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Thursday, January 30, 2014

Beans, Beans, More Beans and Place Value

I know letting kids discover math through hands-on,  meaningful, inquiry-based activities is the goal. But can I just say that for the past three days I have been wavering on whether I should reconsider that goal? I have had some serious second thoughts on how to introduce place value. I don't know why but this year was just a bit harder than most. Same project, but different students, lack of sunshine? Whatever the case, on day one I thought tomorrow will be easy. On day two, I thought....oh, no, what was I thinking? Day three...I debated whether they might be getting it....maybe, maybe not. Day four....envision a happy dance, bundles of ten everywhere and students with proud smiles on their faces.

So what are we doing here? Simple, but oh so meaningful for young mathematicians who are just being introduced to the concept of place value. Grab a few pounds of beans, portion cups, place value mats and you are ready to go.
See the clothespin at the top? It helps keep their record sheets from sliding down, also when we clean up, we roll them up and use the clothespin to hold them together. The numbers on each pin are student numbers, so we know which record sheets belongs to whom.

We never, ever dump the hundreds cups from day to day. But we do dump the tens.

Look below his desk. His record sheets are long now. He is at 249 here.  We use scotch tape to add on record sheets.
Students put one bean on, write down what they have, then repeat.  The key here is that they must look at what they have. We spend a lot of time repeating, "Put a bean on, write it down" and "What do you do when you get a ten? BUNDLE!" This activity is really about learning to see that 53 is  having 5 tens and 3 ones. On day 1 we go up to 12 or 15 together, then I let them take off on their own. I case the room, monitoring that their record sheets match the beans on their mats. If not, we start over. When day 2 rolls around, everyone has to read their record sheet, build back up to the number shown and after I check their building, they start back up. The goal is for everyone to get to at least 120. Today the largest number was 483 when my last student hit 120. Directions and record sheets are included in my free download from TpT. Click below to go to my store. 

The best part of today's math was when we started looking for patterns in the numbers. After discovering the pattern of 0-9 in the ones and just as we started to talk about the pattern shown in the tens, one of my young mathematicians yelled out, "There must be one hundred zeros, then one hundred ones, and one hundred twos in the hundreds." Even young mathematicians can begin to notice difficult number patterns. Now if we can only get all those beans cleaned up off the floor.


Thursday, January 23, 2014

Can a First Grade Student Help Change the World?

With Martin Luther King Day and Black History Month I think it's a great time to introduce my first grade class to the topic of civil rights. I love that they are growing up in homes and communities that teach them that everyone should be treated fairly. I often wish for a little more diversity in our community, but even still my little guys are appalled to hear how people were treated in the 1960s. I always start with the story of Ruby Bridges. I can't think of a better way to introduce this than a first grade girl who goes to school all by herself. This is an amazing true story that really makes my students think.




Here is another version written by Ruby herself. It's written as an "easy reader" version.

The Story of Ruby Bridges lends itself to plenty of discussion. How would it feel to go to school alone? Do you think Ruby's parents were afraid for her? Why was it a brave thing for Ruby to go to the new school? Would you do what Ruby did? Most of all I think this book shows that even a small child can stand up for what is right.

You might also like White Socks Only. This fictional account of a young girl who makes a difference in her southern community also lends itself to some great critical thinking and discussion. 

We used The Story of Ruby Bridges for interactive writing too.


Tuesday, January 21, 2014

Nonfiction Text Features Anchor Chart








Grab a pile of nonfiction books from the library and let your students dig right in to discover nonfiction text features. As you can see by our anchor chart, we are almost finished finding the features and trying to discover why an author would use each feature.  We still need to add some examples for the last few. This is a great activity for allowing students to discover the features on their own.


Monday, January 20, 2014

You Can Retell It!

This past week one of the district literacy coaches came into my room and gave a short lesson on retelling. She demonstrated how to retell a story, had a group practice with a familiar story (The Three Little Pigs) and then gave students a retelling bookmark, a partner and off they went to retell The Story of Ruby Bridges to each other. We had been reading and talking about Ruby Bridges all week so they knew the story well. But I was amazed at how well they told the story when using her bookmark to remind them of all the parts they needed to retell. Here comes my obsessive side, but I thought I could make a cuter bookmark and I did. This is a great way to help them with the second CCSS in reading literature.
https://drive.google.com/file/d/0ByE-sRWWGhWZbDdGRjI0UlhVNVU/edit?usp=sharing


Key to bookmark:
Book - What is the title of the book you read?
Compass - Where did the story take place?
Kids - Who are the characters in your story?
Problem
B - What happened in the beginning?
M - What happened in the middle?
E - What happened in the end? (The end should contain the solution.)
Author's Message- What is the author trying to tell us? What is the author's message?


Happy Retelling!

Wednesday, January 15, 2014

CGI Word Problems

I have to say that I am sold on Cognitively Guided Instruction. I love problem solving in the CGI way. Ready to try it yourself? Enter to win my Sliding on the Ice - Penguin Themed CGI Word Problems on Teacher's Notebook.  Enter by Monday, January 20 for a chance to win. 10 winners! Click here to enter.




I also have a free sampler of problems available on TpT.


 I think you will love these!


Friday, January 10, 2014

Help Your Neighbor - Addition to 12 Game

Help Your Neighbor
A good friend, fabulous overload technician and former parent of a student or two taught me this game. It's a great game for adding numbers up to 12 and can be played with 2-4 students. Perfect for first grade. I play it with face cards, but I have also included number cards for you to print and laminate. Click here to download the game.



Thursday, January 9, 2014

Problem Solving the C.G.I. Way

Have you tried problem solving in the Cognitively Guided Instruction (CGI) way? One of the books that made the largest impact on math instruction in my classroom is Children's Mathematics: Cognitively Guided Instruction.



The main idea behind this book is that children enter school with a great deal of intuitive knowledge about mathematics. CGI uses problem solving to help students continue to develop and refine their intuitive problem solving abilities. What do I love about CGI? I love...
  • watching students discover answers in their own way
  • hearing "Oooohhhh, now I get it."
  • to hear students explain their problem solving strategies to each other
  • to see a student try and solve a problem in a new way
  • the flexible groupings - sometimes I group my students who all use the same strategy comfortably together to try something with more difficult numbers, other times I group students who use different strategies together so everyone can learn from each other
  • how easy it is to differentiate - I choose the numbers for the actual problems according to  my students' needs
  • that I can sit back, watch, and listen to my students as they work, explain and teach each other
  • that while listening and watching I have time to take notes on their strategies, reasoning and problem solving abilities. Later I use my notes to regroup, choose numbers and decide problem types.
  • how much growth I have seen in their abilities in just a few months
  • the mathematical discussions that so naturally happen between my students
  • integrating our problem solving with other topics/subjects we are learning about
  • having all of the various problem types identified and knowing that I can track which problems I use to ensure that everyone gets experience with all types of problems
  • writing new problems in all of the various problem types (see my TpT and TN stores if you are interested in purchasing)
Another book that has had an impact in changing my teaching is Math Exchanges: Guiding Young Mathematicians in Small-Group Meetings. 
 This book has really helped me put CGI problem solving into action. With practical insights and examples of problem solving in action I felt like it really opened my eyes to how this could look and work. Plus the appendix with examples of the 14 problem types is so useful. If you want to make problem solving a larger part of your curriculum, check out these titles. You'll be glad you did.



Tuesday, January 7, 2014

How do we play that again?

Halfway through the year and the question of the hour during math centers is "How do we play that again?" Not that I mind answering the same question 100 times a day. After all I'm a first grade teacher. I'm used to it. But as we have added more and more games the question comes up more and more. Even though I take away the games that have become too easy, with 10-12 options I get that question a lot. I don't know why I didn't think of this sooner, but I took a picture of each game while it's being played and I now hang up the picture with the title of the game for students to see. Not only has it stopped the dreaded question, but students are looking up on the wall and choosing games they forgot about or hadn't played in a while. Such a simple yet wonderful solution.






Sunday, January 5, 2014

Helping All Students Discover Math Concepts

Thanks to Beyond Traditional Math for asking, "How do you help your students discover concepts on their own?"

Some students may learn from listening and watching but all students learn from doing. I think the key is to get students actively engaged in doing math. In my mind doing math means a lot of things. It can mean inquiry based lessons, math games, authentic math experiences, real world problem solving.

One thing I have implemented in full force this year is using math games to teach and practice basic facts. I'm sure you use games too, but I'm not talking about here and there or once in a while but every single day.

Dr. Constance Kamii gives the research behind using math games on a daily basis in her book Young Children Reinvent Arithmetic. She recommends 40 minutes per day.  When I started thinking about her research findings which showed that children will invent their own strategies, I ended up going back about 10 years to when my oldest was about 7 years old. We were trying to teach her some games that we thought she could play with us (Hearts, Yahtzee, Cribbage) and needed a fourth player. We recruited our 4 year old. By the time my youngest hit kindergarten and first grade she was not only a pro at playing these games but had become efficient and proficient at her basic addition and subtraction. She was definitely ahead of many of her peers. To give a little more evidence to further back the research by Dr. Kamii, I must confess that I have never purchased  workbooks, math activity books, flashcards, computer games, get your child ready for K products, etc. Good children's literature, math games, puzzles and trees and trees worth of paper. That was it. If research backs it and it worked with my daughter, then why not in the classroom?

To take this argument even a step further, the NCTM has an article by Dr. Kamii on their website. To summarize her article, it is either superfluous or premature to teach children to solve 3 + 4 by teaching them to count out 3 and then count out 4 and finally count them all up. The same goes for teaching children to count on. Either they are have constructed their logic to sufficiently understand this already or they simply are not ready for it yet.

So, what does this mean for the classroom teacher? We need to find ways to help students discover math concepts. Engaging, active, authentic, motivating, inquiry based learning.

What else does "doing math" mean to you?

References:
Kamii, Constance. Young Children Reinvent Arithmetic. 2nd ed. New York:Teachers College Press, 2000.

Friday, January 3, 2014

Let Them Discover It

"Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely."   Piaget


This year I decided to live or die by this Piaget quote. (Also known as Pea-ag- it to my favorite college niece.) I decided to bypass the direct instruction of addition and subtraction strategies in favor of letting the kids discover them for themselves.  The first thing I did was purchase a Rekenrek. 
We spent a good 5-10 minutes everyday on a number sense activity, either a counting circle, the Rekenrek or visual images. After about 8 weeks I decided to not just ask what they could see on the Rekenrek but to ask how they saw it. Sure enough someone used one of the traditional addition strategies that I normally would have taught. I try repeating the strategy in a little more concise language  and asked if anyone thought they could solve another problem in the same way. So I slid over a different set to add and everyone tried to solve it in the same way. We gave it a name and moved on to another student's idea. After about 3 days of 10-15 minutes of this, we had come up with this chart.
All strategies I could have taught, but instead they were discovered by the students. The best part is that my students are still talking in terms of strategies when they problem solve. And the next best thing is that when I gave my first grade level common assessment in a worksheet format everyone passed, even though it was the first worksheet experience of the year. I know I learned all about Piaget in my college and graduate days but somehow I hadn't discovered for myself all of the wisdom in his ideas. Each time one prematurely teaches a preservice teacher something they will have to learn for themselves the time and effort are wasted. Is that too cynical? Maybe.  If you haven't used the Rekenrek for mathematical discussions, you should give it a try. 

Electronic Rekenrek available from the Math Learning Center. It is a free app that my students love to use on the iPad.
Number Rack App