Chapter 17 discusses developing concepts of decimals and percents. I think that the number one thing to keep in mind when teaching this is that students must understand that all of these things are connected. Fractions connect to decimals and decimals connect to fractions and so on. If students don't understand this they are going to spend a lot of time extremely confused! Students also need to know that numbers not only go one way on the number value line, they go the other way too and that puts a decimal in front of it. Percentages can be very difficult for a student to understand as well. That is why it is so important for students to see the connection that is there!
I found the material in chapter 17 to be incredibly helpful to help students develop number sense when it comes to understanding the connections between fractions and decimals. I also found it interesting that the text specifically mentioned that teaching to divide the numerator by the denominator was not going to be suggested in the text- nor should it be taught. That is the way I was taught, granted it wasn’t very effective for me- which is probably the case for most of us. The suggestions about using a number line were wonderful, and I like that they focused on relating this new concept to old information and allowing the students to come to their own explanations for understanding fractions and decimals. I can’t imagine how this would have changed my understanding of mathematics. Understanding basic concepts is such a HUGE focus in this text and I am thrilled and excited to be taught to teach this way. This is such a fundamental yet not underused idea in teaching- it just makes more sense. I am thrilled that the text focuses so much attention on allowing student to develop number sense. The models and activities suggested within this chapter were, like always, wonderful and provided future teaches with many ways of accessing and connecting student knowledge.
In response to Kristle C: I agree with you about the importance of students seeing the ‘big picture’ and realizing how all components of mathematics are related. I’m in a first grade classroom and the number line is used heavily in there. We haven’t yet broached the subject of negative number yet, because it is a very difficult concept for most of them, but I would love to be there to see them figure it out. Thanks for your thoughts on this, I too agree that the number sense a student develops is critical in their lifelong understanding of mathematics.
Adrianne- I agree with you on the importance of understanding basic concepts! If students don't get it, they are going to struggle with math for their entire lifetime! There is no way to get around it, every educator needs to strive to find a way to help students "GET IT!" when it comes to basic concepts in mathematics!
Chapter 17 is about developing concepts of decimals and percents. This is one topic in math that I am not afraid of, and I think that's because I'm a big shopper that is always looking for the best deal. I can always make it relate to me, so I understand it. The students in my internship class have been working on decimals and there is one student who is really struggling he always sees the thousandths spot as being larger than the hundredths spot. Once you are able to explain it once and it seems like he gets it, the next question he is right back to not understanding. I can see how this can be really confusing to students. According to the book, he needs to work more on developing a better decimal number sense. This chapter gave some great ideas, activities, and strategies to help student like this one to understand number sense with decimals.
I also was taught to divide the numerator by the denominator, and am surprised that it is suggested to not teach that way anymore. I also liked the suggestions for using a number line. Using a number line is something that I have no experience with, and I have enjoyed see all the activities and strategies that go along with using it because I think it can be very helpful.
Chapter 17 Developing Concepts of Decimals and Percents I have never seen the hundredths disk before; it really looks like it could be very useful as a teaching tool. (pg. 329) I have found that using a hundreds chart paper and having them color in a certain amount of squares really helpful in teaching them fractions and decimals. I think fractions and decimals might be something that you would want to work on everyday with the children, maybe in calendar time. Knowing where the decimal goes and lining it up is also a very big struggle for children. I can imagine why, in multiplication we count how many digits, in addition we bring it straight down, it can really be confusing. Seems like estimation is very important, because it seems to come up over and over again in our book.
Elizabeth, I think your right it comes right back around to the point that we need to make everything we do in mathematics mean something to them. It has to be something that they will see themselves using over and over again in their lives. Get to know your students. Know what their parents do for a living. If mom works at Walmart how many times does she use this type of math that your working on. Use that reference when making up problems. Sally went to Walmart and saw a dress that was 10% off. If the dress is $12.00 at regular price what will it be after the 10% off. Use real life situations, real to them.
The way I learned to add and subtract decimals was lining up the decimals that way all of the place values line up with each other. That way made the most sense and was the easiest for me to understand. But I do understand that for some students that strategy will not be the best strategy. The one strategy that I found the most interesting was estimating. I thought this was an interesting strategy because it gets students to learn how to round to the nearest whole number and work on estimation skills all at once. This allows the students to come close to the correct answer. Teachers have to remember though that when you estimate the answers are going to vary between what could be a wide range depending on the equation being solved and how far the students are rounding to: ones, tens, hundreds.
Elizabeth Sills I think your shopping ways are the best way to relate decimal computation to students because money is an everyday part of life. In my math internship when we were working with decimals every student seemed to understand things instantly when relating it to money just because they have already had to do a lot of math with it and know, for example, how many quarters equal a dollar or nickels in a quarter, etc. An educator can come up with several activities relating decimals to money. One way that I remember using in elementary school was we had to buy something, using monopoly money, and then the other student had to count back the correct amount of change.
Under the Big Ideas the author states that decimal numbers are simply another way of writing fractions. A huge learning point when teaching is to make sure this point is taught. All of the points made in this section are critically important when teaching decimals and percents. Making the connection between the two will allow students to make the real world connection between there percentage grade and the number as a decimal. Base Ten fraction models is new learning for me. For example in figure 17.1 the picture shows the manipulative being shown in various configurations. I find that using a number line to begin talking about percentages is a way of visually showing students the range of percentages that can occur between 1 and 100%. A review of decimals in addition, subtraction, multiplication, and division is essential when beginning to compute decimals together. Overall, this was an informative chapter with two great literature suggestions in the literature connections section.
I didn’t think about using snap cubes to solve decimal problems. Now that I see it, I think it would be a great idea! It would be a great way to visually show the students a part of something. I think that decimals are tricky for children. Before they start decimals, they are taught using whole numbers. To break it down (i.e. .75, .35, .01) can be mind-blowing for some of them! Later on in the chapter, the author talks about estimating. My internship teacher just went through the long and strenuous process of teaching the students the concept of estimating. For some reason, they had difficulties rounding up or rounding down a number. The book said that starting with decimal computations is a good place to start estimation skills with the students because they begin to develop reasonable ranges of where the number might be, or should go.
Comment for Lane A. I completely agree with your point about answers varying when asking students to estimate. If we do not ask students to estimate to a certain digit then answers will certainly be different. Teachers must take this into consideration when grading. I believe that there are many ways to compute decimals. I find that following the rules I learned are easy for me but I will encourage my students to use a strategy that works best for them. The correct answer may be achieved through different avenues.
In response to Lane- I learned how to add and subtract decimals the same way. I, for one didn’t find it too difficult. As you said, every student is different. I may become a challenge to incorporate all the different strategies for the students but it is important that we do.
Percents and decimals can be a lot of fun to teach because there are so many ways to involve fun activities into teaching these concepts. Using the base ten blocks and snap cubes are great ways to get students hands-on learning as well. I think that by using graph paper can also be a good alternative. Converting fractions to decimals is a fun transition. I remember when I learned how to do this it was a big deal, at least to me, because I was converting different types of numbers that would equal the same thing. I guess I am weird like that. It will be a fun challenge to teach to different types of learners but will be rewarding for the hard work, hopefully.
I agree that it will be a challenge to use multiple strategies and it is important that we do so. It is important as well that we recognize the learning types that we have in our classrooms and try to decipher which strategies may reach those students, teach that strategy then continue to introduce a different strategy. Anything hands-on always engaged me as a learner so that is something that I will most likely always do.
Chapter 17, developing concepts of decimals and percents is the last chapter we are blogging over and is probably my favorite. I love working with decimals and percents and feel that this is one of the most practical applications in math. We all deal with both decimals and percents on a daily basis, weather we are talking about money, sales, grades, or measuring. There are so many different methods to teaching decimals and percents but the best way is by connecting fractions to decimals and then decimals to percents. This will give the students a complete understanding of the connections that the all share. When I was in school we were taught decimals and fractions simultaneously, doing worksheets were we converted decimals into fractions and vice versa. Then we added in percents so by the time we were done the class was able to say ¼ is the same as .25 and 25%. The two key points in this chapter is extending the place-value system so that students understand the number in relationship of other numbers and teaching decimals with familiar fraction, this means ones that are commonly used a easy to solve for. Both of these are important because it helps students take a realistic approach to math concepts; for example students need to learn that .07 is very different than .7, one is only seven cents while the other is seventy cents. Overall this chapter has a lot of very good activities but I found it odd that didn’t have any activities dealing with money. Have a great Holiday Season!
In response to Joel Stucky, I totally agree with you, I love decimals and fractions, and I remember feeling so smart when I was able to convert a fraction into a decimal and then into a percent. You get the feeling that you can actually see how all the different math concepts tie together. Also I love the many different activities you can do with decimals and percents, I remember this being the section where we always got to use different types of manipulative.
Chapter seventeen was very interesting to me because it was based on a topic I greatly struggled with as a child, decimals and percent’s. I don’t really know why but decimals and percent’s were very hard for me to grasp. ¾, ½, ¼, 75%, 50%, and 25% were all easy for me to grasp because it was like counting the parts of a dollar. It was all the number sin between that confused me. I really liked the friendly fractions to decimals activity in 17.4. I like the thought of introducing “friendly” fractions to students. Even just this simple term might put a more enjoyable spin on working with fractions. The other part I really like about this specific activity is that it uses models to guide students in converting fractions to decimals. This friendly fraction idea is re-enforced through many of the activities in this chapter.
One other section I really liked in this chapter was the models and terminology section. I feel like maybe I didn’t have enough visual aids when I was a child. I really desired models but I didn’t have many and I think that’s why I want to use them as much as possible in my future classroom. Like the chapter says, models provide a clear link among fractions, decimals, and percent’s. Hearing the term 3/4 can be a bit confusing but when you see what ¾ actually is you can put an actual size to it. Models are a great tool for understanding and a great connection for fractions, decimals, and percent’s.
Joel, I like how you mentioned how decimals and percent’s can be fun to teach. I had trouble with them as a child, but you are right in the sense that there are so many manipulatives I will be able to use as an educator to make them fun or “friendly” for my students. Manipulatives such as popcubes and base ten blocks are really helpful in making connections between fractions, decimals, and percent’s. I think these manipulatives are the only things keeping me excited about teaching decimals and percent’s. I may not have had the best learning experience with this concept as a child but I definitely have the tools to give a more meaningful experience to my future students. Good post!
Decimals and percentages don’t bother me to much but reading through this section made me realize how confusing they can be in their relationship together. The chapter begins introducing the base 10 way. I understand how they figure it but I for some reason just don’t feel it’s the best way to accommodate all types of learners. It was funny, just as I was thinking to myself how great money is to use in this concept I read “Don’t use money”! I do love the idea of putting decimals and fractions in number lines. For me this is how I learn, seeing the physical amount of the value. The chapter moved on deeper in percentages which I think I understand pretty well. It did however bring back a nightmare of a concept for me- the 3 percent problems. I can’t stand those problems, they just never made since to me. I remember having a cheat sheet with each way the question could be presented and having to look off that on every problem. For some reason it just never stuck with me. Now once I saw the illustrations of the same thing I was like ok…………that’s when I could use this. As a teacher I need to highlight this segment to remind myself to never do this to another student. The picture just explained it without having to get my calculator out to figure the correct amount. It was easy and made since what they were asking. If we are in the store and something is on sale, I usually make him do it in his head. I hope our kids get his math skills!
I think that the truth in this chapter is that children start with base ten blocks to help with decimals. That means that no matter the grade you teach you are going to build a base for decimals. That kind of makes decimals very important. Just like reading it advances as you move from grade to grade. This chapter gives many ideas on how to use decimals in the classroom and also how to teach them. I think one difficult part of decimals is putting them in order from least to most or most to least. This can become difficult, as students get older. It definitely gets harder when negatives come into the picture. I sometimes get confused with fractions and decimals in negatives. I think when taught correctly decimals can become second nature to most students.
The concept of estimating is kind of confusing for children. Which I think once they get it though it comes easier for them. I think it is just one of those concepts that is kind of hard to explain on how to estimate.
When reading chapter 17 over developing concepts of decimals and percents I was able to learn some helpful information to use in my future classroom. I liked how the chapter focused on the fraction-decimal connection and how students should be able to make the connections between the two of them. I liked the figure 17.11 called a decimal number line. The picture did a great job of explaining how to make the decimal number line. The chapter did a great job also of showing me as a future teacher some tips of how to teach percents to my students. One very important tip when teaching percents to students is to limit the percents to familiar fractions or easy percents. The part of the chapter I found the most interesting was the area of estimation. I feel that students need to know how to properly estimate and make an educated guess when referring to math problems and in real world situations. I liked how the book talked about it relationship to estimation about percents that if the percent is not a “nice” one then substitute a close percent that is easy to work with. This is such an important statement to tell the students at the beginning of the lesson so that the students are not struggling with tough percentages. Overall I liked all of the different activities presented in chapter 17 and I feel that I learned lots of information about decimals and percents in order to become successful teaching it in my future classroom.
In response to Kristle C., I agree with you Kristle 100% that it is so important for students to understand that decimals and percentages are all connected together. This is so important for students to understand in order to become successful in this area of math as well as make the math experience easier on them. Students are going to become confused if they don’t see that fractions are connected to decimals and decimals are connected to percentages. I agree with you that overall percentages can be a very confusing concept for students to understand and it is up to the teacher to help the student to be able to understand the concept. Overall the main focus of the chapter I agree with you is to make sure that the student sees the connection!!!
Chapter 17 Chapter seventeen of the text book Elementary and Middle School Mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discusses how students learn decimals and percents and how teachers can explain these different concepts to their students. The textbook states “this fractions first, decimals-later sequence is arguably the best approach” (Van de Walle et al., 2010, p. 328). Van de Walle et al. textbook also mentions “linking the ideas of fractions to decimals can be extremely useful, both from a pedagogical view as well as a practical view” (Van de Walle et al., 2010, p. 328). This is why it is important for teachers to go into a sequence of what they teach to their students. A piece of information that I learned from chapter seventeen was of Van de Walle et al. textbook was when the textbook states “many teachers use money as a model for decimals, and to some extent this is helpful. However, for children, money is almost exclusively a two-place system (Van de Walle et al., 2010, p. 330). I often do explain fractions as money amount because students can relate to that better but I do understand what the book is explaining that this only can take the students so far. Something interesting mentioned in chapter seventeen of Van de Walle et al. textbook was on page 335 of Van de Walle textbook that mentions “only 51 percent of eighth graders selected ½” when asked the problem “What fraction would you say approximates the decimal 0.52” (Van de Walle et al., 2010, p. 335). This was actually surprising to me because I thought that would be an easy problem for students especially eighth graders to get. Chapter seventeen of Van de Walle et al. made me think about all the different examples that I can use to relate this material to the students everyday life. I can use signs that they may see, sales that stores may have percentages students get on assignments etc. I think that having students relate to these different concepts really gives them higher understanding of the certain concept. Something from chapter seventeen Van de Walle et al. that I would like to use in my classroom is the different manipultives and hand on materials that were described in the textbook. It is so much easier when students can actually explore with these different concepts and can see why there is or isn’t correct. References: Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Jennifer Pen reply to Shannon, I agree that there different parts of fractions that make sense to me and then there are parts that do not. I always looked at decimals like they were money and fractions like they were a piece of a pie because that is what makes sense to me.
Chapter 17 was very interesting! I like the big idea that decimals are simply another way of writing fractions. I probably love decimals more than I love fractions! Dr. Stramel has shown us the rational number wheel and I think it would be something that would be a fantastic manipulative. One thing that I am not so confident about is the base ten blocks. I have seen them used but I am not so confident about them. In figure 17.8 where they showed decimals to fractions on a base ten flat I think would be a bit confusing for students. I think it will be as difficult to teach decimals as it is fractions!
@ Jena Simms We both liked the same big idea! I would agree that this is so important for students to understand. It should be our main point that we push to our students!
I too agree that percentages are easier for me than other topics (like fractions). I think it’s because percentages are everywhere. Last weekend over Black Friday my e-mail inbox was swamped with sales fliers from various stores stating how much you could get off of your purchase or particular items.
In regards to your student that is having a hard time with decimals and the values… I saw a great idea on the Internet using Styrofoam cups. (I’ll post the link at the end of this.) This idea was for just number value, but I bet it can be modified to use larger numbers like 7.874. You would stack 5 cups… one for ones, one for the decimals, and 3 for the other three decimal places. Around the rim you write numbers 0-9 (so you don’t waste materials), and the student spins them while stacked to get the correct number being asked for. It would make for a great manipulative if something like if the base-ten blocks aren’t working! (Did an awful job explaining, sorry!)
Chapter 17: This class has opened my eyes to so many new ways to teach math concepts. I remember way back in grade school watching my teacher do math problems on the chalk board. It got very long and boring. Math can be fun if teachers utilize the right resources. It is amazing how the base ten blocks can be used for so many different examples. I guess I would try to find other manipulatives because I wouldn't want to keep using the same things over for different concepts. I really liked the use of the number line to demonstrate to students where decimals and fractions belong. I think it allows the students to visualize the range between some of them.
To Lindsay H: I think as teachers we need to be careful not to use the same manipulatives for different concepts because we may confuse the kids on how we use them. This is just my opinion. I would try to use different items I am comfortable with.
To Amanda L. I agree putting decimals in order is very tough. I think that is why the number line is such a good tool. I think if students can visualize where they are on the number line it makes it a lot easier.
Chapter 17 was about developing concepts of decimals and percents and I think these concepts can be a bit challenging for some students. It was interesting to read about how the base ten blocks can be used to show that decimals can be represented as fractions and vice versa. Having the students label decimals as well as fractions on a number line can help them to compare the two. It's important for students to know that 3/4=.75=75% and this can be shown through a variety of diagrams and manipulatives. Percents can be very useful in the real world, especially when there is a sale at the grocery store or mall. If a bag of oranges is 20% off, it's important to know how much it will actually cost.
I thought that the "friendly fractions" activity would be beneficial to students as well. I liked how you mentioned the terminology of this chapter and how some students might get confused hearing 3/4. As we discussed in class, the fraction 3/4 can be stated as three-fourths or three quarters and this can definitely be confusing for students. It's important for teachers to use these terms interchangeably so students are aware that they mean the same thing. I think that teachers should also be sure to use a variety of models in order to ensure that students are able to visualize these concepts.
The way I learned how to add and subtract decimals is to line up the decimals. I never thought about using snap cubs with the decimals. This is a great hands on learning material. Estimating decimals for me comes easy just round to the nearest whole number. I thought it was interesting in class to hear how people did it different.
To Andrew: I thought that the snap cubes were an interesting way to help students with decimals too. Estimation can be hard for students to get the concept of. I think that using math manipulatives is a great tool for students to visually see.
Chapter 17 – Developing Concepts o f Decimals and Percents This chapter really pushing the idea of making sure our students get that whether it a decimal or fraction, its related. A fraction can mean the same thing as a decimal but they look much differently. That can be very confusing for kids, heck, that’s confusing to me at first. It is also so important to make sure kids are understanding what the decimal really means, what does it look like on a number line? I really like the idea of using the yard stick. This is something that kids struggle with, so I believe this is something that as teachers, we need to make a special effort to really spend the time to get the key points across to the students. The text mentioned that using money early on is not suggested. I would not have thought of this until reading about it, but it really makes sense. When students are just learning, dealing with money can make things more confusing. Using realistic problems when teaching can be helpful and in my opinion just makes sense. If students can see that learning this information is important, they may be more likely to actually do their work.
@ Kristie C I feel like you really summed this chapter up well. I completely agree about the numerator/denominator – that is the way I was taught and so that is the way I did it – but I didn’t really know why I was doing it. I failed to learn that deeper, conceptual knowledge. That is why I think the text book really hit the nail on head by suggesting not to teach our students that method. I also like what you said about the importance of number sense and making sure students are understanding that the numbers continue on both sides of the number line on each side of the 0.
This chapter was over decimals and percents. I really enjoy doing percents. Many times when I am given a decimal I convert it to a percent first thing when solving problems. It was fun to see the variety of ways to solve problems when we had the snap cubes in class. Everyone learns differently and having manipulatives really helps students. It shows how fractions, decimals, and percents are all connected and I think if a student doesn't understand one of these forms, they have two others to show them how. I really thought this chapter had great information in it!
I agree with you that percents are very important in our everyday lives. We always use them ESPECIALLY when shopping! How often do you see a sale that says 3/4 off? Never! It would say 75% off! Many times we use percents without even realizing it! I have read many posts about using percents for shopping! This is so true and such a great example to use!
I too have experienced children have a great struggle learning how to estimate. They also have a hard time knowing whether to go up or down. Actually both of my children had a hard time with this concept in math, and I consider both of them very intelligent children. I am glad to have this book as a resource to help with teaching these concepts.
Chapter 17 discusses developing concepts of decimals and percents. The book states that the best approach is to teach the fractions first, decimals-later sequence. It goes on to state that linking the ideas of fractions to decimals can be extremely useful. I remember being taught the old way, both of them as separate entities. This entire chapter is spent teaching us how to teach the fraction-decimal connection with lots of hands-on activities to achieve that goal. This will probably be one of the most valued books in my collection. I have learned so much this semester on how to teach math. Thanks to this class, I have begun to develop the confidence I needed to teach math.
Chapter 17 covers Developing Concepts of Decimals and Percents. I liked that the chapter had a section on connecting fractions and decimals. I can remember growing up and learning about fractions and decimals and having a hard time finding the connection. I enjoyed reading the activities that were listed on base-ten fractions to decimals. I thought that it was a great way to help me apply it to the classroom. In Response to: Angela S. I agree! I feel much more prepared to teach math after going through this course!
Chapter 17: One thing I loved about this chapter was figure 17.1. It showed us how to make rational number wheels. I think it is such a clever idea and I think it will work great for teaching. One thing this chapter focuses on is converting decimals to fractions and vise versa. I remember learning this in school and our teacher told us to try and memorize the basic fractions. (.75= 3/4 and .5 = 1/2, etc) I didn't really realize how to figure it until later on in school. The book mentions using a number line and I think this is a great way to teach it.
In response to Tammi Whi: I agree that when I was younger I didn't know how to find the connection between the two. It was great to read the parts in this chapter about relating the two. I haven't had the chance to read those two articles yet but I'm excited to see what they talk about.
This chapter was all about decimals and percentages. When I was in school, I struggles with converting decimals to percentages and vise-versa. Now, I don't really know how I got confused. It seems so simple as an adult, that I worry I might have difficulty breaking it down and teaching it to a child that has a hard time understanding it. I loved the teaching ideas that were given in the chapter though! Also, my internship class never taught decimals and percentages while I was there, so I look forward to seeing at some point. I may even teach it before I see it taught!
Chapter 17 was all about developing concepts of Decimals and percents. Decimals and Percents are very intimidating to students and students are immediately apprehensive about completing any assignments that involve either of these types of numbers. One thing I found very informative about this chapter was the different ways to look at the information. But most especially for this semester I found the activities given very useful.
Activity 17.2 was especially interesting to me because it deals directly with the relationships between fractions and decimals. This activity may be very helpful to the students that don’t always understand why they are needing to learn this information. This use of as many manipulatives as possible to learn the same information can be very helpful and informative to the students. It gives them different ways to view and see the same information.
I haven’t personally seen either of these being taught in my internship but I know from experience how difficult it can be for students to positively embrace this information and use these numbers to help them.
In response to Kymberly R... I feel the same way at times. That I may have trouble breaking down the information to an easy-to-understand level for the students. Luckily there are strategies that we can all use to teach many different levels of information.
In response to Carrissa Kruse: I agree with you that the use of manipulatives with this topic is very important. Manipulatives always give students a visual and a hands on way to understand the subject better. I have always learned better with manipulatives.
Chapter 17 was over developing concepts for decimals and percents. These both can be very challenging concepts to students. In my internship class they have just started learning decimals and percents and there are some students who are struggling. I believe in order for students to understand these concepts, the teacher needs to be able to teach at their level. They are closely related so if a student does not understand one concept, they are more than likely not going to be able to understand the other. There are many methods and strategies you can use to teach this as well as many different online games that the students would have playing on the Promethean Board, etc. This just gives they more practice and they do not see it as an assignment. After reading this chapter and watching Professor Stramel teach her class, I am excited to teach these concepts in the near future to my students!
Kymberly--I completely agree with you, converting decimals and percents does seems so much easier now that we are adults but really it is all the same concept. My internship class is learning this now and it does seem so easy but I truly believe it is how you go about teaching these concepts. Teachers need to make sure they are at their students level and are not teaching way over their heads. Great post!
This chapter was about decimals and fractions. Teachers need to make sure that students know that fractions and decimals work together. Sometimes you have to know the decimal before you go to the fraction and vice versa. Using the number line to teach fractions was really interesting to learn. Sometimes teaching a concept in many different ways can help students. Some learn easier one way and others learn from another method. I have always hated fractions and decimals and now after this semester, I feel a lot better about the topics. I still have a little fear, but I think if I keep maintaining my learning about mathematics in general but especially fractions and decimals, I will feel better as time goes on in teaching the different topics.
In response to Kristi P. – I agree that these are topics that are one of the most struggling concepts. I think as long as the students know one concept, they will most likely know the other concept as well. This is not always the case of course. I know there are some students that are able to write fractions, read them and reduced them and all, but they are not able to deal with fractions as easy.
Chapter 17 discussed developing concepts of decimals and percents and connecting them to what the students previously learned about fractions. This chapter was useful to me because this is what the students were learning in my internship class this last week. However, I have not ever seen decimals taught the way that this chapter shows, but I think it is great because it gives meaning to the decimals and decimal places instead of them just being arbitrary numbers. I like the idea of expanding the place value system as a way to show this. As always, this chapter also included many fun activities that can be used to teach students the concept of both decimals and percents, including computation. Overall, I found this chapter very useful and hope to be able to try some of the activities that it mentioned in my classroom someday.
I agree that teachers must have an understanding of how fractions and decimals relate to teach other in order to be able to successfully teach them. I also had a little bit of fear about the concepts of fractions/decimals, but after learning about them in my internship class I feel I have a much better understanding of how they all relate.
Chapter 17 Base ten fractions are an easy thing for me to teach, but the strugglers in math really have difficulty with it. The chapter discusses keeping it simple and using colored disks. It is good to use real life experiences as well, things the students can relate to! The chapter discussed also using place value strips as well as using square models. We are so fortunate to have manipulatives to help us teach this strategy. The chapter provides us with many techniques and activities to teach fractions and percents. I chuckled when I was reading about teaching them about things on sale. Last week, I was working with some fourth graders who were struggling with sale items. I used the example of video games on sale at black Friday, and though they laughed they all seemed to get it!! Estimation is easily taught when using traveling examples. The students seem to relate well when the problem uses nearby towns and though they don’t know the exact number of miles, they are able to estimate how long it takes to get there.
Chapter 17 discusses fractions and their relationship to decimals. There are several ideas presented in this chapter I believe will be very helpful for teaching these concepts to students. For instance, I like the idea of using the calculator to add by .1 up to whole numbers. I also like the idea of having students say fractions, represent them with models, write them, and give them in decimal form. This gives them a lot of practice in various ways. I didn’t realize before how important the use of a number line is in helping students understand decimals and their relationships to whole numbers.
Michelle A., I agree with you that real life examples are important. They give the children information they can relate to and are motivated to use and learn. This is a strategy that is helpful for teaching all subjects, and not just mathematics.
One of the most important take aways from this class has been the importance of manipulatives. Sadly, I don't remember using manipulatives. Like nearly everything we have covered, manipulatives bring mathematical concepts to life. Within my unit we used the fraction wheel. The fraction wheel is great. It is a super simple manipulative that students can make (two round pieces of paper working together). I downloaded mine from the illuminations website (an amazing website) http://illuminations.nctm.org/lessons/6-8/numbersense/BigSmall-AS-FracCircle.pdf
@Shawna My fifth grade mentor uses the concept of money all the time. All she has to do is rub her fingers together (symbolizing money) and the student immediately can relate the decimal to money. It has even helped me have a better understanding.
Chapter 17 discusses the idea of developing concepts of decimals and percents. I think another reason why fractions are so hard to understand is because after a certain time, we convert them to decimals so we have “whole numbers” to add, subtract, multiply, and divide. I remember when I was in high school I would use my graphing calculator and divide all the fractions to make them decimals. I would them complete the problem and them convert the decimal into a fraction. Another challenge is remembering that decimals are hundredths, and tenths. I think we reach a certain point where we stop recognizing the place values and just say “point”. They say that mathematics is the pursuit of laziness, but after being lazy for so long, I am afraid its just because we do not remember the correct terms for everything.
In reply to Brandi: I so agree with you. I know I have never used manipulatives. Using the manipulatives in class was really hard for me because I was so used to using pencil and paper and the standard way of finding the "right" answer. I think that is why it is hard for teachers to teach the non traditional way because we did not learn with manipulatives.
Chapter 17 discussed teaching the concepts of decimals and percents. Personally, these concepts were much easier for me than fractions, but I realize that is not the case for everyone. I remember learning to work with decimals by lining up the “dot.” I wish I would have been given manipulatives like the hundredths disk or the tower cubes. These are both great options for visual learners. This chapter also suggested using base ten blocks to represent decimals. The 100 block now represents 1, the rods represent tenths, and the squares represent hundredths. Personally, I think this might get confusing for children to suddenly change what a block they have been working with for so long represents. I would probably try using the other manipulatives first before using base ten blocks.
I did the same thing you did. If I came across a fraction, I would automatically enter it into my calculator and convert to a decimal. It was just so much easier for me to work with decimals than fractions.
Chapter 17 is about developing concepts of decimals and percents. For me it is sometimes easier to make the fraction into a decimal and then work with the decimal to add, subtract, multiply or divide. The chapter talks about how a teacher should review whole-number place value before working with decimal numerals with students. It also shows how to make the connection of fractions with base-ten fractions and how students can relate to a problem by using real life examples. Models are a great way to introduce fractions, decimals, and percents. Students are able to use these and figure out the answer to a problem. The activities in this chapter are very useful for teaching the above concepts.
To teach decimals and percents to students can be very difficult for some students. I really like to explain it the way Dr Stramel did in class. "Oh look, the 100 is already there (in the percent) Take the back slash and put it for the one and the two '0's next to that to make the 100. I then tell the students that you move the decimal over two spots to make it into a decimal. Other times I have told the students that the number remains the same i.e. .55 = 55/100 - 55% It just a matter of what to do with the decimal or 100 (%)
Michelle A. I like to use real world problems with the students as well. It helps them to associate and thereby it might stick a little better. One of my absolute favorite real world idea is money! 4 quarters = 1 dollar. What is a quarter worth? 25 cents. When we go to a store and buy something for 1 dollar and 50 cents it is written $ 1.50 that is... Chapter 17 has a lot of wonderful idea's. Good post Michelle
Chapter 17 discusses developing concepts of decimals and percents. I think that the number one thing to keep in mind when teaching this is that students must understand that all of these things are connected. Fractions connect to decimals and decimals connect to fractions and so on. If students don't understand this they are going to spend a lot of time extremely confused! Students also need to know that numbers not only go one way on the number value line, they go the other way too and that puts a decimal in front of it. Percentages can be very difficult for a student to understand as well. That is why it is so important for students to see the connection that is there!
ReplyDeleteI found the material in chapter 17 to be incredibly helpful to help students develop number sense when it comes to understanding the connections between fractions and decimals. I also found it interesting that the text specifically mentioned that teaching to divide the numerator by the denominator was not going to be suggested in the text- nor should it be taught. That is the way I was taught, granted it wasn’t very effective for me- which is probably the case for most of us. The suggestions about using a number line were wonderful, and I like that they focused on relating this new concept to old information and allowing the students to come to their own explanations for understanding fractions and decimals. I can’t imagine how this would have changed my understanding of mathematics. Understanding basic concepts is such a HUGE focus in this text and I am thrilled and excited to be taught to teach this way. This is such a fundamental yet not underused idea in teaching- it just makes more sense. I am thrilled that the text focuses so much attention on allowing student to develop number sense.
ReplyDeleteThe models and activities suggested within this chapter were, like always, wonderful and provided future teaches with many ways of accessing and connecting student knowledge.
In response to Kristle C:
ReplyDeleteI agree with you about the importance of students seeing the ‘big picture’ and realizing how all components of mathematics are related. I’m in a first grade classroom and the number line is used heavily in there. We haven’t yet broached the subject of negative number yet, because it is a very difficult concept for most of them, but I would love to be there to see them figure it out. Thanks for your thoughts on this, I too agree that the number sense a student develops is critical in their lifelong understanding of mathematics.
Adrianne- I agree with you on the importance of understanding basic concepts! If students don't get it, they are going to struggle with math for their entire lifetime! There is no way to get around it, every educator needs to strive to find a way to help students "GET IT!" when it comes to basic concepts in mathematics!
ReplyDeleteChapter 17 is about developing concepts of decimals and percents. This is one topic in math that I am not afraid of, and I think that's because I'm a big shopper that is always looking for the best deal. I can always make it relate to me, so I understand it. The students in my internship class have been working on decimals and there is one student who is really struggling he always sees the thousandths spot as being larger than the hundredths spot. Once you are able to explain it once and it seems like he gets it, the next question he is right back to not understanding. I can see how this can be really confusing to students. According to the book, he needs to work more on developing a better decimal number sense. This chapter gave some great ideas, activities, and strategies to help student like this one to understand number sense with decimals.
ReplyDeleteIn response to Adrianne,
ReplyDeleteI also was taught to divide the numerator by the denominator, and am surprised that it is suggested to not teach that way anymore. I also liked the suggestions for using a number line. Using a number line is something that I have no experience with, and I have enjoyed see all the activities and strategies that go along with using it because I think it can be very helpful.
Chapter 17 Developing Concepts of Decimals and Percents
ReplyDeleteI have never seen the hundredths disk before; it really looks like it could be very useful as a teaching tool. (pg. 329) I have found that using a hundreds chart paper and having them color in a certain amount of squares really helpful in teaching them fractions and decimals. I think fractions and decimals might be something that you would want to work on everyday with the children, maybe in calendar time. Knowing where the decimal goes and lining it up is also a very big struggle for children. I can imagine why, in multiplication we count how many digits, in addition we bring it straight down, it can really be confusing. Seems like estimation is very important, because it seems to come up over and over again in our book.
Elizabeth, I think your right it comes right back around to the point that we need to make everything we do in mathematics mean something to them. It has to be something that they will see themselves using over and over again in their lives. Get to know your students. Know what their parents do for a living. If mom works at Walmart how many times does she use this type of math that your working on. Use that reference when making up problems. Sally went to Walmart and saw a dress that was 10% off. If the dress is $12.00 at regular price what will it be after the 10% off. Use real life situations, real to them.
ReplyDeleteThe way I learned to add and subtract decimals was lining up the decimals that way all of the place values line up with each other. That way made the most sense and was the easiest for me to understand. But I do understand that for some students that strategy will not be the best strategy. The one strategy that I found the most interesting was estimating. I thought this was an interesting strategy because it gets students to learn how to round to the nearest whole number and work on estimation skills all at once. This allows the students to come close to the correct answer. Teachers have to remember though that when you estimate the answers are going to vary between what could be a wide range depending on the equation being solved and how far the students are rounding to: ones, tens, hundreds.
ReplyDeleteElizabeth Sills
ReplyDeleteI think your shopping ways are the best way to relate decimal computation to students because money is an everyday part of life. In my math internship when we were working with decimals every student seemed to understand things instantly when relating it to money just because they have already had to do a lot of math with it and know, for example, how many quarters equal a dollar or nickels in a quarter, etc. An educator can come up with several activities relating decimals to money. One way that I remember using in elementary school was we had to buy something, using monopoly money, and then the other student had to count back the correct amount of change.
Under the Big Ideas the author states that decimal numbers are simply another way of writing fractions. A huge learning point when teaching is to make sure this point is taught. All of the points made in this section are critically important when teaching decimals and percents. Making the connection between the two will allow students to make the real world connection between there percentage grade and the number as a decimal. Base Ten fraction models is new learning for me. For example in figure 17.1 the picture shows the manipulative being shown in various configurations. I find that using a number line to begin talking about percentages is a way of visually showing students the range of percentages that can occur between 1 and 100%. A review of decimals in addition, subtraction, multiplication, and division is essential when beginning to compute decimals together. Overall, this was an informative chapter with two great literature suggestions in the literature connections section.
ReplyDeleteI didn’t think about using snap cubes to solve decimal problems. Now that I see it, I think it would be a great idea! It would be a great way to visually show the students a part of something. I think that decimals are tricky for children. Before they start decimals, they are taught using whole numbers. To break it down (i.e. .75, .35, .01) can be mind-blowing for some of them!
ReplyDeleteLater on in the chapter, the author talks about estimating. My internship teacher just went through the long and strenuous process of teaching the students the concept of estimating. For some reason, they had difficulties rounding up or rounding down a number. The book said that starting with decimal computations is a good place to start estimation skills with the students because they begin to develop reasonable ranges of where the number might be, or should go.
Comment for Lane A.
ReplyDeleteI completely agree with your point about answers varying when asking students to estimate. If we do not ask students to estimate to a certain digit then answers will certainly be different. Teachers must take this into consideration when grading. I believe that there are many ways to compute decimals. I find that following the rules I learned are easy for me but I will encourage my students to use a strategy that works best for them. The correct answer may be achieved through different avenues.
In response to Lane-
ReplyDeleteI learned how to add and subtract decimals the same way. I, for one didn’t find it too difficult. As you said, every student is different. I may become a challenge to incorporate all the different strategies for the students but it is important that we do.
Percents and decimals can be a lot of fun to teach because there are so many ways to involve fun activities into teaching these concepts. Using the base ten blocks and snap cubes are great ways to get students hands-on learning as well. I think that by using graph paper can also be a good alternative. Converting fractions to decimals is a fun transition. I remember when I learned how to do this it was a big deal, at least to me, because I was converting different types of numbers that would equal the same thing. I guess I am weird like that. It will be a fun challenge to teach to different types of learners but will be rewarding for the hard work, hopefully.
ReplyDeleteAndrew,
ReplyDeleteI agree that it will be a challenge to use multiple strategies and it is important that we do so. It is important as well that we recognize the learning types that we have in our classrooms and try to decipher which strategies may reach those students, teach that strategy then continue to introduce a different strategy. Anything hands-on always engaged me as a learner so that is something that I will most likely always do.
Chapter 17, developing concepts of decimals and percents is the last chapter we are blogging over and is probably my favorite. I love working with decimals and percents and feel that this is one of the most practical applications in math. We all deal with both decimals and percents on a daily basis, weather we are talking about money, sales, grades, or measuring. There are so many different methods to teaching decimals and percents but the best way is by connecting fractions to decimals and then decimals to percents. This will give the students a complete understanding of the connections that the all share. When I was in school we were taught decimals and fractions simultaneously, doing worksheets were we converted decimals into fractions and vice versa. Then we added in percents so by the time we were done the class was able to say ¼ is the same as .25 and 25%. The two key points in this chapter is extending the place-value system so that students understand the number in relationship of other numbers and teaching decimals with familiar fraction, this means ones that are commonly used a easy to solve for. Both of these are important because it helps students take a realistic approach to math concepts; for example students need to learn that .07 is very different than .7, one is only seven cents while the other is seventy cents. Overall this chapter has a lot of very good activities but I found it odd that didn’t have any activities dealing with money. Have a great Holiday Season!
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteIn response to Joel Stucky,
ReplyDeleteI totally agree with you, I love decimals and fractions, and I remember feeling so smart when I was able to convert a fraction into a decimal and then into a percent. You get the feeling that you can actually see how all the different math concepts tie together. Also I love the many different activities you can do with decimals and percents, I remember this being the section where we always got to use different types of manipulative.
Chapter seventeen was very interesting to me because it was based on a topic I greatly struggled with as a child, decimals and percent’s. I don’t really know why but decimals and percent’s were very hard for me to grasp. ¾, ½, ¼, 75%, 50%, and 25% were all easy for me to grasp because it was like counting the parts of a dollar. It was all the number sin between that confused me.
ReplyDeleteI really liked the friendly fractions to decimals activity in 17.4. I like the thought of introducing “friendly” fractions to students. Even just this simple term might put a more enjoyable spin on working with fractions. The other part I really like about this specific activity is that it uses models to guide students in converting fractions to decimals. This friendly fraction idea is re-enforced through many of the activities in this chapter.
One other section I really liked in this chapter was the models and terminology section. I feel like maybe I didn’t have enough visual aids when I was a child. I really desired models but I didn’t have many and I think that’s why I want to use them as much as possible in my future classroom. Like the chapter says, models provide a clear link among fractions, decimals, and percent’s. Hearing the term 3/4 can be a bit confusing but when you see what ¾ actually is you can put an actual size to it. Models are a great tool for understanding and a great connection for fractions, decimals, and percent’s.
Joel,
ReplyDeleteI like how you mentioned how decimals and percent’s can be fun to teach. I had trouble with them as a child, but you are right in the sense that there are so many manipulatives I will be able to use as an educator to make them fun or “friendly” for my students. Manipulatives such as popcubes and base ten blocks are really helpful in making connections between fractions, decimals, and percent’s. I think these manipulatives are the only things keeping me excited about teaching decimals and percent’s. I may not have had the best learning experience with this concept as a child but I definitely have the tools to give a more meaningful experience to my future students. Good post!
Katie Coulter
ReplyDeleteChapter 17
Decimals and percentages don’t bother me to much but reading through this section made me realize how confusing they can be in their relationship together. The chapter begins introducing the base 10 way. I understand how they figure it but I for some reason just don’t feel it’s the best way to accommodate all types of learners. It was funny, just as I was thinking to myself how great money is to use in this concept I read “Don’t use money”! I do love the idea of putting decimals and fractions in number lines. For me this is how I learn, seeing the physical amount of the value. The chapter moved on deeper in percentages which I think I understand pretty well. It did however bring back a nightmare of a concept for me- the 3 percent problems. I can’t stand those problems, they just never made since to me. I remember having a cheat sheet with each way the question could be presented and having to look off that on every problem. For some reason it just never stuck with me. Now once I saw the illustrations of the same thing I was like ok…………that’s when I could use this. As a teacher I need to highlight this segment to remind myself to never do this to another student. The picture just explained it without having to get my calculator out to figure the correct amount. It was easy and made since what they were asking. If we are in the store and something is on sale, I usually make him do it in his head. I hope our kids get his math skills!
I think that the truth in this chapter is that children start with base ten blocks to help with decimals. That means that no matter the grade you teach you are going to build a base for decimals. That kind of makes decimals very important. Just like reading it advances as you move from grade to grade. This chapter gives many ideas on how to use decimals in the classroom and also how to teach them. I think one difficult part of decimals is putting them in order from least to most or most to least. This can become difficult, as students get older. It definitely gets harder when negatives come into the picture. I sometimes get confused with fractions and decimals in negatives. I think when taught correctly decimals can become second nature to most students.
ReplyDeleteIn response to Andrew D.
ReplyDeleteThe concept of estimating is kind of confusing for children. Which I think once they get it though it comes easier for them. I think it is just one of those concepts that is kind of hard to explain on how to estimate.
When reading chapter 17 over developing concepts of decimals and percents I was able to learn some helpful information to use in my future classroom. I liked how the chapter focused on the fraction-decimal connection and how students should be able to make the connections between the two of them. I liked the figure 17.11 called a decimal number line. The picture did a great job of explaining how to make the decimal number line. The chapter did a great job also of showing me as a future teacher some tips of how to teach percents to my students. One very important tip when teaching percents to students is to limit the percents to familiar fractions or easy percents.
ReplyDeleteThe part of the chapter I found the most interesting was the area of estimation. I feel that students need to know how to properly estimate and make an educated guess when referring to math problems and in real world situations. I liked how the book talked about it relationship to estimation about percents that if the percent is not a “nice” one then substitute a close percent that is easy to work with. This is such an important statement to tell the students at the beginning of the lesson so that the students are not struggling with tough percentages. Overall I liked all of the different activities presented in chapter 17 and I feel that I learned lots of information about decimals and percents in order to become successful teaching it in my future classroom.
In response to Kristle C.,
ReplyDeleteI agree with you Kristle 100% that it is so important for students to understand that decimals and percentages are all connected together. This is so important for students to understand in order to become successful in this area of math as well as make the math experience easier on them. Students are going to become confused if they don’t see that fractions are connected to decimals and decimals are connected to percentages. I agree with you that overall percentages can be a very confusing concept for students to understand and it is up to the teacher to help the student to be able to understand the concept. Overall the main focus of the chapter I agree with you is to make sure that the student sees the connection!!!
Chapter 17
ReplyDeleteChapter seventeen of the text book Elementary and Middle School Mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discusses how students learn decimals and percents and how teachers can explain these different concepts to their students. The textbook states “this fractions first, decimals-later sequence is arguably the best approach” (Van de Walle et al., 2010, p. 328). Van de Walle et al. textbook also mentions “linking the ideas of fractions to decimals can be extremely useful, both from a pedagogical view as well as a practical view” (Van de Walle et al., 2010, p. 328). This is why it is important for teachers to go into a sequence of what they teach to their students.
A piece of information that I learned from chapter seventeen was of Van de Walle et al. textbook was when the textbook states “many teachers use money as a model for decimals, and to some extent this is helpful. However, for children, money is almost exclusively a two-place system (Van de Walle et al., 2010, p. 330). I often do explain fractions as money amount because students can relate to that better but I do understand what the book is explaining that this only can take the students so far.
Something interesting mentioned in chapter seventeen of Van de Walle et al. textbook was on page 335 of Van de Walle textbook that mentions “only 51 percent of eighth graders selected ½” when asked the problem “What fraction would you say approximates the decimal 0.52” (Van de Walle et al., 2010, p. 335). This was actually surprising to me because I thought that would be an easy problem for students especially eighth graders to get.
Chapter seventeen of Van de Walle et al. made me think about all the different examples that I can use to relate this material to the students everyday life. I can use signs that they may see, sales that stores may have percentages students get on assignments etc. I think that having students relate to these different concepts really gives them higher understanding of the certain concept.
Something from chapter seventeen Van de Walle et al. that I would like to use in my classroom is the different manipultives and hand on materials that were described in the textbook. It is so much easier when students can actually explore with these different concepts and can see why there is or isn’t correct.
References:
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Jennifer Pen reply to Shannon,
ReplyDeleteI agree that there different parts of fractions that make sense to me and then there are parts that do not. I always looked at decimals like they were money and fractions like they were a piece of a pie because that is what makes sense to me.
Chapter 17 was very interesting! I like the big idea that decimals are simply another way of writing fractions. I probably love decimals more than I love fractions! Dr. Stramel has shown us the rational number wheel and I think it would be something that would be a fantastic manipulative. One thing that I am not so confident about is the base ten blocks. I have seen them used but I am not so confident about them. In figure 17.8 where they showed decimals to fractions on a base ten flat I think would be a bit confusing for students. I think it will be as difficult to teach decimals as it is fractions!
ReplyDelete@ Jena Simms
We both liked the same big idea! I would agree that this is so important for students to understand. It should be our main point that we push to our students!
@ Elizabeth Sills
ReplyDeleteI too agree that percentages are easier for me than other topics (like fractions). I think it’s because percentages are everywhere. Last weekend over Black Friday my e-mail inbox was swamped with sales fliers from various stores stating how much you could get off of your purchase or particular items.
In regards to your student that is having a hard time with decimals and the values… I saw a great idea on the Internet using Styrofoam cups. (I’ll post the link at the end of this.) This idea was for just number value, but I bet it can be modified to use larger numbers like 7.874. You would stack 5 cups… one for ones, one for the decimals, and 3 for the other three decimal places. Around the rim you write numbers 0-9 (so you don’t waste materials), and the student spins them while stacked to get the correct number being asked for. It would make for a great manipulative if something like if the base-ten blocks aren’t working! (Did an awful job explaining, sorry!)
http://mysecondgradejournal.blogspot.com/2011/11/im-such-bad-blogger-but-i-have-goodie.html
Chapter 17: This class has opened my eyes to so many new ways to teach math concepts. I remember way back in grade school watching my teacher do math problems on the chalk board. It got very long and boring. Math can be fun if teachers utilize the right resources. It is amazing how the base ten blocks can be used for so many different examples. I guess I would try to find other manipulatives because I wouldn't want to keep using the same things over for different concepts. I really liked the use of the number line to demonstrate to students where decimals and fractions belong. I think it allows the students to visualize the range between some of them.
ReplyDeleteTo Lindsay H: I think as teachers we need to be careful not to use the same manipulatives for different concepts because we may confuse the kids on how we use them. This is just my opinion. I would try to use different items I am comfortable with.
ReplyDeleteTo Amanda L. I agree putting decimals in order is very tough. I think that is why the number line is such a good tool. I think if students can visualize where they are on the number line it makes it a lot easier.
ReplyDeleteChapter 17 was about developing concepts of decimals and percents and I think these concepts can be a bit challenging for some students. It was interesting to read about how the base ten blocks can be used to show that decimals can be represented as fractions and vice versa. Having the students label decimals as well as fractions on a number line can help them to compare the two. It's important for students to know that 3/4=.75=75% and this can be shown through a variety of diagrams and manipulatives. Percents can be very useful in the real world, especially when there is a sale at the grocery store or mall. If a bag of oranges is 20% off, it's important to know how much it will actually cost.
ReplyDeleteIn response to Shannon H.:
ReplyDeleteI thought that the "friendly fractions" activity would be beneficial to students as well. I liked how you mentioned the terminology of this chapter and how some students might get confused hearing 3/4. As we discussed in class, the fraction 3/4 can be stated as three-fourths or three quarters and this can definitely be confusing for students. It's important for teachers to use these terms interchangeably so students are aware that they mean the same thing. I think that teachers should also be sure to use a variety of models in order to ensure that students are able to visualize these concepts.
The way I learned how to add and subtract decimals is to line up the decimals. I never thought about using snap cubs with the decimals. This is a great hands on learning material. Estimating decimals for me comes easy just round to the nearest whole number. I thought it was interesting in class to hear how people did it different.
ReplyDeleteTo Andrew:
ReplyDeleteI thought that the snap cubes were an interesting way to help students with decimals too. Estimation can be hard for students to get the concept of. I think that using math manipulatives is a great tool for students to visually see.
Chapter 17 – Developing Concepts o f Decimals and Percents
ReplyDeleteThis chapter really pushing the idea of making sure our students get that whether it a decimal or fraction, its related. A fraction can mean the same thing as a decimal but they look much differently. That can be very confusing for kids, heck, that’s confusing to me at first. It is also so important to make sure kids are understanding what the decimal really means, what does it look like on a number line? I really like the idea of using the yard stick. This is something that kids struggle with, so I believe this is something that as teachers, we need to make a special effort to really spend the time to get the key points across to the students. The text mentioned that using money early on is not suggested. I would not have thought of this until reading about it, but it really makes sense. When students are just learning, dealing with money can make things more confusing. Using realistic problems when teaching can be helpful and in my opinion just makes sense. If students can see that learning this information is important, they may be more likely to actually do their work.
@ Kristie C
ReplyDeleteI feel like you really summed this chapter up well. I completely agree about the numerator/denominator – that is the way I was taught and so that is the way I did it – but I didn’t really know why I was doing it. I failed to learn that deeper, conceptual knowledge. That is why I think the text book really hit the nail on head by suggesting not to teach our students that method. I also like what you said about the importance of number sense and making sure students are understanding that the numbers continue on both sides of the number line on each side of the 0.
This chapter was over decimals and percents. I really enjoy doing percents. Many times when I am given a decimal I convert it to a percent first thing when solving problems. It was fun to see the variety of ways to solve problems when we had the snap cubes in class. Everyone learns differently and having manipulatives really helps students. It shows how fractions, decimals, and percents are all connected and I think if a student doesn't understand one of these forms, they have two others to show them how. I really thought this chapter had great information in it!
ReplyDeleteIn response to Sarah,
ReplyDeleteI agree with you that percents are very important in our everyday lives. We always use them ESPECIALLY when shopping! How often do you see a sale that says 3/4 off? Never! It would say 75% off! Many times we use percents without even realizing it! I have read many posts about using percents for shopping! This is so true and such a great example to use!
In response to Andrew Dempewolfe,
ReplyDeleteI too have experienced children have a great struggle learning how to estimate. They also have a hard time knowing whether to go up or down. Actually both of my children had a hard time with this concept in math, and I consider both of them very intelligent children. I am glad to have this book as a resource to help with teaching these concepts.
Chapter 17 discusses developing concepts of decimals and percents. The book states that the best approach is to teach the fractions first, decimals-later sequence. It goes on to state that linking the ideas of fractions to decimals can be extremely useful. I remember being taught the old way, both of them as separate entities. This entire chapter is spent teaching us how to teach the fraction-decimal connection with lots of hands-on activities to achieve that goal. This will probably be one of the most valued books in my collection. I have learned so much this semester on how to teach math. Thanks to this class, I have begun to develop the confidence I needed to teach math.
ReplyDeleteChapter 17 covers Developing Concepts of Decimals and Percents. I liked that the chapter had a section on connecting fractions and decimals. I can remember growing up and learning about fractions and decimals and having a hard time finding the connection. I enjoyed reading the activities that were listed on base-ten fractions to decimals. I thought that it was a great way to help me apply it to the classroom.
ReplyDeleteIn Response to:
Angela S.
I agree! I feel much more prepared to teach math after going through this course!
Chapter 17: One thing I loved about this chapter was figure 17.1. It showed us how to make rational number wheels. I think it is such a clever idea and I think it will work great for teaching. One thing this chapter focuses on is converting decimals to fractions and vise versa. I remember learning this in school and our teacher told us to try and memorize the basic fractions. (.75= 3/4 and .5 = 1/2, etc) I didn't really realize how to figure it until later on in school. The book mentions using a number line and I think this is a great way to teach it.
ReplyDeleteIn response to Tammi Whi:
I agree that when I was younger I didn't know how to find the connection between the two. It was great to read the parts in this chapter about relating the two. I haven't had the chance to read those two articles yet but I'm excited to see what they talk about.
This chapter was all about decimals and percentages. When I was in school, I struggles with converting decimals to percentages and vise-versa. Now, I don't really know how I got confused. It seems so simple as an adult, that I worry I might have difficulty breaking it down and teaching it to a child that has a hard time understanding it. I loved the teaching ideas that were given in the chapter though! Also, my internship class never taught decimals and percentages while I was there, so I look forward to seeing at some point. I may even teach it before I see it taught!
ReplyDeleteCarissa Kruse
ReplyDeleteChapter 17-BLOG
Chapter 17 was all about developing concepts of Decimals and percents. Decimals and Percents are very intimidating to students and students are immediately apprehensive about completing any assignments that involve either of these types of numbers. One thing I found very informative about this chapter was the different ways to look at the information. But most especially for this semester I found the activities given very useful.
Activity 17.2 was especially interesting to me because it deals directly with the relationships between fractions and decimals.
This activity may be very helpful to the students that don’t always understand why they are needing to learn this information.
This use of as many manipulatives as possible to learn the same information can be very helpful and informative to the students. It gives them different ways to view and see the same information.
I haven’t personally seen either of these being taught in my internship but I know from experience how difficult it can be for students to positively embrace this information and use these numbers to help them.
In response to Kymberly R...
ReplyDeleteI feel the same way at times. That I may have trouble breaking down the information to an easy-to-understand level for the students. Luckily there are strategies that we can all use to teach many different levels of information.
In response to Carrissa Kruse:
ReplyDeleteI agree with you that the use of manipulatives with this topic is very important. Manipulatives always give students a visual and a hands on way to understand the subject better. I have always learned better with manipulatives.
Chapter 17 was over developing concepts for decimals and percents. These both can be very challenging concepts to students. In my internship class they have just started learning decimals and percents and there are some students who are struggling. I believe in order for students to understand these concepts, the teacher needs to be able to teach at their level. They are closely related so if a student does not understand one concept, they are more than likely not going to be able to understand the other. There are many methods and strategies you can use to teach this as well as many different online games that the students would have playing on the Promethean Board, etc. This just gives they more practice and they do not see it as an assignment. After reading this chapter and watching Professor Stramel teach her class, I am excited to teach these concepts in the near future to my students!
ReplyDeleteKymberly--I completely agree with you, converting decimals and percents does seems so much easier now that we are adults but really it is all the same concept. My internship class is learning this now and it does seem so easy but I truly believe it is how you go about teaching these concepts. Teachers need to make sure they are at their students level and are not teaching way over their heads. Great post!
ReplyDeleteThis chapter was about decimals and fractions. Teachers need to make sure that students know that fractions and decimals work together. Sometimes you have to know the decimal before you go to the fraction and vice versa. Using the number line to teach fractions was really interesting to learn. Sometimes teaching a concept in many different ways can help students. Some learn easier one way and others learn from another method. I have always hated fractions and decimals and now after this semester, I feel a lot better about the topics. I still have a little fear, but I think if I keep maintaining my learning about mathematics in general but especially fractions and decimals, I will feel better as time goes on in teaching the different topics.
ReplyDeleteIn response to Kristi P. –
ReplyDeleteI agree that these are topics that are one of the most struggling concepts. I think as long as the students know one concept, they will most likely know the other concept as well. This is not always the case of course. I know there are some students that are able to write fractions, read them and reduced them and all, but they are not able to deal with fractions as easy.
Chapter 17 discussed developing concepts of decimals and percents and connecting them to what the students previously learned about fractions. This chapter was useful to me because this is what the students were learning in my internship class this last week. However, I have not ever seen decimals taught the way that this chapter shows, but I think it is great because it gives meaning to the decimals and decimal places instead of them just being arbitrary numbers. I like the idea of expanding the place value system as a way to show this. As always, this chapter also included many fun activities that can be used to teach students the concept of both decimals and percents, including computation. Overall, I found this chapter very useful and hope to be able to try some of the activities that it mentioned in my classroom someday.
ReplyDelete@ April B
ReplyDeleteI agree that teachers must have an understanding of how fractions and decimals relate to teach other in order to be able to successfully teach them. I also had a little bit of fear about the concepts of fractions/decimals, but after learning about them in my internship class I feel I have a much better understanding of how they all relate.
Chapter 17
ReplyDeleteBase ten fractions are an easy thing for me to teach, but the strugglers in math really have difficulty with it. The chapter discusses keeping it simple and using colored disks. It is good to use real life experiences as well, things the students can relate to! The chapter discussed also using place value strips as well as using square models. We are so fortunate to have manipulatives to help us teach this strategy. The chapter provides us with many techniques and activities to teach fractions and percents. I chuckled when I was reading about teaching them about things on sale. Last week, I was working with some fourth graders who were struggling with sale items. I used the example of video games on sale at black Friday, and though they laughed they all seemed to get it!! Estimation is easily taught when using traveling examples. The students seem to relate well when the problem uses nearby towns and though they don’t know the exact number of miles, they are able to estimate how long it takes to get there.
@ Lindsay,
ReplyDeleteI agree that if we can give our students something to relate to it makes teaching easier for us and learning easier for them!!
Chapter 17 discusses fractions and their relationship to decimals. There are several ideas presented in this chapter I believe will be very helpful for teaching these concepts to students. For instance, I like the idea of using the calculator to add by .1 up to whole numbers. I also like the idea of having students say fractions, represent them with models, write them, and give them in decimal form. This gives them a lot of practice in various ways. I didn’t realize before how important the use of a number line is in helping students understand decimals and their relationships to whole numbers.
ReplyDeleteMichelle A., I agree with you that real life examples are important. They give the children information they can relate to and are motivated to use and learn. This is a strategy that is helpful for teaching all subjects, and not just mathematics.
ReplyDeleteOne of the most important take aways from this class has been the importance of manipulatives. Sadly, I don't remember using manipulatives. Like nearly everything we have covered, manipulatives bring mathematical concepts to life. Within my unit we used the fraction wheel. The fraction wheel is great. It is a super simple manipulative that students can make (two round pieces of paper working together). I downloaded mine from the illuminations website (an amazing website) http://illuminations.nctm.org/lessons/6-8/numbersense/BigSmall-AS-FracCircle.pdf
ReplyDelete@Shawna
My fifth grade mentor uses the concept of money all the time. All she has to do is rub her fingers together (symbolizing money) and the student immediately can relate the decimal to money. It has even helped me have a better understanding.
Chapter 17 discusses the idea of developing concepts of decimals and percents. I think another reason why fractions are so hard to understand is because after a certain time, we convert them to decimals so we have “whole numbers” to add, subtract, multiply, and divide. I remember when I was in high school I would use my graphing calculator and divide all the fractions to make them decimals. I would them complete the problem and them convert the decimal into a fraction. Another challenge is remembering that decimals are hundredths, and tenths. I think we reach a certain point where we stop recognizing the place values and just say “point”. They say that mathematics is the pursuit of laziness, but after being lazy for so long, I am afraid its just because we do not remember the correct terms for everything.
ReplyDeleteIn reply to Brandi: I so agree with you. I know I have never used manipulatives. Using the manipulatives in class was really hard for me because I was so used to using pencil and paper and the standard way of finding the "right" answer. I think that is why it is hard for teachers to teach the non traditional way because we did not learn with manipulatives.
ReplyDeleteChapter 17 discussed teaching the concepts of decimals and percents. Personally, these concepts were much easier for me than fractions, but I realize that is not the case for everyone. I remember learning to work with decimals by lining up the “dot.” I wish I would have been given manipulatives like the hundredths disk or the tower cubes. These are both great options for visual learners. This chapter also suggested using base ten blocks to represent decimals. The 100 block now represents 1, the rods represent tenths, and the squares represent hundredths. Personally, I think this might get confusing for children to suddenly change what a block they have been working with for so long represents. I would probably try using the other manipulatives first before using base ten blocks.
ReplyDeleteDeidre --
ReplyDeleteI did the same thing you did. If I came across a fraction, I would automatically enter it into my calculator and convert to a decimal. It was just so much easier for me to work with decimals than fractions.
Chapter 17 is about developing concepts of decimals and percents. For me it is sometimes easier to make the fraction into a decimal and then work with the decimal to add, subtract, multiply or divide. The chapter talks about how a teacher should review whole-number place value before working with decimal numerals with students. It also shows how to make the connection of fractions with base-ten fractions and how students can relate to a problem by using real life examples. Models are a great way to introduce fractions, decimals, and percents. Students are able to use these and figure out the answer to a problem. The activities in this chapter are very useful for teaching the above concepts.
ReplyDeleteTo teach decimals and percents to students can be very difficult for some students. I really like to explain it the way Dr Stramel did in class. "Oh look, the 100 is already there (in the percent)
ReplyDeleteTake the back slash and put it for the one and the two '0's next to that to make the 100.
I then tell the students that you move the decimal over two spots to make it into a decimal.
Other times I have told the students that the number remains the same i.e. .55 = 55/100 - 55%
It just a matter of what to do with the decimal or 100 (%)
Michelle A.
ReplyDeleteI like to use real world problems with the students as well. It helps them to associate and thereby it might stick a little better.
One of my absolute favorite real world idea is money! 4 quarters = 1 dollar. What is a quarter worth? 25 cents. When we go to a store and buy something for 1 dollar and 50 cents it is written $ 1.50 that is...
Chapter 17 has a lot of wonderful idea's.
Good post Michelle