standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
The purpose of this activity is for students to think about different activities they might participate in during free time, to define a smaller set of categories, and to collect data. A significant part of this activity is the definition of the categories, which is an important aspect of mathematical modeling (MP4). Encourage students to convert the time for their activities from minutes to hours. Students may notice that some fractions are more meaningful in the context of time such as half, third, and quarter of an hour. Students will further explore the relationship between time and fractions in the activity synthesis.
If a student sees that a specific activity is not on the poster, have them consider if there is an umbrella activity. For example, “What category, that is on a poster, might talking to your friends go under?”
Engagement: Develop Effort and Persistence.
Invite students to generate a list of shared expectations for group work. Record responses on a display and keep visible during the activity.
Supports accessibility for: Social-Emotional Functioning, Attention
Launch
Groups of 4
“What are some things you do or like to do if you have free time on the weekend?” (sleep, play video games, play sports, spend time with family, social media, read, go to the movies)
Activity
“For this activity, you’ll think about how you might spend 2 hours of free time and then we’ll record the time we spend for some of those activities.”
“As you work, I will write down the different categories of your responses on the posters hanging around the room. You will record your times on the posters.”
As students work, monitor for 4–6 popular activities and write the titles of these activities on the large pieces of poster paper. If necessary, list some examples of the umbrella category.
8–10 minutes: independent work time
Monitor for students who record using multiples of
\(\frac{1}{2}\)
,
\(\frac{1}{4}\)
, and
\(\frac{1}{8}\)
of an hour.
Student Facing
Imagine on the weekend you have 2 hours of free time that you can spend any way you like.
How would you spend it? Record your answer in fractions of an hour. Show your reasoning.
Record the time for each activity from your list on the appropriate poster, if there is a category for it.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“Look at the data of the different categories around the room. What do you notice?” (Most people recorded using halves and fourths. More students play games than read books. There is more data on one poster than on another. There are more small numbers on one poster, it’s hard to compare because there are so many numbers and they are not in any order.)
If it doesn’t come up, ask, “Why did most people record time as multiples of
\(\frac{1}{2}\)
and
\(\frac{1}{4}\)
?” (Because half of 60 minutes is 30 and half of that is 15. I can easily see that on the clock.)
“Does it make sense to talk about time using
\(\frac{1}{8}\)
or
\(\frac{1}{7}\)
of an hour?” (Yes but it’s not a whole number of minutes like
\(\frac{1}{2}\)
hour or
\(\frac{1}{4}\)
hour.)
“What are some ways we can organize the data?” (Bar graph, line plot, chart, list the numbers in order.)


aligns: no