Megan Sexton Blog Post #3

The learning goal of this task is for students to understand order of operations and to be able to work backwards and opposite form a starting number. This activity falls under the common core standard of 2.NBT.7- “add and subtract within 1000, using concrete models of drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.” The big idea is to get students to understand that given a starting number the problem may need to be worked on backwards and how and what strategies to do that involve addition or subtraction. This task is a high-level task in that it encourages the students to elicit their thinking through the use of adding or subtracting backwards or having to rearrange by if it asks to add they will be challenged to realize its really making them do the opposite and subtract.

There are many ways to go about solving this problem. One way to solve this would be to start at the number that is given, 139, and notice that the arrow that is dotted is asking to add 2. So then I would add 2 to 139 and get 141 to go in the next bubble. I would then see that the arrow from 141 to the next circle is asking to subtract 10 so I would subtract 10 from 141 and get 131. Then go back to the number 139 and see that the arrow from the circle next to it to the 139 circle says to add 10. I would realize that since it’s not asking to subtract 10 from 139 but really add 10 to 139 so I would get 149. I would check my work to see that 149-10=139 and that is correct. Another way to go about this problem could be start at 139 and fill in all the empty circles before it then proceed to do the last two circles, basically just start at different positions.

I anticipated the students to solve the problem using the ways I provided above. Although I anticipated multiple errors to occur in the process. Some of the errors include: the students would put either +2 or -10 in the circles given the correct arrow and not actually solve for the problem. Another error is I could see the students being able to work forwards starting at 139 then adding 2 then subtracting 10 and getting those last two circles correct but not being able to work backwards and do the opposite of what is being asked. I could see the students getting very confused at this problem.

I am just using this students work to show the problem but I did not specifically tune in on them. I observed all the students working on this problem and every single student had problems with solving it so there are technically no steps taken by any specific student. Once I saw the whole class struggling I told them to skip the problem and finish the work page and we will go over it as a class. So I will explain the steps I took to show the students how to solve this problem.

•  I said let’s start at the number 139. I asked what arrow was leading to the next circle and pointed. The class responded with a +2 arrow. I then asked so what should we do to 139? They responded with add 2 so I asked them to add 2 and got 141.
• I continued on and asked what arrow was leading to the next circle and they responded with minus 10 from 141 and you get 131. This shows me that they understood this part.
• Now was the tricky part that the majority of the students struggled with. I said to go back to the starting number the book gave us, 139. I said what arrow is from the circle before it to the circle with 139 in it. They said minus 10. I then asked ok so do we minus 10? And the majority said yes. This is when I caught them and explained if it asks us to work backwards from a number we actually do the opposite and add 10. So we add 10 to 139 and get what? They responded with 149. I then said let’s check our work. Does 149-10=139? They all said yes and proceeded on with the rest of the circles. The students were able to understand that we had to do the opposite and understood to check their work to see if they did it correct.

One hypothesis I have about the students current mathematical knowledge with this specific problem is that the students may not have been introduced to working backwards and doing the opposites with adding and subtracting numbers. I feel the students were struggling with this problem because they saw the arrows, they saw whether to add 2 or subtract 10 based on the type of arrow so they did that whenever necessary but they did not comprehend that the problem needed to be solved by working backwards and opposite. Another hypothesis I have is that the students may not know at all that problems such as these involve closely reading the problem and figuring out to do the opposite. This is a higher task for them as it showed when the majority of the class struggled with solving the problem.

One way to advance the students thinking with this task is to set it up differently and maybe use only add 2 or minus 10. Such as: use the arrows to show minus 2 or add 2. Using smaller numbers could help and teach them how to solve it also say the dotted arrow is add 2 the non-dotted is minus 2 and then the students could solve it easier. Another way is that I could have the students take a different approach to this task. The students could be given a number and I would have them add a number to it and get that number then subtract a number and get that number. Then have that starting number and ask that if it asks to add 5 do the opposite. I think that if I explicitly state to do the opposite in certain times then the students will catch on easier and then understand what the problem is asking then have them come back and redo the problem given in their book and see if they understand how to solve it then.