The Elementary Math Maniac: 2014

Tuesday, December 30, 2014

Monday, December 29, 2014

Monday Math Literature: Place Value Story Problems with Snowmen at Night

Happy Monday! Today's post isn't getting done until late because I have been enjoying my vacation a little to much! If you are still on vacation, I hope you are enjoying your final days and if you are already back to school, I hope your return went smoothly. I will be finishing up our book study on Children's Mathematics this Sunday and I have some great plans for January including a book study on Number Talks.
If you have been following along with our Children's Mathematics book study and the past few Monday Math Literature posts than you know we have been looking at the importance of using multiplication and division story problems with primary students as a way to develop base-10 place value concepts. This week, I once again choose one of my favorite winter stories to write some multiplication and measurement division story problems focusing on place value concepts. These are meant to be used with primary students! This week, I picked a new favorite, Snowmen at Night by

Caralyn Buehner

If you have not read this book, you really should! It is a great story for stretching kids' imaginations. It is about what snowmen do after it gets dark and why they end up looking shorter, crooked or missing some parts. It is a fun book to read aloud because it is written poem style and the illustrations are a lot of fun.

I wrote two multiplication and two division problems based on this story to use with primary students. I again focused on place value ideas and wrote 3 of the problems to be about grouping into 10's.

You can grab a free printable copy of these problems from Google Drive!

If you missed the last 2 week's installments of Monday Math Literature, you might want to head over to read more and grab more freebies! I did The Mitten and The Bear Snores On. You can grab a set of problems to go with each book.

If your students are working on equality or addition facts, or you are looking for more snowman themed math, you might want to check out my Addition Fact Equality product.

Saturday, December 27, 2014

Children's Mathematics Book Study: Part 4

Welcome to the second to last week of our book study on Children's Mathematics. If you missed this week's Monday Math Literature post, you might want to check it out. I took a suggestion from the book about using children's literature to inspire story problems that help build place value understanding and wrote some story problems to go along with Bear Snores On. Head over to read more about it and grab a free set of problems.

If you are just joining us, it is not to late to join our book study. Grab a copy of the book and maybe a friend or two and jump in when you are ready. Also, if this December is just to hectic for you, I will be starting another book study the second week in January. Read more details about both book studies here.

Here is the posting schedule for Children's Mathematics:
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13

I will post each Sunday morning and share it on my Facebook page. Please join in by leaving a comment on my blog post or Facebook page. If you have your own blog and want to write a post about the book that works too! Add your link in the comments section here. Thank you to all who shared last week!

Chapter 8: Problem Solving as Modeling

To me, this chapter is kind of the anthem to who I am as a math teacher. I so strongly believe that kids learn best through problem solving and modeling situations rather than learning procedures and then applying the procedures to solve problems. While working with kids of all ability levels I have seen that "Children who are progressing more slowly than their classmates are better served by being supported in generating their own models to solve problems than by being taught problem-solving strategies that have no inherent meaning for them and simply become procedures to follow." One of the things that saddens me the greatest as a teacher is when I find a kid who is so far removed from this sense making idea that they solve a problem like 300-299 using a procedure. The fact that math has become all about procedures to them is just a shame.

Chapter 9: Developing Classroom Practice: Posing Problems and eliciting Thinking

I think starting Cognitively Guided Instruction can be intimidating. When teachers first see CGI being done it can look effortless but it certainly takes a change of practice for most teachers to get to that level. Moving your classroom to one where kids are sharing strategies and a range of ideas are celebrated certainly takes some effort but is so worth it in the long run. The ability to know what problems to pose, how to unpack those situations and how to question kids about their strategies develops over time. There really isn't a wrong way to do these things. If you are new to CGI, the hardest part can just be getting started.

Chapter 10: Developing Classroom Practice: Engaging Students with Each Other's Ideas

I love listening to students share ideas about math. I think it is such a vital part of getting kids to develop a conceptual understanding of a topic. There is so much power in hearing kids talk to each other about math and to make statements that compare and contrast strategies. I love the ideas in this chapter about getting kids to think about other students thinking.

One thing that has made having students share strategies easier over the last few years is the availability of document cameras. When I read the first edition of this book, I had an overhead projector and a small chalkboard. Now many classrooms have access to document cameras thus allowing kids to share their work instantly without having to copy it to the board or a transparency. While watching the video of Mr. Graces's class, I was thinking about how nice it was that the entire class of students could see multiple strategies at the same time and how the kids who were not writing on the board were talking about different strategies while they were being written up there. I think I have gone a bit to far away from this with using document cameras and need to remind myself that the time invested in having kids show their work on the board is valuable in itself. I need to find a better balance between the efficiency of the document camera and the breadth of possibilities I get by having multiple kids show their work on the board.

What are your thoughts about this week's reading? Feel free to comment below or head over to Facebook and leave your thoughts there!

Sunday, December 21, 2014

Monday Math Literature: Base Ten Story Problems with The Bear Snores On

Happy Monday! If today is your first day of winter break or summer vacation, I hope you are enjoying it! If you are in school for a few more days, remember that the end is in sight. I have some fun holiday plans coming up in the next two weeks so expect to see less posts from me for the next 2 weeks. I will be posting on Sundays for our Children's Mathematics book study and I have some great plans for January including a book study on Number Talks.

If you have been following along with our Children's Mathematics book study and last week's Monday Math Literature post than you know we have been looking at the importance of using multiplication and division story problems with primary students as a way to develop base-10 place value concepts. This week, I have chosen one of my favorite winter books by Karma Wilson.

Bear Snores On

This was the first book written in the Bear series and is such a fun read aloud. There is lots of action in the story and it is a great way to demonstrate what a fluent reader sounds like. Kids of all ages love this book and it lends itself well to solving math problems. I wrote 4 different multiplication and measurement division story problems mostly focused on base-10 concepts that you can use with your students this winter. These problems are a great way to build and assess place value understanding with your students. The process of writing such story problems is a good one and I encourage you to grab one of your favorite read alouds and write some of your own problems.

Here are the 4 problems I wrote to accompany a reading of Bear Snores On. Click here to grab them from Google Drive!

What story problems can you write to go along with Bear Snores On? Please share in the comments below!

Saturday, December 20, 2014

Children's Mathematics Book Study: Part 3

Welcome to week 3 of our book study on Children's Mathematics. I was so excited to dig into the chapter on base 10 concepts after last week's reading. I also really liked all the strategies shared in chapter 7 and I love watching videos of kids solving problems. If you missed this week's Monday Math Literature post, you might want to check it out. I took one of the questions from last week's chapter about writing story problems based on a children's book and applied it to The Mitten. You can check out my process and grab the set of problems I wrote.

Chapter 6: Base-Ten Number Concepts

After being introduced to the idea last week of the importance of exposing kids to multiplication and measurement division problems I was very excited to explore this chapter in more detail. There are some excellent videos to watch and some great examples of problems that get kids thinking in tens. I love the range of problems presented in this chapter and the examples really got me thinking about how I can ask more base ten multiplication and measurement division problems of kids at all grade levels.

Teaching Concepts versus Teaching Procedures

I have seen time and time again how powerful it can be for students to construct their own knowledge and I love how the paragraph as the top of page 91 supports this idea. It is so tempting to teach kids a procedure or a rule and tie it into a cute jingle because then it seems like they "get it" right away. It is also the way most teachers were taught themselves and the only way most adults have ever experienced learning. As someone who works with kids over a span of 7 years, I have seen first hand how these rules don't hold up over time. It certainly takes longer to let kids develop a good conceptual understanding of math concepts, but it pays off big time later when they can add to their knowledge rather than throwing out old rules and learning new ones.

Number Words

When I first started teaching math at the primary level, I remember feeling very frustrated by the lack of understanding in reading and writing numbers. Even very small numbers seemed to be super challenging for some kids to read and write. It just seemed like such an easy skill to me because I had been doing it for so long. "As adults, we have used number words and pace value for so long that we no longer pause to think about the fact that there is a difference between spoken number words and written numerals or that the same symbol can have many different values depending on where it is placed in a numeral." After I took some time to stop and think about all the nuances of place value and of the English language, I realized why my students were struggling with this so much. I have to say that arrow cards have really changed the way I teach number words and can make a huge difference for your students.

Chapter 7: Children's Strategies for Solving Multidigit Problems

This chapter opens with this statement: "Problems with two- and three-digit numbers actually provide a context for children to develop an understanding of base-ten number concepts. As children solve and discuss these problems, their understanding of base-ten number concepts increases concurrently with an understanding of how to apply this knowledge to solve problems." I love this statement and think it sets a great tone for the chapter. I have spent a great deal of time developing better ways guide my students through multidigit problems over the last 3 years. When I first started my blog, I wrote this post about how I presented a group of second graders with a problem that involved them solving 1000-668 without ever having "taught" them how to do it. I was so impressed at the time with how well my students did with this and how many strategies they had. Now I do these types of problems a lot more with kids. It really helps them cement their place value understanding while building their own strategies for multidigit computation.

There are so many excellent examples and videos in this chapter that I could spend a full week talking about all the great ideas. Similar to the earlier chapters, it is important to remember that kids move from direct modeling to more efficient methods over time. If you change the numbers or the context of the problem, they might revert back to direct modeling. It is not a linear progression where kids graduate from one type of problem solving and never use it again. They will move up and down in terms of efficiency based on the problem type, the numbers and the language in the problem.

What are your thoughts on this week's reading? Please respond in the comments below or head over to Facebook and leave your thought there!

Monday, December 15, 2014

Monday Math Literature: The Mitten Story Problems

Happy Monday! Yesterday, in my post about our book study on Children's Mathematics, I mentioned that I loved one of the review questions from Chapter 4 that suggested looking at a book or a unit of study you are working on and writing some story problems based on that book or unit. I thought this was a great idea and will be posting my problems and books for the next few weeks as part of my Monday Math Literature series. If you haven't read Children's Mathematics, they make some great arguments for exposing primary students to multiplication and division story problems as a way to build their understanding of place value. Today I wrote some problems to go along with a treasured favorite in the primary grades.

The Mitten

It is hard to believe this book is celebrating its 20th anniversary! It is a wonderful adaption of a Ukrainian folk tale. If you haven't read it, you should definitely check it out! If you use this book with your students already, here are some math story problems you could pose as a follow up. One of these problems is a multiplication problem, one is a partitive division problem and two of them are measurement division problems. If you don't know about these different types of problems and why they are important for primary students to be exposed to, check out the Children's Mathematics book study.

You can grab these problems for free from Google Drive

Remember that problem solving is a process. The range of solutions you will see will depend on where your students are on the problem solving progression. If you don't see a range of strategies, these problems might be to hard or to easy for your students.

Your turn! What math story problem would you write for your students based on The Mitten? Please respond in the comments below or head over to Facebook to share your idea!

Sunday, December 14, 2014

Children's Mathematics Book Study: Part 2

We are on to week 2 of our book study on Children's Mathematics. I am so enjoying this book and this week's chapters really made me think about how I teach kids and what kind of problems I expose them to. It also helped me see how far I have come in my teaching practice and how much of what I have done has been based on Cognitively Guided Instruciton.

Chapter 4: Multiplication and Division: Problem Types and Children's Solution Strategies

3 Possible Unknowns

I loved the way the chapter started with the big ideas around multiplication and the 2 different types of division problems. When I first learned about partitive versus measurement (sometimes called ) division, it completely changed my teaching practice. Upon examining the problems in my math program and supplemental materials I was using with students, I came to the conclusion that most of the division problems were partitive or sharing problems. When I first started asking different problem types, it was hard for my students who had not been exposed to these types of problems. Now I make sure kids have experience with the 9 different problem types for multiplication and division whether we are working at the fact level, with double multiple digits or even with fraction and decimals.

Primary Students Need to Solve Multiplication and Division Story Problems

Reading page 71 was a big wake up call for me. I have been so focused on making sure my primary students are moving along with their additive reasoning and being exposed to the 12 problem types for addition and subtraction that solving multiplication and division types story problems with primary students as kind of fallen by the wayside. Reading about how these problems support place value development and how "base-ten problems are essentially multiplication or division problems involving groups of 10" reminded me how important it is for primary students to solve more than addition and subtraction problems. A resource I used a great deal when getting started with problem solving with little kids was the Kindergarten Kindergarten blog and it is definitely a resource I need to revisit.

Further Reflection

I did take a peak at the questions for further reflection in the back of this chapter and LOVED number 2. "Choose a book that you are reading with your students or a topic that you are studying. Write one problem for each of the problem types that relate to the story or topic." I think this will be a great way to ensure my students get experience with these types of problems. I will be choosing a few books and doing this and will be sharing these with you as part of my Monday Math Literature posts. Check back on Monday to see the results!

Chapter 5: Beginning to Use Cognitively Guided Instruction

When I first started using Cognitively Guided Instruction it was hard. I felt like I wasn't teaching. If I didn't tell kids how to do it, how would they learn? It definitely took some time and a few disastrous lessons before I realized that by allowing my students to construct their own learning was giving them a deeper, more meaningful understanding of math. This chapter had some great ideas for getting started. Here is what I think the 5 most important things are to remember if you are just starting out.

1) It is your job to stop "teaching" and start listening. You REALLY need to listen to how your students are solving problems and not just assume you know what is going on.

2) Make sure you are using problems of different types.

3) Be strategic in who you choose to share their thinking with the entire class. Make sure you get a variety of ideas. This is not the time to use call sticks or other random generators.

4) Talk to your students about efficiency. When multiple kids share strategies talk about how efficent each one was.

5) The hardest part can be starting!

I am looking forward to hearing your thoughts on this week's reading!