Teaching Maths through Powerful Learning

APR-mathsTo enable students to develop their knowledge of Maths, it is essential that they acquire the conceptual understandings which underpin the subject. Conceptual understandings are the meaningful ideas and multiple representations that allow students to connect their learning and facilitate collaborative discussion and personal success.


An example of this conceptual understanding is evident in the Year 1/2 unit on Fractions. To ensure that the students experience success in this unit, it is essential that they recognise:

Key Mathematical Conceptual Understandings:

  • Fractions are numbers.  They are equal shares or equal sized parts of a whole, the whole can be one object or a collection of objects.

Key Mathematical Knowledge:

  • Fractional parts have special names that tell how many parts of that size are needed to make the whole, for example, in thirds we need three parts to make the whole.
  • The more fractional parts used to make the whole the smaller the parts.
  • The size of a fraction is determined by the size of the whole and by the relationship between the numerator and the denominator.


This week the Year 1/2 teachers planned the lesson below:


Stage of Lesson

Teaching Instructions/Prompts


How will the teacher activate prior knowledge?

Kings and Queens – Halving

Flash a card and the first to halve the number wins that round. If you win three in a row you are a king/queen.

Aim is to practise fluency of halving.

Learning Intention To be able to find fractions of a collection

How will the teacher explicitly teach the concept/knowledge/skill?

½ or not ½ – Show different collections. Partition the collections in different ways. Some that represent halves, some that don’t. Ask students to sort collections into showing halves or not showing halves. Ask students to justify why they sorted the collections into halves or not halves.
Guided Practice/Teacher Group

Who will attend?  How will you support their practice?

If I can find ½ of a collection how could I use this information to find ¼ of collections? How about 1/8 of a collection?

If students are making this connection easily – Can you find 2/8 of a collection?

Independent Practice

How will the students apply the skills in different contexts?

Some people came to visit our classroom. Half of them were wearing hats, half were wearing blue t-shirts, half were wearing socks. Draw a picture of what the people might have looked like.
Reflection/Drawing the lesson to a conclusion

How will students reflect on what they have learned?

Comparing some answers from the independent work. Did people have different answers? Were they all correct?  Why/why not? What if one person in the group wasn’t wearing any of the items? Would that still work? Could we still show half?


Jourdan and I team taught this lesson and encountered some deep, rich discussion with 1/2D students about the value of a half. The students believed that in Figure A (below), half of the people are wearing hats, but in Figure B it is not half of the people who are wearing hats. This misconception provided an opportunity to identify their next stage of learning.



Specialist Timetable

Following parent feedback, we have attached the specialist timetable for Term Three. Every grade attends a PE, Performing Arts, Visual Arts and French lesson. There may be occasions when the timetable is changed due to school events.