patterns, estimation, communication (ideas for a grade 1 math course) (draft)

*UPDATE* this is not a class we are going to teach, but the ideas behind it and spirit inform the activities we do with the children.

Spirit of the class 1: "It is good to be confused."
Quote from Glenn Stevens (and Arnold Ross?) My initial thought on a Thai version is:

 ความสับสนเป็นสิ่งที่ดี

The goal is to operate within a realm of difficulty where the students are making some mistakes. From a music teacher, I got the heuristic that roughly 10-20% of the time is a reasonable target.

Students should be praised and encouraged when they say they don't understand something, when they ask questions.  Typical cues:
- show excitement (smile, eyes wider, raised voice pitch)
- emphasize this is where we get to learn
- ask them to explain how they are thinking, use words, symbols, numbers, draw a picture, etc
- ask other students for their thoughts
- ask everyone (including the original student) approaches for how they think we could figure out an answer

Spirit of the class 2: Always looking for patterns.

Communication
Throughout, emphasis is placed on having the students talk to each other about what they are finding, organize some of their thoughts, share with the class, write down what they think.  Written material will include:
- equations
- diagrams/pictures
- words (Thai and English)

Practice comparisons:
- X is similar to Y because A, B, C
- X is different from Y because A, B, C

Later, ask for things they know that are similar (and how those things might be different).  When appropriate ask for things that are close but different.

Patterns
Starting discussion:
- What is a pattern?
- What patterns do they know?
- What do they do with patterns?

using single trio blocks hidden in a paper/cardboard tube. For all, questions are

1. can they guess a pattern.  
2. how many patterns they can guess that fit the existing data. 
3. how much more data they need to see to test their hypothesis (confirm or reject).
4. For the pattern they guess, what color comes 30th in the sequence? What about 191st? or some other numbers that are moderately and then very large.

- repeated AAA etc pattern
- repeated ABAB pattern: what color is the 30th in the sequence?  What about the 191st?
- repeated (ABC)^n pattern: what color is the 30th in the sequence? What about the 191st?
-  prod_i=0...inf (A(B^i))
- prod_i=0...inf (A(B^(2i))
- random
- (AB)^8C: to show that there could be something else going on

Using a piano or violin, play patterns like:
- aural versions of the patterns above
- jumping up an octave
- CDCECFCGCACBCcCdCeCfCgCaCb
- CEDFEGFA etc
- CDEDEFEFGFGA etc
- forte, piano, forte, piano (single note or chord)
- different rhythms
- play a simple piece (e.g., twinkle) and stop before the last note.  Is there a pattern.  How do they know that the song doesn't feel finished?  This is just for discussion, no real expectation to have deep answers.

Movement patterns
- movement versions of some of the block patterns
- follow the leader patterns (everyone assigned to follow someone else, someone assigned to follow the teaacher, then teacher slowly walks a loop to allow the snake to form up)
- 2 separate snakes
- wall and monster: everyone assigned another person who is a monster (to them) and another person who is a wall (to them).  They try to walk so that their monster is on the other side of their wall.  Discussion: did it look like there was a pattern?  We had a rule about what was going on, but it was very complicated.  If another teacher came to watch, could they guess our rule?

Ending discussion:
- What other places can they find patterns?
- What are their favourite patterns?  What do they find appealing about those patterns?
- Are there any patterns they don't like?

Homework:

1. Find patterns in new places: movement, colors, shapes, in language
2. Find new patterns: for something they thought they already knew the pattern, can they find another rule that fits the data?  Maybe this one is too hard

Follow-up activity: 

Here are 4 things, find the one that doesn't belong.  

• Why doesn't it belong? What is the pattern or rule that the other three fit?
• Now, can you find another rule or pattern that kicks out a different object?
• For each of the four, can you find a rule that excludes it from the other three?

Estimation/Measuring
Note: other quantities to measure are listed here: http://3jlearneng.blogspot.com/2014/06/getting-started.html

How many are in my jar/box each day at the beginning of the day (can be something left out for the whole school to enter a figure.)

Temperature using the infrared thermometer gun
Distance using the tool

School run: give the students a gps to measure the following
- Time: how long does it take to get to school? Does it vary from day to day? How does it look over the course of a week?
- Distance: how far do they travel? Again, does it vary from day to day and how does it look over the course of a week?
- Speed: average and max speed as measured by the gps.  Which varies more over the course of a week?
Each day, ask for the data of the day and then ask for an estimate for the following day. Rotate through the students who has the GPS.

These will also be good for introducing graphs. I would just show the picture and explain what it meant, but not dwell on the graph.