Today I was working with a year two class on understanding tens and ones. We used a hundreds chart as a tool to help the students develop deep understanding of two digit numbers. Key questions included “what is missing?” and “how are the numbers kind of the same?”
The four photographs below show the development of Emilie’s understanding of how numbers are structured over the course of a single hour. At no point was she corrected. At no point was she told what to think. We simply asked her to evaluate her answers and consider the patterns in the chart. Questioning led her to self-correct, and then to further develop a much more robust understanding.
This is Emilie’s first attempt. The number that she was given initially was the 16.
This second photo shows how much Emilie learned simply by asking how 16 was kind of the same as 26. Notice how much further developed her understanding of the underlying structure of mathematics has become.
This is Emilie’s third question. Notice how much harder this question is when only given the 16 in the centre. She could not simply follow the pattern of tens to fill the spaces, but needed to think beyond this pattern.
In this last question, Emilie was initially only given the 82. She worked forwards and backwards, and self-corrected her attempts to work it out. This shows advanced understanding and reasoning skills.
It is amazing to consider where Emilie will be in a year’s time if her teacher continues to ask these kind of questions that prompt development of understanding even just once per week!