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Showing posts from October, 2011

Pentominoes!!

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Today was all about spatial awareness and resilience.  Before the activity started, we shared strategies with each other on how we can deal with a situation that is very hard, and when we feel in over our heads.  Students made suggestions like;

Walk away from it and think about something else
Don't pay attention to other people
Ask others for help
Sing a song while you work
Try and switch between using your hands and your head
Let your hands think, and clear your mind
Set a reward for yourself if you finish

With that in mind, we started what was a very difficult activity.  The subject was Pentominoes.  Pentominoes are shapes made of 5 squares, where each side of one square touches another side of one square.  Here is what we did with them;

1) Using your blocks, find out how many possible shapes you can make with 5 squares.  Flips and rotations count as 1 shape, not two.  When you have found all the possible combinations, draw them in your math journal.

2) Using the shapes you made, make a r…

A Reflection on Anxiety

I try to manage my classroom with as little stress and anxiety as possible.  I do this by:

No grades of any kind, just feedback
Almost no Homework
Collaborate activities and almost n0 competitive elements to the classroom
Freedom to opt out of doing anything at anytime (if students don't want to do something, they don't have to)
Weekly Free Time periods where they can explore and play whatever they want to

During the past three weeks we have been diving into the world of Graphic Novels and the Elements of a Story.  We have read a heap for pleasure, for analysis, and for research.  We have looked at the characteristics of GN, the art, the speech bubbles, etc.  We researched our own myth from an Ancient Civilization, and then planned and planned.  Plot, theme, character development, narration, setting, time, etc, etc.  We have reams of notes, and have gone through two rough drafts,  and finally are ready to get started on the good copy.  Everyone was very engaged, very interested, and…

Finding Pi

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Pi is an interesting mathematical idea for young kids.  The thought that a measurement can be same, everywhere in the world, every time, is a hard concept to grasp.  I came across this activity in the great Teaching Student Centered Mathematics by John van de Walle.

1. Ask the students to measure the Circumference and Diameter of 5 circles in and around the classroom.  Try and get a variety of sizes of circles.

2.  Make a Table to record your work

3.  Once finished measuring, find the ratio of Circumference to Diameter by dividing C by D.  Add this information to your table.

4.  Take you data and record it on a large, class sized Scatter Plot.

5.  Analyze data from Scatter Plot and Tables; look for conclusions or patterns



This should lead into a discussion about why all of the numbers for the ratios are close to 3.14.  Once we see this, you can introduce the concept of Pi.  From there, this lesson could fractal out into so many different dimensions and independent inquiries.

To further excit…

Face to Face

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This a nice little activity I picked up from a Paul Ginnis workshop.


Students sit with a partner and choose who is A and who is B
Person A,  grabs a clipboard and a pencil and sits with their back to the screen; person B sits in front of their partner, facing the screen
Teacher puts an image up on the screen
Person B will explain to person A what the image looks like; Person A will draw the image
RULES!
Only use words, no hand gestures of any kind; sit on your hands!
No looking at, or showing the paper until finished
Person A, no turning around and looking
Both A and B are allowed to talk, and ask each other as many questions as they want

Very effective for Geometry, shapes and oral explanations.  Also useful as a diagnostic to see what students already know.

Simple Math Assessment

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Today was test day in my class.  We have been deconstructing Triangles and Quadrilaterals, and I needed to pause for a second and make sure they were getting it.  Instead of doing the standard pencil and paper test (which I have vowed to not do even once this year!), I used this little exercise;

Each child gets a Geo-Board and a pile of elastics and finds a quite spot in the room

Students are given a list of instructions
1.Make a right angle triangle
2.Make a triangle with an obtuse angle
3.Make a triangle with three acute angles; What type if triangle is this?
4.Make a Scalene triangle; why is it Scalene?
5.Make a quadrilateral with four equal angles; what shape is this?
6.Make a quadrilateral with two sets of equal angles; what shape is this
7.Make a quadrilateral with two obtuse angles; what shape is this?
8.Make a quadrilateral and two triangles and have them overlap; how many shapes can you now notice?

When each step is finished, students bring their geoboard to the teacher and check their …

Sticks, Rocks, Housing, and Fun

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We are currently studying Ancient Civilizations in our Unit of Inquiry.  To delve into this topic, we are creating our own civilization, and jumping around the history of past civilizations to better understand the imaginative one we are building.  I am trying to keep the learning as Emergent as possible, and letting the kids take their world in any direction they want.  One of the inquiries they raised was that of ancient housing;  How did people live back then?  What did their houses look like?  Why did they look that way?  To help the kids get a close up, hands on perspective into this topic, we undertook the following series of lessons.
Step One - Research Jigsaw

I set up four stations around the room and put the students into teams.  I told them that they were construction engineers and they were doing research.  At each of the four stations were pictures of housing in the ancient world.  The students then travelled from station to station, and made notes about the characteristics …

The Chessboard

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I introduced the Polya Problem solving steps to the class and we talked about how we would implement such a framework.  As a class, we recollected our golf ball math problem, and applied these steps to the learning that took place during that problem.  Once we had a good idea of how it could help us, I introduced a new problem for the day, and asked them to keep this framework in the back of their mind while they worked through it.  At this point in our classroom growth, this is not something that I am going to force on them, but something that I will bring up and talk about after and before we embark on  complex math puzzles.

Today, we had a great problem that I picked up in The Elephant in the Classroom, by Jo Boaler.  The problem is simple, and the introduction is easy.

How many squares on a chessboard?

At first glance, this is easy.  64, you say!  Well, what is a square?  The board is a square.  2x2 squares.  3x3 squares.  And so on.  Also, they overlap!  This simple counting activit…

George Polya and Mathematical Problem Solving

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George Polya was a Hungarian mathematician who penned a book titled How to Get it.  In that book, we comes up with a four-step guide to mathematical problem solving

Understand the problem.
Make a plan.
Carry out the plan.
Look back on your work.



I am going to try and adopt this to a grade 5/6 class, with level friendly language to help guide them through the process.  Here is what I have so far;
I hope start doing a weekly Problem Solving class, where we work through the steps and train ourselves to think like problem solvers.
I would love some feedback.  What do you think?  Is there anything wrong with what I have up there?  Anything I should add?  Anything that is unclear?  Put your thinking hats on and deconstruct it.

A Golf Ball Mathematics Inquiry

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This series of lessons started with a simple premise, but with a deep desire to get my students thinking more mathematically; and reflecting on their thinking.  I have been trying to get more Meta-Cognition (or Meta-Learning, as I frame it with my students) into the classroom.  This was something that I tried to weave into the activity, and not necessarily tack it on at the end as something to think about.

As for the subject of golf, there was no particular reason to choose it.  I am not interested in golf.  My students are not interested in golf.  Their parents are not interested in golf.  The reason I choose it was because I found a bucket of golf balls in our school’s multi-purpose room, and it sparked a question in my head (which I explain below).  Here, I am trying to model inquiry in daily life for my students.  These things make me curious, what makes you curious?



The actual work that was done in this series of lessons took place over several days, but for the sake of distilling …

An Idea that is Emerging

I don't usually give homework on the weekends (to be truthful, I don't like giving homework at all, but external.... well, you get it).  This weekend though, I changed it up a little and tried something new.  My instructions were incredibly simple, very clear, yet at the same time, incredibly confusing.  In their homework agendas, I asked them to write this simple task:

MAKE SOMETHING

I had no idea what would happen.  They asked me what I meant, what they should do, can I give more clarification, what does that mean?  I resisted the urge to give ideas, and told them that the task was pretty self explanatory.  Just make something.

Well, Monday morning rolls around I go outside to pick up the kids as they stand in line and wait for me.  All of them, the whole class, is standing there in line with boxes, and shopping bags, and folders, and photos.  They are enthusiastically waving their creations at me trying to get my attention.  Sometimes, the things that children can come up on t…