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Monday, October 4
	Topic: Place value
	Topic: Mental Arithmetic, Estimation
	Read: VdW 10
	Read: LDT 3.5
	Act: A14-15: FUNN @ handouts/activities-b.txt

	Intro to mental math
	    when to teach
		spread throughout curriculum
		as it arrises
		before pencil-and-paper algorithms are learned
		    standard algorithms are "unnatural"
		    avoid "mental blackboard" methods
	    how to teach
		let it arrise naturally
		encourage multiple answers/methods
		explain reasoning
		provide some examples/suggestions

	    prerequisites
		number sense
		operator sense

	    example
		Extending Basic facts to tens, hundreds, etc.
		    fen + threefy = fourfy
		    threefy + threefy = alf fen = figgle fen (110_5)
		    estimation: threefy-one + threefy-three 
			is approx threefy+fourfy = bet fen = figgle twofy = 120

Tuesday, October 5
	Topic: Meaning of Addition/Subtraction
	Act: A16: Add/Sub Word Problems@ activities-b.txt
	Read: VdW 7 (thru 126)
	Read: LDT 2.3

	quiz 4
	    other models for place value
		not proportional (money, washers, chips, abacus)
		groupable, proportional 
		    (counters & cups, bundles of sticks, unifix cubes)  
		pregrouped, proportional (beans on sticks/rafts)
		
	Finish FUNN, if necessary
	Meaning of addition/subtraction
		categories: situation & unknown info
		    dynamic
			join (init, change, result)
			separate (init, change, result)
		    static
			part-part-whole (part, whole)
			compare (large, small, difference)
	
Thursday, October 7
	Topic: Meaning of Multiplicaiton/Division
	#Act: A17: Meaning of Mult/Div @ activities-b.txt
	Read: VdW 7
	Read: LDT 2.4
	Due: HW6 @ hw02.shtml
	Due: A12-15: FUNN @ handouts/activities-b.txt


	Models for addition/subtraction

	Meaning of multiplication/division
	    categories
		equal groups (whole, group size, number of groups)
		multiplicative comparison (product, set size, multiplier)
		cartesian product (product, size of a set)
		product of measures (product, one of the measures)
	    models
		any model for addition/subtraction
		    counters (in piles), etc.
		    numberline (with hops)
		    multibase blocks (for place-value algorithms)
		array

	equal groups (repeated subtration vs. fair share) for division
	    models and word problems

	discussion of remainders
	

Friday, October 8
	Topic: Basic Facts
	Read: VdW 8
	Act: A18: Basic Facts@ activities-b.txt

	review from thursday

	quiz 5

	Basic Facts 
	    def'n
	    approach to teaching
		0. understand operations and number relationships
		1. develop strategy ("discover" strategy)
		2. practice strategy
		3. practice strategy selection		
		
	    (strategies for addition facts)
		0
		1 more/2 more
		doubles
		near doubles
		make 10 (elevator strategy)
		6 (pairs of)  remaining facts

	    (strategies for subtraction)
		think addition
		benchmark 10
		
	    (strategies for multiplication facts)
		0,1
		2: doubles
		5: fives
		9: nifty nines
		remaining 25 facts (10 pairs plus 5 squares)

	    strategies for division facts (why not on worksheet?)
		think multiplication
		near multiplication facts

	    operation tables (in vdw) show which facts can be done with which
		thinking strategies 

	Mult/Div
	    Division ideas
		missing factor
		fair share
		repeated subtraction

	        Important properties
	            (inverse relation)
	            order
	            (0,1)
	    Postpone this until division algorithm
	            distributive law


======================================================================

Monday, October 11
	Topic: Addition Algorithms
	Read: VdW 11 (thru 221)
	Act: A19: Addition Algorithms @ handouts/activities-c.txt

	a few arithmetic properties
	    why did add/sub and mult/div go in pairs? -- inverses
	    commutativity
	    0, 1

	Mental Math - Extending Basic facts to higher decades

	algorithms for arithmetic operations
	    def: step by step procedure, recording scheme
	    emphasize algorithms as recording schemes

	use of models
	    do then write
	    problem solving with models available

	recording schemes
	    partial sums
	    crowded house (overloading columns, then exchanging)
	    "standard algorithm"

	prerequisites
	    meaning of operations
	    place value (exchanging)
	    basic facts
	    

Tuesday, October 12
	Topic: Subtraction Algorithms
	Act: A20: Subtraction Algorithms @ handouts/activities-c.txt
	Read: LDT 3.3

Thursday, October 14
	Topic: Test 2 @ test-info.shtml
	Notes: covers thru 10/8 
	Notes:


Friday, October 15
	Topic: TBA
	Notes:
	Notes: MCTM in GR
	Due: HW7 @ hw02.shtml