Authentic Student Work

What the student understands?

This student (my fourth grade sister), appears to understand how to multiply single digit numbers. Without any instruction, the student began the problem with a visual representation to begin her solving technique. This first step allows us to see that this student understands what the question is asking and how to visually show what the question is asking. I actually was quite impressed when I saw her begin the problem by visually setting up four rows of nine without any instruction to. I enjoyed seeing her do this because we have actually looked at many examples and student work similar to the diagram she drew throughout this quarter. This made it apparent that what we have been learning throughout the past few months is extrememly prevalent and will aid in our successes as future teachers. While utilizing the visual to arrive at the answer of 36, the student also checked her work by doing the multiplication on her hands as well. Based off of her work we can assess that she understands what the problem is asking, how to set up a visual diagram for the problem, how to correctly solve a multiplication problem with two single digit numbers and how to arrive at an answer correctly re stated in a full sentence.

What the Student is Ready to Do Next

This student, although initally struggling with whether the question was asking her to multiply or divide, was able to understand and arrive at the correct operation for the problem through a visual and thoroughly complete the problem in the correct manner. Given the students work, I believe that this student is ready to begin solving bigger multiplication problems; such as a single digit number and a two digit number. This students work, although providing the visual where she could have simply counted up the 36 dots and simply left that as the answer, shows both the vertical and horizontal line up of 4x9 as well. Although solving through a visual, when doing this problem the student also checked her work by doing the multiplication of 4 x 9 on her hands. Through these two mechansims, we can see that the student does know how to multiply single digit numbers in her head/by counting her fingers and also understands the need to vertically line up the 4 on top of the 9- which will become extremely important as she begins to multiply multiple digit numbers. Through her multiplication skills and her understanding of the need to vertically line up the two numbers, I believe that this student is ready to advance on to multiplying a two digit number by a single digit number.

What the Student is Struggling With

Although the students work shows her to be struggling in esentially no aspect of this problem, what is not pictured is the question she asked before attempting the problem. After handing her the question, she asked "Is this multiplying or dividing?". Instead of telling her what operation needed to be used, I told her to re-read the question again and try her best. Still slightly confused, that is when she began to draw out the diagram. Through the utilization of a visual, she was able to visually see the problem and then understand what the problem was asking and what operation needed to be used.

Next One on One Steps with the Student

This student, although I am 90% certain incorrectly lined up the solution to the equation simply due to rushing and knowing the correct answer, did misplace place value in her solution with the vertical representation. Although correctly lining up the 9 under the 4, when multiplying, she puts the 3 (30) directly below the 4 and 9, which is the column representing the ones place. Although I do think that this mistake was made due to paying little attention, my first steps with this student would be to have her re do the vertical multiplication and show where the 3 should be placed and where the 6 should be placed. Once correctly executing her understanding of the 6 in the ones place and the 3 carried over to the left and dropped down to the tens place, I would then continue on to a problem like 14x4. A problem like this causes the student to have an increased understanding of place value and multiplication. A problem like this requires the student to show her understanding of correctly lined up place value, carrying over, and completely multiplying through-so multiplying the ones place (the 4) by the tens place (the 10 in 14) and then adding the carried over 1 (10). I believe that this is the next one on one step that should be taken because it requires the student to exhibit an increased understanding of multiplication, place value, and carrying over but is not too much more difficult than the 4 x 9 problem to where the student will be completely lost at where to begin the problem.

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