How to Make Problem Solving More fun : Turn it into a Game

When I taught 3rd grade, sometimes my students would get overwhelmed with problem solving days.  I remember when they would turn to the next lesson in their problem set, and they see that it is a day of complex word problem after complex word problem and they would groan.  

I looked at the teachers manual, and it wanted me to walk through problem after problem with the students and no independent work. Blah.  Definitely not my favorite, or the kids' favorite, until I turned it into a game I named, "Level Up!"

The game is quite simple, all I did was take the word problems in the problem set, put in my students 's names and type them on new paper. Each problem got a different color and a different level.   Student worked in partners, and when they solved a problem, they would bring it to me and I would check it.  If they needed help, I would help, and then I would exclaim, "Level Up!!"

The students loved it.  They enthusiastically worked on word problem after word problem to Level Up! in the game. It was the simplest and easiest tweak in the world, and all of a sudden my kids were eagerly solving math problems, drawing models and collaborating on solving challenging problems.  

I am turning my Level Up! game into a problem solving game for St. Patrick's Day in case someone else is interested in trying it out.  I am trying to make each level a little harder than the last, and include some communication problems, open problems (with lots of answers), modeling and other compare and contrast problems.   

Additionally, when students Level Up! with my new game, they get a puzzle piece and when they collect them all it says, "Happy St. Patrick's Day!"

I'm looking forward to playing my game again soon. :) 

What Does Digging Deeper In Math Mean for Gifted?

 When I go online to a Facebook Group on Building Thinking Classrooms and mathematical mindset, I see teachers often giving each other advice about gifted kids.  I hear the phrase, "Go deeper with your kids rather than accelerate." However, I find that many people aren't sure what going deeper means or how to teach in that manner.

When I think about how to go deeper in a concept, the Math Practice Standards come to mind.  

Many times my students have memorized an algorithm that is above their grade level and know when to apply it, but don't understand what is happening with the numbers within the algorithm.  It becomes apparent when I ask them to explain why the partial product strategy works, or why you can take a one away from the ten.  This is why place value charts, models, labeled diagrams, and the like are important. 

In this dynamic world, my students need to be flexible thinkers and problem solvers as they work on complex problems.  It is imperative that they explain their thinking to others, so collaboration can occur and we, as a society, can discover multiple solutions to problems and chose the most effective one.

One way we work on this is through Math Talks in the debrief section of my lesson, which gets at Math Practice 3.  I ask students to explain someone else's work based on their notes on a whiteboard or worksheet.  Students have to be able to interpret what the student understood and find places to "nudge" them a little further in their learning journey.  

For example, yesterday I pushed into a classroom for some problem solving.  I allowed students to chose from 4 different problems and work in partners or groups on the problems.  There was a problem about splitting brownies, which was similar to one we already worked on, a complex problem about how many ways can you solve a problem, a communications problem where student wrote a fraction story, and finally one with constraints and rules to find a mystery number.  To find similar problems, click here.

During the debrief, I asked for students who were willing to put their work under the document camera to be talked about.  A few students raised their hands and wanted to share.  I placed their work under the document camera, and had the student take a seat and sit silently.  The work had great ideas in it and small errors as well. 

When the first student placed her work under the document camera, I asked, "What does this student understand?"  We would talk about how the student was dividing brownies correctly, writing fractions accurately, and distributing them evenly.  Then I would ask, "What could we say to this student to nudge them a little on their learning journey?" Students shared that we need to consider the last brownie (which was left out). 

We did this again with a student attempting to add fractions, but was needing to consider how unlike denominators affect the addition.  I like how students are oriented toward each others' work and communicating clearly, and I also like how many notes need to be on the page for someone else to analyze the work. Students talk with one another and the class as we look at each other's learning journeys and offer tips and tricks. 

It's a work in practice.  Every day I get a little better at facilitating and the kids push their learning a bit further, but its productive and helpful in the long run.  

Math Contracts for Gifted Students

For Free Contracts Click Here.

Sometimes teachers ask me how to differentiate in math.  One of the ideas I suggest is to put that student on a contract.   What this means is that students can test out of a unit of math, or a part of a unit in math, if the teachers administers a pre-assessment and the student passes certain domains.  

Contracts are documents that ask the students to do a few of the problems in the problem set rather than the whole problem set.  Sometimes if a teacher notices that a student knows the majority of the content but needs work in an area or two, they can ask a student to stay with the class on those particular lessons and work on extensions at other times.  

For example, I am working with a fourth grade teacher at Creekside right now who used to teach gifted students with me.  She gave the end of module test to her class before the unit even began to see where all students were at and what their prior knowledge was.  This pre-assessment showed her that all of her gifted students already knew the content.  She also learned that an unidentified student also knew all the content for the upcoming fraction module.  

My teacher friend was able to "put them on contract," so those students could work on extension resources on fractions, while other kids were following along the Eureka lesson.  The gifted kids were able to expand their thinking by applying their knowledge of fractions to a project, in depth problem solving problem, or more complex task.  The rest of the class was able to follow the lesson planned in Eureka.

Now, I am checking in with those students in SAGE (our gifted pull out program) regarding their project and the homeroom teacher checks in with them as well. We are differentiating our content to meet the needs of all students and making sure all kids get what they need to be successful.

That said, it is also important to acknowledge the Practice Standards in math as well.  All students need to be able to engage in mathematical discourse, debate, kindly questioning ideas, developing strategies and finding patterns in math and explaining them.  Sometimes it is necessary for students who contract out to also engage in some math discourse in the lesson to deepen their understanding and push their math behavior forward. 

 I see it as an intricate dance, balancing the needs of all students, which can be done with precision and care.

Here are some free Eureka contracts.

Using Science to Teach Math: Launching a Inquiry Science and Math Unit for Gifted

 Today we dove head first into inquiry in science and math.  We used purposeful play to help students begin to explore and question bubbles.  I watched as my students made bubble mountains, bubble chains, bubbles inside bubbles and the biggest bubble ever!  They broke up into pairs and then decided ultimately to work collaboratively as a group to make the biggest pile possible.  

The whole thing reminded me of how important it is for students to play with the world around them, experiment without direction, try new things, and collaborate with others.  Students develop a curiosity of the world around them and notice things.  

I have been watching a Ted Talk with the older kids this week.  It talked about how creativity was being drained from students and how they are learning to be more and more afraid of making mistakes.  We don't know what the world will bring in the next five years or ten years or twenty years, and in order to meet those needs, one of the most important characteristics a child can have is the ability to problem solve and think flexibly without an adult showing the way step by step.  Actually, many of the students asked me to share the video with their parents.  It can be found here: Ted Robinson. 

We collectively gathered our observations and questions about bubbles.  I will guide the students into developing testable questions and we will create experiments and observations and do research to answer their questions.  Today was a jumping off point for their minds and was used to hook them into the unit.  It worked!

With squeals of delight and sayings, "This is the best SAGE day ever!" I knew it hit the mark.  Now, we begin the harder part of research and tying our findings to math and science.  

Math Talk in the Classroom

 My third graders were excitedly sitting in their seats filling in their mood meter.  I was about to try a new Math Talk routine Thursday, one they hadn't seen yet.  I projected the image onto the screen from this amazing website called NTimages and waited in anticipation:

I asked students to look at the picture and notice and wonder.  What do you see?  What do you wonder? Turn to a partner and talk about it.  The students noticed the characters on the pins, but soon they were seeing the math. 

 It's always so interesting to me to see the way their minds work. I thought they would start seeing fractions in the picture and analyzing the fractions, but instead they found commonalities in multiplication.

Before I knew it, my students got together and were creating and solving their own math problems.  They looked at the image and saw (4 x 2) + (5 x 2) +6 = 24. Next, they pushed each other to represent their thinking with parentheses, arrays, and word sentences. Another student, always the daring rebel, stated that she was going to solve it her own way and said the equation really was (9 x 2) + 6.  

The students talked about how they were both right and how numbers can be decomposed in a multitude of ways. The differences in ideas moved our conversation forward as my students challenged each other, pushed mathematical models, and are learning to respectfully disagree with one another as well.  

At the end, we filled out a Math Talk Checklist, where the students self-graded. If you are interested in the Math Talk Checklist, you can click here to get it for free.  I will send other free resources,  tips and tricks there as well.

The Math Talk is so important because it simulates conversations they will have as adults one day.  They will all have to be in meetings at some point in their life, and they will need to know how to listen, problem solve, interact respectfully, help one another and solve company problems. Math Talk Routines are integral to math but also life outside of school.

Happy Mathing! 

Integration: Dry Ice and the Coordinate Plane

 

One of my favorite units of all time is Dry Ice and the Coordinate Plane. Soap is everywhere.  Dry Ice gas fills the air. Students are inevitably laughing and thinking and shrieking with delight.  They get to touch the dry ice bubbles and plan future investigations.  Students think about the properties of matter before, during, and after the dry ice hits the soapy water and watch suds enter the air.  

 I teach it to my 5th graders usually, and we investigate the properties of dry ice through mathematics.  We launch the unit by watching a really funny video by Steve Spangler on Youtube, and then we talk about which experiments we want to recreate, and what control and manipulated variables we will use to investigate them.   

Next week, we are going to graph the different rates of sublimation on a coordinate plane.  We will measure out various sizes of Dry Ice and see if the rate they sublime varies according to original size. The students will determine the exact experiment and flush it out accordingly.  I'm looking forward to seeing my kids' thinking and what they come up with!

Waiting for the Data

One of the coolest parts of my job is meeting the needs of my students academically.  I feel fortunate that I am able to work with small groups of kids and assess them to figure out where they are at and make a plan to push them further.  But that also means that January is a waiting game.  All the students are completing their i-ready diagnostics in school right now.  I keep checking and checking, and waiting so I can plan upcoming units and figure out my next move as a teacher.  

I get to figure out cool puzzles like how can I place coordinate plane learning and dry ice together to come up with some amazing lessons?  How do I help my students learn to listen to one another and from one another during discussion in class?  What can I do to facilitate learning?

When the i-ready data comes in, I will look for trends and develop units around it.  I have my data for third grade and it looks like fractions are next on the list.  I love fractions!  I am super excited to dive into them with the kids.  I think we will break out play dough, recipes, number lines, maybe string and paper as well.... we will look at math talks and can even break out the counting collections to help us identify fractions out of a whole!

There are so many fun manipulatives that we can play with.  I am really looking forward to the coming month or so and playing math with my kids.