Behrman: Student Work- Week 9

            Today, since it was a festive holiday, we integrated Halloween into our math and literacy activities (which the kids obviously adored). Since our kids have been working with the 100s chart quite a bit and working with double-digits, we decided to do a listening activity centered around this chart. I instructed students on what color to use (green, gray, or black) and which number to color. In the end, if students followed directions, they ended up with a Frankenstein 100s chart. Since they were using crayons or colored pencils, it was obvious who either struggled to identify the numbers solely based on listening (no visual assistance was supplied), or who struggled with following directions. This activity was especially beneficial for my student population since the overwhelming majority of them are ELLs. It is important for them to be able to quickly identify numbers provided in both written and spoken form.
          I walked around and monitored students as I was calling out numbers and observed students at work. One of our lowest students who we are vigilantly progress monitoring (in red for both math and literacy), had several errors. When I directed students to color the number 23 green, he colored the number 43 green instead. This occurred while several other numbers during this activity. Since there wasn't a long pause or request for repeating the directions, this reveals to me that his errors weren't due to struggling to follow directions. Instead, this seems to point towards a lack of understanding of number names and their corresponding written representation. For this particular student, it could be a lack of English language proficiency (his parents don't speak any English), or a lack of prior academic experience working with numbers.
          In order to determine the underlying issue for this student's struggle, I would assess the student by having him repeat a similar activity of pointing to/coloring in numbers on a 100s chart that I say aloud, but give him the choice of whether I give directions in Spanish or English. Giving him the opportunity to perform this task using his L1  would provide me with information as to whether their is a linguistic gap or an academic gap. If he excels with identifying numbers when spoken in Spanish, I would then be able to work with him using various TESOL strategies so that he is able to communicate his intellectual understanding in English, as well. If he struggles with identifying numbers when spoken in Spanish, then I would be able to work with him on his numbers and point out patterns between the names of one and two-digit numbers (for example, two-->twenty, three-->thirty), and using numbers in word form, digits, or spoken.

Cosmas Student Work

This piece of student work is from one of my first grade students and is a practice sheet about nickels and pennies.  The side of the sheet I will focus on is the side about nickels.  The students were given this practice during their independent math work time and had to count by 5’s to write the amount of nickels shown.  There is a small blank box with a cent symbol next to it for students to record their answers.   In the first problem, there are 3 nickels with a blank box, and the lines to “count ___, ___, ___” are already filled in (5, 10, 15).  This student wrote “20” in the blank box.  This leads me to believe that the student thought she was supposed to fill in the next number that comes in that sequence of counting by 5’s.  Several other students in the class did the same.  If there were 4 nickels they wrote 25 instead of 20.  When asked about this, one student said they thought they were supposed to count the box too even though it isn’t pictured as a nickel.  I would imagine this was a common thought throughout.

              However, this student only followed this “pattern” on the first example.  On all the rest, she simply counted the number of nickels present and put that in the blank box as “2 cents” or “5 cents”.  Interestingly enough though, on the lines where she was supposed to count up by 5’s, she counted sometimes by 2’s or 5’s depending on what number she put in the box.  For example, the box where she put a 7 (because of the 7 nickels pictured) she started counting “7, 9, 12, 14, 16, 18, 20”.  Though this isn’t a correct sequence of counting by 2’s, she still thought she was supposed start counting at 7.  This tells me first, that she didn’t understand that she was supposed to count each nickel as its own entity equaling 5 instead of counting how many nickels were pictured.  She may understand that a nickel is worth 5, but not that when we see multiple nickels we are to count them by 5’s to determine the worth of that grouping. 

              My second thought on this child’s work is that she may have been confused by the picture of whether this was a nickel or a penny.  I do not typically like to give sheets about money money because the student can be easily confused (especially when they are first learning the coins) which coin is pictured.  Manipulative coins will be extremely beneficial to getting this student to explain her thinking.  She may see the way a nickel looks and feel the way it feels as a 3-D coin and have no trouble counting them by 5’s.  it is possible she thought she was counting pennies, in which case the “count __, __,” lines would be confusing.  If I thought they were pennies I would be confused what to count by as well.  It is possible she did this and just counted by 2’s or 5’s depending on the number she placed in the box.

 In addition to manipulative coins, another thing that I think would help gain insight into this child’s thinking would be to have her use pennies and nickels in this case to set out, for example, 40 cents.  I would then be able to observe how she approaches the coins.  She may make a decision that counting by 5’s and using all nickels is the best way to arrive at 40 proving that she understands how much a nickel is worth.  This student may also not know how to approach these coins and I would be able to learn about the sense she makes of them blindly. 

Markert-Week 9

For my student work blog this week I will be looking at one of recent homework assignments. This homework assignment was given during my GLT and is about nickels and pennies. I wanted to look at this homework and see if there were misconceptions in the students work. This homework assignment asks the students to answer two short word problem questions that involve counting nickels and pennies. The third question asks the students to count the pennies and nickels shown. Overall the students did a very good job at this homework assignment and were few errors. The one particular student work made a mistake with the first question.

The question states: “Sabine grabbed 2 nickels and 7 pennies. She had (blank) cents. Tony grabbed 3 nickels and 1 penny. He had (blank) cents.” The students were asked to fill in the blank to the problem. For the first blank this particular student wrote the answer “9.” I believe that this students’ misconception is coming from counting the number of coins rather than the value of the coins combined. I’ve generated this conclusion also from the students work next to the problem. Next to the problem the student wrote “2+7=9.” This tells me that the student saw the two numbers and simply added. I like that the student knew to add the numbers since the problem says grabbed, but he maybe didn’t think about what the cent notation meant. However the second part of this question the student answered correctly. He also displayed “15+1=16” next to the question. This shows me that he knows 3 nickels is worth 15 cents and one penny is worth 1 cent.

The rest of the homework sheet was done correctly, which makes me think that maybe this first question he didn’t think thoroughly through the problem. He may have rushed and immediately assumed to just simply add. This is mistake doesn’t make me think that this student needs further understanding behind the value of these coins since he did correctly answer the other questions that were similar. I believe that this may have been a careless mistake. I was very interested in the students’ use of number models. Prior to this homework we had a lesson on change-to-more number models and this student demonstrate an understanding for these models in his work alongside the question. This student clearly understands the grabbing more coins means addition and he also is using the addition sign and equals sign appropriately. He shows that by grabbing more coins we are going to add these two numbers together and those two numbers are going to equal the third which is also the answer. Even though the first part of the first question he did not get the correct answer he used the number model correctly and correctly added those two numbers together. One way I can advance this students thinking is by asking him questions about why he chose to add these two amounts together? Or why did he not convert the coins in the first problem? I would also like to see the student explain how he came to the result that he did? This would force the student to think about why he is doing what he is and why it is important. It would also show me the students thinking and what he actually is gaining from this homework and lesson. 

Week 9 Bode

          This week I want to focus on a piece of student work that displays a low level student while working with a middle level student. Both these students I have observed during math and helped them quite a bit; one struggles with the math content while the other tends to get distracted and off task. The activity was called Penny Grab where students have 20 pennies that they put in a pile between them. One student grabs a handful of pennies and the other student takes the rest. Both students count how many pennies they have. Once they have counted their pennies, the partners have to decide who has more pennies. While I was watching these partners working together I was noticing the middle level student was doing all the answering for who had more. I wanted to monitor this because I felt it was important for the low level student to answer too. When I asked the lower level student to count with us and see who has more she could count how many she had and how many her partner had but she got shy when she was answering who had more. She answered that she had more (she had 8 pennies while her partner had 12) but then looked up at me to see if her answer was correct or not. Instead of me telling her no she is wrong I asked her partner to explain who has more and how he knows that. Her partner was successful at explaining because he was able to say “well I have 12 and she has 8 and I know that 8 is more than 12 because on the number line, 8 is less than 12.” After that I had the girl try to answer again and this time she had 11 pennies and her partner had 9. I saw her look down at the number line and take a minute to see which number was larger. She answered 11; I was so impressed to see that a student gave another student a successful strategy to use.

            In order to advance this students thinking (the low level student) I really think that partner working is successful but it has to be an appropriate partner whom I know will not just give her the answers. She tends to get really shy around teachers because she’s timid to answer so I believe that when she works with a partner she can see their strategies and learn how to use them herself. Another strategy I would do is have students share strategies they use on a problem in a whole group discussion. This way students are sharing their ideas (which we already do) however to make it different I would want to maybe demonstrate having other students, like this struggling girl, come up to the board and solve the problem by using the strategy another student explain. If the student doesn’t understand the strategy than I would have the child who thought of the strategy explain it to the child who is solving the problem. This is not a way to text students or scare them, it’s to demonstrate and have low level students work our problems using strategies they may not have thought of that can be helpful to their learning.

McCormick Student Work

One piece of work that I examined this week is a homework assignment where students worked with nickels and pennies to determine the amount shown. The problem read "Sabine grabbed 2 nickels and 6 pennies. She had ____ cents." This student said that she had 8 cents. This reveals that she knows how to count amounts of coins, but cannot yet determine the value of the nickels. She knows how to count pennies, assuming that she thought all coins were pennies. She may have thought that all coins are worth the same as a penny. She does not yet know how to count nickels and pennies together.

One way that I might advance this students thinking is by creating a chart for her to visually see the differences between different coins. I can display the faces of each coin and how much it is worth. I can also display the conversion between 5 pennies and 1 nickel. This might help the student to see the  difference between pennies and nickels. Another way that I might advance her thinking is by explaining orally the difference between the values of the coins. I might explain that the number of coins is not the  same as the value of the coins. If I could ask her a question, I might ask her to explain how she reached the number 8. If she explains that she counted the number of coins, then I could explain the values of the nickels. A future math task that may be beneficial for her is using actual coins while solving the problem. This would help her to see the problem shown visually instead of just stating the names of the coins. She may be able to solve the problem given the coins as a resource.

Marie Lewis week 8 work blog

I am starting an afterschool math club to help students who are in need of extra support.  This past week I gave another pre-assessment to see what students knew about addition, subtraction, and multiplication.  The reason I tested these specific areas was because their NWEA standardized test scores fell below the “meets” category, putting them below where they need to be at the beginning of fourth grade in these areas of math.

One question on my pre-assessment asked the students to write a multiplication and addition sentence for an array that had four rows of 7. One of my students wrote the multiplication sentence as 4x7=28. Her addition sentence was 4+7=11. 

Although her multiplication sentence matched the array, her addition sentence held misconceptions that intrigued me.  She could have thought she was supposed to use the 4 and 7 to represent a multiplication sentence and an addition sentence, not recognizing she was supposed to end with a product of 28 for both.  This also tells me she may have a misconception with skip counting since she was not able to write 7+7+7+7=28.  This shows me she knows her multiplication facts, since her 4x7=28.  She also recognized the correct number of rows and items in each row.

When working with her, I think it will be important to ask her to skip count by various multiples.  This will show me whether or not she understands that multiplication is repeated addition or has simply memorized her multiplication facts.  

Bullying projects

This week my favorite part was seeing my students bullying projects come together! We did not have any explicit math instruction for me to review their work other than homework, however it was just a review of each type of graph they have learned. So I decided to write about their amazing projects!

 I could not believe that finally after two weeks of explicit instruction my students were able to put together posters that looked amazing! It showed off all their math skills that they have been learning, bar graphs, line graphs and line plots. It also was cool to see the different types of titles that they chose for their titles. The best part of the day for me by far would have been seeing the look on each students face as they completed their project. They were so happy and felt so accomplished they could not believe that they finished a fourth grade project and saw all the work that they have been doing come together and really mean something.

It was also very interesting to see the students really check their grading rubrics with each component of the project to make sure they had every piece and that they clearly labeled every part of their poster. My students are all dying for their posters to be hung up in the wall because each of them is so proud of their work. That to me is so important because they will now want to try hard on each project because they will want to have that same feeling again and now that they are creating something that truly is a reflection of what they have learned and have done.

Maxwell-week 8

This week was the last week of my GLT.  While examining student work I recognized that many of my students would get the ones place of a subtraction equation's solution correct, but the other numbers were off.  After further analysis, I recognized many of my students were not following correct borrowing procedure.  For instance, they would correctly carry a tens to the ones place, however, they would forget to reduce the number in the higher place value position.  Many of my students erase their borrowing work when working through an equation, which may have led to them forgetting the correct procedure.  However, we went over borrowing procedure as a whole class review, and many of the errors were corrected.

King Math Conversation GLT Week 1

This week I was able to teach a small group lesson to a pair of girls who were struggling with understanding the procedures for doing lattice multiplication. One of the girls just needed to hear the procedures more slowly and be given time to work through a problem while getting confirmation that she is doing the procedures correctly.

The second girl is very low level in her math understanding. Her strategy for simple multiplication (i.e. 7x8) is counting up on her fingers starting at 1. While making sure she understood the procedures for lattice multiplication and helping her through the multiplication, I made an effort to help her understand some other methods for solving simple multiplication, such as solving 7x8 by splitting it into 5x8 and 2x8. I introduced this method to her because she does pretty well with multiples of 2, 5, and 10. I also introduced the method of solving 7x8 by finding 7x10 then counting backward 2 sets of 7. She responded well to both of these methods and understood how to use both. I did not have enough time see if she was able to take these methods and apply them to other 1 diget multiplication, but the unit 2 summative assessment is on Monday, so I will be able to assess her growth and understanding of multiplication.

Delise Week 8 Student Work

This week we taught two things in math that were brand new for the students. We talked about name collection boxes and frames and arrows. The students really impressed me when coming up with different names for numbers. For example, in the math message, students were to come up with different names for 10. Students were coming up with ideas such as various subtraction problems and addition problems, the word ten, ten ice cream cones, ten tally marks, and the roman numeral for ten. All of the different ideas seemed to help the students see the relationship between addition and subtraction, since we have been easing into subtraction. The students would see that 30-20 equals 10 and 9 + 1 equals 10, the answer is still 10, but they are opposite operations. When students were assessed on this concept, they did extremely well!

With the frames and arrows lesson, students really understood when the rule was adding. The part that students did not grasp as easily was when it would look like _ 24 _ _ _. And the Rule was -6. So for the first blank, the student would need to add 6, so that going right the numbers decrease by 6. To help students with this, I had them do all of the blanks after 24 and then use those numbers as clues to find out what the blank before 24 was. On the assessment, there was  a problem that was _ 20 _ _ _ and the rule was -2.  I think this really seemed to help students because on their assessment, some students wrote out the work for numbers after the 20 and had the 22 correct as well.

Cosmas Student Work

The piece of student work is from a lesson I just recently did on time using both the hour and minute hands.  My first grade students caught on very quickly to telling time to the hour.  They are able to identify “o’clock” times with the minute hand pointing straight up very quickly.  However, they have trouble using the minute hand as well to make a complete time.  The students (for the most part) understand and can show me by pointing how each number stands for an interval of 5 minutes when the minute hand is pointing to it, however, they have difficulty taking that knowledge and constructing a time out of it such as 6:15 or 9:30. 

              This piece of work is particularly interesting because I had a side conversation with this student after they completed it that contradicts their written work.  The sheet depicts four clocks that are blank and students need to draw the hands for 6:30, 5:40, 6:00, and 6:20.  After the hands are drawn there is a space for them to write the time out in ___:___ notation.  This student’s sheet has hands drawn on the first clock to show “6:00” which is incorrect for 6:30.  Then, the times he depicted read 6:3, 3:5, 12:6, 7:3.  From this work I am to assume that the student doesn’t understand the counting by 5’s interval to find what the minute hand is pointing to.  However, once I saw this I had a conversation with him about what we had learned about finding the number that the minute hand represents.  He repeated to me that we count by 5’s and did so with his fingers for the first example arriving correctly at the 30.  I then told him to put it together piece by piece, the hour then the minute and he arrived at 6:30.  What was most interesting though was that after he turned this in I noticed he made a mistake on the 6:00 example which we had been over numerous times and he had demonstrated he understood.  This was the problem where he wrote 12:6.  Even though he knew one hand should point to the 12 and the other on the 6, he flipped them when writing it out and was confused again about what the minute hand represents.

              When thinking about this student’s work first I think that there is an obvious misunderstanding of how the numbers on the clock face could mean anything else.  This is a difficult concept for any first grader to handle.  Though he knows how to count by 5’s around the clock, he hasn’t concreted the idea that when the minute hand points to those numbers, they are read differently.  I think one thing that would help this student would be using real-world examples of times to rule out “non-sense” times.  For example, ask him if he has ever heard of a time that is 6:3 or 3:5.  The answer will (hopefully) be no, and we can then take a more logical look at what the clock is trying to tell us.  Giving him a way to self-check whether what he has come up with makes sense will be a great tool for using some problem solving to arrive at the correct answer. 

Markert-Student Work Blog

This week I collected one of my homework assignments from my unit. This homework assignment asked the students to look at 5 dominoes and count the number of dots on each. Then it asked the students, on the back, to draw the dominos in order from the least to the greatest number of dots. It also asked the students to write under the dominos the number of dots prior to redrawing them and ordering them in the back.  The student was able to accurately count the dots under the dominos and write the number under the corresponding domino. On the back the student drew the dominos in order from least to greatest number of dots. However, her homework proved to be really interesting. The student looked at the domino but only the bottom half of the domino. The student ordered these dominos from least to greatest but only looking at the dots on the bottom half not the number entirely. Even though the student was able to see on the front of the sheet the number of dots each domino has. The student ordered the dominos on the back starting with the domino that had no dots, then the domino with one dot, then the one with two, then three, then four, and finally five. This is not incorrect because she did follow the instructions of ordering but she didn’t look at the whole domino. This makes me wonder if maybe she thought the domino is two separate parts or didn’t really understand the question. She may have also felt that this question allowed them to choose which half they order.

I would have liked to seen a question asking the students for an explanation. This would have allowed me to see what the student was thinking when she was ordering the dominos. This homework was in direct correlation with the student’s exploration day. This day the students were asked in class during a center to organize the dominos from least to greatest. This was the first time that the students were introduced to dominos so there is a chance that she may not have known the domino was all the dots as a group. I do not think that this student has a problem with ordering numbers since she was able to accurately do it based on the dots on the bottom. She also was able to answer the second half of the homework correctly. The second part of the homework asked the students to write a number that comes before and after the one printed. This is also an insight as to whether or not the student understands ordering of numbers. As a result I think her misconception of ordering the entire dominos number of dots has more to do with her unfamiliarity with dominos or the questions wording. To help this student understand this it would be beneficial for her to have a better understanding of dominos. This would allow me to see if this was the problem. It would also be helpful to higher her level of thinking by asking her to explain her reasoning and thinking behind her ordering. 

Bode Week 7

          This piece of student work is from a low level student in math, which I know this based on working with this student and observing them in all subjects not just math. This student goes to an interventionist (for reading and math) during the reading and math time. Normally my MT has the student go at the second half of the class so that the student still gets to sit in on the math lesson and then gets some extra help for the individual work time. Both these pages are pages from the Everyday Math Student journals and these were completed by the student during the time she sees the support teacher. I can tell that her answers for the clocks page are correct but have several eraser marks which I know, from the past, that she had attempted this problem many time and got assistance with the answer. Her numbers are still being worked on since you can tell she is practicing writing them still. The right page is the work I saw her doing today. She was sitting at a table with the support teacher and she would sit not doing anything unless the teacher was helping her answer. This would be the answer for why she only has number 1 done and number was attempted but erased by her. This student severely concerns me because she is at such a struggling level that even with the assistance she is getting she still struggles with the content and severely needs one on one help. I know from observations that most of these answers she could only do because the support teacher walked her through the entire problem. The gaps in her thinking are really below grade level and even somewhat below a lot of other students in the class. It is clear that one on one attention is desperately needed for this little girl.
          For a student like this who really needs one on one help I am at a lose for what I could do to help her. During students individual work time in math (working on worksheets or games) I am always trying to stop at this students table to make sure I check in on her. More than half the time she is not doing the work and I spend the remainder of my time working with her. What encourages me that she can do the work is that she obviously knows how to answer, although it is with much one on one work, she still has the capacity to answer the problems. Two ways I would help would be to continue monitoring her in the classroom activity time and if we have partners than I would want to strategically partner her up with someone who I know will be a leader and support/guide her, I have several students in my class who I think could do this. Next I would want to send home some work for her to try to do at home and to have her parents sign it so I know it has been checked and worked on with them. Her parents seem a little bit uninvolved so having them sign it and making it a priority would encourage her to do work at home.

Today I taught my first "real" math lesson (I say real, meaning that I am the one who wrote up the plan and enacted it. I have taught math before this year in this placement just when my MT tells me what to do right before). The math topic for today was patterns. Most students had never heard of patterns before. (or at least did not articulate that they had when asked). I started by a brief discussion, asking students if they have ever heard of the word repeat before. One student raised his hand and said it was when you mock someone, which he is correct. After this student said this, noone else was able to come up with something else that repeats, even with prompting. I tried to get students to think of their daily activities (brushing teeth, getting dressed, waking up, going to bed). Those are all activities that students repeat. After we talked about the word repeat, I asked if students had ever heard of the word "pattern" before and if they had, tell me what the pattern was. A few students were able to correctly identify what a pattern was (a student example was i did my sisters hair with barrets-yellow blue yellow blue yellow blue.)

Next, I continued by reading a book about patterns. Throughout the book we talked about the different patterns that appeared, focusing on the AB patterns. After the book, we worked on coming up with rhythmic patterns and translating rhythmic patterns into concrete patterns (using halloween cut outs). I gave several students chances to try to come up with their own rhythmic pattern. Several were able to, several were not.

Next, I modeled how to create an AB pattern with the halloween cutouts and we made one together as a class. Then I set the students free to create their very own patterns. The directions of this ended up being for students to create only an AB pattern which I feel like made the task not so high level. Students were not able to go about the question in an open ended way. This was not the way I set up the lesson so I was frustrated with having to teach it this way. My MT told me that I needed to only have them do AB patterns since they havent done patterns yet. So they were only given 2 different colors of halloween cut outs to create their pattern, not giving them much room to show their understanding of patterns.

After looking at the patterns that the students created, all but 9 students successfully created an AB pattern. Some of the work that students did show that they clearly did not understand how to create a pattern, others look as if they may have known but didn't have room to continue to pattern. Therefore, it would be beneficial for me to have a chance to talk with the students (time ran out so I did not get the opportunity today but will try to do so later in the week if possible) about the pattern they created and why they did it the way they did. If they had a reason and can tell me what would go next in the patterns that they did (not necessarily AB), that would tell me that they may actually know how to create a pattern and just did not listen to the directions of creating an AB pattern.

One student did orange pumpkin, white ghost, orange pumpkin, white ghost, white ghost, white ghost. This is a student who is very low in terms of academics therefore, I expected this to be kind of challenging for her. This activity shows me that she needs more opportunities to explore AB patterns to gain a deeper knowledge of patterns.

Student Work Week 7

This past week, I worked with one student, Dave, individually. This students has struggled with reading and writing and gets frustrated when he doesn't know how to spell words, so he often gives up. During math time, this student seems confident and thrives on getting the answers correct in class, however, he cannot read the directions, so he becomes even more frustrated when the problems aren't verbally said to him to solve. This week, the students were filling out their math boxes in their math journal. While walking around the room, I realized many, if not all, of the students had the first problem in the math box incorrect. The problem said, "Count by 6s." It looks like this: _,12,_24,_,_. We haven't taught counting by 6s, and have only been working on counting by fives and tens so far this year. When the students add, they normally use their fingers. I helped the students who had this math box incorrect, and showed them that we were counting by sixes, since many of them had 11, 12, 24, 25, 26 on their papers. When I got to Dave, I was completely shocked! He had the entire problem filled out correctly. I found this amazing because I know that Dave could not read "count." I asked him how he did the problem and he told me that he saw "6s" and so he went down 6 from 12 and up 6 from 12. He also told me that he realized that there was 12 from 12 to 24 so the middle number had to be 18. This justification was so great! Instead of giving up and saying that he couldn't read the problem, he used the clues in the directions, and in the problem itself to work out the problem. When explaining what he did for his problem to me, he stated HOW he solved the problem, and that he was able to realize the relationship between the 12 and 24, and had to find the middle number, 18, when he realized that he is supposed to be counting by sixes. He didn't just say, "I saw 6s, so I counted on my fingers until I got to the number." This is ultimately the goal of all my students! I want them to be able to tell me why and how, and not that they just arrived at the number by counting on their fingers. I would want my students to see the patterns and relationships between numbers, in order to solve the problems.

Student Work: Week 7

          The past two weeks in math, we have been learning about writing multiplication number sentences. The students worked with manipulatives to put the cubes into groups in order to get a total number (which was given). We taught students about what happens when there are remainders. The students did not have to group the cubes into equal groups; rather, they had to group them into groups of the same amount, whether or not they had a remainder. We were working on a calendar multiplication chart where the students and I filled out the calendar according to the days in October. After modeling and working on problems together, I allowed the students to fill out box 21 with a partner.

          While walking around the classroom to hear student strategies and student thinking, I came across with more than one group that wrote their multiplication problem 11+10=21. Although I told the students that this was true, I asked the students to think about this same sentence using multiplication. I asked, "How many groups of 11 do you have?" I was looking for the students to write multiplication sentences. The next steps of subsequent lesson plans may be to write division sentences and to further discuss division.

Jones- Week 7

At this point my students are working on fact families and identifying different ways to arrive at a given answer and identify how numbers are related. My MT introduced fact families Monday and Mondays homework included writing addition and subtraction number sentences involving three numbers. An example was 75, 50 and 25. The students had to write 2 addition number sentences and two subtraction number sentences using those numbers. Also as a part of the homework, the students had to choose their own three numbers and create 2 addition number sentences and 2 subtraction number sentences. The 3rd graders did very well with this. They understand the concept of fact families and were able to.create true number sentences when given a set of numbers. On October 16th the students had to again practice writing true number sentences based on.a family of numbers. In addition this, the worksheet asked the question " Why is it important to know the basic base 10 addition and subtraction facts? Students either did not.respond to this question or wrote something to this effect " so you will know them if someone asks". I wish that students would have put more effort into answering this question.
A future task that students can do with this concept would be to again discuss the importantce of knowing fact family information. It is important that students know why they are learning something. If they do, they are more likely to internalize the information and are able to recall it at a later date.

Berger- week 7 student work blog

The students received a homework packet on Thursday to work on over their fall break next week. The packet has questions on everything that they were studying about fractions, from reducing to lowest form, to adding & subtracting and multiplying & dividing. I was walking around the classroom while the students were working on their packets before they went home for the day and I stopped at one student's desk to watch him do his work. I noticed that he was counting on his fingers so I asked him what he was doing. He explained that the fraction was 74/3 so he was using long division. I asked what he was using his fingers for and he said he was counting by 3s to get to 74. I immediately saw what he was thinking and asked him if he thought the 3 had to go into the 74, not just the 7. It took no time at all for him to see what he was doing was unnecessarily difficult and he immediately wrote down 2 and multiplied that by 3 to bring below the 7 to subtract.  He then continued through the rest of the problem to find the answer. After he got his correct answer, he asked if that would have worked, what he was doing before. I explained to him that it would work, but it is just a lot more work and very time consuming to have to count up to big numbers by a small number. I noticed he was counting on his fingers again and asked what he was doing. He said he just wanted to make sure and check his answer.

This was an example of a mathematical error, but not necessarily a misunderstanding. I think that the student knew the general way to do this operation because as soon as I pointed it out, he jumped right into doing it the correct way without any hesitation. I think that this shows that the student had an understanding of how to long divide, but definitely has not mastered it yet. What I would offer him as some extra help would be showing him how and why long division actually works and giving him practice problems to work on. I think with problems like long division, one of the best ways to become good and quick at it, is practice.

Week 7

This week my students worked on their bullying project and were making line plots and bar graphs to represent their data for their posters.

The students had explicit instruction on how to make line plots as we did an example as a class and were given the information necessary to make their graphs. However, one student (at a lower level) began making x and y axis, which a y is not required for that. The student then drew half x's and half bar graphs on their paper thinking that was the best way to represent this data.

It was evident that the student heard the two types of graphs that they would be making however, I think they misunderstood that the graphs were to be separate and not one graph. When the student was told to correct their mistake they went off on their way. When we got the papers back after the lesson was over and analyzed the paper again, the student had now made a line graph and not a line plot.

Looking at the paper I made a few conclusions,  one this student does not understand the differences between these graphs, the kind of information each of these graphs show and finally, the way in which each of these graphs represents the information.

I think explaining the project altogether in the beginning threw the student off as they heard too many graph names and mixed them up. Adding that on top of their misconceptions of the graph did not help the student overall when it came to making the graph.

After seeing the students mistake my mentor and I decide it would be a good idea to sit with them next class and find out what they think they know about each graph and clarify and fix the misconceptions accordingly.

Week 7-Ricchio student work blog

This week in math my students are working on place value. They're working on understanding the value of a digit and its place in the number (ones, tens, hundreds, or thousands). The work I’m reviewing is the Homelink homework from their Everyday Math Journals. Many of my students are struggling with the concept of zero and how it still stands even if there are zero in the tens place. For example, if the problem says there’s 7 hundreds, 0 tens, and 4 ones, instead of writing 704 I had a few of my students writing 74 like the zero didn’t exist. This shows me that students are confused with the idea that zero can be a placeholder. I think my mentor teacher and I need to reiterate how zero can be in a number at different places. After going over corrections, one student stuck out to me the most.  This student did not appear to have a good grasp on the concept, either because he was extremely confused or just not paying attention and decided to write random answers. The question I am looking at is number 1, which has a visual representation of the 10-base blocks. The problem showed 3 hundred blocks, 7 ten blocks, and 4 one blocks. Instead this student put 102. This is one problem I was not completely sure how to analyze unless I have a conversation one on one and ask him again and see if he still thinks the answer is 102.

Behrman-Student Work Wk 7

              Today I was grading students' tests that they took yesterday while I was at our MSU classes. I was unaware that we were even planning on assessing students yesterday; the majority of the assessment was over material that we have been working on, such as writing numbers in different ways, skip counting, etc. However, there were certain questions that our students haven't explicitly been exposed to. Although they have the conceptual knowledge to solve these, they clearly struggled with the format in which they were asked to apply these skills. A trend I saw on several students' tests was that they were extremely confused about tables comparing the number of stamps two different students owned. Each picture of a stamp was worth ten stamps, as noted by the key underneath the table. Although my students are entirely capable of counting by tens and determining the difference between how many each student owned, the majority of students answered this incorrectly. It was a fill-in-the-blank question, so students put what they thought was the obvious answer and just counted how many more pictures of stamps the one child had.
             I think that if my students would have had more experience working with tables and understanding that keys even exist, they would have been able to be successful. Since I wasn't there during the actual testing session, I'm not sure how my MT explained it or what clues she gave. This reveals to me that my students understand one-to-one correspondence, but were not aware that these everyday object pictures could represent different values (although they do understand this when related to base ten blocks). A next would be to present a similar type of a problem comparing number of objects between two people; however, I would use base ten rods as the objects. I would start by asking students how many more rods person A had than person B. This would transition into a discussion about what each base ten rod really represents (10 units). We could then make our own key about what each rod represents and scaffold this idea to real-world objects in tables. Another next step would be to present the same problem to students and have them in their table groups talk about how they would each solve it. Since I didn't grade all the tests, I would be curious to see if other students did answer it correctly, or what misconceptions they had. While monitoring these student discussions, I would determine whether to select individual students' ideas and sequence them, or each group's strategy.

King Student Work Week 7

This week I led the Fast Math lesson warm up in which students were asked to round various decimal numbers to the nearest whole number. The students were given 2 minutes to complete the task then I led a class discussion to find the correct answers. During the class discussion I called on a student to read the unrounded decimal number and the rounded answer. I then asked the student, whether their answer was right or wrong, to explain why they rounded up or down. Being asked to explain their thinking was something that many students struggled with, but after talking to my MT I found out that the students are not used to having to explain their thinking.

In order to have students be more successful in the future during class discussions that require deeper explanation of why they did what they did, I will need to scaffold their thinking and give them some sentence starters. With this particular class discussion, there is little I can do to further their thinking because the concept being discussed is pretty straightforward and there is really only one way to come to the correct answer. One thing I can do to advance student thinking is to add additional digits to the numbers I am asking the students to round, which will create a situation where students will potentially have to round twice.

Note: Since this lesson and discussion was taught, the class has had more practice with rounding and seems to have a better understanding of rounding.

Marie Lewis Student work blog week 7

     My students were given this question as a quick check after learning how to create line plots.  One of my students responded with this:

     The student plotted his graph by putting an x for every page read on the noted day of the week. He is on the right track because he understands the layout of a line plot and was capable of drawing the x's as he thought acceptable.  This work is wrong because the line plot is supposed to have a scale along the x-axis that includes the values in the problem.  For example, a good scale would have been from 1 to 20. This student does not have a scale, rather he listed the days of the week.  It seems as if the student thought he was supposed to keep track of how many pages were read each day.
     If I were to talk with this student, I would ask him his reasoning as to why he labeled each day of the week.  I would ask him to explain to me what he knows about what a line plot entails.  I would then restate this question, taking the days of the week away from the number values.  I think this is confusing because the student could have thought he had to keep the day and the value together.  The question would be better phrased as, " Throughout the week, Consuela read a different number of pages from her book each night.  She read 8 pages, 11 pages, 10 pages, 7 pages, 8 pages, and 8 pages. Create a line plot of this information." The specific days of the week are irrelevant, confusing the student to think he needed t keep track of how many pages he read each day, rather than focusing solely on the values.

Maxwell week-7

Erin Maxwell

10-18-12

This week, I assigned a particular workbook page for in class work to review the fact extension lesson from the previous day. I was particularly interested in student success in completing the portion of the worksheet shown in the photo below, as it using a math fact to work through a sequence of related equations.  This student receives special education support and often as challenges with concentration during whole group lessons.  Questions three and four on the worksheet below were answered incorrectly, however, after analyzing these solutions, I recognized a repeated problem solving strategy.  Instead of borrowing, this student subtracted from bottom to top, therefore he did not recognize the larger number being on the bottom to be problematic.  In question three, subtracted five from seven, then one from seven. Question four’s solution was gathered from a similar strategy, subtracting three from eight and one from eight. Although this strategy provided the target student with incorrect solutions, he managed to work correctly from the ones place onward showing a command of proper problem solving direction. Yet, this strategy may have developed from an intimidation or unfamiliarity with proper borrowing procedure.  An interview with this student to better understand their rationale would be very beneficial.  This could help clarify if the problematic strategy was developed out of carelessness or misunderstanding. 

15-7=62

13-8=75

Cosmas Student Work

The sample of work I chose this week is a worksheet from the Everyday Math curriculum my class uses about counting up and counting back on the number grid.  With my first grade students we have been working a lot on counting our hops up and back on the grid using their fingers so the concept is definitely familiar. 

This day, I conducted a whole group lesson specifically about counting on the number grid and this sheet was given for independent work after the lesson.  As I was walking around I noticed this student understood what each problem was asking him to do (count up or back), referring to the number grid to count, and filling in his responses.   However, each response was 1 off either too high or too low.  At first I thought maybe he was making the common mistake of saying 1 before he even made a hop making the final answer 1 too low  (Ex: start at 27, count up 10.  Student puts their finger on 27 and says 1, hops to 28 and says 2, etc.).  However, when I asked him to show me how he arrived at his answers he did something really interesting.  He did not do what I had anticipated.  He correctly started his hops, but when he arrived at the end of a row (10, 20, 30) he did two things: he either didn’t count the first number after the sweep (11, 21, 31) and moved on to the next number (12, 22, 32) leaving his answer 1 too big OR he counted the sweep AS a hop resulting in his answer being 1 too small.

In the photo included of his work his answers were erased and corrected after talking it through with me and modeling again how we make a sweep when counting on the number grid.  Once we worked together on this he completed #6 on his own and correctly.  This leads me to believe two things about his thinking.  First would be that in a whole class setting he didn’t receive the individualized attention he needed to understand fully how to maneuver the number grid.  There is a large class number grid next to the smart board where I model how to count on and each student uses the back page of their math journal for an individual copy.  I observed him complete this process in class  a couple times, but he may have just been going through the motions as I did them instead of making a conceptual understanding of how the “hop” helps us count up and back.  I think one way to push his thinking further or to make this concept come to life and make sense would be to incorporate this number grid into more of an addition problem and having him use manipulative on the grid itself.  From getting to know this student, I know that at home he works with his parents on simple addition problems and having a student start at a point and move 10 spaces to see where they end up on a grid is essentially an addition problem phrased differently.  I think this student would benefit from seeing what he is adding on to with some type of counters. 

Second, my observations and this sample of work leads me to believe that this student may not understand that counting on the number grid is the same process of adding on as counting on our fingers or with counters would be.  He may be actively paying attention to the hops he is making but not understanding that each hop is how we add 1 to a number.  If he understood that this is just another way of counting to add on or take away maybe he would have been able to self-correct that starting at 24, counting up 10, and ending at 33 doesn’t quite make sense because that only adds 9.  I believe that using the number grid as a reference and instead counting with fingers or counters may be more beneficial for this particular student to understand.  Also, I think that practicing the way we sweep our finger down a number grid would help with this student too.

Student Work Blog- Markert

 Abby Markert

One of the lessons that my first grade class had this week was on clocks and time. Students were introduced to clocks, both analog and digital, during a mini lesson. This mini lesson showed the students how we tell time and what the hands on the clock stand for. The students asked questions that were insightful to their learning like “why do some clocks not have numbers?” or “what are the other numbers on the clock (i.e. the 30, 45, 50, etc)?” My MT did an excellent job answering these questions and the students seemed to grasp the concept. After the mini lesson the students were asked to go back to their seats to work with their own personal analog clock. The students had a few minutes to work with their clock on their own and explore them. Then my MT asked the students “can you show me 4 o’clock?” The students would then have a few seconds to get show this time on their clocks and hold it up. My MT did this a few times with different times all ending on “o’clock” or to the hour.

            During this time I walked around looking at the clocks and seeing what the students were doing. I also wanted to hear what the students were talking about and observe their thinking getting to a particular time.  One student in particular grabbed my attention with the times that she was showing on her clock. One of the times that she showed was “4:30” instead of “4:00.” I noticed that she did this and decided to ask her “why she showed this on her clock?” She responded to me that it shows “4:00.” I asked her again “how do you know that this shows 4:00?” She looked at me for a second and said, “Because the hour hand is on the 4.”

            I believe that this student realizes that the hour hand must be on the 4 for it to be “4:00” but I think confusion arises with WHY it must be on the 4. I think that she has a misconception that the only hand that matters is the hour hand on the four. This tells me that the student does not fully understand the reasoning behind why the clock works the way it does. Meaning I do not think she realizes that there are 12 hours in a day and that the minutes in the day add up to hours. She only saw the one large component of the “hour.” I think that to help assist her thinking it would be beneficial to explain these key concepts to the students. Another small misconception that I saw a lot of that still goes off this same misconception is that the students just knew that “big hand on the 12, small hand on the 4.” I would have like to see some questions about why this means 4:00 not just “that’s what we have to do.”

            This lesson was an introduction to the lesson on clocks so it may become clearer about the different parts of a clock and why it works the way it does. I think that in later lessons it may be useful to ask the students more questions about the clock. This would allow the task to become higher level and also will help the students understanding of the different areas. 

Wek 7- Patterns HW Robb

Student Work Blog Week 7

After giving my students the opportunity to create their own Halloween patterns and introducing them to “A-B-C” patterns, I followed up with the following sheet for homework. Students had the opportunity to produce several different kinds of answers for their problems, which allowed me to understand their thinking about patterns. Students came up with many ways to complete the patterns in “part A” and also created a variety of patterns in “part B”. Some students thought about patterns based on the shapes/pictures and completed their patterns by drawing the picture that came next and using solely illustrations in creating their own patterns. Student 1 took this a step further and used a combination of both illustrating and labeling the patterns.

            What this example of student work is showing me is that this student has a very full understanding of patterns and pattern creation. Without much prompting, this student recognizes that their pattern is an “AB” pattern.

            Student 2’s work is unique. She is the only student who solely used letters to represent her patterns. She is an ELL who primarily speaks Spanish at home. All of her answers are correct. 

            I wanted to make this task open ended. I did not direct students to “draw” or “label” or “color” their patterns. My only directive at the top of the page was “what comes next?” This student interpreted that to mean that she could use letters to represent the next “piece” of the pattern, and I think it is just as bright of an answer as the students whose pages are full of color. Her answers are quite formulaic, and I will be interested to hear her thinking when we discuss our answers.

            Student 3 used colors in completing her task. “Part A” of her task is very well done, her color scheme is logical and her answers are correct. However when give the opportunity to create her own pattern, her work reveals that her knowledge of pattern concepts do not extended into a realm that is just a bit more abstract.

            This student shows that she needs more practice with creating her own patterns and applying the concepts she uses to solve “part A’s” problems to part be. With a class discussion and presentation of other students thinking, and another group task, I think shoe could achieve this handily because she does express that she has enough knowledge to complete pattern sets.

McCormick Student Work 10/18

The student sample that I chose was from the student's homework this week. The homework assignment had students draw a picture of an interesting clock or watch that they see in their homes. The student drew a clock with roman numerals on it. Each roman numeral was written correctly around the outside of the clock. The student also drew two hands on the clock, one shorter and one longer. I was very surprised that the student drew this because students have not explored roman numerals at this time. A family member could have assisted the student with finding the interesting clock, but I still think it's a very interesting sample of work.

This reveals that the student currently understands that other symbols can be on clocks and watches and that they are still clocks and watches without visual numbers on them. The student also understands that there are two hands on the clock, with one shorter and one longer. The sample reveals that there are gaps in this students thinking. The student was not required to locate this clock on her own, so an adult may have assisted her. She could have simply copied down the symbols of the roman numerals without having understanding that they represented numbers.

If I could ask this student a question about her work, I would ask her what the symbols mean that she drew. I would see if she knew that roman numerals corresponded with numbers. A way to advance this students thinking would be to show her many clocks that have different numerical values (one with only the 12, 3, 6, 9; one with no numbers but tick marks; one with only the 12 and 6; one with roman numerals). I would have this student compare the clocks to see what she noticed and if she thought they were all still clocks even though they looked differently. I might advance her thinking about what the two hands on the clock mean in a more complex way. In class, we talked about the minute and hour hands, but we mostly explored telling time to the hour. I would work with her to practice telling other times than just to the hour, so that she is using the minute hand, as well. A future math task that she might benefit from is telling time on one of these less common clocks. This would help her to estimate time by using a clock with only 12, 3,  6, and 9.