Math Tip Monday: Ways to Keep Math Meaningful... and a FREEBIE!

K's Classroom Kreations and I would like to thank you for joining us for another edition of Math Tip Monday!

Wow! I can't believe it's already December!

Wait, I take that back. The way my kids have been acting, I definitely know it's December!

Are your kids as crazy as mine are?

Keeping kids on track during the holidays can be difficult. So much excitement. So many interruptions. Rehearsals, programs, holiday parties....it can get pretty crazy.

Unfortunately, I can't just stop teaching and do stuff that's just for fun. I have to keep teaching the curriculum. Our school pacing guide doesn't allow time for much holiday fun. Math still must be taught. Rigor must be maintained. Assessment must continue to guide instruction.

My math time is in the afternoon, so I already have a hard time keeping the kids focused during math instruction. When holiday time rolls around, I have to pull out every trick in the book to keep them engaged.

One of the ways I encourage engagement is to design activities that, while they continue to teach concepts, also incorporate holiday themes.  This week, we will be playing 120 Race in one of our math centers. I've designed a couple of winter-themed 120 charts for my students to use to play the game.

The game is easy to play.  Students use two dice, two different colored counters or game pieces, and the 120 charts to play. Each player takes turns rolling the dice and moving their game piece the appropriate number of spots. After each move, the players must tell each other how much farther they have to go before they get to 120.  Once a player gets close to 100, s/he may switch to using just one die. Players must land on 120 in order to win.



In our latest math unit, we've been reviewing skip counting and learning strategies for repeated addition. We are also building on the place value concepts students learned in first grade and earlier this year. I've found that many of the students in my class really need some extra practice with these skills. For morning work this week, we will be using 120 charts to practice locating and writing numbers that are missing from a 120 chart.

You can get a FREE set of these Winter Theme One Hundred Twenty Charts in my store.

For our math talks, we're continuing our focus on problem solving. However, this time of year, I try to make the problems engaging by connecting them to students and their experiences. Here's an example:

I've found that kids love seeing their own names in the story problems. They also like solving problems that are relevant to their own lives. Little things really matter when it comes to getting and keeping the attention of a group of second graders!

I hope you find these ideas helpful with your busy class.

How do you keep your kids engaged in math activities this time of year? Please share in the comments.

Don't forget to check out the other great ideas from my fellow bloggers below.

An InLinkz Link-up

Math Tip Monday: Operations & Algebraic Thinking

Welcome back to Math Tip Monday, a monthly blog hop filled with wonderful ideas and resources for teaching Mathematics.  This month we're focusing on Operations & Algebraic Thinking.

I remember seeing the Common Core State Standards for the first time a few years ago. When I saw that standard, I shook my head in disbelief. "Algebraic thinking," I thought incredulously, "but these are first and second graders!?" I don't think I realized then how much my instruction formed the foundation for what my students would be expected to do years in the future. I tend to overlook the label now and focus on making sure my students understand these important math concepts.  For the purposes of this post, I am providing tips for the three second grade standards included in this thread.

Represent and solve problems involving addition and subtraction.

CCSS.MATH.CONTENT.2.OA.A.1

Story problems can be so challenging for students at all grade levels. To me, the most important way I can help my students to solve them is to help them to understand the problem. I don't believe in teaching key words, because sometimes those words can be misleading in a story problem. Instead, I help students use reading comprehension strategies to understand the problem before attempting to solve it.

During our math talk time, I introduce a story problem. We read and reread the problem. I ask students to restate the problem in their own words. We visualize the problem or we act out the problem, both physically and by using math tools (counters, cubes, etc.).  Only then do I ask students to tell me what operation would help to solve the problem. I always ask them to explain why or how they know that's the correct operation.

It seems like a lot of work to solve one problem, but I think these strategies are crucial to helping my students become successful mathematicians.  So many times, I've seen excellent math students bomb a test because they added the numbers in subtraction problems or vice versa. Emphasizing comprehension of story problems helps prevent this type of error. Here's a poster I made to remind my students of the steps to solving story problems.

Add and subtract within 20.

CCSS.MATH.CONTENT.2.OA.B.2

Teacher confession: I hate the traditional use of flash cards and timed fact tests. I think they are tedious and, for students who have difficulty with memorizing (like myself, in third and fourth grade), they make math seem more difficult than it is.  The key to this standard is teaching students effective and efficient mental math strategies and then providing them with ample opportunities to practice using those strategies. Here are three ways I help students with fact fluency.

1) Make Mental Math Visible

As part of our math talks or my math mini-lesson, I often help students to "show their thinking." I'll ask them to explain how they got the answer to a problem. I'll then draw an empty number line, break down the equation, or jot a quick picture to show that thinking.

Here are some ways we might show 8 + 7.

In this example, the student used a known doubles fact to help solve the problem. I would rewrite the problem as above to help students to visualize the strategy.

I often use empty number lines to show student thinking. This is one way I might show how a student used the Making 10 strategy to solve the problem quickly and accurately.

2) Help students to see and use number patterns. 

When we teach fact fluency, we start with the Plus 1 facts. Then we move on to the Plus 2 facts. Next, we focus on doubles. Then, we introduce near doubles.  One of the ways I help students to see the patterns for each of these facts is by giving them time to explore the answers on their own. We use math tools, such as cubes, counters, number lines, and the one hundred twenty chart. I allow my students time to find the answers to the equations on their own. Next, I make an organized list of the facts.

I ask students to look for patterns in the list. What do they notice? How does that help them to solve this type of problem? I love it when the kids get excited at discovering the patterns on their own!

3) Use math games to practice!

I shared this idea last month. Check out my post for some great games to use for practicing fact fluency.

Work with equal groups of objects to gain foundations for multiplication.

CCSS.MATH.CONTENT.2.OA.C.3

Patterns, patterns, patterns! Whether you're working on even versus odd numbers, repeated addition, partitioning, or rectangular arrays, helping students see and understand number patterns is crucial to building algebraic thinking.

Just as I use an organized list to help students to find number patterns and increase fact fluency, I often have students look for patterns as they work on this standard. We list even numbers and odd numbers, comparing them and looking for clues to identify each. We use objects and draw pictures to demonstrate why a number is even or why it is odd. Students have to justify their thinking to demonstrate understanding. Here's one way to help your students see patterns during a math talk.

Write on chart paper or create a slide with a question similar to this one.

 

Some of my students can tell you the answer to the first question in two seconds. Because of this, I always put more emphasis on the second question than the first. We draw pictures and write equations (often students will use doubles facts to explain) to "prove" that the number is odd. By focusing on the "why" or the "how do you know" part of the question, you are encouraging your students to share their strategies with their peers. You are building conceptual understanding, rather than a surface recall of whether a number is odd or even.

During math talks for our multiplication unit, I also encourage students to discover patterns. We build arrays using cubes or counters. We draw them on grid paper. We record repeated addition equations. We look for patterns and draw connections to what we already know. I love to give my students 24 color tiles and ask them to make rectangles. 

We draw our solutions on grid paper. Then we record the repeated addition sentences.

I help students to see that this array represents 4 + 4 + 4 + 4 + 4 + 4 =  24. Often students notice that it can also represent 6 + 6 + 6 + 6 = 24. In this way, my students are already internalizing the commutative property of multiplication. They are building connections that will help them when they begin multiplication in earnest in third grade.

So these are just some of the ideas that I use in my classroom to help students build a foundation in Operations and Algebraic Thinking. I hope you find these tips helpful. You may also want to check out the variety of math products I have available in my TPT store. 

In the meantime, I hope you'll hop to the next blog to find more tips about this important math topic.

An InLinkz Link-up

Until next time, 

A Hard Job, A Little Patience

Some days it is really hard to be a teacher.

You work as hard as you know how. You fill out paperwork. You collect and record endless amounts of data required by your school, your district, and your state.  You tie shoes, clean up messes, mediate conflicts, search out support for students, reinforce good behavior and correct misbehavior, complete more paperwork, supervise recess and lunch, answer parent emails and, in between, you try to teach.

Because teaching is what you love, what you were born to do.

But it's hard.

Some days it can be overwhelming. The mandates, the paperwork, the behavior concerns. You find your fuse getting shorter. Little things start getting on your nerves more than they used to. You fight back tears, and you keep on teaching.

And some days, you lose it.

You yell.

You cry.

You respond in a snarky, impatient way.

You say words you can't take back.

And you feel absolutely horrible.

Because you know it's not your students' fault.

You know that some of them come from situations that are insecure and even unsafe. They've seen violence and they've known fear. They've known hunger and want. It's not their fault your job is stressful.

Some of them come from secure homes, but are overindulged, spoiled, and entitled. Their parents blame you or other students for infractions or bad reports. It's not their fault that you can't make them take responsibility for their actions. It's not their fault the parent has the principal on speed dial.

Some of them seem unreachable. You try to motivate them, engage them, and help them to progress. Nothing seems to be working. It's not their fault you haven't found the answer yet. Yet.

You need to find patience and hold onto it for all you're worth. You need to try again. And again. And keep coming back, even though it's hard.

Your work matters. Even when progress is slow, you're making a difference.

So you pray for patience. You count to ten. You take deep breaths. You walk away.

Because everything you say matters. Everything you say can be the one thing that gets through. So it needs to be the right thing. The thing that helps. Not the thing that hurts.

Patience.

A little patience.

Even when it's one of those days, you need to find it.

Especially when it's one of those days, you need to find it and hold onto it for all you're worth.

Even when it's hard.

I wrote this poem for myself. Because some days are just really hard and I need the reminder sometimes. I thought other teachers might like it, too. If you'd like a copy of this poem, please download it for free from my TPT store.

And  because we don't hear it enough...

Thank you for the work you do every day. Thanks for coming back for more even when others don't. Thanks for making a difference in the lives of the children you teach. Even on those days when it seems impossibly hard. Thanks for finding that patience.

Math Tip Monday: Addition & Subtraction Basics

Welcome back to Math Tip Monday. Once again, I am teaming up with K's Classroom Kreations to bring you a blog hop full of great ideas for teaching math. This month's topic: Addition and Subtraction Basics. After giving it some thought, I decided to share with you three ideas that I've found extremely helpful in my classroom.

Math Talks

Several years ago, I discovered a resource that began to transform my mathematics teaching. The book, Teaching Student Centered Mathematics Grades K-3 by John A. Van de Walle and LouAnn Lovin, helped me to see that the old model of teacher directed instruction (direct instruction, guided practice, and independent practice) did not help students to construct their own understanding of concepts. As a constructivist in my literacy instruction, I found the practices suggested in this book more closely matched my philosophy of teaching than traditional mathematics instruction.

Van de Walle suggests creating a "mathematical community of learners." I've shared how I do that in a previous post. He suggests that "classroom discussion based on students' own ideas and solutions to problems" is a critical component of the mathematics classroom. Well, math talks provide a forum for students to share ideas about their thinking and learning with their peers.

Van de Walle also advises that instruction that is based on problem-solving engages students and helps them to make sense of ideas. Math talks allow students to discuss ideas about concepts, strategies, and barriers to problem solving. They are a great way to teach students how to choose effective strategies for addition and subtraction. They are also great for helping students to use mistakes as tools for learning. Finding the right answer is never the goal of a math talk. Instead, the class focuses on understanding real-life problems and finding effective and reliable strategies for solving them.

So how does a math talk work in my classroom?
First we have to establish the expectations for the math talk. After we've started to come together as a classroom community, I gather the students together on the carpet and tell them about math talks. Since we are all mathematicians, we can all help each other learn math. I tell them that when we have a math talk, we will work together to understand a problem and share ideas for how to solve it. I ask them what we should do to help each other learn. Together, we create an anchor chart like this one.

Our first few math talks usually focus more on practicing the expectations than solving the problems themselves. Once we've got an established procedure, a math talk might go like this.

I bring students to the carpet with their math journals and a pencil. I share a slide that has one problem posted on it.

We read the problem together once. Then I ask students to visualize as we read the problem a second time, one sentence at a time. I then ask a student to restate the problem, (i.e. Johnny, what's going on in this problem?). I ask guiding questions such as,

•  So what do we need to do?
•  How do you know? 
• Are you sure it's addition/subtraction? Why? 
• What would be a good strategy to use to solve this problem?
• What is another strategy we could use?

Once we've discussed the problem, students work to solve the problem in their math journals. After a couple of minutes, I choose two or three students to share their strategies. Here are some my students used:

I keep sharing limited to two or three students. Otherwise, the math talk can drag on too long. 

After sharing our strategies, I then briefly review our learning about the problem and end the talk. From beginning to end, the math talk should take about 10 minutes.

Here are some common problems that have come up during our math talks and how I've solved them.

• Problem: Students begin to solve the problem before you've discussed it as a class.
• Solution: Have students place closed journals and pencils behind them on the carpet. I've even had students sit on their journals until we are ready to solve.
• Problem: Students blurt out the answer before you've analyzed the problem.
• Solution: Either acknowledge it or ignore it. Students gradually come to realize that the answer is not the most important part of a math talk. If you choose to acknowledge it and the student has the correct answer, you can simply say, "Yes, the answer is 23, but as mathematicians, we need to understand how we get the answer." Then redirect to the question at hand, "So how did you know that you needed to add?"
• Problem: The same students participate all the time and others seem disengaged.
• Solution: Use cold calling or a bucket of names to randomize student participation. If students know they might be called on at any time, they are more likely to be prepared. Refer to the anchor chart to remind students that all mathematicians participate in the math talk.
• Problem: The math talk drags on too long.
• Solution: Decide what to focus on before the math talk. Spend more time on that. For example, if you want students to understand different strategies for subtraction, spend less time analyzing the problem and more time discussing the strategies. You may need to draw or record the strategies if time is running short. Just ask students to tell you what to write. Keep the pace moving. Set a timer if necessary. Your students will tune out after ten minutes, so you really don't want this part of your lesson to take too long.

Strategy Board

A strategy board is a great resource that has really helped my students. As we learn new strategies for addition or subtraction, we add it to our board. The board stays up in our room. When students are stuck, I often refer to the board. Choosing a strategy helps them to get started. Here's one that I've made. Yours can be as fancy or as basic as you like. Use whatever works for you.

Fact Fluency Practice using Math Games

In my school, second graders are expected to be fluent with addition and subtraction facts to twenty. While to some this might mean memorization, to me that means students have become so efficient with their mental math strategies that they are quickly and easily able to solve these problems with accuracy.

One of the ways that students gain this proficiency is they have multiple opportunities to practice these facts. While flashcards can be useful, especially when you make a game out of it, I've found that games provide students with multiple opportunities to practice facts in a fun and meaningful way. Luckily, the math program we use, Investigations, emphasizes the use of math games to practice fluency. While I can't share their copyrighted games with you, here are a few others that I've used.

Fast Facts:
In this game, students use a timer and a pair of number dice to practice facts with a partner. The partner turns over or starts the timer, says when to start and stop, and checks the answers. The player begins rolling the dice and adding the digits, writing only the answers in his/her math journal. Once time is up, both partners count how many problems were successfully solved. Then, partners switch roles. This is a great activity for early finishers.

Flash Card War:
This game is based on the classic card game, War.  The students divide the flash cards evenly among each player. Each player turns over the flash card on the top of their pile and places it in the center of the group, Players add their own cards. The player with the greatest sum collects all cards played. If players have sums of equal amounts, there is a "war." Saying, "I declare WAR!" each student places three more cards, then adds the last one placed. The player with the greatest sum collects all cards played in the round.  Play continues until time is up or players run out of cards. The player with the most cards at the end of the game wins. Note: You can also play this game for subtraction. Just have students who have the smallest difference win the round.

Domino Addition:
Use dominoes to play a variety of addition games. They can be a simple as having students try to match dominoes that have the same sum. You can also have them create an addition "train," each time they add a domino they add the pips on the touching sides of the dominoes.

Invent a Game:
This is a great way to challenge your high-achieving math students or to involve all students in being creative mathematicians. Ask them to work together to invent a game that helps them to practice their facts. They need to use materials that are in the classroom such as dice, cards, counters, or dominoes. They need to play the game with a partner to make sure it works. Finally, they need to write the rules and directions so someone else can play. You'll be amazed at what your students come up with!



There you have it. My ideas for teaching basic addition and subtraction in your classroom. I hope some of these will be useful to you. Don't forget to check out the other great ideas from my fellow bloggers below.

An InLinkz Link-up

Five for Fraturday

I've been away from my blog for a couple of weeks, so I thought I'd jump back in with a Five for Fraturday post. :)

I had planned to write this last night, but I'm a bit tired exhausted comatose by Friday nights. I'm sure you understand.

We had our Curriculum Night on Thursday. Ugh! I teamed up with two colleagues to present the information to parents. I'm usually the one who does most of the speaking. I've been teaching so long now that talking to parents doesn't bother me as much as it used to. Both of my colleagues are relative newbies, so it makes them more nervous to do the presentations. 

Actually, it wasn't bad. I only had five parents show from my classroom (two of them were there for one student). We don't have a huge turnout at our school. Sad.

Of course, I really stress about Parent Nights beforehand. Does my room look clean? Is it welcoming? Do I have all my handouts? Do I have enough student work up?

I was running out of wall space and time, so I decided to use an old standby for highlighting student work - Class Books! They don't have to be super-fancy and are as easy-as-pie to put together. I had two students create the cover illustrations. Then I took a large piece of construction paper, folded it in half and hole-punched it. I used a Sharpie to write the title and to credit the authors and the cover illustrators.  I hole punched the student pages and placed them inside. Three brads later and I was done. I think they look pretty good. My students and their parents enjoyed looking through them.

This one is our Constitution Day response to my poem, Our Constitution. It's part of my Constitution Day: A Celebration for Primary Grades.  It can also be found in my Patriotic Poems and Activities for Primary Grades.

The other book is student responses to my I Can Be a Scientist poem. It's part of my Science Poems and Activities for Primary Grades.

I have a confession to make. I am a piler. Yup. If I have a surface, I can put a pile of papers on it. The piles get higher as the week goes on and then I make a new pile. I would say I know where everything is, but that's not exactly true. I've searched many a pile of papers for that one important form that's due in the morning. It doesn't help that I moved rooms this year and ran out of time to set up my filing cabinet. Life is hard when you're a disorganized teacher. On the other hand, when you've got parents arriving in less than 30 minutes, that means you've got an empty file drawer in which to stuff and stash your piles. :)

So I followed up my 13-hour day on Thursday with a rainy Friday. You know what that means - the dreaded indoor recess.  Thank goodness for GoNoodle! We started out with one of the shorter Indoor Recess Mega Mixes. 

After the kids worked off some of their excess energy, I got out some of my indoor recess games for them to play with. Aside from some minor squabbles, a good time was had by all. 

These are student created pieces that the students created in art class.
A few of my kids enjoyed making new sculptures with them.

After a rather tiring week, it was nice to spend my Saturday doing little more than going to the grocery store and then coming home to watch my Gators play beat Tennessee! It was a close one, but we pulled it out in the end. Go GATORS!

I updated my Facebook profile picture to show my support.

Well, that's it for today. I hope you all have a great week!

Five for...Sunday?

It has been such a busy week! I'm joining the linky party a little bit late. Can I have a Five for Friday on a Sunday? Or would that make it a Five for Funday?  In any case, here are my five for this week.

We celebrated my mom's 72nd Birthday last weekend. Or, as the baker wrote on our custom order cake, the 72th. Oops!

My sister and I arranged a mini-family reunion as a birthday surprise. Two of my nieces came up from Florida with three of the great-grandchildren. My brother and niece came over from Tennessee. Mom was surprised and very happy. We spent the weekend hiking, looking through pictures, talking and reminiscing, going to Carowinds, and eating...a LOT!  No wonder I was tired this week.

After three weeks at school and I finally feel like I'm getting finished with the beginning of school stuff. On Monday, we finally finished decorating and filling our book boxes. This is the first time I'm using the cardboard magazine holders from IKEA. I like that the kids are able to decorate the boxes and make them their own. I even put their pictures on the front to make identifying ownership easier. However, I confess that I am a little worried about them lasting the whole year. We'll see. Here are a few of them before I put on the student pictures.

I'm loving my Owl theme this year. I was able to update a lot of areas in my classroom thanks to K's Classroom Kreations. I used her Classroom Decor & Organization: Owl Theme to update my schedule, "I Can" display, word wall, and clock display. Doesn't it look cute?

I've found yet another resource on TPT that makes my life easier. This one is a freebie from Reagan Tunstall.  I printed these Voice Level Charts on blue cardstock and then laminated them. For every activity, I move my magnet to the appropriate chart. If students don't use appropriate volume, I move the magnet to a lower level. If they can't reduce their volume, they lose the privilege to talk and the magnet gets moved to zero. Works like a charm!

We have a large population of English Language Learners at my school. Most of them speak Spanish in their homes. I've found it's helpful to include Spanish translations in much of my classroom decor. Here's a picture of my Color Words in English and Spanish.  After I took this picture, I found out that some of the students use naranja for orange, while others use anaranjado. The kids voted to include both in our display.

Check out my other Bilingual Resources in my TpT store!

That's it for this week. Make sure you check out all of the other great bloggers on the Linky. Thanks always to Doodle Bugs Teaching for hosting!

Until next time,