1-2 Nim (Videos included)

I don't fully understand the name of this game called 1-2 Nim, but I understand how much my mathematicians enjoy it. I also understand how much it helps develop not only their mathematical minds, but their love for math. 

(I learned it from Dan Finkle who provided a math games webinar on Christina Tondevold's Build Math Minds site. Please consider following her work if you're an elementary math teacher.) 

• Grab a partner and a collection of counters. (I use cubes, but it really doesn't matter.)
• A player has to take 1 counter on his turn but can take 2 if he chooses.
• The player who takes the last counter wins.

Ways to change it up:

• Use more counters.
• Play 1-2-3 Nim. (The player can take 1, 2, or 3 counters on his turn.)
• Poison: The player who takes the last counter loses.
• Use a ten frame. The player who puts the final counter in the ten frame wins.

My kids have the stamina to play this game and its variations for a good while. Though simple to play, it's so engaging. It's easy and fun enough for kids to teach family members at home too. 

Here are two videos of 1-2-3 Nim in action. Enjoy. :)

Give Nim a shot, and don't be surprised if a little person beats you a time or two! (Not that I would know anything about that.)

Stand Up, Sit Down

When the children cheer at the mention of a game, you know it's a good one. I learned Stand Up, Sit Down from Dan Finkle when he offered a math games webinar on Christina Tondevold's site, Build Math Minds. (If you're an elementary math teacher, you should be following Christina's work.) 

Stand Up, Sit Down is basically a quick mathematical brain break. It sounds so simple that it almost seems impossible that my students love it so much. Tis true though.

• The teacher picks a number. 
• The teacher then states other numbers one at a time.
• If the numbers are above the original number, the students stand. 
• If the numbers are below that number, the students sit.

For example:

T: 9 is my number.
T: 4
S: sit
T: 14
S: stand

It's that simple.

But wait, there are variations.

• Choose a smaller or larger first number.
• State the numbers in the form of an equation. (ie. 4+4, 8-1) 
• Play the game with multiplication, division, fractions...

Give this one a try. Maybe your students will end up cheering too.

Thanks Dan and Christina!

Commonly Held Beliefs

This summer I read Regie Routman's newest book, Literacy Essentials. The book overflows with poignant stories, quotes, research, and suggestions. I found myself especially drawn to the chapter titled Embedding Professional Learning. Her wisdom helped launch my school into the year with a focus on learning and growing professionally together in a new and refreshing way. Regie has perfect timing. 

We began the year with this quote in mind from Regie's book. "Perhaps more than any other dynamic, positive and lasting change in a school accelerates and takes hold only when the principal and staff come together on commonly held beliefs that align with research-based practices." Based on Regie's work, my brilliant instructional coach and I designed three PD opportunities that led our staff to create six to seven common beliefs for reading, writing, and math.

For example, following a DBI on balanced literacy (borrowed from our generous Idaho Coaching Network friends), staff members individually brainstormed their reading beliefs. Vertical teams then created posters of their common ideas. Each person used sticker dots to vote for her top six beliefs. After some revisions, staff members had the opportunity to provide feedback.

reading

writing

math

The final beliefs for all three areas are now on our wall where we will be able to intentionally interact with them throughout the year. I'm excited to see where these important building blocks lead us.

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Trust

Even though I tell my students that mathematicians love to count things, I also make sure to let them know the other side of the story. Sometimes there's literally just way too much counting. Sometimes counting is the last thing a mathematician should do.  

This year I have been emphasizing trust during math time. In fact, it might be my new favorite math word. Trust is the thing that can keep kids from counting when it would be inefficient to do so. Trust helps them recognize five-ness and ten-ness.  Trust helps them subitize. Trust makes them more efficient. Trust takes away some of the guess work. Trust helps them see that math makes sense. Trust shows them that numbers can be very predictable. Trust is a necessary piece of the puzzle.

I can thank Christina Tondevold from Build Math Minds for helping me understand the importance of explicitly teaching my mathematicians to trust. 

Visualizing: A Mathematical Must

Close your eyes. Visualize 8 on a ten frame. What do you see? How many are on top? How many on the bottom? How many blank spots are there? Turn and describe what you see to your neighbor. Go. 

This kind of thing has been happening often during the past few weeks in my classroom. Through the guidance of Christina Tondevold from Buildmathminds.com, I have seen the light, and the light is called visualizing. The results leave me wondering, Why haven't I been doing this for 24 years? It seems so obvious now that it's officially become a staple of number sense in my room.

Asking my mathematicians to visualize and to visualize within the structure of a ten frame is helping them make huge connections. For one thing, it helps them with facts. If a child can visualize 8, he can see the extra 2 spots that are needed to make 10. Today my class used visualizing in order to use the Make 10 strategy. After days of visualizing, ten frames, scaffolding, and a gradual release of responsibility (all credit goes to Christina Tondevold), a majority of my students were able to explain how to solve the problem below. In fact, my notation came directly from their mouths.

"Give 2 to the 8 to make 10. That leaves 2 left out. 10 plus 2 equals 12." 

(Do not try this at home without all the essential conceptual steps.)

Why can they do this? Because they can visualize. When one of my mathematicians decided to use her free time to solve an additional problem (9 + 5), she knew to give 1 to the 9 but then got stuck in her notation. She didn't automatically know what was left from the 5. As soon as I said, "Visualize 5 on the ten frame. Now take one away. How many are left?" she instantly wrote 4. It was kind of magical.

I will forever now promote visualizing as an essential math strategy. It gives all kids access to numbers. It's really a must. Thank you Christina for leading me to the light!

P.S. It's possible I'm the only one on the planet who didn't know this already, so thanks for celebrating with me regardless. :)

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If Not You, Then Who?

You know you're investing a lot of time into something when it sneaks into your dreams. Last week's subitizing dream confirms where my attention has been of late. I've been immersed in math, specifically number sense.

How long have we teachers been saying that students lack number sense? Don't we say this every year? It's certainly the pattern in my experience. Truthfully, I haven't felt equipped to know how to fix the issue. Number sense has been nebulous and difficult to assess. Well, I've been digging deep into Christina Tondevold's number sense videos via Build Math Minds. She's inspiring and challenging me to know better so I can do better on behalf of my mathematicians.

Here are a few takeaways from her videos that are challenging me to approach number sense and math instruction from a new and better angle.

• Build knowledge through experiences.
• Number sense cannot be taught. It's caught.
• Relationships between numbers are more important than strategies.
• If kids don't have number sense, strategies are useless.
• Focus on sense, not strategies.
• Textbooks teach strategies and not sense.
• It's about fidelity to students, not a math curriculum.
• If kids have great number sense, they won't count as much.
• Counting can become a substitute for sense making and teaching them strategies won't fix this.
• Kids have to be able to subitize. Subitizing will move them from the counting phase to using derived facts.
• Kids must learn to visualize numbers.

and finally...

• If not you, then who?

I really must stop being the one who says that kids don't have good number sense and then proceed as always. I'm educating myself and giving myself permission to slow down in order to build a strong number sense foundation so that later I can speed up. If not me, then who? 

Thanks Christina!



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Number Sense Videos

I recently stumbled across a brilliant math teacher leader who  you will want to hook up with. Her name is Christina Tondevold from Build Math Minds. You can find her on Facebook, twitter, and her website buildmathminds.com. I really can't say enough great things about her.

She's sharing a lot about number sense right now and is offering a four-part free video series on the topic. Two of the videos are available now, which I've watched and LOVE. The other two will be available soon. The catch is that they won't be available forever. If you're going to watch them, and you should, you'll want to start watching soon.

So go here and get busy. 

10 More 10 Less

We're working on ten more and ten less. Today I took the kids through an activity with three levels. It went rather well.

Level one: 

Each partnership was given a large poster of sorts with twelve boxes and one numeral written in the top box. Their task was to repeatedly add 10 until all boxes were finished. In the end, each poster looked like a column from a 120 chart.

Level two:

Their second task was to cut their column apart into boxes. Then each partner got to travel around the room to other "puzzles" and put the pieces together in the correct order. 

Level three:

I borrowed the premise from another game for this phase. With the use of a +10 and -10 spinner (which can be seen in the picture below) and counters, the pairs raced to the bottom of their column of numbers. 

I love how this activity was easy to prepare. I also love that it progressed in levels. It allowed for lots of practice but in a way that kept things fresh. 

Snowballs and Math

We have plenty of snow outside. We just can't play with it, because it's just been way too cold to go outside. Fortunately, though cooped up inside, they're hangin' with me fairly well. It helps that we take lots of breaks. Today we took one that they'd love to repeat often. I didn't invent the idea, but I did take it up a notch by adding a simple math component.

I split the group in half and sent them to opposite sides of the room with their paper snowballs. At my signal they let them fly. The winning team is the one with the fewest number of snowballs on their side when time is up, so they did their best to get those snowballs on to the opposite side of the room. At my signal, they stopped throwing and two chosen collectors gathered up each team's snowballs. Here's the best part. Instead of simply counting them up, we created a visual. It was easy, meaningful, and so quick, we grabbed our snowballs and played one more time.

The Evils of Scissors and Glue

Today my mathematicians worked on the concept of equal and unequal when it comes to 2D shapes. I perused the internet for ways my students could practice this concept, but I was mostly disappointed and reminded of how we need to be careful how we ask students to use their time. 

If I want my mathematicians to look at shapes and identify whether they've been partitioned equally or unequally, then I'd best not instead ask them to spend their time cutting and glueing. A sheet divided in half, labeled equal and unequal with shapes at the bottom that need to be cut out, sorted, and glued on the page, is going to prevent mathematicians from quality time spent practicing the actual skill I need them to learn. 

Here's how I handled their practice time. Each of my mathematicians was giving one shape, like in the examples below. They met up with others, identified their neighbor's shape as equal or unequal, swapped shapes, and visited someone else. This continued until I knew they had ample time to practice. Their final task was to write "equal" or "unequal" on the back of the last shape in their possession and give it to me. Voila.

I just think we need to be wary of allowing cutting, glueing, or some other random task from preventing what's truly most important from happening.

Parent Math Night

My school had our first Parent Math Night this week, and I was in charge. That's what happens when you share your vision at a leadership team meeting and people like what they hear. I've had this vision for three or four years now, so even though it's taken some work to pull off, it's rewarding to finally see it become a reality.

My vision originated from the very first night of MTI (Mathematical Thinking for Instruction) provided by my state. (Pre-Common Core, Idaho required all math teachers to take this course.) The very first thing my instructor did was give us a math problem to solve in any way, shape, or form. I believe it was a 3-digit problem, but I can't remember if it was addition or subtraction. While we were computing, he was moving around the room, interacting with teachers, and asking certain ones to write their strategies on the board. Once there were about five strategies up, he asked those teachers to describe their thinking. There was much interaction between the instructor and the group as he facilitated making connections between each strategy. This whole experience kind of blew my mind. I got great grades in math but was a huge rule follower, so I had no idea there were so many ways to solve a problem. I was immediately won over and could envision giving the same experience to my own mathematicians. And I did just that. I still do.

This is what I also wanted for parents. While parents want and need strategies for helping their kiddos, more importantly, they must be won over. They must understand why math looks different now than when they sat in a math class. They must be able to see the rewards of their own children learning a different and better way. With all the negative voices on social media adding to their already growing confusion, teachers must give them a reason to not believe everything they read and hear. What better way to be won over than to experience a piece of it themselves.

We only had the parents for 60 minutes, and we crammed a lot in. Here's a simple outline.

* We asked them to quickly jot down a math memory (good or bad) and place it on a happy/sad continuum, followed by a great discussion.

* We asked them to solve the problem 61-19, sent certain parents to draw their solutions on the board, and asked those parents to explain their thinking. Most importantly, we then had a discussion about the benefits of experiencing math this way.

* We asked them to read some research about math instruction, and we facilitated a conversation about what they thought.

* We showed them a video of children in a 6th grade math class learning about area and perimeter in a real-world, engaging, hands-on way, and we facilitated a conversation about what they noticed.

* We shared specific grade-level tips and typical models and asked for questions regarding both. (Each grade level presented on their own. This was the only part of the presentation that was grade-level specific so that no matter what grade level a parent went to, they basically experienced the same presentation. This definitely helped solve the problem for parents who have children in multiple grades.)

* We asked parents to fill out a reflection form so we could know what they found most helpful and where they still need assistance. That way we can prepare for next steps.

Here is the slide presentation. Click on the graphic to view. Notes are also included.

This is the first parent handout.

This is the research page that parents read, copied onto the back of the first page.

This is the first grade tips and models page. Each grade level had their own version of this sheet. 

The models were handwritten. You'll see first grade's below.

This is the reflection page that parents filled out.

Click here to see these parent handouts.

Our numbers were smaller than I would have hoped, but we didn't invite children, who are typically good at dragging parents to events. (We did provide childcare though.) This night was all about meeting the needs of parents, so we wanted them, as well as teachers, to be free of distractions. Regardless of the small crowd, I've heard positive feedback from those who were there. 

Our parents really do deserve to be educated, so my hope is that we do something similar in the future. At the present, parents are stuck in a place of ignorance, which is not their fault, and ignorance leads to frustration for both them and the little people who they are trying to help at home. Schools have a responsibility to step in and change that.


P.S. I had a helpful team of people helping me along the way too. Our instructional coach was a great collaborator on the event.

Intro to the Bar Model

I taught my best math lesson of the year last week. This was quite unexpected for three reasons. 1) Math has been my nemesis this year, (I'll refrain from explaining all the reasons why. It's complicated.) 2) I've never taught this lesson before. 3) Beyond a few pointers, I've never had the training to teach it. 

For several years I've heard heard bits and pieces about the bar model - how it teaches our youngest mathematicians to visualize problems and transitions them into the number line. I never felt like I had enough information to introduce the concept though. This Fall I got a few pointers which helped me develop this lesson, and it really did work. Phew.

I developed the above Google slide presentation which took my kids through the lesson. (Click on the graphic if you'd like to see it.) 

Other than the presentation, it was a simple lesson to plan for. My kids had access to red and blue cubes as well as blank paper. This is what one mathematician's final product looked like, although it probably won't mean much unless you check out the slides above.

I had the opportunity to share this lesson with a math guru from BSU a few days ago. He was very pleased with the components of the lesson and how I took my kids through the process of discovering the bar model. The only recommendation he made concerned the first row of cubes seen on the child's paper. Instead of labeling the individual cubes from 1 to 5, he suggested they be labeled each as 1s since they are units of 1, and I totally agreed. (I edited the slide presentation accordingly.)

Maybe this information will be helpful for someone out there who has been wanting to introduce the bar model to their little mathematicians as well. I'm also in the process of developing further lessons. I'd be happy to share those in the near future as well. Happy bar modeling!

Comparing Names (Freebie)

Keep it real. Keep it relevant. 

That's one of my math mottos this year. I'm not sure how well I'm doing on that, but it's a most worthy goal to keep in mind.  

Names are always real and relevant for first graders, so I invented a way for my kids to compare numbers using symbols with teen frames and their names. Click on the graphic below for your own copy.

Free Exploration

Many years ago during Math Their Way training, I learned about the power of free exploration. Before I ever ask kids to use math manipulatives for a specific reason or in a specific way, they get to use them for their own purposes. They can explore, be creative, use their imaginations, and play. It honestly does lessen the amount of issues we might have later when I really do need them to use the tools for particular  objectives. 

There are only two rules:

• We never toss, drop, or throw manipulatives.
• We never take apart someone else's creation unless they give permission.

I love that the kids use their math skills during free exploration without even trying. They naturally sort, count, build, compare, create patterns, etc. They also use the same creative imaginations that they'll be using in the near future to make up their own math strategies. Also, they must rely on those all-important social skills. It's difficult to successfully pull off free exploration without cooperation and the ability to share.  

Whether at the beginning of the year or at the start of a new unit with new tools, free exploration is a great strategy. 

Saturday Sayings: Math Immersion

Reading Recovery training taught me to be mindful of the print-rich environment I surround my students with. They need to see, hear, and experience words at every turn. Cambourne calls it immersion, and that's exactly what I hope my young literacy club members experience in my room. I've never thought about immersing my students in numeracy though. I'm not even completely sure what that looks like, but I'm interested in finding out.

If the same principles for literacy apply to numeracy, then these are some of my guiding questions. 

Are students surrounded by math?
Do they constantly hear the language of math?
Do they see math in the room and on the walls?
Is math something that is addressed throughout the day or is it isolated to a specified time?

Honestly, I'm left with more questions than answers. How will these questions transform the look, feel, and language of my room this year? If I'm mindful, they'll help me navigate my way into a classroom where math is not separate from but is an authentic and natural part of the world of my classroom and of my students. 

Saturday Sayings: Radar Awareness

If my numbers are right, I've read six books about math this summer. One repeated theme throughout much of my reading is the need for math to become part of our student's worlds instead of an isolated skill set that seems unrelated to daily life. Fosnot repeatedly uses the word "mathematize." With purpose and intentionality, we math teachers can ramp up the authenticity factor for our students and invite them to mathematize their worlds. Many of them will not independently make this leap though. We are the linchpin, which brings me to the thought above by Sammons. I desire this radar awareness that she speaks of. 

In order to purposefully teach my kids how to mathematize their worlds, they obviously need to be given the opportunities to tackle math in ways that are personally relevant. I also think Sammons might be encouraging me to teach with eyes wide open, seeking out the teachable mathematical moments throughout the day that I previously might normally have overlooked. I imagine that with a radar awareness, they would abound. 

Is there math in that read-aloud? What about a class dilemma? Maybe a problem-solving situation arises out of a typical classroom routine. Obviously there's not time in the day to stop at every math situation that presents itself, but I wonder if a few might be worth tackling in order to help kids see, feel, and hear how math is personal and real lifelong tool.