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Eclectic Topics for  Primary Math Teachers Eclectic Topics for  Primary Math Teachers

Eclectic Topics for Primary Math Teachers - PowerPoint Presentation

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Eclectic Topics for Primary Math Teachers - PPT Presentation

Dr Sharon WhitehurstPayne swhitehucsusmedu Outline Professional Growth Common Core State Standards ThinkPairShare Summary Evaluation Personal Professional Growth Have you ever thought about the connection between simple multiplication and algebra ID: 272416

mathematical ways students mathematics ways mathematical mathematics students number algebra share standards understanding student understand core concept rule teach

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Slide1

Eclectic Topics for Primary Math Teachers

Slide2

Dr. Sharon

Whitehurst-Payne

swhitehu@csusm.eduSlide3

Outline

Professional Growth

Common Core State Standards

Think-Pair-Share

Summary

EvaluationSlide4

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.Slide5

Example

35

x 17Slide6

Example

35

x 17

(30 + 5)

X (10 + 7)

7x5 35

7x30 210

10x5 50

10x30 300

595Slide7

Alternative Way

BTW, what is a “quick and dirty” way to multiply this if you were doing simple multiplication?

35 x 20 = 700

35 x 3 = 105

700 – 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.Slide8

Another Example

241

x13Slide9

Another Example

241

x13

(200+40+1)

X (10+3)

3x1 3

3x40 120

3x200 600

10x1 10

10x40 400

10x200 2000

3 1 3 3Slide10

Algebra Example

(x+3) (x+9)Slide11

Algebra Example

(x+3) (x+9)

X+3

X+9

9 times 3 27

9 times x 9x

X times 3 3x

X times X

x

squared

X squared +12x+27

It’s the same process.Slide12

Another Algebra Example

(2y+3) (y+5)Slide13

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+15Slide14

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. Slide15

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, 2009Slide16

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.Slide17

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. Slide18

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.

2 + 3 + 2(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. Slide19

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.Slide20

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.Slide21

Learning Opportunity Enhancements

Remember to find ways to emphasize the big picture.

Allow students the opportunity to explore (THINK, TALK, DISCUSS, INTERACT) concepts. Slide22

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. Slide23

Evaluation

Go on-line and evaluate the course.

www.pollev.com

/gsdmc

Session Evaluation Code: 31362Slide24

Thank you

Thank you and

best wishes

on success for your students.