How long does it take?
This unit involves students in looking at the lengths of time various activities take and calculating how long is spent on these activities in a week.
- estimate the time taken for daily activities in hours and minutes
- use advanced counting or partitioning strategies to solve problems involving minutes and hours
- check the reasonableness of answers obtained using a calculator
Two aspects of mathematics are explored in this unit on time:
- investigations of the length of time taken for various activities, working in hours and minutes.
- calculations involving hours and minutes. It is anticipated students would be at the advanced counting or early additive strategy stages of the number framework and could use repeated addition, skip counting, multiplication or division to solve these problems.
time, hours, minutes, estimate, estimation, reasonable, unreasonable, most, least, compare, activities,
- Begin a discussion about activities that students are involved in every week.
- Brainstorm a list of things such as sleeping, playing, and eating.
- Once the list is complied discuss how often the activities occur. Are they daily, just on school days or a few times a week?
- Explain that this week they are going to look more carefully at some of these activities and work out how long they spend on them over the course of a week.
- Have the students work in pairs to choose one of the activities from the list, and calculate how long they spend on this activity each week. Copymaster One can be used to help guide this process. You may need to help the students select which activity to focus on to ensure the process is not too complicated.
- As students work, help them with the numbers involved and discuss the strategies they are using.
How could we work out what seven lots of 2 are all together?
How do you know 5 lots of 5 minutes is 25 minutes altogether?
How could you check?
- Encourage students to discuss the methods they are using. If students are familiar with the + and - symbols and their meaning use the calculator as a way for students to confirm their answers. Encourage students to check the answers the calculator gives them are reasonable.
If we know 2 lots of 5 are ten is it reasonable for 5 lots of 5 to be 8 which is less than that?
- At the conclusion of the session bring all students together to report their findings and discuss these.
How long do you think you would spend brushing your teeth in a week? What did Jane’s group find out?
From our calculations which activity takes the most of our time over the course of a week? Which takes the least?
Emphasise that the calculations they have done are based on estimates and are not statements of fact.
- Show students Copymaster 2.
- Over the course of the next few days look at the statements individually and assess whether or not they are reasonable. You need not look at all the statements, but work at the pace of your students and cover as many as appropriate.
- For each statement have the students work in pairs to do their own calculations to check the statements. Copymaster 3 can be used to guide this process.
- Encourage the students to compare their ideas about what times they think are reasonable for the various activities as well as their methods for calculating to check the statements.
- A calculator could be used as a final check with students encouraged to confirm the reasonableness of the answers provided with mental calculations.
- At the end of each session have students share their findings. The types of questions you might use to help develop students understanding include:
How many minutes in an hour? In half an hour?
How did you work out how long she spends each day?
How could you check your calculations?
Is it reasonable to spend that long to brush your teeth? How long do you think it takes you?
- Show students Copymaster 4. Use the same process as above to decide which statements are reasonable and which ones are unreasonable.
- Compare the times taken by Sally for the various activities, with those taken by Hone.
Who takes the longest?Copymaster 5 can help in these comparisons.
How much longer do they take?
How does this compare with how long you would take to do that?
- Have students work in pairs to write their own set of statements about the time spent on different activities in a week.
- Get the students to write three statements but make only two of them reasonable and one unreasonable. Copymaster 6 can be used to record their statements.
- Once the statements are written have the pairs of students swap statements and work out which one of the other group’s statements is unreasonable.
- Can they describe to the other group how they found it and why they think it is unreasonable? Does the other group agree?
- As a conclusion to the session have students share their experiences.
Did you find the statement that was unreasonable? How?
What made you think it was the unreasonable one? How did you check?
- Discuss both the strategies used in calculations to check the reasonableness of the answers and the lengths of time taken for various activities. Discussion may cover debate about what is a reasonable length of time taken for a particular activity if required.