In Calculate Blog, Teacher PD

“Wow Michael, so much I didn’t know about clocks. Sometimes we do get caught up in teaching the skills and forget about the interest factor. Thanks for a great lesson today. Kind regards,”

This was a reply I received recently, after running a class on time for a year 3 class. The teacher and I had spoken briefly before the lesson and she mentioned that the class were struggling with the concept of to and past the hour. This had been the concept covered by the text book the day before. As we talked we both agreed that we shelve the planned lesson on addition, and revisit time.

Reaching in to my kit bag I pulled out a packet of circle papers for the students to make clock faces with.


Folding a circle in half and opening it up again, “what goes at the top?”

“The o’clock”

“And what does o’clock mean?”


“Does anyone know?”

Shaking of heads

“Ok. It stands for ‘of the clock’. So 12 o’clock is the hour 12 of the clock, and so 1 o’clock is …”

“1 of the clock”

“And 2 o’clock is?”

“2 of the clock”

“Wonderful, so what do we call it when the minute hand is down the bottom?”

“30 minutes”

“Or …?” Folding the paper along the crease and out again a few times, “what is this fraction?”


“Half what?”

“Half past.”

“Yes. Or more completely, half past the hour of the clock.”

There were a few “oh”s and “wow”s at this point.

“Now,” folding the circle to show just the upper right hand quadrant, “what time is this?”

I should also point out that I was choosing a different student to answer each question and selecting from both those who had raised their hands and those who hadn’t. In each case I did not move on until the chosen student had given me an answer.

“A quarter…” “To.” “Past.”

And here was the threshold, or liminal point, of their confident knowledge. There is only one “o’clock” every hour, and only one “half past” but there are two quarters? Many young children do not discern the difference between the two.

“Hmm,” raising my arm so that the elbow is at chest height and my hand is in front of my face, “what is the hand doing?”


“Is it moving to or from?” The first time I ask this question I don’t provide a reference point. I wait a few seconds and then elaborate, “Is it moving up to the hour or down past the hour?”

“Down past!”

Holding up the quarter circle, “so this is?”

“A quarter past!”

“Past what?”

“The o’clock” and “of the clock” are both heard.

Quickly flipping the quadrant around, “and this is?”

“A quarter to”, then less loudly “the o’clock”

“Wonderful! Next then, what else is half past called?”


“How many minutes in an hour?”


“So how many minutes is half past?”


“And a quarter past?”


“And a quarter to?”

“45” and a couple of unsure “15”s.

“How many to the hour?”

“15” more confidently and supported around the room by nods.

Moving to the whiteboard and drawing a circle, “what numbers go between the o’clock and the quarter past?”

At this point I look around and comment to the teacher that there is no clock in the room for the students to use as a reference point. This is neither good nor bad but does help to explain the puzzled looks. A little more prodding elicits the appropriate responses and it is now time for the students to fill in the remainder of the clock faces by themselves. This allows for a couple of minutes to chat with the teacher about where to next.

Where to next is suggesting that smaller circle paper is now used in the same way to model the hour hand. The teacher immediately indicates that she has some and collects it from a storage tub. A few more questions and the students are able to complete the second clock face as well. All that remains is to guide the reflection time by asking the class what they learned during the lesson. The previous sticking points are all gone and a few added pieces of vocabulary and insight.

I do not expect any teacher reading this to be surprised by the materials used. They are standard for primary classrooms. Further the only point of difference between my approach and the regular teacher of this class was to add a second “face” to highlight the different numbering systems for minutes and hours. So why then did she find observing the lesson to be so valuable?

It begins with her own ability to recognise that even though she and the students had already worked through a lesson on the same material they had not reached a point of understanding. Then, having an opportunity to collaborate with another teacher and the confidence to postpone the planned lesson in favour of review and consolidation allowed the class to dig deeper into the meaning of how we measure time.

From this point on, everything about the lesson was centred on the students. Every question stepped out the path from general to specific knowledge and the responses were all genuinely those of the students. Thinking time, both for the students and the teacher asking the questions facilitated dialogue. Silences indicated confusion at one point, concentration at another and dawning awareness at a third. The feedback was in real time and paced to bring the entire class along together. At points where some students were still confused, their classmates chatted with them and retraced the most recent movement until both could continue.

Of course the students will now need to cement their understanding and improve their fluency over coming weeks. One way to do this is to explore the origins of clocks and the word clock. Painting the picture gives greater vibrancy to the image than just sketching it. In this case the painting includes history, etymology and science as well as maths.

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