Guided Math In Action Book Study - Chapter 7

Chapter 7 of Guided Math in Action looks at the opportunities teachers have to build mathematical proficiency while having small groups. The chapter is broken down into five sections. These include:

• Conceptual understanding
• Procedural fluency
• Strategic competence
• Adaptive reasoning
• Mathematical disposition

Let's examine each one briefly.

Conceptual Understanding. Conceptual understanding is when students know what they are doing on a conceptual level. This is often what we teach in our small groups. Dr. Newton give the example of using coins to help teach dividing decimals. There is also a sample lesson that shows how one teacher used this strategy, giving students 28 pennies and asking them to put the pennies into 4 groups. This portion is where manipulatives and the teacher toolkit comes into play.

Procedural Fluency. Procedural fluency is knowing how to do mathematical procedures. It is when the students know how to do math. The example that is given in the text is adding numbers with 8 (a concept that I am totally going to "steal"). Students know the procedure of adding 2 to a number that ends in 8 to help make the number friendlier.

Strategic Competence. Strategic competence is when students are able to solve a problem and then explain their thinking as to how they were able to solve that problem. Students don't just jump straight for the answer, but they can show someone what they did to solve that particular problem. This can include using number lines, grids, or arrays. It is important for students to have a number of different ways to solve a problem.

Adaptive Reasoning. Adaptive reasoning is when students can think logically about math and then explain and justify why they chose that specific course of action. These mathematical discussions should allow the students to talk in an environment where they know their thoughts have value and they will not be made fun of because of the way they did a problem.

Mathematical Disposition. This area focuses on what students believe about math. How many students do you have that believe they are bad at math? As teachers, we need to promote perseverance, so that students will understand that some problems just take longer to solve. This involves scaffolding and helping student to stick with a problem or concept. Reflection is also a big part of this area.

I am only going to focus on answering the second question today. In my math classroom, we focus a lot on problem-solving. One of the key aspects is what we call the "Wrap Up." The Wrap Up is a concluding question (based on the day's lesson) in which students are asked to explain their thinking about a particular question. They are given the opportunity to solve the problem using words, numbers, or pictures. At the beginning of the year, the vast majority of the students will write one or two words. As the year progresses and the students become more adept at answering and solving math problems, their thinking becomes more elaborate and I begin to see longer explanations and pictures to illustrate their thinking. Of course, this type of thinking requires a good deal of scaffolding. Many third grade students try to take the easy way out when it comes to math, so building their perseverance is a huge part of teaching.

Be sure to join us on Sunday for Chapter 8.

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Two for Tuesday - Great Place Value Activities 50% Off Until Friday

It's Tuesday, so that means it must be time for another...

Two for Tuesday

To celebrate the fact that it's Tuesday (and school is about to start for most of us...sad but true), I've put two of my place value activities on sale for 50% off until Friday, August 1! Just click on any of the pictures below to go to my Teachers Pay Teachers store to take advantage of these great offers.

Place Value Scavenger Hunt

The first activity I have listed is the Place Value Scavenger Hunt. My students loved Scavenger Hunts! This particular activity had 28 questions that were related to place value concepts. The students were asked to round numbers, compare numbers, and write the numbers in different formats (standard, written, and expanded form). Each of the cards has a unique QR code associated with it.

The Place Value Scavenger Hunt makes a great center. I prepare the cards on cardstock and laminate them for durability. Then I cut out the cards and hang them randomly around the classroom. The students use the included recording sheet to write their answers down. After completing the activity, the students would use the classroom iPad to scan the QR codes using an app installed on the iPad. The QR code would provide the students with the correct answer, making the activity self-checking. Of course, the Scavenger Hunt can be used without an iPad as well.

This product normally sells for $3.50, but you can purchase it through Friday for just $1.75.

Check Writing - A Place Value Activity

The second activity is Check Writing - A Place Value Number Writing Activity. This activity is designed to student to the real world concept of check writing. The students are given the option of choosing from 24 different task cards and they are also given a blank check. The students are to fill out the check with the information on the card.

This was one of my students' favorite activities during our place value unit. They felt so grown up writing checks to me, their parents, and to the principal. One student even asked if she could take her checks to the principal. Too bad the checks weren't real.

Check Writing normally sells for $3.00, but, until Friday, it is on sale for $1.50. Please don't miss out and definitely share this with your friends and fellow teachers.

These are great activities to start the school year with, especially if your first unit is place value. You can also visit my Teachers Pay Teachers store for other great math activities. You can also follow my store to get updates when new products are available.

Guided Math in Action Book Study - Chapter 6

Chapter 6 is all about how to plan a Guided Math lesson. It was relatively short, but there was some really good stuff inside. I especially enjoyed the "peek in" of a Guided Math lesson.

Dr. Newton provides a framework for guided math that is broken into 3 sections. These sections include the mini-lesson, student practice, and share time.

• Mini-Lesson In the mini-lesson, it is our job as teachers to hook the students into that day's learning. We do this by making some kind of connection. I like to make the connection by telling a story. My students love to hear stories about my life or when I was a student in college and I always do my best to tie the story back to the lesson. After the hook, it is time to demonstrate the material.
• Student Practice After the teacher demonstration, it is time for the students to practice the skill being taught. This is the part of the lesson where the teacher and the student interact and discuss what they are doing as they work through the lesson. This would be a time for using whiteboards or playing games.
• Share Time The final part of the lesson is the share time, where students are asked questions about what they did during their practice time. Students can be interviewed one at a time or they can be asked to retell the main points of the lesson. The share time is then concluded by reinforcing the concepts one more time to clarify any confusion the students may have. The math centers are then explained and that group of students is released to go work.

The key take-away from this chapter is the need to plan out the lessons. Guided math is not something that can be done by the seat of your pants. It takes careful planning to be effective

Question 1: I have never been one to use a Guided Math lesson plan. Because of the way I build my small groups, I tend to do many of the same things each time I meet with a group. The key thing is that I already include all of the aspects of a guided math lesson when I meet with my small groups. We begin by reviewing the material. I show the students a couple of examples. The students are then given the opportunity to practice the lessons. Finally, we discuss what was done. I would like to become more conscientious about doing a more formal plan.

Question 2: When teaching from the concrete to the pictorial to the abstract, I always start with manipulatives. This can include base-10 blocks or coins or even cards. The students need something to hold in their hands. After they are used to moving the objects around, I show them how to draw pictures. A good example of this is showing the students how to draw arrays for multiplication. I also show the students how to use large squares, lines, and dots when using base-10 numbers. I have a blog post that I really need to write on how I teach my students to solve multiplication problems. I've been trying to write it for months.

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It's hard to believe that we are almost finished with this book. Be sure to leave a comment about how you plan your guided math lessons or ways that you move from concrete to pictorial. I would love to hear some new ideas.

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Teaching Multiplication With Arrays and a Freebie

I have a confession. I absolutely love teaching multiplication with arrays. I love to draw them and I love to see my students drawing them, especially when they are attempting to solve a fact that they have not memorized yet. One of the projects that I am excited to have my students work on this coming school year is a giant multiplication chart where each space on the chart is filled with an array. I'll post pictures if/when we get it finished.

I realize that arrays may not be the most time efficient way of solving multiplication facts, especially when you get to larger facts like 11x12 or 12x10, but I think they provide students enough support and scaffolding as they learn their "smaller" facts to provide the foundation for those "bigger" facts.

One of the games that I will often have my students play in math centers (regardless of the topic) is Matching. Some people call it Memory, but I think that term may be copyrighted, so I call it Matching. The way the game is played is to have all of the cards turned face down on the table or floor. Students take turns flipping over two cards at a time. If the two cards are a match, the student keeps the cards. If not, he has to turn them back over. The key to the game is to keep an eye on the cards that have been flipped so that when a player's turn comes up, he can flip over cards he already knows. The player that makes the most matches is the winner.

       

I created a small freebie of this game and I want you to have it. Obviously you can use it as a Matching Game, but there are many different uses for it. If you do use it as a Matching Game, I would recommend printing it on card stock, but you probably know that already. Just click on the image below and it will download the activity.

If you are looking for other multiplication activities, I have several available in my Teachers Pay Teachers store. To take a look, click on the images below and it will take you to the product for more information.

I hope that you enjoy the freebie and I would love to hear how it works for you. Please leave a comment below to let me know how it is working for you and your classroom. You can also follow my blog or follow me on Facebook for other updates.

Five For Friday - Five Things I am Thankful For

It's time once again for Five for Friday, hosted by Doodle Bugs Teaching.

This week, I think I am going to write about five things I am thankful for.

My beautiful family. If you recall from last week, my wife just had a baby. She is a beautiful little girl, a true answer to prayer. In addition to my daughter, my wife and I also have four boys and they are just as amazing as you can imagine. Yes, they can be a handful at times, but they are wonderful little boys and I couldn't ask for a better family. Right now, as I type this, I am sitting in the garage, watching them ride their bikes. I am beyond blessed. And, while I don't want you to leave my blog, here is a link to my wife's blog where she wrote about our daughter in a much more beautiful way.

My health insurance. If you turn on the news, you are probably aware that healthcare and health insurance are big news lately. I have no desire to make political statements here, but I do want to say that I am thankful for the health insurance that my family has. Right now, our daughter is dealing with jaundice. I know that's not a serious thing, but her levels have been slowly increasing each day. As a result, she has had to have daily blood tests at the hospital and has been wrapped in a blue light blanket almost every hour of the day (I'm not a doctor, so I don't know the name for all of these things). Anyway, without our health insurance, I can't imagine what the costs would be.

Our trip to Disney World. This is a strange one for me to be thankful for today, but hear me out. I love Disney. I love Disney World. My wife and I took our boys to Disney World in June 2013 and we had a blast. We rented a van and drove from West Virginia to Orlando. That was an adventure in itself. Right now, we are planning another trip in June 2015. Yes, I realize that it is a little less than a year away and that I have an entire school year to get through between now and then, but it is giving me something to look forward to. Having a goal (and a pretty heft one at that. Have you seen how much it costs to go to Disney recently?) is helping to push me into working harder and to be a little more frugal with our funds. My wife and I have a goal of paying off our credit card before the trip and my desire to get to Disney is causing me to work on that even more. If you are interested, I recently wrote a post on ways that I am saving for my Disney trip. It might help you start saving for a trip of your own.

Running. I have mentioned running in each of the three Five for Fridays that I have participated in so far. Today, I am thankful for running because I am able to do it without it hurting. Earlier this year, I developed a really, really nasty case of tendinitis in my lower left leg. It hurt to walk or even stand up sometimes. Do you know how difficult it is to be a third grade teacher and not be able to walk? I kept trying to run and had to wear fancy compression sleeves on my leg in order to help alleviate some of the pain. Fortunately, most of the pain is gone. I ran almost 4 miles today and don't feel any discomfort. It's a great feeling. Now, if I could just get a little faster and go a little farther.

My Teachers Pay Teachers store. I am incredibly thankful for my Teachers Pay Teachers store. Having this store has done two things for me. First, I think it has made me a better teacher. By creating materials for the store, I have really "upped my game" because I want to make certain that the materials I am posting of top quality. Everything that I make for my store is something that I use with my own students and I want them to have the very best. Second, the money that I have made has helped as we have been paying off our credit card and saving for different things as a family. I am incredibly humbled that there are teachers who spend their hard-earned money on products that I have made and trust me to make products for them to use in their classrooms. It has been and continues to be a wonderful experience.

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So, another week is in the books. Hard to believe that a few more of these and we will be back in school. I hope you enjoyed reading about the things I am thankful for. I would love for you to share something you are thankful for as well. It reminds me of that song we used to sing in church. "Count your blessings, name them one by one..."

Guided Math in Action Book Study - Chapter 5

Our book study continues with Chapter 5: "Balanced Assessment - The Key to Grouping Students." This chapter was all about using different assessment to help group students for small group instruction. Dr. Newton discusses ways for pre-assessment, ongoing (or formative) assessment, and evaluative (or summative) assessment. This chapter was chock full of practical ideas, but there were some things that I was left wondering about. More on that in just a bit.

Now, on to the questions.

Question 1 - The way our math framework is set up at my school, we do a "pre-assessment" every day. In third grade, we call it the problem of the day. This consists of 3 questions. The first question is a question from the previous day's lesson. It helps us to determine who is still understanding the material from the day before. The second question covers the new material we are learning that day. The final question is of a cyclical nature and can be from any topic we have covered up to the point, usually place value, multiplication, or fractions. These questions help us to determine who will be working with us in which groups that day. This is a bit different from the way Dr. Newton describes her pre-assessment. I love many of the ideas that she shared, but the sad reality (at least in my context) is that I often cannot fit all of those pieces in.

For on-going assessments, I use many of the centers activities that the students complete, as well as the first section of the problem of the day. I also give several written quizzes throughout the unit. These activities are designed to help me understand how the students are progressing. Our county recently began adopting a collection of questions (for lack of a better term) that are collected online. This allows us to create quizzes and tests that can be taken online. However, adoption of this practice has been slow. I guess old habits (written tests) die hard.

The summative assessments tend to be your typical paper and pencil tests.

Throughout the year, usually three times, our entire school gives a test that helps us to determine where a student is according to a benchmark score. It is the same test each time and the students are expected to make growth on the test throughout the year. This test is not without weakness, but it does allow me to determine what students may be falling behind in particular areas. The two main weaknesses are that the test includes questions that are not covered by our learning standards and the test is timed. Some students just don't test well when under time pressure.

Question 2 - There were a number of great ideas in this chapter. First, I am going to have to find some time to make versions of the interview forms Dr. Newton has in the book. I am reading my copy of the book on my iPad, so the formatting is a bit different.

Second, I need to find out what Math Running Records are. If you know, can you please leave a comment and direct me to the right place.

Finally, I am interested in putting together student portfolios. I will be working with special education students next year and this data will be necessary for IEP meetings. As I mentioned before, Evernote will be perfect for working on this. There is a feature on the app that allows Post-It notes to be photographed and cataloged. Perfect for anecdotal records and portfolios.

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This brings us to the end of another chapter. If you haven't heard, there is a Q&A with Dr. Newton happening at Guided Math Adventures. Head over there for all the details. Thanks for participating.

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Two for Tuesday - Save 50% Through Friday

Today, I'm going to do something different. I'm going to offer two of my best-selling products from my Teachers Pay Teachers store at 50% of the regular price. I don't usually sell my products here on my blog (at least not this blatantly), so that's why it is different. So, I am linking up with the wonderful ladies of The Teaching Tribune for Two for Tuesday.

Subtraction Across Zeroes Task Cards

The first product is a set of task cards to help students practice subtracting across zeroes. A number of my students had difficulty with this particular topic, so I wanted to make something for them so that they could have extra practice during centers. It turned out that this product struck a nerve with others and it has sold more than any other product in my store. I recently updated the product and added several other items to it. Subtraction Across Zeroes sells for $4.00, but through Friday, July 25, it is on sale for 50%.

Identifying Fractions on a Number Line

The other product that is on sale is Identifying Fractions on a Number Line. To be honest, I was pleasantly surprised that this activity has been so popular. This is a set of 32 task cards that ask students to identify a fraction based on where the X is on the number line. It can be challenging because students have to determine how many sections the line has been divided into (the denominator) and find the position of the X (the numerator). This set of cards (like all of my task cards) are perfect for play Scoot, scavenger hunts, math centers, or for use in small groups. Identifying Fractions on a Number Line is normally $3.00, but is marked down to $1.50 until Friday.

I know that most of us still have a couple of weeks before school starts, but it is never too early to start planning ahead, especially when you can get an awesome deal like this. Hurry, these special prices are only available until Friday, July 25. And, while you are looking for great deals, be sure to head over to The Teaching Tribune to see other great offers.