Professional+Development

=Summer Session June 3, 2008 Notes=

Counting in K vs. Counting in 1st:

The Number System 1. Natural Numbers 2. Whole Numbers 3. Rational Numbers 4. Integers
 * start w/ 1 to infinity
 * aka counting numbers
 * add "zero" to the natural numbers
 * come between the natural numbers
 * numbers to represent "betweenness"
 * natural numbers, their negatives and zero

3 x 2 "3" is the multiplicand "2" is the multiplier in terms of counting -"count by 3, 2 times"

4 x 1/2 in terms of counting -"count by 4, one half of a time"

Base ten starts in first grade cuz we are expecting them to now think in groups and that is where subitizing comes in.

__Enter the blue binder__ Read Counting section pgs 2-3, then Additon and Subtaction sections pgs 3-6.

Comments from Reading:
 * The number 10: seems to be a goal
 * set = group. We should use the mathematical term set alongside group
 * How can we facilitate counting in groups? Manipulatives come in ones. We need a manipulative that comes in groups. Grouping manipulatives into groups of 2s, 5s, and 10s. (Bead strings?)
 * When is the algorithm for addition taught? Not till fourth grade. You want them to have a firm foundation in number sense before you teach them the procedures of the standard algorithm. Once taught the SA, they will use it almost exclusively as the "right way".
 * Many activities involve: comparing, combining 2 amounts ( joining (CGI) ), removing 1 amount away from another ( separating (CGI) )
 * Derived facts strategy: 4+5 = 9 because 4+4 =8 and 5 is one more than 4.
 * **Most first graders will be counting on to solve addition problems by the EOY.**
 * Strategies for subtraction: see pg. 9. Subtraction is hard so its development is usually a grade level behind. Standard addition algorithm is taught in fourth grade. Standard algorithm for subtraction is taught in fifth grade.

Counting
• Count a set of up to 20 objects C10 • Compare and order quantities up to 12 C13 CO11 • Count a set of 40 to 50 objects C15 • Rote count, read, and write numbers up to 65 C16 • Begin to use groups in meaningful ways C18 S8 COM3 • Identify, read, write, and sequence numbers up to 105 C22

Addition and Subtraction
• Find more than one combination of two addends for a number up to 10 AS 5 • Find at least 5 two-addend combinations of 10 S7 • Interpret (retell the action and sequence) and solve addition and subtraction story problems • Find at least five combinations of two addends for a number up to 15 COM5 • Subtract one small quantity from another S8 AS4 • Represent numbers using equivalent expressions • Combine two small quantities by at least counting on • Demonstrate fluency with the two-addend combinations of 10 AS9

Very vigorous debate on scoring of EOU 1 assessment. What constitutes a "4?" What constitutes a "3?" Why do we give 4s? How important is it to "explain your thinking?" What does "explaining your thinking" look like?

+++++++++++++++++++++++++ Afternoon ++++++++++++++++++++++++++
Do a study on how much actual repetition of a concept occurs during a center

Three Towers will be done with 3 ten frames rather than asking students to build 3 towers