This week my students are working
with even and odd numbers. As part of this lesson the students continued
working with counting by 2’s. To begin this lesson the students sat on the
carpet for a mini lesson on what it means to be an even or an odd number. To
introduce this my MT had the students count by 2’s starting at 2 then from 20
then from 40. This gave the students practice counting by 2’s but also a way to
introduce what kind of number “2” is. Then my MT had two students stand up and
explain that these two have a pair then had a third stand up and explain that
this student is the “odd one out.” We did this has a group until we had 6
students standing. Then we began discussing what numbers are even and why as
well as what makes an odd number. We went over that all even numbers end in a
0,2,4,6, or 8 and all odd numbers end in the remaining numbers (showing the
students on the board.) The students really seemed to grasp the idea of an even
versus odd number throughout the mini lesson. We did a few examples of writing
a number on the board and asking the student if they are even or odd. The
students all called out the answer and seemed relatively confident in their
response. The student’s were then asked to go back to their seats and get a
personal white board, marker and eraser.
Once back at their seats the
student’s were asked to write the numbers 1-6 down their boards. My MT then
explained to the students that she is going to say a number and they are to
write that number down and then write an “O” or an “E” next to the number if
they are odd or even. I decided to circulate the room and see what the students
were doing and see how they were thinking. I got to one student for number
three who wrote the number “16” with a “E” next to it. This is correct, however
the number they were asked to write was number 19. This student is one of the
lower students who is going to RTI for math. I believe that she wrote the
number 16 thinking that she had down 19 and made a relatively common mistake of
flipping her number. I then realized she looked up at the board and saw that
the number “6” is one of the numbers that is always even. I am glad that I saw
her use her resources to answer the question and she did do that correctly
however she wrote the wrong number, which would have been an odd number. The
importance of knowing your numbers is crucial at this point because it is hard
to build knowledge when the framework is not secure. To make this task a high
level task I believe it would have been beneficial to have the students explain
why the number that they have written is even or odd. Another way that students
could demonstrate understanding of even or odd would be to have the student
draw a picture or use manipulatives to show that a number is even or odd. Having
the student explain the reasoning would be helpful because then I would also
know how the student is thinking about even and odd. Did she know that 6 is
even because they each have a pair or because it is on the board and the
teacher said so? Did she truly mix up her number or was she just not really listening?
There are so many questions that could be answered if the students were asked
to explain their reasoning. This was a quick lesson due to a field trip and
other time constraints so I will be interested in what this particular student
does next. I also will like to see how the students grow in their understanding
of even and odd numbers.
These are all good analyses and recommendations. I would suggest that you think of ways in which you might construct an open-ended, high-level task that allows not only for students to come up with different representations of the concept, but also to share this different representations with each other. This is implicit in your analysis above, but I also want to encourage you to think about how you as the teacher might explicitly connect these different representations in the most powerful way that scaffolds thinking towards the big idea...again, such a sharing-out can be accomplished through a whole class discussion.
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