Mult-e-Maths



Time problem-solving 5MEA6

National curriculum objective

Pupils should be taught to:

• solve problems involving converting between units of time.

Prior knowledge and skills

• Convert hours to minutes, minutes to seconds, years to months, weeks to days.

• Solve problems involving converting hours to minutes, minutes to seconds, years to months, weeks to days.

Vocabulary

second, minute, hour, day

Resources

• DVD boxes (3 per small group)

• calculators (optional)

Oral and mental starter

Groups

Give each small group of pupils three DVD boxes and ask them to find the running time printed on the back of the boxes. They should order the DVDs by running time, then talk together about how to change the times into hours and minutes.

Remind pupils that when converting whole hours into minutes there will be a whole number of minutes. Ask pupils to recall how many minutes there are in 1 hour, 2 hours and 3 hours. Explain that when converting minutes to hours, unless the number of minutes is a multiple of 60, there will be a whole number of hours and some minutes left over. One way to convert from minutes to hours is to divide by 60 to find the number of whole hours (find how many 60s there are in the total number of minutes), then the remainder is the number of minutes.

(Activity 1 on whiteboard: screen 1)

Q Which film has the shortest running length? (B; 89 minutes)

Q Which film has the longest running length? (A; 136 minutes)

Ask pupils to order the films from shortest to longest running length (ADECB). (If desired, you can write the correct order using the ‘Pen’ tool on the board.)

Q How long does each film last in hours and minutes? (A: 2 hours 16 minutes; B: 1 hour 29 minutes; C: 1 hour 38 minutes; D: 2 hours; E: 1 hour 43 minutes.)

Main teaching activity

Pairs or small groups

(Activity 2 on whiteboard: screen 2)

Explain that the table is meant to show the finishing times of a group of friends who have run a marathon. The names and finishing times of each friend are on the right, but they are not written in the correct order. Some of the times are written in seconds, some in minutes and seconds, and some in hours, minutes and seconds.

Pairs or small groups of pupils should discuss how they could start rearranging the runners according to their times so that they are in the correct order, from fastest to slowest. As necessary, encourage pupils to start by ordering the times that are expressed using the same units, then pupils can convert the times in minutes and seconds into hours, minutes and seconds, and finally explore a way to convert seconds into hours, minutes and seconds.

Ask volunteers to give you the solution. Drag the blue labels (or ask pupils to) into the table as pupils suggest the correct order (the name and associated time are a single label).

(Solution overleaf.)

|Position |Runner |Time |

|1st |Tasha Tuttle |14329 secs (3 hours 58 minutes 49 seconds) |

|2nd |Tareq Toure |239 mins 13 secs (3 hours 59 minutes 13 |

| | |seconds) |

|3rd |Ted Tovey |4 hours 15 mins 3 secs |

|4th |Tyler Twigg |277 mins 10 secs (4 hours 37 minutes 10 |

| | |seconds) |

|5th |Tahira Tamer |4 hours 39 mins 58 secs |

|6th |Tim Tanner |288 mins 54 secs (4 hours 48 minutes 54 |

| | |seconds) |

|7th |Troy Tagg |18088 secs (5 hours 1 minute 28 seconds) |

|8th |Tiffany Truman |5 hours 13 mins 32 secs |

Whole class

Ask pairs or small groups to explain how they attempted to convert seconds into hours, minutes and seconds and share successful methods.

(Activity 3 on whiteboard: screen 3)

Explain to pupils that they are going to expand their understanding of converting between units of time to the larger units of days, weeks and years. Discuss and complete the sorting activity on the whiteboard, asking pupils for their reasoning and methods for placing words and numbers in the spaces. Answer:

Equal to 1 year: Equal to 1 week:

365 days 7 days

8760 hours 168 hours

525600 minutes 10080 minutes

31536000 seconds 604800 seconds

Individuals

Ask individual pupils to work on one or more of the following problems, using the conversions on the whiteboard, and whatever information they have, to make it as accurate as possible. Pupils should be encouraged to understand that, as with all measurements, the solutions will be approximate and they should decide on the appropriate accuracy.

Q How long have you spent brushing your teeth in the last year in hours or minutes or seconds?

How long have you slept for in your lifetime?

How many days is it until your 18th birthday?

Other tasks

You could ask pupils to:

• pose their own questions that involve converting between different units of time.

• create a classroom time line, showing the relative time in different units.

Review

Pairs or individuals

Ask pupils to use what they have learnt to solve the following problem, either in pairs or individually as appropriate:

The heart of a 9 to 10 year-old child beats approximately 90 times a minute on average. Investigate approximately how many times your heart beats in an hour, a day, a week and a year.

Key idea and assessment

There are 60 seconds in 1 minute and 60 minutes in 1 hour; you can convert a time given in seconds to a time in hours, minutes and seconds using this knowledge. There are 24 hours in 1 day, 7 days in 1 week, 52 weeks in 1 year; you can use this information to convert between these units of time.

Can pupils:

• convert between different units of time?

• solve problems involving converting between different units of time?

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