## Enquiry: Is the 'mountain-hill-rock' strategy effective?

We began with some simpler questions to try to solve independently such as:

° How long have you been awake for today?

° How long ago did we last have a maths enquiry?

° In how long will you be asleep?

After a few minutes, students were invited to share with us on our whiteboard the strategies they used in their maths books. We discussed the strategies and in particular, we focused on the use of a timeline like some students had used.

### Investigation:

I then explained to the class that I will try to introduce and teach them a strategy for measuring elapsed time without saying a word. They said they were up to the challenge. I began showing the 'mountain-hill-rock' on the board by drawing a timeline and wrote the current time at the end. I then drew some mountains (representing 1 hour each), some hills (representing 10 min each) and some rocks (representing 1 minute each). I then wrote a time that they measured.

I then mimed to the class to show with a thumbs up, a shaky thump to the side or a thumbs down as to whether they understood what I was doing. A few had thumbs up, we had a lot of shaky side-thumbs and quite a few thumbs down.

So, again, without speaking, I drew another time line and showed the strategy. This time, a few more thumbs up were shown.

After the third silent example, about two-thirds of us had thumbs up indicating they understood the strategy. At this point, we could start speaking and students shared their understanding of the strategy. There were a few varying understandings and they found it interesting to work out exactly the strategy I was using.

### Investigation:

We then tested how effective this strategy was for measuring elapsed time. To test its effectiveness we decided upon the following questions:

1. Does the strategy help us to solve the problems mentally?

2. Does it complicate the thinking or make it easier?

3. Can we use this strategy for all types of elapsed time problems?

With these 'testing' questions, we then began trialling the strategy with the following questions. As usual, the students have a choice of an easier or a more challenging question to solve. They need to decide where their abilities are at and to choose questions that will challenge them, but at the same time help them to feel like successful mathematicians. (see below)

They then solved the questions using the 'mountain-hill-rock' strategy on paper.

### Reflection:

Afterwards, we discussed our initial 'testing the strategy' questions. We agreed it was an effective strategy for mentally solving elapsed time. A few of us felt that there could be easier strategies though so we left question 2 as a 'maybe yes, maybe no'. After that discussion, for question 3, we felt it was too early for us to decide or not so we a few students suggested we should try to solve some questions with longer time periods. A suggestion of Mt Everests could be used to represent a whole day and another student suggestion we could draw a rocket flying to the moon on the number line to represent a whole year.

With those ideas, we will test this strategy out further next week.

 Easier More Challenging The time is now 10:30.   What will the time be in 3.5 hrs? The time is now 22:45.   What will the time be in 3.5 hrs? It is now 15:15.   What time will it be in 2 hr 35 min? It is now 15:15.   What time will it be in 4 hr 55 min? Gaby was going to the cinema. The film at the cinema starts at 11:30 and lasts for 1 hr 25 min.  What time does it end? Yasmin was going to the cinema. The film at the cinema starts at 14:40 and lasts for 1 hr 25 min.  What time does it end? Florence went for a hike in the Alps. She started the trail at 13:40 and it took her 3 hr 25 min to finish the hike.  What time did she finish? Jack was taking the TVG train from Lausanne which leaves at 15:50 and arrives in Paris 3 hr 55 min later. What time does it arrive in Paris? Isabel’s flight to Naples has a stopover in Rome. Her flight leaves Geneva at 10:30.  It lands in Rome 2 hr 15 later.  Her stopover in Rome is 1 hr 20 min. The next flight from Rome to Naples takes 55 min.  What time will she arrive in Naples? James’ flight from Geneva to Melbourne has a stopover in Singapore.  His flight leaves Geneva at 14:30 and lands in Singapore 16 hr 42 min later.  He will have a stopover for 1 hr 15 min and then it will take 8 hr 15 min to arrive in Melbourne.  How long is the trip? We start school at 8:30 and finish at 3:40. How much time do we spend at school in one day? We start school at 8:30 and finish at 3:40.  How much time do we spend at school per week? Micah’s family drove to Munich for a holiday. They left their house at 10:40. It took 7.5 hrs to drive there. What time did they arrive in Munich? Carlijn’s family drove to Berlin for a holiday. They left their house at 8 a.m. It took them 7.5 hrs to drive to Munich. They stopped for a half hour lunch and then continued to drive another 6 hr 15 min. What time did they arrive in Berlin? Chloe flew to Cape Town in South Africa for a holiday. Her direct flight left Geneva airport at 22:20 and took 15 hr 15 min.  What time did she arrive in Cape Town? Nolan flew to Cape Town in South Africa for a holiday. His flight left Geneva airport at 22:20 and took 15 hr 15 min.  The flight included at 1 hr 20 stopover in Dubai.  What time did he arrive in Cape Town?