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Today’s Agenda 8:30 - 10:00  Personal Strategies   Addition - Subtraction - Multiplication - Division   10:00 - 10:30 Nutrition Break SHSS Look at Resources 10:30 - 11:30 Virtual Manipulatives   11:30 - 1:00  Lunch   1:00 - ?  Assessment
"Mathematics, as a body of knowledge,
 can be lost.  But numeracy is the set of proficiencies  that, once
gained, are forever with you.” Dave Van Bergeyk
 
Young Mathematicians at Work
If learning doesn’t happen, there has been no teaching. The actions of learning and teaching are inseparable. - Catherine Twomey Fosnot
Procedural  versus  Conceptual?
Ma and Pa Kettle
[object Object],[object Object]
The Sub Question
17 submarine sandwiches - 22 students.  How much for each?
Which group got the better deal? What would have been fair?
Math Congress ,[object Object]
"Mathematics is not a spectator sport!"
 
What’s at Stake? ,[object Object],[object Object]
[object Object],[object Object]
How do these textbook problems not help students develop their understanding of operations? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object]
Cookie Problem ,[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object]
[object Object]
[object Object]
[object Object],[object Object],[object Object],Addition ,[object Object],[object Object]
[object Object]
[object Object],[object Object],[object Object]
Subtraction? ,[object Object],[object Object],[object Object],[object Object]
-secret # p 43 -focus on operations p 47
Personal Strategies
[object Object]
 
Informal Methods? Working from left to right is  perfectly acceptable if the  student is able to keep track.  (Front End Approach)
Temporarily adding or  subtracting numbers. . . 673 + 99 673 + 100 then take 1 away.
Breaking a number into  Appropriate parts.  307 + 424  300 + 1 + 6 + 424
16 X 25 =
16 X  25  4 groups of 25 is $1.00  so  . . . 16 groups must be 400. 16 X  25 80  five 16” are 80 320   twenty 25’s are 320 400
Addition
[object Object]
Explore ,[object Object],[object Object],[object Object]
 
Algorithm? ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object]
So . . .  How do we teach subtraction of multi digit numbers?
[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
How does subtraction by decomposition work? ,[object Object],[object Object],[object Object]
[object Object]
Misconceptions and gaps. ,[object Object],[object Object]
Multiplication  and Division ,[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Potato Soup (Serves 8) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Our Job? ,[object Object],[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Multiplicative ,[object Object],[object Object],[object Object],[object Object]
The Distributive Law ,[object Object],[object Object],[object Object]
Try these two questions using the distributive law. ,[object Object],[object Object]
What is multiplication? ,[object Object],[object Object],[object Object]
26 x 34 ,[object Object],[object Object],[object Object],20 x 30 6 x 30
Using the .5 cm paper try: ,[object Object],[object Object]
[object Object]
Dividing numbers is useful  when we: ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Game ,[object Object],[object Object],[object Object]
Broken Keys ,[object Object],[object Object],[object Object],[object Object]
Game - Concentration ,[object Object],[object Object],[object Object],[object Object]
Game - Pass the # ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object]
Just the Facts Please ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Drill? ,[object Object]
Madison, Wisconsin, Longitudinal Study 4: strategies, facts 3: counting on 2: counting all 1: incorrect Strategy use across grades 1-3
Assessment
GAMES ,[object Object]
Every classroom should have: ,[object Object],[object Object],[object Object]
[object Object],[object Object]
Quotes to Ponder ,[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object]
"A man is like a fraction whose numerator  Is what he is and whose denominator is what he thinks of himself.  The larger the denominator, the smaller the fraction.” -- Tolstoy
"Five out of four people have trouble with fractions."  -- Steven Wright
And my favourite …
"Math class is tough.”  -- Talking Barbie Doll (1992)
Continued Readings Continued Readings ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object]
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