standard_description: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
problem_activity: Narrative
The purpose of this activity is for students to find the missing value in equations involving a whole number and a fraction. They find missing factors or products to make equations true. Many of the problems encourage students to think in steps, interpreting a fraction
\(\frac{a}{b}\)
in terms of division by the denominator and multiplication by the numerator.
Representation: Internalize Comprehension
. Synthesis: Invite students to identify which details were most important to solve the problems. Display the sentence frame: “The next time I solve multiplication problems of a whole number by a fraction, I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing, Memory
Launch
Groups of 2
Activity
5–8 minutes: independent work time
1–2 minutes: partner discussion
Monitor for:
partners who use different strategies.
students who are challenged but persevere and arrive at a viable solution.
Student Facing
Fill in the blanks to make each equation true. Be prepared to explain your reasoning.
\(\frac{1}{3} \times 18 =\underline{\hspace{0.7cm}}\)
\(\frac{7}{9} \times \underline{\hspace{0.7cm}} = \frac{21}{9}\)
\(\frac{1}{15} \times \underline{\hspace{0.7cm}} = 2\)
\(9 \times  6 \frac{2}{3}  = \underline{\hspace{0.7cm}} \)
\(14 \frac {99}{100} \times 10 = \underline{\hspace{0.7cm}} \)
\(7 \frac {3}{5} \times 6 = \underline{\hspace{0.7cm}}\)
\(4 \times 6 \frac {9}{10} = \underline{\hspace{0.7cm}}\)
Student Response
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Advancing Student Thinking
If students do not get the correct solution for the missing factor problems, ask “How would you represent this expression with a diagram?”
Activity Synthesis
Ask previously selected students to share their responses.
“What was different about you and your partner's strategies?”
“Which problem did you find most challenging and why?”
“Which problem made the most sense to you and why?”


aligns: yes