When teaching any mathematical concept, it is essential that you collect some evidence of students prior knowledge, to ensure you implement the right content at the right time, in addition to the best possible pedagogy. One suggested introduction to this topic is to discussing how many numbers are on a traditional analogue clock face. Ask students to articulate and explain what they think these numbers mean and represent.

 

From this discussion it is important students are explicitly aware that the numbers (symbols) on an analogue clock face have 2 meanings:

 

• representing the hour – via the hour (shorter) hand; and

• representing the duration of minutes that have passed within this hour – via the minute (longer) hand

 

The focus for this resource and suggested activities is on the latter of these two symbolic meanings.

 

The following resource and activities involve creating a number line. Using the numbers that are found on a traditional clock face (1-12), students will build a number line to explore what relationships and patterns they can find within an hour of time.

 

To create this resource you will need the following materials:

 

• A consistent unit of measurement to represent '5 minutes' (Unfix cubes, Magnetic rods, Cuisenaire rods, match sticks etc)

• Sticky notes

• Paper

• Long strip(s) of card 

• Textas 

• Straws

 

With the selected unit of measurement explain that one of these units represents a group of 5 minutes (or connect 5 together to represent 5 minutes). Here are some examples as listed above:  

 

 

 

 

 

 

 

 

 

 

                         Unifix Cubes           Cuisenaire Rods         Magnetic Rods        MAB units

 

Place one group of 5 minutes down horizontally for all to see (for the purposes of this demonstration I am using Unifix cubes). Ask students to identify how many groups of 5 are present. After they answer “1”, place a sticky note at the end of this group. Then ask a student to add another group of 5 minutes to the number line and ask: how many groups of 5 are there now?, and add a second sticky note to label. Continue to model up to three groups:

 

 

 

 

 

 

 

 

 

 

 

Using these materials and reinforcing to students that they are only labelling their groups with the numbers found on a clock face (1-12), students can complete their own number lines independently.

 

Next, ask students to make a minute hand to help identify different segments and fractions of time. Here is an example made from a straw and paper arrow:

 

 

 

 

 

 

 

 

 

 

 

 

 

With explicit instruction and scaffolding where applicable, here are some examples of questions you can ask students to explore, with emphasis on noting their strategies for solving.

***Creating a mental schema that illustrates the multiplicative nature of time is the first building block in understanding time. 

 

• How many groups of 5 are in your number line?

• How many minutes in total are around your clock?  

• How did you count these?

• What’s another way of naming this duration of time? (one hour)

• How many groups of 5 (minutes), make up 25 minutes?  - You can ask any multiples/ variations here.

• If you divided your number line in half, how many minutes would be in each half? How could we name this duration of time? (30 minutes, Half an hour)

• If you divided your number line into quarters, that is 4 equal groups, how many minutes would be in each group?

• How many minutes are in 2 quarters, 3 quarters? (30, 45)

• Can you see any relationships with other time fractions explored so far? (some students may see thirds - 3 groups of twenty minutes, 6 groups of ten minutes etc).

• If my minute hand lands here (point to say minute 42,) how many minutes have passed? How many more are needed to complete the hour? (18). How did you work that out?

• What are the patterns and relationships you can see between the number of minutes and the number of groups (of 5 minutes) in your number line?

 

Finally, ask students to record this information on a long strip of card. If students use disposable materials as their unit of 5 minutes (such as match sticks) the can stick these directly onto the paper. Alternatively, having a BLM of the materials chosen will ensure students can record their number lines accurately and proportionately. Grid paper has been used in the following example to represent Unifix cubes:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Once students have recorded this information on their length of card, ask students to spend some time folding their number line in half and in half again. Explore what fractions have been created and ask them to label appropriately. Refer back to the questions posed above so students can practice and build these mental referents for understanding the relationships and fractions associated with time. 

 

Some further explorations for the linear clock:

Connecting to the digital clock.

When we read the minute hand on an analogue clock, we are referring to the amount of minutes that have passed during the present hour.  On a digital clock, the minutes are represented by the value after the colon. Consider the following times on these digital clocks:

 

 

 

 

 

 

 

 

 

 

 

 

Using your minute hand (pointer),  find the following minutes on your hour number line: 32, 40 59, 20 etc.

With a friend, challenge them to identify where different durations of minutes would be on their number line – eg 24 minutes, 53 minutes etc.

 

There are two variations for where you can now take this resource for students to represent

their thinking and understanding about the part-whole relationships of time. What's important to remember is that your students may need one, or they may need both of the representations to explore and construct their understanding. This gives you, the effective maths educator, some flexibility to meet the learning styles and needs of your students.

 

The first variation of this linear clock as constructed above is to connect both ends of the number line to create a cyclical model of an hour: 

 

 

 

 

 

 

 

 

 

 

 

 

By transforming their number line with all fraction representations  into a cyclical clock-like model, allows students to visualise concretely the relationships between the minute fractions in a cyclical formation which is required when reading an analogue clock.

 

The second variation to this resource is to construct this numberline in 2D form using the same BLM of the minutes units, but in a circle to mirror the traditional position of an analogue clock :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If we consider the suggested pedagogical experineces above and how they support and develop the conceptual development of time, we refer back to the schematic diagram we explored in the "Professional Learning" section to see the distinct relationship and interconnectedness between the concepts addressed in these learning experiences:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

As illustrated by this section of the schematic diagram, the pedagogical approaches above support the construction of a mental schema that enables students to not only perform and undertake surface level tasks (such as those in pink) but apply this knowledge in a range of different contexts becuase they have developed deep conceptual knoweldge and understanding (illustrated in blue) to support this learning  

 

These linear clock variations provide students with a range of concrete resources they can use and refer to endlessly. I hope it also inspires you to create many more investigations in your own classrooms implementing this teaching and learning tool!