NS.1 - DIVIDE FRACTIONS AND INTERPRET THE MEANING OF THE QUOTIENT USING MODELS AND EQUATIONS
warm-up
mini lesson - independent work/share out/discussion
1) Emilia and her mom bake together every weekend. Now, it is her mom's birthday, and Emilia would like to bake her mom a cake on her own. The recipe calls for 2/3 of a cup of sugar. Emilia has 1/2 of a cup of sugar. How much of the recipe can Emilia make?
2) Matt is running a frozen yogurt shop for the summer. At the end of a Saturday night, there is a long line outside of the shop, but Matt is running low on yogurt. The meter on the yogurt machine says it has 1/2 gallon left. Each cup of yogurt is 1/8 gallon. How many more people can Matt serve?
3) A recipe calls for ¼ lb of potatoes to make 3 servings of soup. Jim has 1 ½ lb of potatoes. How many SERVINGS can Jim make?
2) Matt is running a frozen yogurt shop for the summer. At the end of a Saturday night, there is a long line outside of the shop, but Matt is running low on yogurt. The meter on the yogurt machine says it has 1/2 gallon left. Each cup of yogurt is 1/8 gallon. How many more people can Matt serve?
3) A recipe calls for ¼ lb of potatoes to make 3 servings of soup. Jim has 1 ½ lb of potatoes. How many SERVINGS can Jim make?
team challenge
How many???
Solve each problem using a number sentence involving division.
Baking Cookies
Alice, Raul, and Maria are baking cookies together. They need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. They each brought the ingredients they had at home. Alice brought 2 cups of flour and 1/4 cup of butter, Raul brought 1 cup of flour and 1/2 cup of butter, and Maria brought 1 1/4 cups of flour and 3/4 cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make?
Cup of Rice
Tonya and Chrissy are trying to understand the following story problem for 1÷2/3: One serving of rice is 2/3 of a cup. I ate 1 cup of rice. How many servings of rice did I eat? To solve the problem, Tonya and Chrissy draw a diagram divided into three equal pieces, and shade two of those pieces.
Tonya says, “There is one 2/3-cup serving of rice in 1 cup, and there is 1/3 cup of rice left over, so the answer should be 1 1/3.”
Chrissy says, “I heard someone say that the answer is 3/2=1 1/2. Which answer is right?”
Is the answer 1 1/3 or 1 1/2? Explain your reasoning using the diagram.
Dan’s Division Strategy
Dan observes that:
6/10÷2/10=6÷2
He says,
I think that if we are dividing a fraction by a fraction with the same denominator, then we can just divide the numerators.
Is Dan’s conjecture true for all fractions? Explain how you know.
Making Hot Cocoa
One mug of hot chocolate uses 2/3 cup of cocoa powder. How many mugs can Nelli make with 3 cups of cocoa powder?
a. Solve the problem by drawing a picture.
b. Explain how you can see the answer to the problem in your picture.
c. Which of the following multiplication or divisions equations represents this situation? Explain your reasoning.
3×2/3=? 3÷2/3=? 2/3÷3=?
d. Solve the arithmetic problem you chose in part (c) and verify that you get the same answer as you did with your picture.
Running to School
Rosa ran 1/3 of the way from her home to school. She ran 1/4 mile. How far is it between her home and school?
Traffic Jam
You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to get to the next exit, which is 1 1/2 miles away. You are timing your progress and find that you can travel 2/3 of a mile in one hour. If you continue to make progress at this rate, how long will it be until you reach the exit? Solve the problem with a diagram and explain your answer.
Video Game Credits
It requires 1/4 of a credit to play a video game for one minute.
a. Emma has 7/8 credits. Can she play for more or less than one minute? Explain how you know.
b. How long can Emma play the video game with her 7/8 credits?
Solve each problem using a number sentence involving division.
- How many fives are in 15?
- How many halves are in 3?
- How many sixths are in 4?
- How many two-thirds are in 2?
- How many three-fourths are in 2?
- How many 1/6’s are in 1/3?
- How many 1/6’s are in 2/3?
- How many 1/4’s are in 2/3?
- How many 5/12’s are in 1/2?
Baking Cookies
Alice, Raul, and Maria are baking cookies together. They need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. They each brought the ingredients they had at home. Alice brought 2 cups of flour and 1/4 cup of butter, Raul brought 1 cup of flour and 1/2 cup of butter, and Maria brought 1 1/4 cups of flour and 3/4 cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make?
Cup of Rice
Tonya and Chrissy are trying to understand the following story problem for 1÷2/3: One serving of rice is 2/3 of a cup. I ate 1 cup of rice. How many servings of rice did I eat? To solve the problem, Tonya and Chrissy draw a diagram divided into three equal pieces, and shade two of those pieces.
Tonya says, “There is one 2/3-cup serving of rice in 1 cup, and there is 1/3 cup of rice left over, so the answer should be 1 1/3.”
Chrissy says, “I heard someone say that the answer is 3/2=1 1/2. Which answer is right?”
Is the answer 1 1/3 or 1 1/2? Explain your reasoning using the diagram.
Dan’s Division Strategy
Dan observes that:
6/10÷2/10=6÷2
He says,
I think that if we are dividing a fraction by a fraction with the same denominator, then we can just divide the numerators.
Is Dan’s conjecture true for all fractions? Explain how you know.
Making Hot Cocoa
One mug of hot chocolate uses 2/3 cup of cocoa powder. How many mugs can Nelli make with 3 cups of cocoa powder?
a. Solve the problem by drawing a picture.
b. Explain how you can see the answer to the problem in your picture.
c. Which of the following multiplication or divisions equations represents this situation? Explain your reasoning.
3×2/3=? 3÷2/3=? 2/3÷3=?
d. Solve the arithmetic problem you chose in part (c) and verify that you get the same answer as you did with your picture.
Running to School
Rosa ran 1/3 of the way from her home to school. She ran 1/4 mile. How far is it between her home and school?
Traffic Jam
You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to get to the next exit, which is 1 1/2 miles away. You are timing your progress and find that you can travel 2/3 of a mile in one hour. If you continue to make progress at this rate, how long will it be until you reach the exit? Solve the problem with a diagram and explain your answer.
Video Game Credits
It requires 1/4 of a credit to play a video game for one minute.
a. Emma has 7/8 credits. Can she play for more or less than one minute? Explain how you know.
b. How long can Emma play the video game with her 7/8 credits?