Feedback

We have been working on placing fractions and decimals on a number line as a strategy to help order fractions and decimals. Students use various strategies to do so, sometimes converting fractions into decimals or drawing pictures of the fractions to help them understand what they are looking for. The learning objective for this exit ticket was twofold. First, “I can compare and order fractions and decimal numbers” as well as “I can locate fractions and decimal numbers on a number line”.

The feedback provided to Irvin gave strategies to help him meet the learning objectives. When comparing and ordering fractions or placing them on a number line, Irvin does not yet seem to have a conceptual understanding of fractions. He correctly identified that ⅘ is the same as 8/10. I drew a picture to help show him how he might have come to that understanding. I was hoping that this strength would help him understand his misconception about where to place “A”.

The area for improvement for Irvin is identifying how much 4/4 is equal to. It’s clear that he does not have an understanding that the number line is split into 10ths and not ones. It seems like he placed the 4/4 at the 4/10 place because he might have seen the “4” and made a connection. I drew out an empty rectangle into fourths to have him fill it out and understand that if he filled out all four pieces he would be filling out the entire bar which would be equal to a whole. In my conversation with him and on the picture on the exit ticket we talked about how the number line could be thought of as a bar split into tenths as well. Both the picture split into fourths and the number line split into tenths helped him understand that the section where he put A was less than a whole while 4/4 was exactly one whole. I also wanted to use his strength of identifying that ⅘ is equivalent to 8/10 with the drawing to help him make the same connection to 4/4.

My next steps with Irvin include doing a small, differentiated math group in which we work on conceptualizing fractions and ordering just fractions before mixing fractions and decimals. I will start out with helping him understand visually what different fractions might look like with fraction circles or drawing it out before moving on to ordering them and then placing them on a number line. Once he has a solid understanding of the fractions then I’ll move on to comparing and ordering fractions and decimals in order to place them on a number line.

The feedback provided to Gisselle worked on supporting her understanding of where to place fractions and decimals that are greater than a whole on the number line. She correctly identifies that ⅘ is the same thing as 8/10 by using the strategy of multiplying both the top and bottom by the same number to get a number in the tenths. I drew a picture on the side to help her visualize her thinking too with pictures in the hope that it helps her with her area for growth.

Gisselle incorrectly identified 1.2 as just 2/10. She does not have a solid understanding that place values to the left of the decimal indicate something that is larger than one and place values to the right of the decimal indicate partitioning numbers into less than one. I wrote out what her 1.2 is in words to have her understand that we are talking about one whole and two tenths. Then I drew a picture of what it would look like so she could see that we colored in a full bar and only a small portion of another bar. In my conversation with her, we talked about how that decimal was greater than a whole and where it would go on the number line then. She automatically identified that it would have to be past 1 and then understand that two lines after that would be two additional tenths.

Next steps with Gisselle include similar strategies that I used with Irvin. I am going to do a small, differentiated math group with her in which we conceptualize mixed numbers and decimals greater than a whole in placing them on the number line. I will start out with mixed numbers and have Gisselle draw out pictures of what it would look like. Then after she has a solid understanding of mixed numbers, I’ll add in decimals that are greater than one and do the same thing with drawing pictures of what those look like. Through this she will have a visual understanding of the decimals and fractions and will be able to use that to help her place the numbers on a number line.

 


Something that I will use to support both learners are number talks and math routines as established in “Mathematics Routine Banks” established by San Diego City Schools. I will have a fraction on the board and have students represent the fraction in as many ways as possible. This will include a hundredths chart, other pictorial representations, word form, decimal symbols, and a number line. Each time we find a new way to represent a fraction, I’ll have students record that in their notebooks. This will support Gisselle and Irvin to see that fractions can be represented in a multitude of ways and each way they can be represented can be another strategy for placing them on number lines.