Megan Sexton Post #4

The mathematical objective of the learning task is for students to understand how to share a certain amount of money equally among more than one person. The learning goal of this task is also having students engage in division problems through the use of tiles to help show their work. This task can be under the common core standard of 2.MD.8: solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cents symbols appropriately. This elicits students thinking through the use of dividing a number into many different parts and showing how they did that using drawings or tiles. This is a higher level task in that students are stepping out of addition and subtraction and into division. The students are learning how to break down numbers into equal parts and seeing if there are any remainders.

Let's take problem 1 and the 16 cents are being shared equally by 4 people.  One way to solve this problem could be the students could set out 16 tiles and move tile by tile to 4 different groups and count how many tiles are in each group. Another way this problem could be solved is you could divide 16 by 4 and get 4. 

One way I anticipate the students to approach this problem is by the way above, having four groups and moving the tiles into each group one by one until they get an equal amount in each seeing that there are no remainders. Another way I could see the students solving this problem is through the use of drawing. They could draw 4 circles and put a dot in each circle seeing that each circle gets 4 dots with no remainders. An error that I could see occurring not with this exact problem but with one that has remainders is that the students could get confused and put the remainder with one group and that they would not understand that each person needs an equal amount. 

Steps taken by student:

• She first put out 4 tiles in a column and counted 4.
• She then took one tile and placed it under the first tile and said 5, another tile under the second tile and 6, and so forth until she got to 16 and saw there were no remainders.

One hypothesis is that the student understands how to take a given amount and split it equally among a certain number of people. Another hypothesis is that she understands to start at 16 and split it between 4 people until each person has an equal amount and that there are no remainders. 

One way I could advance the students thinking is I could make it into a word problem. I could say "The kids father has 16 cents. He wants to give it to his 4 kids but wants each child to get the same amount. How many cents does each child get?" Another way I could advance the students thinking is have the problem set up as 16 divided by 4=?