Student Work #5

The purpose of this learning task was to have students learn how to take objects and make a graph out of the amount of each object. The big idea of this task is that understanding how to make a bar graph out of an amount of sorted objects allows for further thinking in their mathematical skills. This activity is under the common core standard; 2.MD.10- Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart and compare problems. This task starts out not as a high level in that it just asks the students to sort the candy hearts then count how many of each color. Then it asks for them to make a bar graph of their sorted candy hearts. Then the problem leads to attempting to get to a higher level task when it has questions to follow. One asks, "How many pink and yellow hearts were there?" This problem not just having them say how many color hearts but an addition problem asking to add the pink and yellow together. Then it takes it to a different perspective and asks the students to come up with their own question to this worksheet. 

For this specific task, there are really not two ways to approach it. They are to just sort the colors and count them then graph them. I will just take question number 4 it asks how many hearts were there altogether. One way the students could have solved this question would be to start at the top their first color, in this case it was blue and there were 5 of them. Then they would go down, adding the number to the previous number. So, it would be 5+5=10 10+8= 18, etc. Then the final number would be how many there were altogether. Another way they could have solved this problem would be to group numbers together then add. This student could have grouped 5+5 knowing it made 10. Then grouped 7+1 knowing it equals 8. Then add 8+8= 16, then because there were two tens they just had to add 10+16=26.

The anticipated student approaches would be the same as above. I would anticipate the students to solve the problems using addition or by looking at their bar graph. This activity is simple in that it requires counting the objects, sorting, and then asking two addition problems. Although, I could see some possible errors. An error that I could see happening is switching the x and y axis on the bar graphs and not knowing whether to put the colors on the x or y and vice versa with numbers 1-10. 

The Students Approach:

• First the student sorted the bag of candy hearts into piles of the colors.
• Then she counted how many were in each color and wrote that next to the corresponding color.
• She then set up her bar graph with the colors on the x-axis and numbers 1-10 on the y-axis. 
• She drew in hearts in each square representing the candy hearts. 
• She then answered the questions that followed (she looked at the most heart on the graph and the least and wrote that color in.)
• She solved number 3 by looking at the pink and yellow and adding together. There were no pink hearts so she just added 0+1 for the yellow and got 1.
• She solved number 4 by adding 5+5= 10, then did 10+8=18, 18+7=25, 25+1=26.
• She then came up with her own problem and solved for it. She used what the previous questions asked and made up how many blue hearts were there? 

The student clearly understands how to sort and count the candy hearts. She knows how to make a bar graph and fill it out. Her mathematical understanding of using addition is clear in that she can answer a simple question asking to add two colors together. 

One way to further this students understanding would be I could make a word problem with the candy hearts. Instead of asking to add two colors together, I could say, "If one person had 8 pink hearts and 5 yellow hearts. Then their friend had 7 pink hearts and 8 yellow hearts, who has the most hearts?" Another way I could get this student to think higher is that I could make a division problem asking them to add all their hearts up then split the total hearts equally among 4 people.