Outline Professional Growth Common Core State Standards Think-Pair-Share Summary Evaluation

Personal (Professional) Growth Have you ever thought about the connection between simple multiplication and algebra? Let’s examine a couple of problems and explore the connection. We get lost in the trees and miss the forest for ourselves and for the children.

Example 35 x 17

Example 35 x 17 (30 + 5) X (10 + 7) 7x5 35 7x x x

Alternative Way BTW, what is a “quick and dirty” way to multiply this if you were doing simple multiplication? 35 x 20 = x 3 = – 105 = 595 And again, 700 – 100, and then take 5 from that. Think about simple ways. This uses the Distributive Property without thinking about it.

Another Example 241 x13

Another Example 241 x13 ( ) X (10+3) 3x1 3 3x x x x x

Algebra Example (x+3) (x+9)

Algebra Example (x+3) (x+9) X+3 X+9 9 times times x 9x X times 3 3x X times X x squared X squared +12x+27 It’s the same process.

Another Algebra Example (2y+3) (y+5)

Another Algebra Example 2y+3 y+5 (5)(3) 15 (5)(2y) 10y (y)(3) 3y (y)(2y) 2y(y squared) 2y(y squared)+13y+15

Summary of Personal Areas These are simplified examples. Notice two things: Stay focused on the big picture of how things connect. Teach rules in the context of the big picture. We have a plethora of rules. We have mnemonic devices. Help the children to understand the bigger picture as we teach the rules. In other words, teach the CONCEPTS in CONTEXT. If they forget the rule, they can go back and reconstruct the rule because they UNDERSTAND the concept.

Common Core State Standards Toward greater focus and coherence Mathematics experiences in early childhood settings should concentrate on (1) number (which includes whole number, operations, and relations) and (2) geometry, spatial relations, and measurement, with more mathematics learning time devoted to number than to other topics. Mathematical process goals should be integrated in these content areas. —Mathematics Learning in Early Childhood, National Research Council, 2009

Common Core State Standards Con’t Understanding mathematics These Standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.

Think-Pair-Share Examine the number 12. Think of 3 ways you can show them 12 physically. Share with a partner. Share with everyone. Homework Assignment: Have them to find 3 ways at home.

The Number 12 After you have explored physical ways, have the students to write different ways to put 12 together. Be bold and allow students to go. For example, if students realize you could physically put fractional pieces together as a part of 12, let them (1/2) + 3(1/3) + 5 Of course primary students will not be able to write this expression, but they can construct a pizza divided into halves and a pizza divided into thirds.

Think-Pair-Share Examine the number 12. Think of 3 ways you can show them 12 physically. Have them to find 3 ways at home. 2 six packs of sodas Dozen of eggs 2 six packs of bottled water 2 six packs of peanut butter /cheese crackers Etc.

Your Choice Chose an example of a concept you teach. Discuss with a partner ways you can focus on the CONCEPT and not just the mechanics. Share with the group.

Learning Opportunity Enhancements Remember to find ways to emphasize the big picture. Allow students the opportunity to explore (THINK, TALK, DISCUSS, INTERACT) concepts.

Closure - Summary We have examined our own knowledge of how we conceptually understand the math concept of multiplication and how it relates to algebra. We looked at the general notion of the Common Core State Standards and the direction of mathematics. We discussed ways we can modify math instruction to facilitate greater conceptual understanding.

Evaluation Go on-line and evaluate the course. Session Evaluation Code: 31362

Thank you Thank you and best wishes on success for your students.