Weekly Blog of Student Work

 This week, my students had an exctivity where they had to choose one shape from 6 choices (circle, square, oval, triangle, rhombas, and heart) and they had to draw a picture about something that has that shape in it. The task that the teacher intended from this was to have children draw intentionally, add detail to pictures, and write a description. For me, the task also had the goal of identifying/recognizing shapes nad being able to connect them to form objects. The "big idea" of this task could be recognizing that shapes have meaning and that most objects we see everyday are made up of a lot of different shapes that are connected. This task allowed the student to not only choose their preferred shape but also allowed them to think of anything they could that has that shape somewhere in it. Two ways the students could approach this task is to make a drawing where the shape is the main focus and the entire object (i.e. a face, a ball etc) or the student could use the shape to make a larger, more intricate, drawing (i.e. a basketball hoop, a flower, a house etc.). My students did both. Some used the shape to make one object and added detail around it (like 1 and 3) while others used it as part of something bigger (like 2). This task showed me that the students are able to identify shapes in a classroom and in the world around them, and are able to think about how people, animals, objects, and the enviornment is made up of different connecting shapes. To scaffold this, the teacher could next time make the students choose two shapes. This would draw more focus to idea of connecting shapes together. The teacher could also have a drawing prepared and have the students identify how different parts of the drawing could be different shapes.



Weekly Blog #5

This week in my 1st grade classroom, the students are working on becoming experts with addition and subtraction problems.  On this day, specifically, the students were given an Addition and Subtraction Facts Table to help them solve the problems.  As you can see in the photo, there is a line highlighted in blue along the top of the table and down the left side which are numbered 1-9.  These lines tell the students where to start with their math problem. 

The objective of the lesson is to have students use the chart to assist them while they solve multiple addition and subtraction problems.  The chart adds a level of assistance, or difficulty, based on the specific students' skills with math.  Based on the current thinking of most of the 1st graders in my classroom, I see this chart as a helpful.  Many students are still struggling with "memorizing" and automatically knowing basic addition and subtraction problems so I feel that this chart makes a great aid.  For this student, Nick, it was clearly helpful.  The page wanted students to use the entire chart to solve the problems, but Nick found that it was easier for him to do so if he took an extra sheet of paper and aligned it with the numbers then drew an arrow to the answer. 

If this chart was not provided, I would imagine that Nick and most of the other students in the class would start to solve the problems using their fingers.  Because this is true, I think that Nick shows an above average level of understanding of mathematical thinking for this problem because he found his own way to alter the chart for what works best for him. 

If I were to suggest approaches to advance Nick's thinking, I would first suggest that he solve a number of double digit addition and subtraction problems with a similar chart that would be altered for larger numbers.  I think that this would help him see that a chart such as this could help with large numbers as well as "easy" 1-digit problems.  I would also suggest that the then try to solve addition and subtraction problems without a chart to help.  This would ensure that Nick really understands the concepts of addition and subtraction and not just relying on the chart to help him find his answers. 

Student Work Blog

 

When the teacher handed out this assignment she told the students "Complete this worksheet as fast as you can. I know we have gone over single digit addition a lot and these numbers are really easy, it will help you to do double digit addition. You need to practice your single digit addition and get really good at it to help you with your double digit addition." Right there, she already challenged the students and put pressure on them. By telling them that the numbers were really easy and to complete it quickly. I think this could have had an effect on this student in particular and other students I saw who missed a few simple problems.
This student overall did a very good job. However, one of the problems I noticed in her work was with the solutions that were in the double digits, and also numbers dealing with 9. I think one of the strategies that could help this student mainly, is to first slow down. I know the challenge was to complete the task quickly, but because she was counting on her fingers, she missed a few of the answers. I also think it would benefit this student to go over adding numbers with 9. Since 9 is a number that children typically learn a pattern with, it might help this student if she thought about a problem such as 9+4, as 10+4-1. Sometimes students have to count over the number first and then take away how many is leftover. I think this student just needs some more practice with these smaller numbers but in a different style. Seeing these numbers in a word problem might also benefit the student instead of having to memorize these numbers even though we typically have them memorized by the time we are out of elementary school.

100th day of school!!!

Today we celebrated the hundredth day of school. Going along with our daily routine, we did the straw count. We got to 101. What my mentor teacher did today was have three students stand in front of the rest of the students. She had the straw bundles and one big rubber band around ten groups of tens along with one single straw. She had the three students and then with the large hundred straw bundles she tapped the student all the way to the left on the head and handed it to him saying "one hundred" and over the middle student "and" and then finally over the last student with the one straw tapped on all three heads "one".  She explained to them that when writing this even though it is 100 and 1 numbers we write it 1-0-1 for one hundred and one.

This is teaching these kindergartners the fundamentals. They are learning the basic writings skills of numbers and counting past one-hundred. To continue with hundred day celebrations we listed out how far one-hundred steps would take us. They made guesses, which my MT wrote down. We then tested out our guesses by having the students line up in their line. From the door one student would take 10 steps then go to the back of the line. Ten students took ten steps  and we realized that all of our guesses were incorrect and that 100 steps gets the students to the 2nd grade classroom. 

This math task I had the students make an estimation and then test their  answer. These tasks did not dive deeper into measurements or anything like that. A way that my MT could have deepened the question was what are other ways that we can measure 100? What 100 things could get us to the rooms that we guessed our steps would.

I was unable to get photos of this task due to the students being in the pictures along with the excitement of one hundredth day I accidentally forgot to snap a photo of the boards but I can do Friday for you!

100 steps

Today was the 100th day of school that the kindergartners had been to! One activity that the students did to celebrate, was to predict what place in the school they would be able to reach in 100 steps. The students brainstormed the different locations they thought might fit this requirement.  The students then tested out their ideas and found that another classroom was 100 steps away from their classroom. In order to count to 100, they counted by ten.  One student would stand at every 10 steps.  When the students came back and discussed this, my mentor teacher asked, "How many students did it take if we had a student stand every 10 steps and we got up to 100 steps?" Many of the students yelled out, "Ten!"  The students are definitely starting to understand multiples of 10 and how they work.  They often count by tens during the calender activity when they are counting how many days they have been in school so far and when they sing the song about counting by tens.  Since the students really seem to grasp this concept, I might start working with them on other patterns of counting you can use. For example, counting by fives or by twos.  This could be modeled when my mentor teacher counts the number of students in the classroom every morning.  Instead of the helper counting each student individually, perhaps, the teacher could have the students grouped, and the helper could count by the number of students in the equally divided groups.

Student Work #5

Today, my MT introduced the topic of measurement. She began by asking the class what types of things/objects they have measured, or think would be important to measure. Next, she displayed how to measure a book with a ruler and explained that the length of a ruler is considered a foot. Following, the students traced their feet, cut them out and compared them to the ruler. Then, they were asked to find something in the room that was the same length as their foot, then something that was smaller and finally something that was larger. The purpose of this task is for students to realize that things can be measured in many different ways, to practice measuring items correctly and compare the sizes of objects.

Students may approach this task by starting their measurements at the heel end of their 'foot' or at the toe-end. They may also cut out two 'feet' and use both of them to measure larger objects. Although not instructed to do so, the children may use a ruler to compare the precise length of their feet compared to other objects.

I anticipated students would struggle measuring items by either not evening out the edges of the paper and the object, or by simply placing their 'foot' next to - rather than on to - the objects. I also anticipated that students would have a difficult time differentiating the difference between items being 'smaller' or 'larger' than their foot due to lack of vocabulary. However, I knew that many students already had experience measuring objects, so I knew that many of them would be able to succeed in completing this task.

This student in particular excelled in this task.  He started off getting a little frustrated because when he traced his shoe on the paper, it did not perfectly outline the shape. However, once he was finished cutting it out, he made markings along the side along with numbers. This displays to me that he is well aware that when we measure things, we use numbers to evaluate them. This also reveals that he has in fact at least seen a ruler, yardstick or some other measuring tool prior to today. In the photo above, he found a book that is the same length as his foot. When asked to find an object that was smaller than his foot, he grabbed scissors and counted (using his markings) how long they were. Finally, when asked to find something larger than his foot, he exclaimed 'the table!' and began to count how many of his feet would fit across the table (even though he was not necessarily instructed to do so).

Evidently, this student has more experience with measuring than most of his classmates. In order to challenge him, I may ask him to measure things around the room and write a numerical value for them (3 of his feet, 1.5 of his feet, etc.). I may also ask the student to use a ruler to create accurate markings on his paper foot. Finally, I may also ask him to create another tool to measure with, or if limited on supplies, ask him to use parts of his body to measure things (hands, arms, legs, entire body length, etc.).

100th day of school Activity

Last week when I visited my placement it was the 100th day of school. This meant that the majority of the activities throughout the day were planned around the number 100. In my class The students had to come up with 100 different math problems that equaled 100. They were allowed to use addition or subtraction. At first this was easy for the students but after a while this became a difficult challenge for some because they were not allowed to repeat any math problems. The students would raise their hand and if the teacher approved their math problem they got to write it on a card and stick it on the display wall in the hall. This math task really made students think. This helped them realize that there are a variety of different ways to make 100. Also as they started to run out of addition problems the teacher asked them to start making addition problems with three numbers rather than two. This allowed more advanced students to practice their skills and not become bored with problems such as 50 +50.  While completing this task multiple strategies were used. Some students used guess and check which meant they shouted out random math facts and hoped that the teacher said that it equaled 100. Other students used their time lines and counted up from different numbers. Some students counted on their fingers. Once the class got closer to completing 100 problems the teacher asked them to think of it in terms of money. The students were then allowed to write that 4 quarters equaled 100 or any variety of coins. The students that were able to think outside the box and add groups of 3 or 4 numbers together to get the answer showed that they were at a higher level of math. Many students raised their hand and stated math problems that had already been said multiple times. This showed that the students understand addition but maybe they are not challenging themselves to think of more difficult problems. The students overall really enjoyed this activity and were very excited when they reached 100 problems.

Student Work #5

The students were working on a math packet today, because there was a substitute teacher in class. This is an excerpt from one of the packets. The students were supposed to figure out when it says "8 tens" what the actual number was. Then the students were to complete the subtraction problem. Most students did fine on this worksheet, but this particular student would sometimes do addition instead of subtraction. Number four, for example, instead of subtracting ten from sixty, she would add it. Then in problem number 5, she subtracted. Again on problem six she subtracted again. I don't really understand why she alternated on some problems doing subtraction and addition. This student just seemed to be confused.
While I was working with her, she would ask me step by step how to do a few of the problems. She was not very confident while answer the problems. I have noticed a lot of the student in my placement class have this issue. They have a low confidence and then tend to get the problems wrong. Once I help them and give them positive feedback, they tend to get more problems right. I think that if my MT would spend more time walking around and looking at what each student struggles with individually, they might improve in their math skills.

Student Work 2/19

I'm sick today, so I didn't go into my placement. But I have a photograph of some math work that I had taken previously:

This task asks how many boys and how many girls there are in the classroom. The students count all the boys, then count all the girls, then add the two together to get the total number of students in the class. Every time a new student joins the class, they do a new equation. At the beginning of the school year there were 18 students in the class, and they now have 24 students, so they have had to do this activity pretty often.

The big idea of this task is to have students add up parts to make up a whole. It is an interactive activity that the class can connect to because it is always interesting for a new student to come to a class. There is only really one way to approach this problem, given the specifics of the task, and that is to simply add the number of boys to the number of girls. But if we wanted to make this task more cognitively demanding, we could use the given equations to make more math equations (e.g., 21-8=13, 24-15=9). And this can lead to students learning the concept of "number families." 

For this task, it is possible that students might add up the numbers incorrectly in their heads, which would lead them to come up with answers that are slightly off. But given their mathematical understanding, most students in the class would be able to correct themselves shortly after.

Student Work 5

            I was unable to obtain a different math task from my students so I chose another word problem application they were assigned last week. Like I explained last week, my students were placed in groups of 3 where they had to solve a word problem by showing their work and explaining how they got their answer. After they group solved their word problem each group had to present it to the rest of class and work through their problem. The question for this specific word problem is, “Linda buys four items that cost $6.89, $4.59, $3.89, and $3.99. If she used her $20.00 bill, will it be enough to pay for all four items?” The big idea for this problem is being able to add money together to get a sum and determine if it the appropriate amount depending on the limits in the problem. The students have to understand the limits of money and how to add decimals. The students have to realize if they spent more than $20.00 that they don’t have enough money and need to subtract some items. This problem can relate to real life such as going to the movies or going to the store.

            One possible approach to this problem is to make manipulatives for each money amount so they represent something concrete. The teacher can also provide actual money manipulatives to help solve the problem. By having actual money bills and change the students can count the actual bills and change to get to the maximum amount of $20.00. One student approach to this problem is what my students did in this problem where they added all the items together to see if it added to less than or more than $20.00. If the sum is less than $20.00 then the students can see that they have enough money and do not need to finish any more steps. Another way the students could have added the items is to separate the decimals. The students could have added the dollar amounts and then separately added the cent amount. Then the third step would to be adding them together to see if they get under or over $20.00.

            These students demonstrated that they can add numbers with decimals. They were able to pull out the appropriate numbers in the word problem and add them together to get a sum. As well, the students demonstrated the knowledge of less than/greater than concept. They were able to put into words that their sum ($19.36) is less than $20.00 so they have enough money. This word problem contains concepts such as addition, money and greater than/less than that the students have already covered and reviewed. The students are able to demonstrate addition with decimals because of previous practice and maybe exposure to actual money before. They demonstrate that there is a limit to money and if they exceed $20.00 they cannot buy all 4 items.

            One way to advance the students thinking is to place it in a real life setting. There can be a picture of a movie theatre with images of items found there such as popcorn, candy, drinks, etc. with individual prices for each. The question can ask the students to come up with combinations of different items that add up to $20.00 and how many combos can they come up with. Another way is for them to start with an amount they think is appropriate to bring to the movies for food. The teacher can obtain actual prices for food items and the students can pick and choose the items they want for the amount they chose. 

Casey Droste Student Blog 2.19

My placement did not have school today so I grabbed a picture of a worksheet I found in their room last week.  I was not present for the specific worksheet but I believe it was put in place to test where students were on understanding the division of fractions.  We have not talked about this yet in our class so I assume this was a pretest before the lesson.  A pretest is helpful to the teacher to be able to see what is the most confusing part about this topic and what she can point out to help them through this lesson.  I believe they must have had some previous exposure to this in earlier grades or lessons but we have not specifically taught this idea yet in the classroom.

I grabbed the work of one student who seems to struggle in school, he is distracted and likes to goof around a lot.  I know this student can pay attention and do well in his course when he puts his mind to it but there are certain classmates that get him off task very fast and it is hard to bring him back.  Since this was a pretest it was individual and very quiet.  The pretests are taken in the homerooms for 6^th grade, not in the normal math classroom so I am thinking he feels more comfortable and at ease in his own classroom and his teacher knows how to deal with the distractions he has quite well.  This student understood this concept extremely well.  This task was not very high level but the repetition shows that he understands you just have to flip the second fraction and then multiply them to get the answer when dividing.  This shows he can do this and that he can do the simple math that is involved here.

Fraction word problems have always been confusing to me so I am not sure I can explain what I am thinking here very well.  I think a way to take this to a deeper level would to make a word problem in which the fractions are in words and it is a division problem, then this would help us see that the student understands what the fraction is, understands it is a division problem and then also knows that they need to flip the fraction and multiply.  Even this seems pretty much just mathematics so taking it a step further and ask students to create their own word problem for division with fractions (something I cannot even do) and have them solve it.  They could have these shared throughout the class and the other classmates would have to solve them.

Student Work Blog - Amy Tenbrink

My elementary didn't have school on Friday, so I'm going to talk about another one of their math stations. The math station that the kids like the most is the computer-based math station. This one lets the students use computer to figure out math problems in a program. The program they were doing the day I observed was one based on figuring out how to bundle tens together. In the program the theme is a candy shop. The customer orders a package of candy in a certain number, say 14. Then, down the convaery belt comes 14 sticks of candy. The child has to then put ten sticks in the 10's column, and the rest in the 1's column. Then, once they have gotten this right, the candy is boxed up and shipped to the customer. This task is not really a high-level task, but it shows the students how to bundle into tens. The repetition and use of different numbers throughout the game shows them that different amounts can still have the same number of tens, like 13, 14, or 15. I asked the students to explain to me what they were doing, and they tried to explain it, but didn't really seem to understand the concept yet, they just knew they dragged candy sticks to one side and the other side until they got it right.

Hannah Parish- Student work

This is a math worksheet the students had to complete. This worksheet has the students practice their multiplication skills, and allows them to begin working with variables and the order of operations. I would say that there are not multiple ways to approach these problems, as there is one correct answer and one way to get there, because one must correctly follow the order of operations. I have noticed that a lot of students forget to carry over, and add or multiply properly.Those are the most common mistakes that I have found when students do not reach the correct answer.

The first thing I noticed about this student is that they do not show their work. I think that it would have helped this student remember to carry over. I think that by having the students show their work, it would improve their scores. I think this student did not show their work, and they forgot to add and carry over. I think that it would benefit this student by going over the order of operations and by having it on a poster in the room so that they have it available to them.

This worksheet could easily be turned into a high level thinking problem. This could be done by having the students come up with their own problem, with large numbers. For the order of operations, I think that after a mini lesson on it, the students should create their own problem that requires students to know the order of operations, and give it to a friend to try and make sure it works.

Liz Slusher- Addition

My MT asked me to work with a struggling student. I pulled her into the hallway and provided her with manipulatives to practice the addition problems. The transcription is below.

Me: "Here are some hearts you can use if you want to help you solve these math problems! Here's the first one, Mary had 3 hearts and John had 2. How many hearts did they have all together?"
Child W: "Umm well 3. 1, 2, 3." (counting out 3 hearts.) "Then two. So that's two. 1, 2, 3. (counting the hearts she already counted  again) the answer's 3."
Me: "Tell me about why you're thinking it's three?"
Child W: "Well because I counted out 3 hearts."
Me: "What about the 2 hearts that John had?"
Child W: "Yeah I counted."

This child is unable to directly represent this simple addition problem. This is very concerning to my MT because she is unable to create two groups of items to count and add together. My MT told me that the next step for this child will be to actually model directly representing addition with objects. She feels that if the student cannot visualize the addition problem concretely, she will not be able to do to in her head; therefore, she needs it to be modeled. Although modeling would not be a high level task, the student seems to be very confused, and I can't think of another way to teach her this without explicitly showing her.

Student Work 5

 

In my kindergarten class last week the children and my mentor teacher worked on putting 100 dots on this Dalmatian doggie. The idea behind putting 100 dots was because it was the 100^th day of school. The learning goal was to see how many dots each student had to cut out in order to achieve the goal of 100 dots on the dog. This activity was designed to elicit student thinking by my MT asking the children to predict how many dots each student would have to cut out. One child said 10, one child said 3 and another child 4. My MT said lets try 4 dots per student and then we will see if we need to add more or less to our collection. There are usually 24 children in the class, but that day there were only 22. After the predictions were made, my MT had the children cut out 4 black dots each. She then went around to each student and counted the dots. The whole class counted to 88. She then asked the students how many more did they need to get to 100. My MT helped them with this problem, since it is kindergarten 100-88 is not the easiest problem for them to solve. So they got 12 as their answer for how many more they needed to cut out. My MT chose 12 more students to cut their 5^th dot and to make 100 dots total for the dog.

            Having the children predict a number of dots for the students to cut out is a good way to approach this activity. This allows the children to recognize that if they go over or less then 100 then they have to figure out how much to add or take away from the dot collection. Another way to approach this activity could be to already have 100 dots cut out and then have the children divide the dots up evenly amongst the class and the figuring out what 12 students will get the extra dots.

            Two anticipated student approaches would be guess that students get a higher number of dots then what it should be. For example some students said 10 dots per student to reach 100 and then another student said 4. The 4 was the closes number. Did the child just guess or did they have some clue of the correct amount per student? Another anticipated approach for the dividing up amongst classmate, I think some students succeed in this and then some students may give up easily. Even though it is a division problem in kindergarten, I think it would be interesting to see if they could figure it out as a team effort.

            Learning from this task, I can see they students are not at the level of subtracting numbers with more then one-place value such as 100-88. I have also learned that maybe this task is not the greatest at learning the students’ mathematical thinking. For the predications at the beginning of the lesson, my MT only asks a couple of student to share their predications.  Also making a predication is confusing because as a teacher you never know if they are just guessing at and answer or if they actually might have an idea.

            Lastly, one way to advance the students understanding could be to ask the student who is predicating, “Why did you choose that number?” Another way to advance the task is to not have a community thing to stick the dots on, but each child could have their own object and then they could decide how many dots/other items they want placed on their object. Then they’d have to collect the items and count and make sure they had the correct amount.

Student Work 5

 Last week, I posted about how my mentor teacher chose to introduce multiplying by multi-digit numbers by first selecting only numbers that have one or more zero(es) at the end of a single digit. For example, she would have the students do set of problems that all look similar to: "19 X 500 / 54 X 20 / 33 X 6,000 / 65 X 50,000 etc." I mentioned that I found it interesting that she did this before teaching numbers that have multiple integers, because this way of teaching does not show place value. This week when I went to my placement, the students had moved on to multiplying two two-digit numbers together. The problem that my mentor teacher found that her students were having was with lining up the numbers in their proper places. For this reason, she had the students finish the assignment they had started the day before, but instead of using just lined notebook paper, she showed them how to use graph paper to better keep track of how to line the numbers up. I chose to upload two pictures to show the differences that I saw with my students attempting to use the graph paper to think about where to place their numbers while multiplying.

A couple different ways that the students could work on these problems are skip counting, using memorized multiplication facts, or using their fingers to count the multiples. However, because the problems are in the algorithm form, there is really only one way to complete the algorithm, and the methods I mentioned are only for solving the individual single-digit multiplication facts involved in completing the algorithm. One of the other problems that the students had with multiplying two two-digit numbers other than lining up the digits in the correct places, was that they didn't understand why they had to always put a zero in the ones place before moving on to multiplying the tens place. As you can see in the bottom photo, this student did a great job of lining up her numbers, but in the second to last problem, she got the answer wrong because she did not use a tens placeholder. As I was worried about in last week's post, the students did not understand that the placeholder was needed because the problem is representative of multiplying by the ones first then by the tens, meaning that there will never be an answer involving ones when multiplying tens. I tried explaining this to the student, but she did not seem to understand what I meant by that. For this reason, I showed her the distributive property of multiplication and split the problem. She was able to solve both of the simple problems when it was separated, but was still struggling when she returned to doing the whole problem altogether. I think that the fact that the students don't understand how zero works as a placeholder and why it is necessary reveals their current mathematical knowledge about the number zero. I learned in a previous math class that one of the most difficult things for children is to understand that once you get to a certain level of operating with zero, it is no longer just "nothing," but instead has a purpose and has a meaning within the mathematics that they need to understand. I think it is clear that these students do not yet have an understanding of zero deeper than "zero means nothing," at least not explicitly. I think it would be worthwhile for my mentor teacher to spend some time talking with the students about their current conceptions of zero and then discuss how to take those understandings deeper, so that it is more meaningful to the students that there needs to be a zero place holder in the second step of the two-digit multiplication algorithm. It seems as though if she explained it further and made it more clear as to why the zero is needed and why it makes sense to put it there, the students would be more comfortable with the algorithm and feel more confident that they understand what they are doing and why.

Student Work #5

For my weekly blog of student work I conducted the Strange Rulers task that we had done within the first few weeks of class. I chose to conduct this task with one of the middle level math students who is also an English Language Learner. The reason I chose him for this task was because I wanted to see his way of thinking when it came to measurement and to see what his reasoning would be because he isn't an native English speaker.

To begin I placed the Strange Rulers sheet in front of him. I then asked him which of the rulers he thought we could not use. He placed an x next to the rulers that he felt could not be used for measuring. I then asked him to explain to me why we would not be able to use the rulers that he placed an x next to.

• For Ruler A, he explained to me that we cannot use this ruler because it goes from 0 to 5. When I asked if this was because rulers must go from 0 to 1 he said yes. 
• For Ruler D, he explained that there was no middle line. When I asked what he meant by middle line he pointed to the space found between 1 and 2.  
• For Ruler D, he said "Yes, we can use that one because it has middle lines."
• For Ruler F and G, he said "No, cause the numbers are not right."
• For Ruler I, he said that there was no middle half. 
• For ruler J, he said originally said no we could not use this ruler but then changed his answer to "Yes, because they have space middle things and half things."
• For Ruler K, he said "The same as I." 
• For Ruler M, he said "It's a tricky one that one, I think... I don't know. I guess no because there should be numbers and half spaces. When I asked about the shape he said "It's weird."

After he explained to me which of the rulers could not be used we went through each of the rulers the he said could be used and gave me his reasonings as to why.

• For Ruler B, he said that we can use it because the numbers go up by one and the spaces are even. 
• For Ruler C, he said "The same."
• For Ruler E, "Yes, because it has a middle line."
• For Ruler H, he originally said no, but changed his answer to yes saying that "It has those things..." while pointing to the fractions between the whole numbers.
• For Ruler L, he said  "I think yes, because they have a half and they have a middle part."

I was rather surprised that although the majority of his reasonings as to why a majority of the rulers wouldn't work was because they were not evenly spaced or that there were no middle lines but he thought that Ruler L would work because it has "a half and a middle part." I understand what he means by middle line but I was not 100% sure what he meant by half. When I asked him what exactly that meant, he showed me what I understood to be the same definition of half (which is equally spaced lines so that one line between two others marks half). Although he is an ELL, I don't believe that affected his responses as much as I had anticipated it to. If I were to have chosen one of the lower math ELL students perhaps they would have had more of an issue with this task.

Student Work # 5

In my Kindergarten classroom, my students play a math game sometimes in the morning. This game is called “monster squeeze”. First, the teacher picks two students to come up to the board and she shows them a number that is on the number line. Then the students sitting on the carpet guess numbers in between the monsters until the pick the right one. It is the job of the monster holders to make sure that when a student guesses a number that is too high or low they put it on the outside of the monster. The purpose of the game is to “squeeze” the number the teacher chose. This task helps students become more familiar with numbers on a number line. It also helps the monster holders to determine if numbers are bigger or smaller than one another.

This task could be used as a quick warm up for a math lesson, but this is usually used for a fun game in between literacy lessons. Students could struggle with determining which numbers are too big or too small. During the activity the teacher has to remind them where to put the monsters on the number line. The task could be problematic for the students guessing if they do not know all of the numbers on the number line. You can eventually guess the number that was picked by the teacher, a student would just have to look at the numbers between the monsters and guess one.

This math task could show the teacher if a student understands the number order and what it means to be “bigger” or “smaller”. Also monster squeeze could show a teacher if their students need to practice their number recognition. A way to make this task more challenging for students is to pick a higher number line for them to work with. A teacher could also make a number line with more numbers to make sure students are able to squeeze the correct number. 

Student Work 5- Emma Cole

This week I worked with the students in centers how reading and using a number line. The numbers were 1-20. There were five centers and each center worked on the number line for about fifteen minutes.

When the students first got to the center I had them write their name on a blank sheet of paper. I then asked one student to be my helper but let the students know that they would all get a chance to be my helper. I asked the students if *my helper were to add or take away so many steps what number would they land on? Before the student took that many steps, I asked the rest of the students to try and guess what number they would land on. Some of the students would physically count the amount of steps on the number line. Others would count in their head while others just knew off the top of their head from previous experience. After the students guessed the number, I would have them count out loud while my helper took the correct amount of steps. For example, say I asked the student to take nine steps, the other students in the group would then predict what number the helper would land on. The helper would then take those amount of steps while the entire group counted out loud. After the students found out whether or not their predictions were correct, they would write down the number the helper landed on. This way the students were also working on number recognition.

After the first number, the student would stay on that number and then I would ask them to either add or take away a number of steps. Again, the rest of the group would then predict the number the helper would land on. This really helps the students read and understand the number line. Depending on whether we were adding or taking away numbers they would have to figure out which way to move on the number line. The students really enjoyed this activity because they were engaged and I had their full attention the entire fifteen minutes. They were interested in the topic especially when they were the helper.  This activity wasn't focused on addition or subtraction but more understanding of how to use the number line and number recognition.

However, to further advance the students learning I could gear the activity towards addition and subtraction or even both. So if the student was on the number nine ask them nine plus four is what? Or nine minus four is what? This way the activity would be so much on the number line but addition and subtraction.

Student work #5

I wasn't able to see math last week.  We did work on making lists of how to complete a task.  The student who completed this work is a student who struggles in most subjects.  As you can see he has not mastered how to write on the lines yet.  I would provide him with a sheet of paper that is not so confusing.  I think this line paper is great for students who already have a strong understanding of writing.  I would provide him with a sheet of paper that has very defined lines.  This student does have an understanding of how to list events (first, next, then, last...).  He was able to use the vocabulary the teacher provided which was peanut butter, jelly, 2 slices of bread, and knife.  The student is not consistently spelling the words correctly. This is a problem because the words were posted on the black board so they could spell them correctly.  I sense that this student does not enjoy school.  My mentor teacher does not always try to connect what the students are learning to real life.  If I were to change this assignment I would not have them only write the steps, but I would have them actually do the steps.  I would allow each to student to pick one task that they wanted to teach the class.  For example if I wanted to make a milk shake I would bring all of the supplies to class and actually show the class how to make the milkshake. Then we could write out the list.  This is a much more meaningful way to create lists.  Another way to help them understand how to use lists would be to reverse the order.  I would give them a list of steps to make a milkshake and have them actually make the milkshake.

Student Work 5 Kaitlyn Flint

This week was the students' 100th day of school so they were doing quite a bit of work with the number 100. On this assignment, the students were asked to fill in the boxes from 1-100. This was to help the students work with writing their numbers and also ordering their numbers. From my observation, the students were able to successfully do this with little support. The only thing I did notice on some of the student's work was some of their numbers were written backwards. This particular student did not have this difficulty.

This particular assignment did not seem to expand their thinking whatsoever. For students who had the order of 1-100 numbers memorized, this was just rote memory. If the students did not have the order memorized, they could use the number line in the room that went past 100 so even if it was not memorized, students could have easily copied the numbers from that line. This assignment did complete the goal of practicing writing numbers, but if a student already knows how to properly write his/her numbers, this assignment seems to be more like busy work.

If the teacher wanted the student to work with numbers up to 100, the teacher could have given a problem such as "using numbers counting by 10's, write a number combination that equals 100 such as 50 and 50 makes 100." This would give students opportunity to play with numbers, addition, and give them exposure to writing larger numbers up to 100. Another thing the teacher could do is use a smaller scale of numbers, but have them larger values, and turn it into a bingo game. That way the students would have to both write the numbers and find the numbers.

I interviewed the student who completed this assignment and it is as follows:
Me: What did you have to do with this worksheet?
Student: You had to write the numbers and that's all
Me: Did you use anything to count while writing or did you count in your head?
Student: I counted
Me: Did you use a number line to help you?
Student: No
Me: Was this an easy task for you or was it kind of hard?
Student: It was really easy

This shows me that this was not a cognitively demanding task in that it was very closed task and it was also not challenging for the student. Two ways to advance her thinking would be to use my teacher suggestions above with the BINGO game or a word problem equaling 100.

(Sorry I couldn't figure out how to rotate the picture)

On this day, the students were working with thermometers. This concept was new to most of the students. Many had never seen a thermometer before, nor have they ever used one. The concept of being given a temperature and then coloring it in on the thermometer was fairly easy for most of the students. Only one or two students seemed to being struggling with this concept.

In this photo students are first given a picture of a there thermometer and then asked what is the temperature. The second part, the students were given a temperature and then asked to color it in. Before the students were allowed to go off and work on this page, my mentor teacher explained to the students what a thermometer was, why, and how it was used. She then presented the first problem to the class and went through it with them. She informed the class that for the first 6 the picture is given and you just have to find where the colored line stops and follow the time to the number on the side. She then went on to explain how the last 3 walked them through number 7. She taught them that it is like the first half, but this time you are given the number and you want to color up the line until you are at that number. While, I think her explanation to the class was important and well thought out, I think that this worksheet does not expand their knowledge on this new topic.

These problems did not seem to expand the students thinking. Nor did it provide the students with any high level thinking. Now, I think these problems were good when the students were first introduced to this topic, but after their introduction they should have been given something a little more challenging. The teacher could have asked the students to use the thermometer into a story problem, or even gave them a more challenging problem such as in the morning the temperature was 55 it increased to 13 degrees through out the day what was the highest temperature of the day? Something like this would allow the students to think deeper then just finding 50 and coloring the picture in.

This student was like most of the other students approach he listened to instruction and then completed the worksheet. When watching the students finishing this worksheet I noticed that most of the students rushed through it with little difficulty. My thinking that this was because the task was just a little to simple for them. I understand that my mentor teacher is following the book like she is told to do, but to make sure that the students had a solid understanding of this task maybe she should have gave them some more challenging problems. However, this is just my opinion as an observer.

Overall, this is an important task to learn and understand, but I feel it could have been a little high level thinking for the students. The worksheet they were given seemed liked busy work rather then understanding an important concept.

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.

Student Work #5

 

This was the first activity the students participated in when first introduced to measurement.  They were asked to use cubes to determine the length of their shoes.  The big ideas for this task would be that shoes are different sizes and that you need to measure the length of a shoe to determine how big someone's foot/shoe are.  This task elicited student thinking becausethe students met in their math circle before jumping right into this task.  The students were asked to talk about what it meant to measure the length of a shoe.  She engaged their thinking by asking, "Where should you start measuring on your shoe and where should you end?" This question opened a lot of different ideas for the students and it was evident when they were asked to work on their own to measure their own shoes.  Because this was the first time the students learned about measurement, different students have different definitions of "shoe length".  Some students flipped their shoes over and measured all the way from the heel to the toe of the shoe.  Some other students went along the side of their shoes and stopped measuring once the shoe started to curve toward the toes. 

This student specifically used his prior knowledge of going to a shoe store and how they measure your shoes.  He created a personal frame of his shoe out of the cubes and figured out that he only needed to count the cubes along the side of his foot to determine how long his shoe was.  Other students were confused about this, so my MT unattached the two strips of cubes attached to the long stick of cubes and attached them to the preexisting stick of cubes, to create one lone stick of cubes.  She then asked the students if this student's shoe was 18 cubes long, and then took off the six extra cubes and asked the students if the student's shoe was 12 cubes long.  The students were able to see that this student's handmade frame enabled him to see where the heel of his shoe started and where the toe of his shoe ended (finding the length of his shoe). 

This student understood that in order to measure the length of a shoe, you needed to measure all the way from the heel to the toe.  He was able to create a frame of his foot to find the correct number of cubes it took to measure the length of his shoe.  To advance his mathematical thinking, I would encourage this student to measure a different classmates shoe length and see if there are any differences in the lengths of the shoes.  This student could also use a different measuring device besides the cubes to measure his shoe length, such as Popsicle sticks or even advance to a ruler. This would show the student that there are other measuring devices that you can use, that will give you a different answer for your length. For example, his shoe may be 12 cubes long but it may only be 2 Popsicle sticks long.

Student Work #5

            The purpose of this worksheet was to see the student’s level of understanding on the concept of joining numbers (addition). This follows under the standard “N.MR.00.07 Compose and decompose numbers from 2 to 10, e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of number systems, e.g., 6 is one more than 5, 7 is one more than 6.”  It is designed to elicit student thinking because students are supposed to individually count the animals and then join the two sets together. This is intended to help students understand how addition “number sentences” are formed and that the numbers represent actual things.

            This worksheet had the student write the number of animals under each group that was shown and then combine them and write the total. There are not multiple ways the student could approach this problem. There are directions given which state to “write a number for each group then have them circle to join the groups and write how many there are in all.” This is the first indicator that this is not a high level task for the student to solve. As a result of this, I could only anticipate that the student was going to do what it says. The only possible errors the student could make would be counting the wrong number of animals, resulting in him recording the wrong number, therefore getting the wrong total.

Steps taken to approach the problem:

(Student counts 2 ducks and writes 2 below them, then counts 5 ducks and writes 5 below them. The student goes back to the first group of ducks, counts them, and then continues counting on, going to the next group to add the 5 other ducks. He writes 7 for the total.)

Me: (first problem) “How did you know how to do that?”

*Mitch: “I just counted quietly.”

(Student solves the second problem just like the first problem)

Me: (second problem) “How did you do this one? Any different from the first one?”

*Mitch: “Well I just kinda actually counted in my brain actually. My brain whispered it to me.”

Me: “Oh. Can you show me how you counted in your brain?”

(Student whispers as he counts off each rooster, starting with the first group and continuing to the second group)

Me: (third problem) “I noticed you were covering up some of the ducks when you were counting. Why did you do that?”

*Mitch: “That’s what my dad does when he is counting a lot of things on the page. I just covered 4 and then I see what it like was. You cover the rest of them, and you have to count all of them, and there’s a lot, and then I can’t remember which ones…if I counted it already or not.

Me: “Oh, I see. So you covered the ducks up as you counted so you wouldn’t accidentally count one again?”

*Mitch: “Yep, that’s what my Daddy does and he showed me that.”

            Something I found interesting that *Mitch did with these problems was that he would write the number for each group, and then instead of looking back at the numbers he had and combining them, he went all the way back to the beginning and recounted all of the animals together. So, for the first problem, he counted 2 ducks, then 5 ducks, and then went back and started counting from 1, touching each of the ducks. I thought he would just look at the numbers he had written and add them. Based on *Mitch’s mathematical thinking, I can hypothesize that, *Mitch can solve addition problems with the numbers 1-10 by counting drawings.

            To advance *Mitch’s thinking, I could ask him to make different groups of animals to represent the total amount. For example, in the second problem, the answer was 9. So, I could ask him to show me how he many ways he could group the roosters to make 9 altogether. I could also add an unknown group into one of the problems and put the total number, asking the student how many roosters would have to go in this group to make the total. For example, there would be the group of 1, the group of 8, the unknown group, and then the total 12. The student would have to figure out that there would be 3 roosters in the unknown group. This is not as high of a task as the other possible question, but would change up what he was doing instead of the same procedure over and over.

Unfortunately due to a snow day last week, I was not able to watch this student complete this task. However, I was able to ask him a few question about how he did complete it. On this day, the students were to find the rule to the chart. This was a new concept that was first introduce at the beginning of the week. Most of the students seemed to catch onto this new topic quickly, however we had a few students struggle. I found this students had really interesting way of solving this problem.

In the photo there are four tables, that have an in side and an out side. Students were to analyze the in side and then look at the outside of the first column and see how many numbers the in is from the out. Students were then to look at the next column and see the number in the in is away form the number in the out. When students have figured out this pattern the would write it in the rule box. The students also had to place a + if the in box counted up to the number in the out box. For example, as shown in problem 1 the in box is 3 and the out box is 5 so the students would count up from 3 to 5 and find that the rule was 2. Since they counted up and not down they would put it as a plus. If the in box was counting down to the out box then the rule would be a negative. Students worked independently on problems 1-3 trying to find the rule by looking at the in and out chart. Once they finished with this they moved onto problem 4 which asked them to make their own.

From walking around the classroom and checking a variety of different students math workbook, I came to the conclusion that all of the students seemed to understand this new concept. I do not think this problem was super challenging for the students, it did require some high level thinking, but once they understood how to figure out the answer then it should have come easier.

Nathans approach to this problem informed me that he understands the task and is on track for a first grader in math. While working on this problem, Nathan told me that he thought it was easy. He said that all he did was look at the in box and then the out box and either counted up or down. Since the first one was 3 he said he counted up to 5. Nathan said this was his guess that it was 2 away. Then he would look at the second column and saw that the in and out were the same only 2 away. Thats how he knew the rule was going to be 2. Nathan's explanation of how he came up with this method of figuring out the problem was very good thinking.

If I were to advance Nathan's thinking I would give him a table that wasn't as simple as going up by 2's, or 10's, but something challenging like 12 or 9. I would also ask him to make another one of his own problems that was not going up by 1,2,5, or 10, cause those are pretty easy and he shows he understands them.

Rachael Boglarsky Student Work 2/12

(A)

(B)

(C)

Math Objective/Purpose: For this task, the teacher cut strips of paper of varying lengths and the students were to measure the strips using various manipulatives from the classroom. Pictured above are Unifix Cubes, People Counters, and Sorting Bears. This task has a few objectives. One, it will assess the students' counting ability and tell the teacher if the students are able to count one-to-one or if they are rote counting. Secondly, the "bigger" math concept of measurement being addressed here is that things can be measured with diferent tools (cubes, people, bears) and the measurements may not always be the same. This is an introduction to measurement and the concept of using a more standardized measurement tool (i.e. a ruler).

Possible Approaches: The students weren't instructed to use a specific method to solve this problem-it was very open-ended. Some students may be more famliar with measurement and might try to use a ruler to measure the strips. Others may choose a manmipulative and estimate the number it would take to fill the strip. Lastly, some may line the manipulatives up until the strip is covered and then count each manipulative one-to-one to measure the stip of paper.
Anticipated Sol'ns: I anticipate my students will use the manipulatives to masure the strips. I anticipate that some students will be confused or frustrated if they do not get the same answer using 2 different manipulatives and might try to change their answer to fit a previous answer.
Actual Student Response: My students, though they were given a multitude of manipulatives, chose to use the unifix cubes to measure the strips.The students who chose to do this activity today used the unifix cubes, lined them up until the strip was covered, then counted one-to-one, touching each cube, to get a number. Then, they wrote the number in ry-erase marker on the black line. Only one student used the bears to count, and we have a conversatiobn with the other students about why her numbers were different. (Her numbers were higher because the bears were smaller than the cubes). Nobody chose to use the people counters or a ruler.
Explanation: This activity showed me the students' ability to count one-to-one. Most students can count to at least 20 or 30 just by rote counting, but one-to-one correspondance is hard for some students. This activity showd me which students understood the concept of one being one block, the number 2 as a representation of two objects, etc. The students also were surprised that the bears and the cubes made different measurements. This shows me that the concept of measurement and a standard measurement unit is still new to these students and that they do not yet have the cognitive/math skills to know that not all objects will make the same measurement.
Suggestions: The students almost all ued the unifix cubes because that is what they have seen most, so I would suggest introducing and using other kinds of manipulatves for the students to explore. Some missed the opportunity to disccus why the measurements were different because they didn't use another strategy. Also, this would show that numbers and math concepts can be represented in different ways. Lastly, to extend this I would have the students measure longer strips or objects with new materials to see how high they can rote count and count one-to-one.

Student Work Blog - Amy Tenbrink

This past week I observed math centers again. This center was themed for geometry. The goal was to have the students use the blocks to re-create the picture on the laminated card. I sat with one of the female students as she did this pattern, seen above. I asked her what she was making, and she said she didn't know. When I asked her why the different blocks fit together, she surprised me by saying "because their sides are the same". I'm not exactly sure how to take her answer. She could either mean that their sides are the same length, therefore the shapes fit together, or she could simply mean that the sides are both flat and not one flat one curved. Either way, she had a rather impressive knowledge of why these puzzles work.

Math Blog #4- Katie Hall

Unfortunately I was unable to actually witness the students work on this math assignment this week. However, after looking at this particular worksheet, it is apparent that this student definitely understands how to read a clock and how to tell time. You can see that on problem #2, there was a slight confusion, and instead of reading "30 minutes before 7" the student thought it was "30 minutes after 7." They originally wrote 7:30, but fixed their mistake and corrected the time to 6:30. 

In addition to filling out worksheets such as this one, I think giving the students paper clocks whose minute and hour hands move would be a very beneficial way to practice telling time. The teacher could announce a particular time, then ask the students to set their clocks to that time as well. When they were finished, the students would hold their clock up in the air to be checked. 

I have noticed that while the students were in their literacy centers, a number of students would come up to me and ask me if it was "2 o'clock yet?" This worries me, because even though the students may be able to fill this particular worksheet out, they seem to still be having issues reading clocks in the real world. Again, the student who filled out this worksheet may have been advanced and have a better understanding of how to tell time compared to the other students in the class. The situation might also be that the students who would ask me what time it was were the few students who have issues with reading clocks and telling time. I plan on attending the classroom next during their math lesson, so I am excited to get a better insight of their skills in this area.

Due to the snowday, I wasn't able to go to my placement this past Friday and collect a piece of student work. I did however recall a moment last semester when I was assigned by my mentor teacher to help two low level English Language learners with their math. The students were having trouble with tenths, hundreths and thousandths placement. In order to clarify, I sat down with the students and wrote down their math problems on a plain sheet of paper and counted with the students to help them their understandings of each placement. I then wrote down the problems for them to see and watched them attempt to solve the problems and then helped the students individually with the issues that they faced from there on out.

Student Work 4

I found this worksheet really awesome because it included both literacy and math at the same time. This student really struglles with number recognition. For this worksheet the student had to match the number with the letter and then group of words spelt a word. The hopes were that if the student recognized that if the word wasn't spelled right than they must have gotten a number wrong. This worksheet may not help a student if the student struggles with letter recognition as well but for this student this was not the case.

While working on this worksheet the student really first struggled with the concept of looking for the letter with the correspondin number. However, once she got the hang of it she really started recognizing numbers that were used multiple times. She was able to use literacy to also work on number recognition. She seemed to struggle more with the numbers in the twenties. She was pretty confident with numbers smaller though.

To further advanced this learner, a next excersise I would doing a number recognition task without relying on letter recognition as well. As well as working with numbers larger than 20. If the student seem to have mastered number recognition you could then move further into advanced math problems such as simple addition.