Question 1

This project helps us understand how we spend our time by collecting data and calculating averages.

Step 1 — Understanding the Project

We need to track our daily activities for a week. Then, we will calculate the average time for each activity. We will create an activity strip to show this average day visually. Finally, we will compare our data with an adult's data.

Step 2 — Data Collection (Example)

Let us choose a set of common activities. We will track the time spent on each activity for 7 days. Let $T_{\text{activity, day}}$ be the time spent on an activity on a specific day. We record this data daily. After 7 days, we sum up the time for each activity. Let $T_{\text{total, activity}}$ be the total time for an activity over 7 days. Here is an example of total hours for one student over 7 days:

• Sleeping: 60 hours
• School: 35 hours
• Homework: 10 hours
• Playing Outdoors: 15 hours
• Screen Time: 20 hours
• Eating: 14 hours
• Other Activities: 14 hours

We check if the total hours sum up to $7 \times 24 = 168$ hours. $60 + 35 + 10 + 15 + 20 + 14 + 14 = 168 \text{ hours}$ The total time is correct.

Step 3 — Calculating Average Time

The average time for an activity is its total time divided by 7 days. Let $A_{\text{activity}}$ be the average time for an activity. $A_{\text{activity}} = \frac{T_{\text{total, activity}}}{7}$

Let us calculate the average time for each activity:

• Average Sleeping Time: $A_{\text{Sleeping}} = \frac{60 \text{ hours}}{7}$

  $\boxed{8.57 \text{ hours}}$

• Average School Time: $A_{\text{School}} = \frac{35 \text{ hours}}{7}$

  $\boxed{5.00 \text{ hours}}$

• Average Homework Time: $A_{\text{Homework}} = \frac{10 \text{ hours}}{7}$

  $\boxed{1.43 \text{ hours}}$

• Average Playing Outdoors Time: $A_{\text{Outdoors}} = \frac{15 \text{ hours}}{7}$

  $\boxed{2.14 \text{ hours}}$

• Average Screen Time: $A_{\text{Screen Time}} = \frac{20 \text{ hours}}{7}$

  $\boxed{2.86 \text{ hours}}$

• Average Eating Time: $A_{\text{Eating}} = \frac{14 \text{ hours}}{7}$

  $\boxed{2.00 \text{ hours}}$

• Average Other Activities Time: $A_{\text{Other}} = \frac{14 \text{ hours}}{7}$

  $\boxed{2.00 \text{ hours}}$

We can sum these averages to check if they add up to 24 hours (approximately). $8.57 + 5.00 + 1.43 + 2.14 + 2.86 + 2.00 + 2.00 = 24.00 \text{ hours}$ The sum is correct.

Step 4 — Representing Data on an Activity Strip

An activity strip is a visual bar graph. It shows how an average day's 24 hours are divided. We can draw a strip of a certain length, say 24 cm. Each centimeter represents 1 hour. Then, we divide this 24 cm strip into segments. The length of each segment will be equal to the average time for that activity. For example, the sleeping segment would be 8.57 cm long. The school segment would be 5.00 cm long. We would label each segment with its activity.

Step 5 — Tracking Adult's Activities and Comparison

We follow the same steps for an adult at home. We track their activities for 7 days. Then, we calculate the average time for each of their activities. For example, let us say an adult's average screen time is 4.00 hours. We compare our average screen time (2.86 hours) with theirs (4.00 hours). We can see that the adult spends more time on screens in this example. We can compare all activities this way.

Answer

(i) For our example, we assume eating and sleeping happen at fairly regular times each day. Typically, we spend about 2.14 hours outdoors on average. (ii) The average time spent per activity is calculated in Step 3. An activity strip can be made by drawing a 24 cm line, where each cm represents 1 hour, and marking segments for each average activity time. (iii) To track an adult's activities, we record their daily schedule for 7 days and calculate their average times, just like we did for ourselves. Then, we compare the average times for each activity to see similarities and differences. For instance, we might find that the adult spends more time working and less time playing.