# A thousand seconds

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Purpose

This problem solving activity has a measurement focus.

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Student Activity

What time is it now?

What will the time be in a thousand seconds?

Specific Learning Outcomes
• Use seconds, minutes and hours.
• Discuss the size of a thousand.
• Read the time in digital and/or analogue form.
• Devise and use problem solving strategies.
Description of Mathematics

This problem builds on students' knowledge of the standard units of seconds and minutes to develop their understanding of the size of a thousand, within the context of time. Students should be challenged to estimate a solution, use multiplicative strategies to solve the problem, and to check their solution with a calculator.

Required Resource Materials
Activity

### The Problem

What time is it now? What will the time be in a thousand seconds?

### Teaching Sequence

1. Introduce the problem by looking at the clock and posing the question: What time is it right now? Write the time on the board using either digital or analogue form.
2. Read the problem to the students.
What do you need to know to be able solve this problem?
3. Make sure that the students know that there are 60 seconds in a minute and 60 minutes in an hour.
4. Challenge students to estimate a solution, use their multiplicative strategies to solve the problem, and finally, check their solution with a calculator.
5. As students work individually or in pairs, encourage them to record their work, and write about the thinking that they used.
6. Share solutions with explanations of strategies used.
How did you and your partner find a solution?
Does anyone have a different answer?
Did anyone use a different strategy to reach their solution?

#### Extensions

What will the time be in a 1000 minutes? How do you know?

How many seconds are there until (give a time 3 hours 15 minutes later)? How do you know?

Are there more minutes in one day or more seconds in 24 minutes? Show how you know.

### Solution

Students are likely to use a range of strategies to divide 1000 by 60. For example, they may use reversibility and ask,  ? x 60 = 1000, or ? x 6 = 100.

1000 seconds divided by 60 = 16 minutes and 40 seconds.  If the students use a calculator to check their solution, they will need to understand how to change 16.66 into minutes and seconds, understanding that  0.66 is the same as 2/3, and that 2/3 of 1 minute is 40 seconds.

Some may double check with a calculator by skip counting in 60s up to 1000.  Using this approach they would get to 960 after 16 minutes and have 40 seconds left.  So 1000 seconds equals 16 minutes and 40 seconds.

16 minutes and 40 seconds will need to be added to the time noted on the board as the problem is set.

#### Solution to the Extensions

1000 minutes = 16 hours and 40 minutes

3 hours and 15 minutes = 3 x 60 x 60 + 15 x 60 = 11 700 seconds.

There are the same number of seconds in 24 minutes as there are minutes in one day: 1440

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