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 relate multiplying a non-unit fraction by a whole number to multiplying a unit fraction by the same whole number. After finding the value of
\(\frac{1}{5} \times 3\)
in a way that makes sense to them, they then consider the value of the products
\(\frac{2}{5} \times 3\)
and
\(\frac{3}{5} \times 3\)
. In the synthesis students address how they can use the value of
\(\frac{1}{5} \times 3\)
to find the value other expressions.
Launch
Groups of 2
Activity
8 minutes: independent work time
Monitor for students who:
draw a diagram
use division to solve
recognize a relationship between
\(\frac{1}{5}\times3\)
,
\(\frac{2}{5}\times3\)
, and
\(\frac{3}{5}\times3\)
.
Student Facing
Find the value of each expression. Explain or show your reasoning. Draw a diagram if it is helpful.
\(\frac{1}{5} \times 3\)
\(\frac{2}{5} \times 3\)
\(\frac{3}{5} \times 3\)
Student Response
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Activity Synthesis
Ask previously selected students to share their solutions.
Display:
\(\frac{1}{5} \times 3\)
,
\(\frac{2}{5} \times 3\)
,
\(\frac{3}{5} \times 3\)
“How are the expressions the same?” (They all have a 3. They all have some fifths and there is a product.)
“How are the expressions different?” (The number of fifths is different. There is 1 and then 2 and then 3.)
“How can you use the value of
\(\frac{1}{5} \times 3\)
to help find the value of
\(\frac{2}{5} \times 3\)
?” (I can just double the result because it’s
\(\frac{2}{5}\)
instead of
\(\frac{1}{5}\)
.)
“What about
\(\frac{3}{5} \times 3\)
?” (That’s just another
\(\frac{1}{5} \times 3\)
.)
Display diagram from student solution or a student generated diagram like it.
“How does the diagram show
\(\frac{1}{5} \times 3\)
?” (There is 3 total and
\(\frac{1}{5}\)
of it is shaded.)
Display:
\(\frac{2}{5} \times 3\)
.
“How could you adapt the diagram to show
\(\frac{2}{5} \times 3\)
?” (I could fill in 2 of the fifths in each whole instead of 1.)
“In the next activity we will study a diagram for
\(\frac{2}{5} \times 3\)
more.”


aligns: no