*Measurement progression, 4th step *

In this activity, the learners become familiar with converting from one unit of time to another.

## The teaching points

- Some ‘conversion factors’ for time are 60 minutes in one hour, 24 hours in one day and seven days in a week.
- When you change from one unit of time to another unit of time, the amount of time stays the same; you are just giving it a different name.
- If you are converting from a smaller unit of time to a bigger unit of time, you expect less of the bigger unit and therefore divide by the conversion factor. For example, to change minutes (small) to hours (big) you divide by 60.
If you are converting from a bigger unit of time to a smaller unit of time, you expect more of the smaller unit and therefore multiply by the conversion factor. For example, to change weeks (big) to days (small) you multiply by seven.

Note: These last three principles apply whenever you want to change a quantity given in one unit of measurement into another unit of measurement, for example, changing a measurement made in millimetres into metres.

- Developing conceptual understanding of division. One of the reasons learners have difficulty solving word-based problems is that they do not have sufficient conceptual understanding of addition, subtraction, multiplication, and division (particularly division) to make correct choices of which to use to solve a problem.
- Discuss with the learners the fact that time is not a decimal system like our number system. When problems with time are solved using a calculator and the answer includes a decimal fraction, this represents tenths, hundredths or thousandths of a unit of time rather than days, minutes, etc. For example, 2.4 hours is 2 and 4 tenths hours (2 hours 24 minutes) not 2 hours 4 minutes.

## Resources

## The guided teaching and learning sequence

1. Write “120 minutes” on the board and ask the learners how many hours it is. When they reply “two hours”, ask “How did you work that out?”

In the discussion, listen for and highlight the fact that you have to know that one hour is 60 minutes and you have to find out how many 60 minutes are in 120 minutes.

Write “How many 60 minutes are in 120 minutes?” on the board and highlight the use of division by writing 120 divided by 60, 120 ÷ 60, and 120/60 next to the question.

2. Write “21 days” on the board, and ask the learners how many weeks it is.

Repeat the process from 1 above.

3. Write “five hours” on the board and ask the learners how many minutes are in five hours. When they reply “300 minutes”, ask “How did you work that out?”

In the discussion, listen for and highlight the fact that you have to know that one hour is 60 minutes, and you have five hours, so that is five times 60 minutes or 300 minutes.

Write the words and the symbols for five times 60 minutes on the board.

4. Write “six weeks” on the board and ask the learners how many days are in six weeks. Repeat the process from 3 above.

(If the learners are able to multiply with multidigit numbers, you could ask how many hours are in six weeks).

5. Ask:

“How do you know when to multiply and when to divide?”

Listen for, and reinforce, the response that you multiply when you change from a bigger unit to a smaller unit, and divide when you are moving from a smaller unit to a bigger unit.

6. Draw attention to the fact that 120 minutes is two hours and ask:

“Is the amount of time the same in both cases?"

Repeat with six weeks is 42 days. Emphasise that although the units are different, the amount of time remains unchanged.

7. Write “144 minutes” on the board and ask the learners how many hours and minutes it is. Ask the learners to share strategies.

Some learners may have used a calculator, or you may wish to ask them to use a calculator if they are likely to in daily life. Using a calculator, 144 divided by 60 will give 2.4.

Ask:

“2.4 what?”

“If I told you to be back in 2.4 hours, would you know what time to be back?”

“What does 0.4 hours mean?” (four-tenths of an hour)

“What is one tenth of an hour?” (6 minutes)

“What is four-tenths of an hour?” (24 minutes)

“What is 2.4 hours in minutes?” (144 minutes)

## Follow-up activity

Prepare some questions for the learners to work on in groups, for example:

- Each learner in the room is going to make a 15-minute presentation to the class, how many hours and minutes will it take for the whole class to present?
- We have two periods of 1 hour 50 minutes for presentations and 10 learners, how long will each learner get?
- A person is to have 240 milligrams of a drug per day in three doses evenly spread throughout the day. How long between each dose and how much is each dose (Extension: If the first dose is at 14:00, what time are the other two doses)?
- I want to set my video recorder to record two programmes, three-quarters of an hour long and the other 1 hour 10 minutes long. There is a 12-minute break in the middle. If I set the recording to start at 20:00, give a time to set it to stop so that both programmes will be recorded.

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