Mathematicians: thinking, sharing, evaluating

Mathematician's take numbers apart.

Based on last week's math learning the students created their own number patterns for different numbers. Later we sat down looking at the work and discussing which representations worked well and how could we improve the pictures.

Mathematicians listen to the advice of other mathematicians.

My favorite part was when half way through the discussion L. raised her hand and said, "I know what advice I would give myself."

Mathematicians evaluate their own work, decide what is well and what to change.

The students decided that to have a good picture you need clear and large patterns that are easy to see,; the patterns have to be clearly separated from each other to avoid confusion; to make everything understandable you need numbers to show the part-part-whole relationship.

Mathematicians use many tools to help them.

We used ten frames to anchor numbers to 5 and 10. Having these relationships to think about a variety of combinations of numbers strengthens the number sense.

Even though using pattern cards and ten frames may seems too simple for third grade I can assure you that these tools are excellent in enriching the understanding of numbers and their relationships. This is basis for operations and measurement.

Number sense is not a topic to learn but a flexible and intuitive way of thinking about numbers. 

Mathematicians use what they know to figure out what they don't know.

On the following days we looked at the part-part-whole idea and used our best math thinking skills to figure out the missing parts. The numbers got increasingly more challenging. It became increasingly harder to explain the thinking and to understand what others were thinking. The students were allowed to leave at any point and practice other math when this became too much for them. I had one student who left quickly but came back to try again.

Mathematicians don't give up easily.

 I know that many adults would be tempted to grab a pencil and calculate some answers in written form. The students found answers by counting, drawing pictures, thinking of ones, tens and hundreds.