Do They Really “Get It?” {3 Ways to Check During Math Class}

April 17, 2016

Has this ever happened to you?

You teach a lesson, let’s say, about adding fractions. As you’re walking around the classroom, lots of kids have correct answers – even a few that you wouldn’t expect. You’re patting yourself on the back and decide to give them a problem that’s just a little bit harder. (At this point, I always think to myself, “They’ve GOT this! We are FLYING through this lesson!”)

After a few minutes, you realize: they don’t really know what they’re doing yet, and you wonder what happened just a few moments ago.

Over the years, this has happened to me so many times that I wondered if there was even a way to really know if they “get” a concept before they crash and burn and I want to cry.

Check out this post for ideas to see if kids are really understanding mathematical concepts.

Here are some ideas I’ve tried to see if kids are really “getting it” in math class:

1. Can they draw a picture or make a model?

Even in fifth grade, the power of visualizing a math problem is, well…powerful! With younger students, I encourage the students to draw exactly what they see when a problem is presented. With older students, I teach them how to use models to represent the parts of the problem they are working on. (Sometimes, they still draw the actual picture, and I think that’s ok too. I just try to get them working towards something that won’t take quite as much time!)

Check out this post for ideas to see if kids are really understanding mathematical concepts.

Check out this post for ideas to see if kids are really understanding mathematical concepts.

If they are having trouble drawing a picture or creating a model or representation, that tells me a lot about how they are processing the problem.

You can see this adding fractions product by clicking here.

2. Can they write a word problem?

This is ALWAYS eye opening for me. I can usually tell right away how students are understanding a problem or equation by how they write their word problems. (I can also tell if they can actually visualize the problem from their number story!)

First, we have to define how to write one – this is key!

Check out this post for ideas to see if kids are really understanding mathematical concepts.

Once the students know what a word problem looks like and sounds like, I can start to see understanding through their stories. This mainly helps me assess whether they know how to properly apply their knowledge of different operations. It’s fairly evident that they aren’t sure what subtraction really means if the story problem written will result in an addition situation!

This student was writing a word problem for 1/2 + 1/3.

Check out this post for ideas to see if kids are really understanding mathematical concepts.

When I read his problem, I could see he understood that he was combining the two fractions since he used the word “altogether.” He also uses an object that can easily be split up into fractions, telling me that he has some understanding of what fractions actually are! (Not to mention he uses cupcakes – which makes his teacher very happy!)

Writing word problems is one of my favorite ways to see if students truly have an understanding of the type of problem they are trying to solve.

3. Can they clearly explain it to someone else?

We’ve all been there, right? You are obviously explaining something in the clearest way possible and the person you are talking to is looking at you with an expression of utter confusion. And this happens to students all. the. time. They think they are being clear, but the person listening has no idea what they are talking about. (This includes me sometimes!) In the upper grades, I think getting feedback and reflecting on their work is essential to learning how to be clear and concise with their mathematical explanations. Besides being clear with their speaking, they also have to learn how to be clear and concise in their written explanations.

One way we accomplish this is by using museum walks to provide feedback to each other and reflect on our own work.

Check out this post for ideas to see if kids are really understanding mathematical concepts.

Each team completes their own work on a poster, then we hang them up and use sticky notes to provide comments and questions about the work on the posters. Each team gets their own poster back and uses the comments and questions to revise their thinking or make their explanation more clear. This has worked wonders for my students! Through this process they often find small mistakes (and big ones) and it helps them to see what others see when they look at their work.

It gives me insight into two things:
1. Can students look at others’ work critically in order to provide useful feedback?
2. Can students use constructive feedback to revise their work?

I know this has been a hit in my classroom, because now they demand request time to get feedback on everything from their math work to their science notebooks! And I can see that they are becoming more clear in explaining and showing how they got their answers.

Check out this post for ideas to see if kids are really understanding mathematical concepts.

Sometimes, it can be really tough to know if kids are really “getting it.” I have used these ideas to help me gather information about my students for several years and I have learned more about them and their mathematical ideas as a result! It really helps me to inform my teaching – or possibly reteaching depending on what I find out. How do you assess your students to find out if they are “getting it” during math? I would love to hear from you in the comments.
Check out this post for ideas to see if kids are really understanding mathematical concepts.
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The 10 Minute Tidy

February 7, 2016

If you’ve ever looked at your desk or table at the end of a long day of teaching and wanted to hide, this is a great tip you can use every day! I learned this SUPER classroom hack from a great friend and colleague a LONG time ago, but it has always stuck with me!

Many moons ago, I was looking with jealousy interest at my colleague’s clean and clear guided reading table. (In my room, it was the table with the most junk piled on it by the end of the day.) She told me that every afternoon, before she went home, she did a “10 minute tidy.” She set her timer for 10 minutes and cleared that table, and anything else that needed tidying, before she went home. Ever since that day, I have been a firm believer in the 10 minute tidy! I do it before I go home – I pick up papers, put away extra supplies (where they belong, not just in another pile), put books back where they belong and make it so my table is clear when I come in the next morning. It’s actually a huge relief to come in to a clean space.

There’s an oatmeal cup on there!!!!
Ahhhhh…..ready for tomorrow.

This tip has helped me breathe a sigh of relief before going home AND when I walk in the door the next day. What is your favorite tip for avoiding that overwhelmed and disorganized feeling?

A Good Reminder

December 2, 2015
A blog post to remind me what my main job as a teacher is.

My students keep their backpacks on the backs of their chairs.

Some are neat with everything in their place. Planners are tucked in a pocket, snacks are zipped neatly into a pouch, and gloves and hats are snuggled into the nooks and crannies.

And then there are other backpacks. The ones that are overflowing, stuffed full and jumbled. Drawings and lunch boxes spill over the sides, and occasionally a pink stuffed animal peeks its head out.

There’s one more category: the ones where I can tell that a child’s life is in disarray. Papers are crumpled, extra clothes are stuffed inside, and it’s pretty clear that no one has looked in their backpack since August.

When I walk around the classroom and I happen to catch a glance inside the different backpacks hanging on chairs, it reminds me.

It reminds me that it’s my responsibility to provide the safety and structure that ALL students need – I know for some students it may be the safest and most structured part of their life.

It reminds me that I have to be patient and kind – I have to keep the whole child in mind, not just the student part I see at school every day.

It reminds me that, first and foremost, the people I share my day with are children – they aren’t just mini-adults. They are still learning (in school AND in life) and I owe it to them to support them when they make mistakes, not turn it against them.

It reminds me to take a step back and *think* about the individuals who lives are represented in those backpacks – they need me to appreciate who they are and what they need.

Every now and again the universe sends me a reminder like this, just when I need it. It stops me in my tracks and makes me rethink. I smile at my students more, really listen when they tell me a story, and make sure that I give them grace when they need it. (And hugs if they want them…)

This beautiful mess of a job is so much more than imparting knowledge…and I appreciate the reminder.

A Word A Day!

October 10, 2015

I am feeling really lucky this year. I have the kind of class that tries everything you throw at them, and does it with gusto.

Like when one of my students who visits our ESL teacher came back to class with a little notebook and explained that he was trying to find awesome and interesting words to fill it with. And he agreed to share this plan with the whole class. And just like that, everyone wanted a notebook to keep vocabulary in too.

Coincidentally, we had also just introduced the CAFE strategy “Tune Into Interesting Words.”

Once this idea started to spread like wildfire, kids were coming up to me left and right wanting to share the words they found in their writing. Since we had a few extra minutes the first day, I let one person share a word they had found.

And since we are such a gung-ho bunch? It’s become a daily routine.

Each day, during Read to Self, each person keeps an eye out for interesting words – they can be words they know, or words they don’t. They record them in their notebooks…

At the end of Read to Self, one person volunteers to share their word, which I record on a sticky note.

Then, they read the sentence where they found the word. We do a quick turn and talk about what everyone thinks the word means based on the sentence.

A few people share out their ideas. We try to decide what part of speech the word is and come up with a possible definition.

Then, we use the classroom iPad to look up what the word actually means. I LOVE this Learner’s Dictionary from Merriam-Webster. The definitions are much easier to use than a traditional dictionary – I hate it when you have to look up words in the definition to understand the word!

Once we know the part of speech and the definition from the website, we come up with a definition in our own words. I record it on a sticky note.

Then later, I will let the student who volunteered the word write everything on a card and we put it up on the board!

This has been such an authentic was to incorporate vocabulary into our day! If we don’t have time to get to a vocabulary word, I hear about it! Everyone is involved, and I’ve already seen some of the words we discuss popping up in their writing.

I’ve never been great at incorporating vocabulary instruction into our days, but my students’ enthusiasm and excitement has made this one of my favorite parts of the day! I can’t wait to see all the words we will have as the year progresses.

If you are interested in your students learning a word a day I created a resource with directions, ideas for extensions and printables to help you get started. You can check it out in my TpT store by clicking the picture below.

How do you incorporate vocabulary into your day? I’d love to hear more ideas to help this time become even more effective!

SLANT Box Exchange Awesomeness

September 7, 2015

If you haven’t had the opportunity to participate in the amazing SLANT Box Exchange put together by Jameson at Lessons With Coffee, I bet you will want to after seeing this!!

I was SO extremely lucky to be randomly paired with the fabulous Rachel from Mrs. O Knows. In case you weren’t sure, SLANT stands for Sending Love Across the Nation to Teachers. And I could TOTALLY feel the love from Rachel. 

We knew each other a little bit already from some collaborative blogs and Facebook groups, but this was an opportunity to get to know each other even better. The theme was Summer Jam, so we decided that we would put together a box to keep summer going. Rachel asked me questions about my favorite music, hobbies, food and activities that make summer what it is. Before I knew it, she sent me an email to say my box was on the way!!!

When I got home and checked the mail, I found this adorable box full of goodies!

Rachel is so crafty! Even the box was super cute!

When I opened the box, I found a sweet note and individually wrapped presents! I’m sure that my mouth dropped open with excitement, because my husband asked me if everything was ok…

Everything was packed in so neatly, I was hesitant to even take stuff out of the box. But, I’m sure you know, I quickly got over it and started opening each one!

Each one had a tag with a note! So thoughtful!

Every gift was SO perfect for me. Rachel really took the time to get to know me, and made sure each present reflected that in some way. I haven’t been so touched by a gift in a long time…I even got a little teary eyed while I was opening them they were so thoughtful. She paid attention to my favorite team (the Broncos), my favorite beverages (coffee and beer), my favorite snack (Chex Mix), my favorite music and more. Even if you didn’t know me, after seeing the gifts in this box, you would totally know me!!

You’ll notice the Chex Mix is missing? Someone else in this house loves it too….

I am so glad I participated in this exchange. I loved getting to know Rachel better, and hopefully making her feel as special as she made me feel!

Thanks so much to Jameson who puts this whole thing together. It’s a lot of work and I’m sure it’s not easy, but I really appreciate it because it gives us the opportunity to get to know other teachers around the world! If you are interested for next time, make sure to watch for upcoming sign ups by following Lessons With Coffee.

 Thanks again to Rachel! You made me feel really special! 🙂

Back to School Blog Hop!

August 1, 2015

I’m trying hard to NOT be in denial that it is August. I’m not actually sure where the summer went. But here we are and back to school season is in full force. I haven’t officially counted the days I left until school begins. But it’s less than I would like to believe.

Luckily, I’m joining up with some incredible upper elementary bloggers for the Upper Elementary Back To School Blog Hop! It makes all this going back to work nonsense a LOT easier to deal with!

Throughout the hop, we will each be sharing some great back to school tips and freebies! Make sure you hop all the way through to take full advantage of everything these wonderful ladies are offering. Oh and did I mention there’s a giveaway?? Make sure you enter at the end of this post!

Be Prepared: But it’s ok to not get carried away. This has been a long time coming lesson for me. Every year when it’s Meet The Teacher night and my room is still a huge disaster and the bulletin boards aren’t done and the desks aren’t just right or I have to shove a pile of stuff into a cabinet, I stress out. Like tears and sweat stress.

But last year, one of my teammates laid this little gem on me. “No one knows what it’s SUPPOSED to look like. Do the important stuff and don’t worry about the rest!” I was floored. Of course kids and parents don’t know that I meant to have 5 more posters hung up or the library reorganized. I figured out what REALLY needed to be done before they walked through the door and everything else was just gravy!

The things I absolutely get done? I put out bins (read: empty cardboard boxes) to collect shared supplies. I write a note on the board directing students where to put the supplies they have brought. I have nametags on desks. I make sure the ugly bulletin boards are covered with paper and a border. I have a table with handouts for parents to take with them, and a bin of pens in case they want to fill anything out right then. I think that’s pretty much it. Everything else is extra at that point!

Full disclosure: I like to make it look nice. But I have figured out that if the library bins don’t have labels on them just yet, that no one notices (or will care!) on Meet the Teacher night.

Handouts: I mentioned handouts above. I usually just have a little table with all the handouts that parents might need before school starts – an information sheet about me, school calendar, extra school supply lists (just in case), and directions to sign up for Remind 101. I saw a great idea recently to have parents fill out a Google form with their information…which I am totally going to try to do this year!

I created an editable Instant Information form for you to fill in with your information and hand out to parents this school year! Quick and easy! Click over to download it from my TPT store. 🙂

Wait, don’t go yet! We are also giving away some TPT money to spend before school starts! Make sure you follow all these wonderful folks to get as many entries as possible!

a Rafflecopter giveaway

I hope your back to school season is smooth and fun!! Make sure you hop over to Tammy’s blog to get some zen into your teacher life!


Asking Questions for Mathematical Thinking

July 27, 2015

Getting 5th graders to think deeply about the mathematics they are learning is a constant challenge. Truthfully? Teaching elementary math is more of a challenge that anyone gets credit for! Thankfully, there are a few tools we can add to our math teaching toolboxes to help students reach that deeper level of understanding.

When I first found about the Common Core Standards for Mathematical Practice I got so excited because of the emphasis on helping students think critically about the math they are undertaking. That being said, after I read them, I sat back and wondered, “Exactly HOW do we support kids to do this kind of thinking?” I could have the greatest, most engaging math problem in the universe, and if I just threw it at them and walked away, I knew the results could be disastrous.

At the time, I was participating in some pretty amazing PD through my district and a local university. It was all about math and how we could improve students’ learning and understanding in a variety of ways. One of the things we discussed was questioning. Once we started having conversations about questioning, I knew that the questions I asked students (and they asked each other) could potentially be the key to the kingdom of having a deep understanding of mathematical concepts.

Have a Plan

ring of cards with questions on them

This was probably the hardest one for me when I first started shifting my thinking about using questions more effectively in mathematics. How was I supposed to know what questions to ask? To begin with, I found a few “go-to” questions – I thought worked well, like “How did you figure that out?” and “Why do you think that idea is working?” Each time I planned a lesson, I kept a few of these types of questions in my back pocket to help kids extend their thinking. I even put them up on posters or cards at the back of the room to remind me! When you know what questions you might ask ahead of time, it helps you to bust those bad boys out when you are circulating around the room or working with a small group of kids.

Think Like Your Students

After you make a list of the questions you want to use, start thinking about what answers kids might have. Think BIG, because you know they will say exactly what you aren’t expecting! I’ve even made plans that go something like this: “If So-and-So says _____, then I will ask _____.” Be prepared for lots of answers, but don’t get thrown off if they say something you didn’t think of! Sometimes, I have to take a minute to think of how I want to answer or what I want to say, and that’s ok! (Don’t tell anyone, but I’ve even said things like, “I don’t know if I completely  understand your idea yet. Can you give me a minute to think about it?”)

Give Them Room to Struggle

As teachers, we HATE to watch kids struggle. It’s painful and we want them to get it! But, I’m here to tell you, it’s ok to let them struggle. That’s where the real learning happens! Questions are a great way to fight the urge to jump in and rescue a child who is struggling. Use your questions as a way to push their thinking, especially when you just want to give them the answer or tell them the next step. Ask them a great question instead, so they can come to the idea on their own.

Let Them Lead

The best kind of questions are the ones where they get to take the lead, not the ones that lead them to the answer. I always know I’ve asked something too leading when the student’s answer sounds like a question! It gets to that point where the student is just saying what they think you want them to. A question that gets them thinking in the right direction, does just that! Gets them thinking and back to working on the task at hand. The more open ended your question, the more thinking will happen!

Listen to Their Responses

Last, but not least, LISTEN. Once you’ve asked them a great question, really pay attention to what they are saying in response. It can be really hard when you have a great toolbox of questions ready to go, but be prepared to just take the time to hear what they have to say. It’s the most important part of the questioning process, in my opinion!

Are you looking for some questions to add to your math teaching toolbox? Check out these math discussion questions from TpT! They come in handy to post on the wall, or to put on a ring for your students or your small group table.

If you are teaching elementary math, I’d love to hear from you! Do you have any questions about this strategy? What questions do you like to use in your classroom? Leave a comment below!

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Classroom Management: A Culture of Respect

July 19, 2015

I will never forget my first year as a teacher. I got a job late – and when I say late, I mean 3 weeks after school had already started. I was lucky though – a friend a knew a principal who was looking for a teacher, and that helped me get an interview. It turned out that the job was a split position – the morning at one school and the afternoon at another. It was one of the hardest years of my teaching career – even harder than the year I taught 36 4th and 5th graders in one room while having a sub once a week while I was mentoring teachers in my building. Well, ok. Maybe they are tied.

Anyway, the main reason I made it through that first year and even considered continuing as a teacher was the amazing support I got from the instructional coaches in both buildings. I know that not every new teacher is so lucky, so today I’m happy to be able to pay it forward (many moons later).

If there is one thing I feel like I handle pretty well in my classroom, it is management. My classroom is (usually) a good place to work, take risks and feel supported. (I think my students would say they feel this way.)

I have done a lot of the usual classroom management things: clip charts, flipping cards, and even points on the board, but I have found that none of these things are particularly effective unless you have some underlying classroom foundations. And that’s where my tip comes in:

When I was a new teacher, I didn’t really understand this idea. In fact, I don’t think anyone ever talked to me about it. I thought respect meant that I was the only person in the room that got a say. I thought it meant classroom control. I thought it meant that everyone was quiet all the time. I remember feeling really panicked if kids were talking at all in my classroom during my first couple years of teaching. I felt like if I let anything go that I would lose complete control of the class. Boy, was that exhausting! (Side note: You know those back to school dreams you start having around this time of year? Mine are ALWAYS about an out of control class that I can’t seem to get to listen to me!)

What I learned was that in order to get respect, you have to give it. I know that sounds simple. But it changed how I ran my classroom.

1. Let It Go
From the very beginning, I let my students know that I am not the only one in charge of things. Kleenex box empty? Grab a new one. No paper in the basket? Open up a new package and fill that bad boy up! Stomach growling for your irresistible snack? Go ahead and eat it. I started to let go of the little things – the things that don’t disrupt others and let kids have the feeling that they can control parts of their day.

This doesn’t mean I don’t have boundaries. It just means that I respect them enough as people to take care of things. I have very clear boundaries. For example, they know that my Teacher Toolbox is for my teacher tools! They have their own supplies, so mine are off limits. But feel free to get in the kid friendly cabinet if you need new glue sticks for your table. They know where the line is because I tell them. No sense in making those things a secret!

2. Get To Know Them and Be Real
The other, even more important part of giving and getting respect is getting to know your students.  Older kids especially are masters at knowing how much you care – or how much you don’t.

Get to know them. Talk to them. LISTEN to them. Understand them. Let them know that you are all on the same team and you have their back. It doesn’t hurt to show them your human side – they love to know you are a real person. Silly, sad, happy, funny…

Fake mustache optional

Sometimes this is simple – lots of kids love to make connections with their teachers. But sometimes it’s hard. Sometimes there’s that kid (or kids) who doesn’t trust adults or doesn’t want to make connections. Guess what? Those are the same kids who need great classroom management the most. They can be your biggest ally or your worst enemy. By making the effort to show those students how much you respect and care about them, you will be improving your classroom culture a million percent. I always find that once they know you they will do just about anything for you, if you just ask. (Side note: This, for some reason, does not apply to asking them to behave for a substitute. I have not figured that one out yet.)

This year, I had that student. Every teacher before me told me how hard he was, and how much trouble he would cause our classroom. I got to know him. I enjoyed his sense of humor and I think he recognized that I wasn’t judging him based on his past. Now, I’m not saying we didn’t have our tough days, but he knew that I had a lot of respect for him and he returned it. The ultimate compliment came at the end of the year. He was sitting at my table working on a project and talking to a friend. He said, “The teacher never likes the class clown.” (He meant himself.) I looked at him and told him I was a little offended by that. He made a face and said, “Well, not you. Regular teachers. You’re not just a regular teacher.” It made all that hard work to get to know him worth it.

As a new teacher, it can be difficult to give up control of those kids in the desks. It can be really hard to get to know the high-flyers who make your life hard. But if you can keep some of these things in mind, you might find that your classroom runs more smoothly!

If you have ideas about classroom management for new(ish) teachers, please add them in the comments!


Whatever Wednesday – Math Shifts Continued!

July 3, 2015

Hello all!! This will be the second post in a short series about MATH! Hooray! (If you aren’t as excited as me, just play along!)

Last week, we started talking about the 3 key shifts required by the Common Core State Standards.

The first shift was all about the focus and you can read about it {here}.

Today’s post is all about shift #2: COHERENCE.

Has this ever happened to you?

It’s halfway through the school year. You’ve already taught a great unit on addition of whole numbers and your class did pretty well. You feel great about their understanding and now it’s time to start on your unit about adding fractions. When you start teaching your lesson, the confused look on your students’ faces tell you that they have no idea what you are talking about.

Teacher Meme - Giving Instructions

Even though it’s frustrating, this feeling isn’t new, right? Every time you start to teach a mathematical idea, your students treat it like it’s the very first time, even if they’ve been taught it before. As the teacher, you know there are connections to what’s been previously taught, but most students act like every day is completely brand new and relates to absolutely nothing they’ve ever seen before. (I’m not blaming the students or the teacher here! It’s just something that happens!)

This is where coherence becomes your new best friend! Coherence is the intentional linking of topics and thinking across and within grade levels. It’s overcoming the idea that mathematics is a set of disconnected procedures and rules, and helping students see how mathematical ideas are interconnected. Coherence allows students to see that each standard is “not a new event, but an extension of previous learning.”

Some very smart people created learning progressions to help design the CCSS for mathematics in a coherent way.

For example:
In third grade, students are introduced to interpreting products of multiplication by thinking about equal groups of a certain number. i.e. 4 X 5 is the same as 4 groups of 5 objects each. (This is 3.OA.A.1, in case you were wondering!)

Fast forward to fourth grade, and students can use what they learned about equal groups in multiplication to help them start to think about how to multiply fractions with a whole number. This foundational understanding about equal groups of whole numbers can apply to “groups” of a fraction. i.e. 3 X (1/6) is the same as 3 groups of 1/6. (This is 4.NF.B.4.A!)
Click the picture to buy the great basketball clipart from Zip-A-Dee-Doo-Dah Designs!

I LOVE that the same representation covers this type of problem with whole numbers and fractions AND it’s easy for kids to transfer that underlying concept from one year to the next. I think this is especially true if we put the problem into a context (read: word problem) but that is a post for another day! 

This is just one example of how coherence appears in the CCSS for mathematics. We could even extend this example to show how this concept supports fifth graders when they begin to learn about multiplying two fractions.

Remember those confused faces from before? With a combination of focus and coherence students can start to see mathematics as a set of interconnected concepts and ideas, instead of a bunch of disconnected topics and tricks. Lessons are extensions of their learning from previous grades and earlier in the year, and hopefully the look of “I’ve never seen this before” will be a thing of the past. 🙂

I’ve linked up with April from Grade School Giggles for

Whatever Wednesdays

Want to learn more? Check out the resources below for more information.

Achieve the Core: VIDEO – The Importance of Coherence in Mathematics

 Achieve the Core: Shifts in Mathematics – At this link, you can find information about the major work of each grade level, and general information about the Shifts.

Core Standards website: Key Shifts in Mathematics – You can read more about all 3 Shifts here.

Are you working towards having a Common Core aligned math classroom? I would love to hear about your experiences with the 3 shifts in the comments or through email!