I am a former math teacher. Don’t run away (yet)…this won’t be a math lesson (or maybe it will…math is EVERYWHERE!). There was a time in my career where I started the class with an “opener,” which was typically the “Problem of the Day.” The problem may have had a connection to the lesson for that day, or it may have been some sort of spiral review. Regardless, a big part of this problem was to provide my learners with a time to start thinking about math.

I tend to reflect, a lot, about how I can continue to improve upon my teaching. One day I had a realization. My learners asked me A LOT of questions, not necessarily related to the “problem of the day” that I had projected. It was more like, “Mrs. Q, why do parents have to go in to the parking lot this way to drop the kids off if teachers have to get in, too?” Another example, “Mrs. Q, do you think I can raise my grade before the end of the quarter?” Or my favorite, “Why do they serve this for lunch if it’s supposed to be “healthy”?” I began to realize that I was spending a good portion of the beginning of class answering these questions. Could my middle school kids have been derailing me to keep the focus off the problem of the day, quite possibly. But they were also genuinely curious about these questions. And these were middle schoolers – I could only imagine how many questions an elementary school teacher must get asked a day with those big imaginations in their classrooms!

I started to move away from giving kids the answers to their questions. I mean, I never simply give an answer to a math problem; they need to persevere and problem solve and analyze their work when it is incorrect in order to understand. So…why would I answer their questions? It’s not meant to be rude at all, but how am I teaching them anything if I keep providing the answers to them?

Out of this reflection, I brought a box into my classroom with a cut out at the top and labeled it, “Problems of our Life.” I started asking kids to write their questions down, the ones they would ask me verbally on a daily basis, and place them in the box. I had paper that was color coded based on when the answer was needed (red – needed ASAP; yellow – needed within a week; purple – needed within the month; blue – doesn’t matter but would like to know). Those “Problems of our Life,” pending they were appropriate, became the starters of our class period. My kids were thinking critically, problem solving, and collaborating. They were learning about real life issues, and were discussing solutions together. They were realizing that in some situations, there were multiple ways to solve these problems. We were even talking about problems that we thought we solved but did not go as planned, and shared our whys. In some cases, we were able to use their problems towards an entire math lesson/unit which allowed them to make immediate connections to their learning. The best part is these problems were coming straight from my students, which made them even more engaged with learning from the start.

Other than learning math, my kids were learning how to handle situations and challenges that happen in life. Some questions that they collaborated on were about how to get to McDonald’s from school to meet their friends, how to finish homework and study when they had to go to play practice, how to make a necklace out of sea shells for a gift, etc. These were all questions that my students generated because they were curious and needed to know; and they wanted to work with others to find solutions.

Don’t be afraid to navigate away from your “content focus.” Your kids are still learning something that they will be able to take and apply somewhere else. =)

 

I’m back! It’s been a while, I know…times have been busy and I apologize (if you’re truly a loyal follower…anyone, anyone??!!). I have been learning, reflecting, engaging, collaborating, and encouraging each and every day. I am happy to be back sharing another little blog with you in hopes to bring inspiration.

Back in November, my daughter approached me and said, “Mom, I want to make pillows for everyone in the family for a Christmas gift.” I thought..wow, that is super generous, but also a very big task! To no surprise, she had already generated a list of individuals that she wanted to make pillows for, which she had shared with me so I knew how many pillows she needed to make. She told me that she saw someone making them at school, and wanted to use her sewing machine that she was gifted last Christmas to try it out. I asked her what was needed, and this is what she said:

“Well I need fabric for everyone, but I want to get everyone fabric that they will like, maybe what they’re interested in. I need the stuffing to put into the pillows, and I need thread.”

She went on to tell me that she didn’t want the pillows to be too big, maybe just slightly bigger than a piece of paper. She went and grabbed this paper and started tracing outside to show me what she was thinking in terms of the size of the pillows. At that point, we had a conversation about how much fabric she would need. “Can’t you just buy it and if we need more we can go back and get some?” She asked. I explained that we want to buy the fabric that we need, and not too much so that there is a lot extra; but we also don’t live particularly close to the fabric store where I can jump in the car and run out if we needed more. So then my 8 year old says, “Well we can measure it!” Next thing I knew, she was going over to the junk drawer (don’t lie – you have one, too ;)!!) to grab this ruler that I know for sure I have not yet taught her to use. She started measuring the paper and figured out how much fabric we would need for each pillow. We also talked about how much stuffing would be needed for these pillows (we already had the thread).

After a trip to the store, she got home and went straight to work to make these pillows…and she did so with minimal help. She began to measure the perimeter of the pillow out, sewed around the outside edges while the fabric was inside out, turned the fabric around, stuffed the pillow, and finished by manually sewing the pillow closed. I was amazed at her creativity, patience, and drive throughout this entire process.

Now, why do I share this story with you today in a blog that is entitled, “Encourage the learning – don’t force it.” My daughter saw someone at school doing this and was encouraged by her observations. Throughout this entire process, I heard and observed my daughter thinking critically, problem solving, and collaborating with me on the steps she would take to achieve her goal. She used the tools that she needed to make this dream become a reality. And those are the “non-academic” skills that she used. I also watched my daughter use her knowledge of math, reading, science, etc. to create these pillows. I also witnessed her creativity and imagination. She learned so much without even knowing exactly what she was learning and the best part – she had fun doing it and it was something she wanted to do.

I want you to reflect on what the kids in your class are doing when learning. Are they watching you teach them, or are they being guided by you as they problem solve and think critically to navigate through their learning? Are they sitting down and filling out worksheets, or are they allowed to demonstrate their understanding in a way that not only makes sense to them, but is how they choose to demonstrate their learning? Yes, we are bound by standards that need to be covered in order to prepare our kids to move on to the next grade; however, are we being creative in the way we are doing this? You may be and if so, I would encourage you to reach out to some of your colleagues who may be having difficulty doing so and partner with them to generate even more ideas! If you’re not, I challenge you to think of how to bring more of these engaging experiences in to the classroom. Let’s put the fun back in learning!

 

Let’s do a thinking activity. Without Googling or asking for help, can you tell me what the names of Christopher Columbus’ three ships were? Most of you likely passed that first question and were able to say the Nina, Pinta, and Santa Maria.

Now, without Googling or asking for help, can you explain to me why there were three ships and the purpose for each one?

This is likely where we lost a few of you who were able to answer that first part of the question. There have been a lot of questions about Common Core state standards and why students aren’t learning like their parents did back in the day. The reason for that is because most of us learned in a way where it was more important to memorize flashcards and facts rather than understanding the information. Not to mention, we were then responsible for regurgitating information back on classroom or state tests. Were we really learning, or were we just really good at memorization? I know there are things today that I cannot remember and I know I received A’s and B’s on my assessments when I was younger. All these grades told me was that I was really good at memorizing most of the time. This is to no fault of the teachers, either; it is just the traditional way that schools have always operated – which is why it is time for a much needed change.

You may see posts like this on social media sites:

Why can’t we answer a basic math question? Most of us learned PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) – which is also why we sometimes get confused when someone says order of operations ;). Unfortunately, this exact order is incorrect; but we were taught Please Excuse My Dear Aunt Sally to help us remember an order (that was not even correct), rather than understanding what and why we were doing what we were doing to solve these problems.

Traditional ways of teaching and learning do not work for our students, not to mention they are not always the most fun way of learning. With the amount of resources at our fingertips, we have an amazing opportunity to allow our students to learn much more than what we have ever been able to do before.

When I was moving into teaching how to find volume of 3D objects, I found a way to help my students make a connection immediately. I noticed that many expressed their interest in the TV Show, Tanked. I decided to use a small clip of this show to introduce the idea of what volume was, and the importance of understanding how to find volume. The end goal of our learning was for students to demonstrate their understanding of learning volume by drawing/building their own fish tank, and it needed to include specific amounts of water and shapes. Throughout this unit, I never just gave them the formula; instead, we explored different characteristics of shapes and what was happening when we poured water into a fish tank in order to understand where those calculations were coming from. Why did I do this? I knew that if I had just given them a formula to memorize, they might memorize it for the assessment; however, would they know what to do when they came across a volume question again in life? This is why it is so crucial to aim for understanding, and not for memorization. I know how difficult it is to not just give the information that is needed; but we need to provide time for our students to work through the challenges. Not only does this make them better learners, but it builds their confidence and allows them to see that they can learn, and that learning is endless! As the teacher, I was there to guide my students along the way and provide support when it was needed and necessary. That is our role as educators: help them to start and provide them the resources, then guide them as they take off on an incredible journey of learning.

I enjoy taking worksheets and finding unique way to have students practice from them without filling out the worksheet itself. Additionally, games are something that always keep my students engaged and motivated to learn. Changing things up allows students to do something different on a daily or weekly basis.

While searching for some new ideas to practice skills in the classroom, I came across another blog that took the idea of bozo buckets and turned it into a math review game. I thought this was an incredible idea; but I wanted something a bit more challenging. I took the buckets and decided to use cups, while using a ping-pong ball for students to toss into the cups. Students toss the ball into a cup, which contains a problem. They solve the problem with their group in order to earn the cup. The team with the most cups at the end wins the game!

Let me break it down a bit more for you:

The Set Up

• Get some cups and ping pong balls. The number of cups depends on how many problems you want to include in the game, as well as how long you want the game to last. The number of ping pong balls depends on how many teams will be in the game.
• For each problem you have in the game (this also depends on how many cups are in the game), write or type it on a slip of paper. Put each slip in a cup (so each cup should have one slip of paper with one problem).
• Figure out where you want to place the cups in your classroom. I pushed a table up against the wall (so that students had a backboard) and organized them in rows and columns. Then, place a piece of tape on the ground where you want the students to stand when tossing the ping pong ball.
• Place your students into groups (I had groups of 3 or 4, based on how many students were in the class). Each person needs paper and something to write on.

Playing the Game

Students will be tossing a ping pong ball into the cups to try and get a question. I told the students that every person needed to toss (so that it was fair for all teams). You may want to have the students figure out an order ahead of time so that it is not confusing while the game is in play.

• The first group of students go up to the line. They all begin tossing the ping pong balls (yes, at the same time; I had numbered them with permanent marker so students were able to tell which ball was theirs). Once they got one into a cup, they took the cup back to their table where the group was sitting. Students continue throwing the ping pong ball until they get a cup. If a student has been up there for a while, they may swap turns with another partner in their group.
• At their table, students work together to answer the question that was in the cup. Once they have agreed on an answer, they bring their work and solution up to me. I check their work and solution. If they are wrong, they bring it back to their group and continue working until they get a correct solution. If they were correct, the next student goes up to toss a ping pong ball. The game continues like this until all cups are gone (or until class ends).
• The team that has the most cups by the end of the game wins!

The students not only enjoyed the challenge of the game itself, but also had fun collaborating and working together to find a solution. Some teams decided to work together to find one way to answer the question, while others decided to work on the problem independently to compare what they had in groups. They also learned a great deal about how rushing to get a problem done typically presents a lot of errors! This one game taught the students a lot, and they had a very enjoyable time playing.

The pairing of two certain words somehow makes blood run cold in most of us: word problems. But, why? How on earth did something that we truly do on a daily basis get such a bad reputation? Is it because we are used to math being numbers and not words? Is it because they take up a lot of time? Think about it.

It is important to consider all of the above factors when helping our students to succeed with solving word problems. Vocabulary is often overlooked, but yet a huge piece in students feeling good about word problems. If they do not understand what the question is telling and asking, how can we expect them to do the math? We can’t. Going over math terms is important throughout our daily lessons, and also providing students with resources (dictionaries, graphic organizers, etc.) to help them understand other vocabulary is going to give them a positive start with solving word problems.

So, then what? Well, then we have to make sure they understand the math! What is it that the question is asking? What information is important to solving the problem? It may be useful to provide students with a graphic organizer that they could follow when solving word problems. I provide spaces for students to show work such as this:

Students also often take out their graphic organizers and they follow along, or double check, as they are working through the problem. Many teachers post solving word problem strategies on their walls, or you can even include it on the graphic organizer or worksheet you give your students. The ‘CUBES’ problem solving strategy has become one of my favorites:

C – Circle the numbers

U – Underline the question

B – Box the key words

E – Evaluate and visualize

S – Show work, solve and explain

Okay, so students understand the vocabulary, they know the math, now let’s talk about that last part of CUBES – show work, solve, and explain. I remember going over word problems with one of my classes early in my career. The word problem ended with, “Justify your answer.” As a middle school math teacher, I had just assumed that my students understood what that meant, and knew how to do it. Boy was I wrong, and shame on me for assuming! It dawned on me that many of my students at the time actually were not sure what “justify your answer” meant, or how to do just that. It was my job to teach them not only how to justify a response, but what that meant as well. After trying many things out and having success with only half of my students, I think I finally found something that helped most of my students understand this concept. Want to know what it is?? Well, you’ve read this far – so I’m guessing you do! Let me explain:

FIRST, I prepped for this activity. A worksheet is not necessarily needed, though I did create one to closely align to what I did in my classroom. All you really need to prep ahead of time is word problems and a response of a word problem (that you can find or create).

I grabbed a word problem that was age appropriate for my students. I solved the word problem in a way that was very detailed and specific (the way a word problem should be solved). Then, I printed out a few more word problems (based on how many groups I was going to have).

 

DAY ONE: On day one, I presented my students with my WORK,

EXPLANATION, and FINAL SOLUTION. That’s it. No, I did not show them the word problem. I gave my students a few minutes to look over and read everything. After that, I asked them to write down what they believed the word problem said. They did this individually first, then worked together in a group to finalize their word problem. After that, the students hung their word problems up around the room. Each group did a “gallery walk” to look at what other groups had to say about the word problem. To the right is an example of a worksheet that I provided my students with:

DAY TWO: On day two, students came back and began class by discussing how they came up with the word problem on day one. They reflected on the work that was presented to them, as well as why they felt it was so easy or hard for them to write the word problem. They were then presented with different work and explanations for the same question (that were not as detailed and specific as the first). Students had time to evaluate and analyze the work and discuss whether or not they would be able to write the word problem [just as easily] if this was the work presented to them from the start. This led to us having a conversation about the difference between showing work, explaining, and writing a final solution, and what we should make sure to include when doing both. After this, groups were given their own word problem to which they had to show work, explain, and write a final answer.

DAY THREE: Some groups had to finish their work from day two, but once they did, we covered up the word problem with post-it notes and worksheets were passed to different groups. Each group had to do the same activity that was done on day 1, but this time they had the work of their peers. Once done, I arranged for each group to meet so that feedback could be verbally presented to each group. Students went through the same reflection and questions they went through on day two, but with the work of their peers.

DAY FOUR: We began class by going over any final thoughts about the activity, as well as what it means to justify an answer to a word problem. To get even more practice with this, students went through the same activity again, only this time they did so independently.

In no way did the activity above help all of my students to perfect solving word problems right away. However, I know that they all showed improvement in their overall understanding of how to solve word problems, and how to justify their responses. On an even bigger note, the confidence levels of my students surly increased after spending a few days understanding how to go through word problems! Cold blood turned a bit warmer!

 

 

 

Welcome to Middle School Math HeadQuarters (HQ – a great combo!). I am excited to share my work and creations with all of you!

 

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Some of my flipped lessons (from early on)