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.  

Project Based Learning and Football

 Today I was so excited to have my students back in my room, as kinder testing is almost completed! (There is still one subtest for one kiddo who was absent but we are super close.)  

It was great to be in the building again, even if the pipes were bursting with water. Students rushed through the door with their noses cold from the fresh air, chatting about their long weekend, eager to share about their latest mini-trip to Mexico, rock climbing, soccer games, and birthday parties over the weekend.  I missed my students and it was great to catch up again.

We started a new mini-unit today on fractions.  Students got to choose whether they wanted to learn about fractions in conjunction to the Superbowl or Humane Society.  They began Project Based Learning, which entailed studying fractions in the world around them and applying math to everyday experiences.  

I was surprised how new the game of football was to many of my students.  Luckily, one of my quieter students was an avid football player and he explained the rules, abbreviations, strategies, and scoring to the group. He was able to lead and shine and help others, which was a cool and unexpected twist.  I didn't realize how unfamiliar the game would be to my students, who were confused by the goal posts and yard lines as well as what a touchdown and interception were.  The students talked to each other, leaned on one another's expertise and began to analyze the game and find the statistics in it.  They watched a clip of the Seahawks from years ago, winning the Superbowl, and began to make sense of it.  

It's interesting to me to find these unknown holes in their learning. My students can analyze a table and find variables and extrapolate theories, but didn't have much knowledge about a common sport in the US. It was cool to watch how they were able to apply their mathematical thinking to this new concept and begin to analyze it and find the beauty in it as well.   I reminded me that my job is to push their learning in many directions, socially as well as mathematically.  Maybe I will be able to expose them to new hobbies or interests that they would not have learned much about otherwise.

We are about half way through, and will continue next week- hopefully the weather and the pipes hold.  If you are interested in seeing the projects- check them out here.   

COGAT Testing in Kindergarten Makes My Thoughts Spiral

 It's that time of year, where the littlest people in our schools come and test for the Highly Capable Program.  Most kids we test have been prepped hard.  I hear exclamations like, "Oh! I love paper folding!" They are more than ready for these tests that are supposed to be conducted sight unseen.

I wonder about the kids who have never seen an analogy and sit the test.  What are the odds that this unprepped student gets to come to PEP or SAGE?  If you look at the data in my school district, certain demographics are qualifying more and more and other demographics are being left behind. 

 Are there long term ramifications of this?  Will the students in the gifted program go farther in life, if they have studied for the test, worked so hard to qualify for a program that is supposed to be based on innate ability?  Is there really such a thing as innate ability or is that a made up construct?

All of my students work very very very hard.  They are often times at the top of their class, but not always.  They go to Kumon and Art of Problem Solving and Russian Math the way other kids go to soccer or baseball. Many of my students compete in rubics cube competitions, Math Olympiad, and get excited for spelling bees. 

Does this ultimately end in more money or more power or a better life?  Does Harvard mean a better life? If it does, many others are being left behind. But my kids won't get into Harvard from just having good grades and good test scores.  They need to develop an app that everyone uses, invent a new drug, find a solution to a complex problem, or almost become famous to get into one of those top universities.  Can you do this if you are in math competitions and worried about rank any more than if you are on a baseball field hitting a ball far and hard?  Neither seems to be the right answer.

How do we help students get ready for life in a well rounded way? How do we teach them to be kind, helpful, gritty, resilient, thoughtful, and hardworking as well?  

In the end, what truly matters? How much money you make or the legacy of family, friends and kindness in your wake? Is there a way to teach both to all students? I will try, one student at a time. One at a time. 

Algebra and Patterning

 

Today, I build a tower under my doc camera of little cubes.  I asked the kids, "What do you notice? How do you see the pattern growing?"  My third graders promptly let me know the the pattern gets bigger! 

 "It looks like stairs," another cried. 

I watched as they analyzed the numbers behind the pattern.  Soon they realized that it did not grow at the same rate each time. Through sheer grit and persistence, they came to find how many cubes would be in pattern 10 and then again in pattern 43.

I saw students drawing diagrams, using arrows, creating a lengthy pattern of growth.  THey were sharing the workload and pen, and also sharing, their thinking with one another in the end.  My students came up with creative shortcuts to adding long strings of numbers on their whiteboards and build towers of blocks with their hands.  

In the end, they explained how another group solved the problem by referring to their whiteboard.  

Things I will consider: I will continually work with my kids on collaboration.  They are bright and capable and often times do not like sharing the workload.  I will also continue working with them on organizing their thinking so when another group tries to understand their thinking, they can, just by looking at it.  I will encourage my kids to continue to use models, whether they are pictures or built, to explain their thinking.  

Here is a link to some similar activities if you want to try them.

Open Problems on Whiteboards

 

Today, my first grader and I grabbed a whiteboard pen and headed to the the carpet.  I drew the problem on the board and she got exploring.  In big black letters, I wrote all the numbers down....

1, 2, 3, 4, 5, 6, 7, 8, 9

Then I wrote _____  _____ + _____ _____ = 100

I said, "You may only use each numeral once to make the statement true."  

She looked at me and batted her beautiful long eyelashes and away she went.  She first wanted to try a one digit number by a two digit number to make 100 and soon realized that it didn't work because both addends needed to be two digit numbers. 

 She frowned a little, scratched her head, and began exploring some more.  

As she wiped off the board, a huge grin spread across her face. "I know!" she shrieked. She proudly wrote 21+79=100.  I gave her a huge high five and we kept exploring.

She wrote the following numbers:

When she was done, I asked her if she saw any patterns.  She noticed that a lot of her numbers had one and nine in the ones place, or two and eight.  I tried to help her make the connection that she made 10 in the ones place and 90 in the tens place.

Next week, I will work on drawing visual models with her to represent how bundling works and why we can group ten ones and make a ten to ensure her understanding of place value and number sense.  We will solve one problem that equals 100 in various ways and see how they connect, and commonalities and differences. 

If you want to try a similar problem, you can find it here. 

Finding Math Around Us: Elapsed Time in Brainpop

Today's magical teaching story is that my fourth graders came up with a mathematical problem without me even prompting them.  We were watching a Brainpop video on goals for the New Year, since we all do goal setting this time of year, and we had to pause it as the kids ran out to recess.  I told them we would finish the video and the goals afterward.

I was letting the kids in from recess, and holding the door open in the hall when a math debate started!  It was my data dream come true!   My little Anna (name changed) pointed to the screen and said, "We have 4 minutes left!"  

Then another student retorted, "No, we have 3 minutes left in our video!"  

I looked at the screen and noticed that this was a perfect time to do some math.  We paused.  I threw pens to the kids, divided them up on whiteboards, and I asked them to figure out how much time was left on the video.  

I saw one group convert everything to seconds since it would be easier to subtract.  Another group used the arrow methods and counted how many seconds until two minutes, how many minutes until five and then added the final 8 seconds.   We talked about how the strategies were similar and different.  

It went so well, that I did the same problem with my third graders! (I did have to remind them that there were 60 seconds in a minute.)  Our math talk was fun and about goals!  

That was my nerdy teacher win for the day. Carpe Diem. 

Patterning

 

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One of my all time favorite activities to teach kids is patterning.  It connects so well to algebraic thinking, graphing, visualizing math, and it requires kids to think outside of the box.  I love having discussions about patterns to launch the activity. 

I always ask my students:

• "What do you notice and wonder about the pattern?"  
• "How do you see the pattern growing?" 
• "What do you think the next figure will look like? and Why?"

My favorite way to launch is to ask a low floor- high ceiling question, like what do you notice and wonder.  There is very little risk with this question because every student will notice and wonder about something.  It engages all students and learning styles.  It also doesn't put an advantage to some students who have been lucky enough to get extra tutoring or support.  This question levels the playing field. 

Then we go into the more in depth questions.  In general, my students love sharing how they see the patterning growing. They want to get up and "be teacher" and explain to the group ways that it is growing.

After I have oriented my students with the Math Talk on patterning, I generally break them up into partners (randomly) and then we start the problem solving on whiteboards. 

With patterns, we start easy and then level up.

Usually, the questions are layered as such: 

1. What would the next figure in the pattern look like?  How many cubes would it have?
2. How about figure #34?
3. Would there ever be 187 cubes in the pattern? Why or why not?
4. Can you make a rule or algebraic sentence for how many cubes would be in any given figure number?
5. What would a graph of this pattern look like?

I give the questions one at a time, as they finish one, they get the next.

As a debrief, we walk over to a board and I ask questions like:

• How is this board similar and different to that board?
• Jimmy (from board A) can you explain what you think this group B was thinking based on the work on their whiteboard?
• What strategy did this group use?
• How is their thinking made visual?/
• (If a group made a mistake) What did this group understand?  What thinking were they trying?

Then, we sometimes take a picture of the work on the whiteboard and I have the kids caption it with what they learned that day.  

If you are interested in this, you can find some lessons on my new website here.