Unit 2 Fractions As Quotients And Fraction Multiplication — Unit Plan

TitleAssessment
Lesson 1
Share Sandwiches
How Much?

  1. Draw a diagram to show how much sandwich each person will get.

    3 sandwiches are equally shared by 4 people.

  2. Explain or show how you know that each person gets the same amount of sandwich.
Show Solution

  1. Sample responses:

    Four squares. 

    Three squares.

    3 ovals. 

  2. Sample responses:
    • Each person gets one fourth of each sandwich. 
    • Each person gets one half plus one fourth of a sandwich. 
    • Each person gets 34\frac{3}{4} of a sandwich.
Lesson 2
Share More Sandwiches
How Much Sandwich?
  1. 4 sandwiches are equally shared by 5 students. How much sandwich does each student get? Explain or show your reasoning.
  2. Write a division expression to represent the situation.
Show Solution
  1. 45\frac{4}{5} sandwich. Sample response: Student draws 4 shapes to represent the sandwiches and partitions them. 4÷5=454\div5=\frac{4}{5}
  2. 4÷54\div5
Lesson 3
Interpret Equations
Share Water
3 liters of water are shared equally by 5 people. How much water does each person get? Write a division equation to represent the situation. Draw a diagram if it is helpful.
Show Solution

35\frac{3}{5} liters of water, 3÷5=353 \div 5 = \frac{3}{5}. Sample response:

diagrams

Lesson 4
Division Situations
How Much Milk?
Complete the table below.
Equation Situation

5 children share 4 cups of milk so each child gets the same amount of milk.
How many cups of milk will each child get?
Diagram

Show Solution

4÷5 =454 \div 5  = \frac {4}{5}

4 diagrams 

Lesson 5
Relate Division and Fractions
Explain It.

Explain why 8÷5=858 \div 5 = \frac{8}{5}.

Show Solution
Sample response: I can divide 8 into 5 equal parts. This is 8÷58 \div 5. Each of the parts is 15\frac{1}{5} of one whole and since there are 8 wholes, 8÷5=858\div5=\frac{8}{5}.
Section A Check
Section A Checkpoint
Problem 1

Five friends equally share 3 liters of water. How many liters of water does each person get? Explain or show your reasoning.

Show Solution

35\frac{3}{5} liter. Sample response:

<p>3 diagrams of equal length. 5 parts. 1 part shaded. Total length, 1 liter.</p>

Problem 2

Write a division equation that matches the diagram. Explain or show your reasoning.

4 diagrams of equal length. 3 equal parts. 1 part shaded. Total length, 1.

Show Solution
4÷3=434 \div 3 = \frac{4}{3}. Sample response: There are 4 wholes and they are divided into three equal shares. One of those shares is shaded and that’s 43\frac{4}{3} total shaded.
Problem 3

Explain why 10÷4=10410 \div 4 = \frac{10}{4}.

Show Solution

Sample response: If I divide 10 things each into 4 equal shares and take one of each, it is 10÷410 \div 4 since there are 4 equal shares in 10. Since each share is 14\frac{1}{4} and there are 10 of those shares, one for each thing, that’s also 104\frac{10}{4}.

Lesson 6
Relate Division and Multiplication
A Different Relay Race
  1. Lin and Han ran a 5 mile relay race as a team. They each ran the same distance. Draw a diagram to represent the situation.
  2. How far did each student run?
Show Solution
  1. Sample response:
    diagram
  2. 2122\frac{1}{2} miles or 52\frac{5}{2} mile. Sample response: The diagram shows 2 whole miles and 12\frac{1}{2} of another mile. 
Lesson 7
Divide to Multiply Unit Fractions
Another Race

Together, 6 children run a 5 mile relay race. They each run the same distance.

Select all the expressions that represent this situation.

  1. 16×5\frac{1}{6} \times 5
  2. 15×6\frac{1}{5} \times 6
  3. 5÷65 \div 6
  4. 56\frac{5}{6}
Show Solution
A, C, D
Lesson 8
Divide to Multiply Non-Unit Fractions
Two Thirds

Find the value of each expression. Explain or show your reasoning.

  1. 13×4\frac{1}{3}\times 4
  2. 23×4\frac{2}{3}\times 4
Show Solution
  1. 43\frac{4}{3} (or equivalent). Sample response: 4÷3=434\div3=\frac{4}{3}
  2. 83\frac{8}{3} (or equivalent). Sample response: I doubled the answer to the first question. 
Section B Check
Section B Checkpoint
Problem 1

3 diagrams of equal length. 5 equal parts. 1 part shaded. Total length, 1.

  1. Explain how the diagram shows 3÷53 \div 5.

  2. Explain how the diagram shows 3×153 \times \frac{1}{5}.

  3. What is the value of 3÷53 \div 5? Explain or show your reasoning.

Show Solution

  1. Sample response: There are 3 whole rectangles and 1 out of 5 equal shares of the rectangles is shaded. So, that’s 3÷53 \div 5.

  2. Sample response: There are 3 shaded parts and each is 15\frac{1}{5} of a whole rectangle. So, that's 3×153 \times \frac{1}{5}.

  3. 35\frac{3}{5}. Sample response: There are 3 shaded pieces and each is 15\frac{1}{5} of a whole rectangle.

Problem 2

Explain or show how each expression represents the shaded parts of the diagram.

  1. 2 ×(4 ÷3)2 \times (4 \div 3)
  2. 4×234 \times \frac{2}{3}
  3. 4×2×134 \times 2 \times \frac{1}{3}
Show Solution

Sample responses:

  1. Each rectangle is divided into 3 equal parts and 2 of them are shaded. So, that’s 2×(4÷3)2 \times (4 \div 3).
  2. There are 4 groups of 23\frac{2}{3} of a rectangle. So, that’s 4×234 \times \frac{2}{3}.
  3. There are 4 groups of 2 small parts and each one is 13\frac{1}{3} of a rectangle. So, that’s 4×2×134 \times 2 \times \frac{1}{3}.
Lesson 9
Relate Area to Multiplication
Fractional Pieces

Find the area of the shaded region. Explain or show your reasoning.

Area diagram, Length, 5. Width, 1 fourth.

Show Solution

54\frac{5}{4} or 1141 \frac{1}{4} square units. Sample response: I counted the shaded pieces which are fourths. I figured out that I had enough to fill one unit square and 14\frac{1}{4} of a second unit square.

Lesson 10
Fractional Side Lengths Less than 1
A Fractional Side Length

  1. Write a multiplication expression to represent the area of the shaded region.

    Area diagram, Length, 5. Width, 3 fourths.

  2. Find the area of the shaded region.

Show Solution
  1. 34×5\frac{3}{4} \times 5 or 5×345 \times \frac{3}{4}
  2. 154\frac{15}{4} or 3343 \frac{3}{4} square units
Lesson 11
Fractional Side Lengths Greater than 1
Find the Area

  1. Write a multiplication expression to represent the area of the shaded region.

    Area diagram, Length, 3 and 2 thirds. Width, 3.

  2. What is the area of the shaded region?

Show Solution
  1. 3×1133 \times \frac{11}{3} or 113×3\frac{11}{3} \times 3 or 11×33\frac{11 \times 3}{3} or 3×113\frac{3 \times 11}{3}
  2. 11 square units (or equivalent)
Lesson 12
Decompose Area
Decompose Rectangles

Find the area of the shaded region.

Area diagram. Length, 3 and 1 fourth. Width, 4. 

Show Solution

Sample responses:

  •  4×3144 \times 3 \frac{1}{4} square units
  • 13 square units
Lesson 13
Area and Properties of Operations
Equivalent Expressions

Select all the expressions that represent the area of the shaded region.

Area diagram. Length, 3 and 2 fifths. Width, 2. 

  1.  (2×3)+(2×25)(2 \times 3) + \left(2 \times \frac{2}{5}\right)
  2.  6256\frac{2}{5}
  3.  2×(3+25)2 \times \left(3 + \frac{2}{5}\right)
  4.  (2×4)−(2×35)(2 \times 4) - \left(2 \times \frac{3}{5}\right)
  5.  (2×3)+25(2 \times 3) + \frac{2}{5}
  6.  2×1752 \times \frac{17}{5}
Show Solution
A, C, D, F
Lesson 14
Area Situations
Find the Values

Find the value of each product. Show your thinking. Organize it so it can be followed by others.

  1. 53×15\frac{5}{3} \times 15
  2. 134×8\frac{3}{4} \times 8
  3. 1025×10\frac{10}{25} \times 10
Show Solution
  1. 753\frac{75}{3} or 25 (or equivalent). Sample response: I multiplied 15 and 5 and have that many 13\frac{1}{3}s.
  2. 14. Sample response: 8×1=88 \times 1 = 8 and 34×8=6\frac {3}{4} \times 8 = 6 and 8+6=148 + 6 = 14
  3. 10025\frac{100}{25} or 4 (or equivalent). Sample response: I multiplied 10 and 10 and have that many 125\frac{1}{25}s.
Lesson 15
Multiply More Fractions
Mixed Number Multiplication

Find the value of each expression. Explain or show your reasoning.

  1. 12×92312 \times 9 \frac {2}{3}
  2. 359×183 \frac {5}{9} \times 18
Show Solution
  1. 116. Sample response: 12×9+(12×23)=108+8=11612 \times 9 + \left(12 \times \frac {2}{3}\right) = 108 + 8 = 116
  2. 64. Sample response: (3×18)+(59×18)=54+10=64(3 \times 18) + \left(\frac {5}{9} \times 18\right) = 54 + 10 = 64
Lesson 16
Estimate Products
Estimate and Solve

Jada says the value of each product is about 20. For each problem, explain why Jada’s estimate is too high, just right, or too low.

  1. 556×4=‾5\frac{5}{6} \times 4 = \underline{\hspace{0.7cm}}

    20 is…

    too low

    too high

    about right

  2. 3×658=‾3 \times 6\frac{5}{8} = \underline{\hspace{0.7cm}}

    20 is…

    too low

    too high

    about right

Show Solution
  1. Too low. Sample response: 5565 \frac{5}{6} is very close to 6, and 6×4=246 \times 4 = 24. So, 556×4=23265\frac{5}{6}\times 4 = 23 \frac{2}{6}.
  2. About right. Sample response: 3×6=183 \times 6 = 18 and 58\frac{5}{8} is a little more than 12\frac{1}{2} so it's a little more than 18+3218 + \frac{3}{2}.
Lesson 17
Mosaic Pictures
No cool-down
Section C Check
Section C Checkpoint
Problem 1

For each diagram, write an expression for the area of the shaded region. Then find the area.

  1.  
    Area diagram. Length, 5. Width, 1 third. 

  2.  
    Area diagram. Length, 3. Width, 2 fourths. 

  3.  
    Area diagram, Length, 4. Width, 1 and 2 thirds.

Show Solution

  1. Expression: 13×5\frac{1}{3} \times 5 or 5×135 \times \frac{1}{3} (or equivalent). Area: 53\frac{5}{3} square units

  2. Expression: 24×3\frac{2}{4} \times 3 or 12×3\frac{1}{2} \times 3 (or equivalent). Area: 64\frac{6}{4} square units

  3. Expression: 53×4\frac{5}{3} \times 4 (or equivalent). Area: 13\frac{1}{3} square units

Problem 2

Clare made a flag that is 2 meters long and 35\frac{3}{5} meter wide. What is the area of the flag? Explain or show your reasoning.

Show Solution
65\frac{6}{5} m. Sample response:  2×35=652 \times \frac{3}{5} = \frac{6}{5}
Problem 3

Find the value of each expression.

  1. 15×10\frac{1}{5} \times 10

  2. 523×45\frac{2}{3} \times 4

  3. 134×5\frac{13}{4} \times 5

Show Solution
  1. 105\frac{10}{5} or 2 (or equivalent)
  2. 208320 \frac{8}{3} or 683\frac{68}{3} (or equivalent)
  3. 654\frac{65}{4} (or equivalent)