1/4, 1/2, 1/3, 2/3, or 3/4 cups of their selected food. Have them write a math sentence using division of fractions to represent what they did.
Assign students to measure the length of their bedroom. Then have them determine how many 3/4 foot tiles they would need to lie tiles across the length of the room. Have them write a math sentence using division of fractions to represent what they did. They could also find how many 1 1/2 foot dressers they could line up, or how many 1/3 foot candy bars, or 3 1/2 ft wide beds, etc.
As students respond and explain their response to you and fellow students, assess their understanding. Their journal entry would be another opportunity for assessment.