Name Date 5.NF.B.4.A 4.NF.B.4.C Class

Multiplying Fractions & Whole NumbersKey Takeaways

Standard: 5.NF.B.4.A: Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

4.NF.B.4.C: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 

Previously, we multiplied fractions and whole numbers in which the number of groups was whole and the size of each group was a fraction. Now, we know that we can multiply fractions and whole numbers in which the number of groups is fractional and the size of the group is whole, as we are finding a fractional group.

Vocabulary: Numerator: The numerator contains the number of those parts being described by the fractionDenominator: The denominator of a fraction shows how many equal parts or pieces the whole has been split intoEquivalent fractions: Fractions that represent the same number are called equivalent fractions.Improper fraction: When a fraction’s numerator is greater than the fraction’s denominatorMixed number: A whole number and fractionConvert: To changeBenchmark/Landmark: Common fractions or numbers that are end points or easy to recognize are benchmark numbers. For example, 0, ½, and 1 are all benchmarks.___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Activating Prior Knowledge

An espresso mug can hold 38 cup of coffee. Ms. Simmons has five of these espresso mugs.

1) How much total coffee, in cups, can Ms. Simmons pour into her espresso mugs? Use the model below to solve.

2) Which values below represent the total amount of coffee, in cups, that Ms. Simmons can pour into her espresso mugs? Select the three correct answers.

A. 158

B. 5+ 38

C. (5×3)8

D. (5+3)8

E. 15× 18

F. 15+ 18

3) What action or relationship is in this problem? What type of conceptual key would we use?

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Let’s Explore!

Micah has 8 pencils in his backpack. He moves 34 of the pencils to his pencil case.

1) How many pencils are in his pencil case? Use the pencil diagram to model and solve this problem.

2) Explain how you used the pencil diagram to model and solve this problem.

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3) Which expression represents this problem?A. 34 +8

B. 34 ×8

C. 8+ 34D. 8× 34

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Reflect:How were the two examples the same? How are they different?

Activation of Prior Knowledge ExploreAn espresso mug can hold 38 cup of coffee. Ms. Simmons has five of these espresso mugs. How much total coffee, in cups, can Ms. Simmons pour into her espresso mugs?

Micah has 8 pencils in his backpack. He moves 34 of the pencils to his pencil case. How many pencils are in his pencil case?

5× 38

34×8

Groups:

Size:

Total:

Groups:

Size:

Total:

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Independent Practice (Mild)Let’s compare each of these problems and their models to put it all together.

Problem 1A pizza shop makes 12 pizzas and sells 23 of the pizzas to a school nearby.

1) Based on the model, how many pizzas did the school purchase?

2) Which expression best represents this problem?A. 23×12

B. 12× 23

Problem 2There are 12 people out to dinner. Each person eats 23 of a small pizza. How many small pizzas were eaten in all?

1) Based on the model, how many small pizzas were eaten in all?

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2) Which expression best represents this problem?A. 23×12

B. 12× 23

How do the solutions to each problem compare? What does this tell us about multiplication?

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Directions: Use the model to solve. Then, write a multiplication number sentence to represent the problem.

3) Find 14 of 8.

Model Multiplication Number Sentence

14×8=¿¿

4) Find 8 sets of 14 .

Model Multiplication Number Sentence

5) Find 56 of 18.

Model Multiplication Number Sentence6

6) Find 4 sets of 56 .

Model Multiplication Number Sentence

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Independent Practice (Medium)7) There are 16 players on Benjamin’s baseball team. For a snack, each player eats

34 cup of pretzels. How many total cups of pretzels are needed for the team’s snack?

8) There are 20 soccer balls in the supply closet. Mr. Condron uses 35 of them during gym class. How many soccer balls were used during gym class?

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Independent Practice (Spicy)9) Three friends went apple picking. Julie picked 25 apples, Erin picked 15 apples,

and Michael picked 10 apples. All of the apples picked were shared equally by the three friends. Which expression represents the number of apples each friend got to keep? Show your work.

A. 43 × 50

B. 13 × 50

C. 34 × 50

D. 14 × 50

10) There are 16 girls on Jamira’s basketball team. 36 of the team

eats an orange at halftime. How many girls ate an orange at halftime?

A. 8 orangesB. 16 orangesC. 32 orangesD. 48 oranges

11) There are 90 students in the 6th grade. 2

5 of the 6th graders buy a hot lunch at school.

16 of the 6th graders buy sandwiches at school.

29 of the 6th graders bring their lunch to school.

Determine the number of students who fall into each category below.

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Hot Lunch Sandwiches Bring Lunch

12) There are 80 students in the 8th grade. They are required to supply their own markers for an upcoming project.

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of the 8th graders bring boxes of markers that hold 12 each.

35 of the 8th graders bring boxes of markers that hold 8 each.

The rest of the 8th graders bring boxes of markers that hold 10 each.

A. Determine the number of students that bring each type of markers.

Boxes of 12 Boxes of 8 Boxes of 10

B. How many markers do the 8th graders bring in all for the project?

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Name Date 5.NF.B.4.A 4.NF.B.4.C Class

Multiplying Fractions & Whole NumbersExit Ticket

1) A bakery makes 12 cupcakes and sells 34 of them to one customer for a birthday party. How many of the cupcakes were sold for the birthday party?

2) A bakery uses 34 cup of sugar for each batch of muffins that it makes. If the bakery makes 5 batches of muffins, how many cups of sugar will it need?

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Name Date 5.NF.B.4.A 4.NF.B.4.C Class

Multiplying Fractions & Whole NumbersHomework

1) A friend has 16 video games and sells 38 of them back to the game shop. How many of the games were sold?

2) One subject of homework takes a student 13 of an hour to complete. If the student has 6 subjects and each takes the same amount of time, how long will all the homework take?

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3) Which expression is equivalent to 6× 23?

A. 3× 13B. 4× 13C. 8× 13D. 12× 13

4) Write a multiplication expression to represent this model.

5) Ms. Simmons was having a pizza party! She spent a total of $36 on pizza. She orders

an equal amount of cheese, pepperoni, and veggie pizza. What fraction of her cost is spent on cheese and pepperoni? How much money does this represent?

A. Use the diagram below to model this problem.

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B. Write an expression to represent the total cost of the pepperoni and cheese pizzas and then solve.

6) Write a multiplication expression to represent this model.

7) Deonte spends 45 of his time at soccer practice practicing passing. His soccer practice is 3 hours total. How many hours did Deonte spend practicing passing?

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