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# Two Clocks

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
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Thank you to everybody who wrote in to tell us what they thought about these clocks. Most children agreed on the answers, and it was interesting to see the different reasons that children gave.

We received a lot of solutions from the children at King's Hedges. Yousuf and Daniel explained their ideas:

D is what time he wakes up as it is the earliest time (7:15). A is the time he gets to school as 8:30 is the average time to go to school and is the second earliest time. B is midday as 12:00 is midday and no other clock shows 12. With process of elimination, that makes C when he turns his lights off (21:45).

On Friday, she went straight home as 30 minutes past 3.30pm is 4. Wednesday she stayed for 5 minutes so it'd be 4.05pm. Tuesday is when she played with a friend as it's 4.35pm and it said she played for around 30 minutes. On Monday, she bought sweets as it doesn't take 50 minutes to get sweets on the way home. Therefore, Thursday is band practice.

I like the way you showed the order in which you answered these questions - often it is easiest to answer one of the questions using a 'process of elimination'! We were also sent in similar solutions by Zoe, Blanka, Mason, Adrian, Robert, Dominika and Neve at King's Hedges - thank you for sharing your ideas with us.

We also received several solutions from the children at Norwest Christian College in Australia. Nathan thought that the hands on the first set of clocks were pointing to the small lines, rather than splitting the hour into quarters:

Part 1:

Each clock interval for the hour clock is 12min so that means:

A Clock: 8:30 (am/pm)

B Clock: 12:00 (am/pm)

C Clock: 9:48 (am/pm)

D Clock: 7:18 (am/pm)

I think D is waking up, just out of personal experience, I think A is going to school because my school starts at 8:35, so getting to school at 8:30am would be the best time, I think C is lights out because around 9:48pm is about the time when I would go to bed, I think that B is of course midday. I think this question is mostly based off your lifestyle and what time school is for you.

Part 2:

If schools ends at 3:30pm and it takes her 30min to get home at least, she must get home at 4pm at the earliest, so when she runs home quickly that means that since the Friday clock is on 4 o’clock, that means that she ran home quickly on Friday. Since the teacher kept the class in for 5min after school and she rushed home, that means that she would get home at 4:05pm, which is the clock of
Wednesday. When she went to play with Sam for about half an hour, that means that the clock should show about 4:30pm, and the Tuesday clock does, so she played with Sam on Tuesday. This is where it starts getting harder, we don’t have a time or how long things took, so we need to guess, from past experiences, going into the shops to get some snacks doesn’t take that long, so I believe that it
only takes about 10min to get it, and that’s what the Monday clock says, so I believe that she went and picked up lollies on Monday. Now, since there is only now one more clock left, it means that the Thursday clock must be the band day.

Well done for using your own personal experiences to put these events into context! Aarnav, Lucas, Diya and Chloe from Norwest Christian College also had some similar ideas.

The children at St Helen's Abbotsham in England sent in their ideas about these questions. Albie, Olivia, Edgar and Sonny said:

Question 1:

B=Mid day because the hand is pointing to the twelve.

D=When he wakes up because school starts at 08:30 so you can't wake up at nearly ten!

A=When he goes to school because I don't think school would start at nearly ten!

C=When he goes to bed because it's too late for school.

Question 2:

Monday (1610) we think is when Julie gets sweets because it takes about 10 minutes to buy sweets.

Tuesday (1635) we think is playing with Sam because it is 4 o'clock plus a half hour.

Wednesday (1605) we think is staying in for five minutes because 30+5=35

Thursday (1650) is band practise 45+30 plus faffing time

Friday (1600) is where she rushes home, taking 30 minutes.

Sam, Ralph, Molly, Amélie, William, Lucy, Amelia, Rosie, Frances, Kacie, Myles, Reuben, Adam, Riley, Aiden, Tommie, Ophelia, Amber, Charlie, Neda, Fraser, Joanne and Oliver from St Helen's Abbotsham also sent in some similar solutions. Thank you all for sharing your ideas with us.

Gabriel and Muhammad from Wembrook Primary School sent in their ideas about these questions. Gabriel said:

Wednesday could be the day that the teacher kept the class in for 5 minutes because she comes home usually at 4:00 and 4:00 + 5 minutes = 4:05.

Thursday could be the day that she practised in the band because the times just tells us that it's XX:50 so it could be 3:50 or 4:50.

Friday could be the day that she hurried straight home because it takes her 30 minutes to get home at least.

Monday can be the day she goes to get sweets.

That leaves Tuesday being the day that she plays with Sam.

Good ideas - how do we know that the time that shows XX:50 can't be 3:50?

Lucy and Ryan from Bishop’s Castle Primary School in the UK had some similar ideas and they used number lines to show how they thought Julie might have spent her time on her way home from school. Ryan sent in this picture:

This method makes it really easy to see where she might have spent some extra time on each day. This is similar to Albie, Olivia, Edgar and Sonny's idea about 'faffing time' - if your home is a 30 minute walk from school, I'm not sure how likely you are to actually get home 30 minutes after school finishes!

Unfortunately we don't have space here to include all the solutions we were sent. We also received excellent solutions to this activity from: Will from P.S.24 in the USA; Chloe, Sophia, James, Zac, Milan, Harry and Dray from Banstead Prep School in England; Om from St Leonard, Exeter in the UK; Sasha from Bilingual International School of Paris in France; Koen from KPS in Scotland; Ci Hui Minh Ngoc from Kelvin Grove State College in Brisbane, Australia; Dhruv from The Glasgow Academy in the UK; and Meriam and Millie.

Josh from Banstead Prep School thought that there could be multiple possible solutions to the first part of the problem:

C shows it's 9:45 since it's $\frac{3}{4}$ of the way to the 10. This can be multiple answers. It can be when he goes to school or when he turns out the light.

D shows 7:15 since it is $\frac{1}{4}$ past the 7 but it could be when he wakes up or when the lights go out.

Good ideas, Josh. I wonder how many different possible answers there are to the first part of the problem, thinking about clocks A, C and D. The only thing we know for definite is that Sam goes to school after he gets up in the morning, not before! I suppose the rest of the solution mostly depends on how much sleep he needs.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?