Unit 3 Multiplying And Dividing Fractions — Unit Plan

Title	Takeaways	Assessment
Lesson 1 One Piece of One Part	—	Macaroni and Cheese (1 problem) A pan of macaroni and cheese is $\frac{1}{2}$ full. Mai eats $\frac{1}{5}$ of the remaining macaroni and cheese in the pan. Draw a diagram to represent the situation. How much of the whole pan did Mai eat? Explain or show your reasoning. Show Solution Sample response: $\frac{1}{10}$ of the whole pan. Sample response: Student may refer to the diagram they drew.
Lesson 2 Represent Unit Fraction Multiplication	—	How Much is Shaded? (1 problem) Write a multiplication expression to represent the area of the shaded region. Show Solution $\frac {1}{4} \times \frac {1}{2}$ or $\frac {1}{2} \times \frac {1}{4}$
Lesson 3 Multiply Unit Fractions	—	Multiplication Equations (1 problem) Write a multiplication equation to represent the shaded piece in the figure. Explain or show your reasoning. Complete each equation. Draw a diagram if it helps you. $\frac{1}{5} \times \frac{1}{4} = \underline{\hspace{1 cm}}$ $\frac{1}{2} \times \frac{1}{6} = \underline{\hspace{1 cm}}$ Show Solution $\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$ . Sample response: There is $\frac{1}{3}$ of a column shaded and that column is $\frac{1}{3}$ of the square. The shaded piece is $\frac{1}{9}$ of the square. $\frac{1}{5} \times \frac{1}{4} = \frac{1}{20}$ $\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$
Lesson 4 Situations about Multiplying Fractions	—	Area of the Park (1 problem) Here is a diagram for a park. Diagram. Rectangle partitioned into 4 rows of 2 of the same size, but different colored rectangles. 3 yellow rectangles, labeled soccer. 3 red rectangles, labeled swings. 2 blue rectangles, labeled basketball. Write a multiplication expression to represent the fraction of the park that is for soccer. How much of the whole park will be used for soccer? Show Solution $\frac{3}{4} \times \frac{1}{2}$ or $\frac{1}{2} \times \frac{3}{4}$ $\frac{3}{8}$
Lesson 5 Multiply a Unit Fraction by a Non-Unit Fraction	—	Write an Equation (1 problem) Find the value of $\frac{1}{3} \times \frac{4}{5}$ . Explain or show your reasoning. Use the diagram if it is helpful. Show Solution $\frac{4}{15}$ . Sample response: There are 4 shaded pieces and each is $\frac{1}{15}$ of the whole.
Lesson 6 Multiply Fractions	—	What is the Area? (1 problem) Write a multiplication expression to represent the area of the shaded region in square units. What is the area of the shaded region in square units? Show Solution $\frac{2}{4} \times \frac{5}{6}$ (or equivalent) $\frac{10}{24}$ (or equivalent)
Lesson 7 Generalize Fraction Multiplication	—	Multiply Fractions (1 problem) Find the value that makes each equation true. $\frac{3}{4} \times \frac{10}{12} = \underline{\hspace{1cm}}$ $\frac{7}{5} \times \underline{\hspace{1cm}} = \frac{42}{15}$ Show Solution $\frac{30}{48}$ (or equivalent) $\frac{6}{3}$ (or equivalent)
Lesson 8 Work with Mixed Numbers	—	Mixed Number Product (1 problem) Find the value of $2\frac{2}{3} \times 3\frac{1}{2}$ . Show Solution $\frac{56}{6}$ (or equivalent expression or value). Sample responses: I made a diagram then added up the partial products: $6+1+2+\frac{2}{6}$ . I wrote fractions: $2=\frac{6}{3}$ so $2\frac{2}{3}$ is $\frac{8}{3}$ , and $3=\frac{6}{2}$ so $3\frac{1}{2}$ is $\frac{7}{2}$ . Then I multiplied $\frac{8}{3}\times\frac{7}{2}$ or $\frac{8\times7}{3\times2}$ to get $\frac{56}{6}$ .
Lesson 9 Apply Fraction Multiplication	—	The Flag of Chad (1 problem) The area of this flag of Chad is $25\frac{1}{2}$ square centimeters. The blue, yellow, and red sections are all equal. What is the area of the blue part of the flag? Explain or show your reasoning. Show Solution $\frac{1}{3} \times 25\frac{1}{2}$ , $\frac{51}{6}$ , or $8\frac{1}{2}$ square centimeters (or equivalent)
Section A Check Section A Checkpoint		Problem 1 Write a multiplication expression that represents the area of the shaded region. Explain or show your reasoning. Show Solution $\frac{1}{3} \times \frac{1}{8}$ or $\frac{1}{8} \times \frac{1}{3}$ . Sample response: $\frac{1}{3}$ of $\frac{1}{8}$ of the square is shaded. So, that's $\frac{1}{3} \times \frac{1}{8}$ . Problem 2 Find the value of each expression. Draw a diagram if needed. $\frac{1}{4} \times \frac{1}{5}$ $\frac{2}{3} \times \frac{3}{4}$ $\frac{5}{4} \times \frac{5}{6}$ Show Solution $\frac{1}{20}$ $\frac{6}{12}$ or $\frac{1}{2}$ $\frac{25}{24}$ or $1\frac{1}{24}$ Problem 3 A rectangular garden is $2\frac{1}{2}$ meters wide and $4\frac{1}{2}$ meters long. What is the area of the garden? Explain or show your reasoning. Show Solution $11\frac{1}{4}$ square meters (or equivalent). Sample response: $2 \times 2\frac{1}{2}$ is 5 so $4 \times 2\frac{1}{2} = 10$ . Then $\frac{1}{2} \times 2 = 1$ and $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ . So, that’s $10 + 1 + \frac{1}{4}$ or $11\frac{1}{4}$ square meters.

Lesson 10 Concepts of Division	—	Reason About Division (1 problem) What new idea did you have about division today? What questions do you have about division with fractions? Show Solution Sample responses: There is a pattern that when the dividend remains the same and the divisor gets smaller, the quotient gets larger. Is dividing fractions the same as dividing whole numbers? How do you divide something by $\frac{1}{2}$ ?
Lesson 11 Divide Unit Fractions by Whole Numbers	—	Share Macaroni and Cheese (1 problem) 6 people equally share $\frac {1}{2}$ a pan of macaroni and cheese. Draw a diagram to represent the situation. Write a division expression to represent the situation. How much of the whole pan does each person get? Show Solution Sample responses: Student may draw a diagram that shows $\frac {1}{2}$ being divided into 6 equal pieces. $\frac {1}{2} \div 6$ $\frac {1}{12}$
Lesson 12 Represent Division of Unit Fractions by Whole Numbers	—	Evaluate Division Expressions (1 problem) Write a division expression for the shaded region. Explain or show your reasoning. What fraction does the shaded region represent? Explain or show your reasoning. Show Solution $\frac{1}{5} \div 2$ . Sample response: The tape is divided into fifths and then the fifth is divided into 2 equal pieces. $\frac{1}{10}$ . Sample response: There are 10 of those pieces in the whole.
Lesson 13 Divide Whole Numbers by Unit Fractions	—	A Different Strip of Paper (1 problem) Han has a strip of paper that is 3 feet long. He cuts it into pieces that are $\frac{1}{4}$ foot long. How many pieces are there? Explain or show your reasoning. Show Solution 12 pieces. Sample response: Each foot will have 4 pieces, so that is 12 pieces all together.
Lesson 14 Represent Division of Whole Numbers by Unit Fractions	—	Solve and Match the Expression (1 problem) A package has 2 cups of raisins. Each serving of raisins is $\frac{1}{4}$ cup. Does this situation match the expression $2 \div \frac{1}{4}$ or $\frac{1}{4} \div 2$ ? Explain or show your reasoning. How many servings of raisins are there in the package? Explain or show your reasoning. Show Solution $2 \div \frac{1}{4}$ . Sample response: The 2 cups is being divided into servings that are each $\frac{1}{4}$ cup. 8. Sample response: Each cup has four $\frac{1}{4}$ cup, so that’s 8 total.
Lesson 15 Fraction Division Situations	—	Match and Solve (1 problem) Match each expression to a situation. Answer each question. $5 \div \frac {1}{4}$ $\frac {1}{4} \div 5$ Han cut 5 feet of ribbon into pieces that are $\frac {1}{4}$ foot long. How many pieces are there? Han cut a $\frac {1}{4}$ foot long piece of ribbon into 5 equal pieces. How long is each piece? Show Solution $5 \div \frac {1}{4}$ , 20 pieces. $\frac {1}{4} \div 5 = \frac {1}{20}$ , $\frac {1}{20}$ foot long.
Lesson 16 Reason about Quotients	—	Both Types of Problems (1 problem) Which is greater, $5 \div \frac{1}{3}$ or $\frac{1}{3} \div 5$ . Explain or show your reasoning. Show Solution $5 \div \frac{1}{3}$ . Sample response: $5 \div \frac{1}{3}$ is greater than 1 because there are a lot more than one thirds in 5. $\frac{1}{3} \div 5$ is less than 1 because $\frac{1}{3}$ is being divided into smaller pieces.
Section B Check Section B Checkpoint		Problem 1 Write a division expression that represents the shaded piece of the diagram. Write a multiplication expression that represents the shaded piece of the diagram. Show Solution $\frac{1}{3} \div 4$ $\frac{1}{4} \times \frac{1}{3}$ Problem 2 Find the value of each expression. Draw a diagram if it helps. $\frac {1}{3} \div 5$ $\frac {1}{6} \div 4$ $\frac {1}{8} \div 3$ Show Solution $\frac{1}{15}$ $\frac{1}{24}$ $\frac{1}{24}$ Problem 3 Kiran made 12 liters of juice for a party. A serving of juice is $\frac{1}{4}$ liter. How many servings of juice does Kiran have? Explain or show your reasoning. Show Solution 48 servings. Sample response: 12 liters is the total amount. If you split each liter into fourths, you'd have four servings for each liter. $12 \div \frac{1}{4}$ is the same as $12 \times 4$ , so the answer is 48.

Lesson 17 Fraction Multiplication and Division Situations	—	How Much Milk? (1 problem) A container has 2 cups of milk in it. How many $\frac{1}{4}$ cups of milk are in the container? Explain or show your reasoning. A container has 2 cups of milk in it. The container is $\frac{1}{3}$ full. How many cups does the container hold? Explain or show your reasoning. Show Solution 8. Sample response: $2 \div \frac{1}{4} = 8$ 6. Sample responses: $2 \div \frac{1}{3} = 6$ or $3 \times 2 = 6$
Lesson 18 Represent Situations with Multiplication and Division	—	Diagrams and Equations (1 problem) Write a multiplication equation represented by the diagram. Explain or show your reasoning. Write a division equation represented by the diagram. Explain or show your reasoning. Show Solution $6 \times \frac{1}{3} = 2$ , the diagram shows 6 groups of $\frac{1}{3}$ and the total value is 2. $2 \div \frac{1}{3} = 6$ , the diagram shows that there are 6 groups of $\frac{1}{3}$ in 2.
Lesson 19 Fraction Games	—	Fill in the Blanks (1 problem) Use the numbers 6, 7, 8, and 9 to make the greatest product. Explain how you know it is the greatest product. $\frac{\boxed{\phantom{\frac{000}{00}}}}{\boxed{\phantom{\frac{000}{000}}}}\times\frac{\boxed{\phantom{\frac{000}{00}}}}{\boxed{\phantom{\frac{00}{000}}}}$ Show Solution $\frac{9}{6} \times \frac{8}{7}$ (or equivalent). Sample response: It’s the greatest because I used the two largest numbers for numerators and the two smallest numbers for denominators.
Lesson 20 Recipes and Fractions	—	No cool-down
Section C Check Section C Checkpoint		Problem 1 Three friends equally share $\frac{1}{2}$ kg of cherries. Write a division expression that represents this situation. Write a multiplication expression that represents this situation. How many kilograms of cherries did each friend get? Explain or show your reasoning. Show Solution $\frac{1}{2} \div 3$ $\frac{1}{3} \times \frac{1}{2}$ (or equivalent) $\frac{1}{6}$ kg. Sample response: I just found the value of $\frac{1}{3} \times \frac{1}{2}$ . Problem 2 The trail is $3 \frac{1}{4}$ miles long. Mai walked $\frac{1}{3}$ of the trail. How many miles did Mai walk? Explain or show your reasoning. Show Solution $1 \frac{1}{12}$ miles. Sample response: $\frac{1}{3}$ of 3 is 1 and $\frac{1}{3}$ of $\frac{1}{4}$ is $\frac{1}{3} \times \frac{1}{4}$ or $\frac{1}{12}$ .
Unit 3 Assessment End-of-Unit Assessment