The first picture here is the directions for the Fact Extension Game. The students were given number cards from 0-9, a six-sided die, a calculator, and a sheet of paper. The object of this game was for the students to have the higher total at the end of the game. Although many of the students cared more about rolling the die and winning this student in particular spent much of her time focusing on the actual addition part of this problem. The teacher allows the students to check their answers with calculators but when I turned my back many of the students used calculators throughout the whole game. However the big idea of this game I think was to get them thinking about addition with larger problem. The teacher wants the children to always show their work and gives them more than one way to solve the problem. Typically I see the students solving the problems much like this student did on the left. She clearly wrote out the problem with the larger number on top to help her add the numbers better. She then added the 2 numbers in the right hand column and put it off to the side with a carrot. Once you are finished you have to bring the number down and add the left hand column. The student here shows that they have a clear understanding of how to set up the problem correctly and where to begin when solving the problem. I am not surprised with the way this student and other students approached this task. Many of them looked at it as more of a game while others focused on getting their addition problems correctly written out to show their work. I would say this student has a high understanding of this task and understands the big idea in being able to solve addition problems with larger numbers.
A great task to analyze here. You say that through your analysis of the work you see that the student understands...But try to go more in depth and in detail. How is the student approaching this problem? What are you still curious about in terms of what they might not yet understand?
ReplyDeleteOnce the student has the two numbers that she wants to add together, she places them on top of one another. The larger number on top and the smaller number on the bottom to make it easier for herself. She approaches this problem like any typical addition problem. She adds her ones column first and then her tens column second. When she adds her ones column up she puts a carrot next to the two numbers and puts the solution on the right side of the problem. She then draws an arrow indicating that she is bringing the number down. Next, she adds up the left hand column. I noticed in this students work that she did not carry her numbers into a third column. Typically with numbers this small students do not need to. However, I am curious to further this students thinking by giving them larger numbers, such as numbers with three or four digits. I think it would be interesting to see their work when they are forced to carry their numbers into the next column over. This student seems to have a very good understand of addition problems. I think it would be interesting to also further their thinking by seeing how they approach subtraction problems and if these types of problems are as easy to them. This is one of the upper level students in the class and she typically does very well on math tasks such as these. Another thing we could possibly try with her is giving her the problems as word problems and seeing if she sets the problems up like she did on the example above or if she solves the problem by counting up and using her fingers or using other material given to her.
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