Therefore I tell you, do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes? 26 Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them. Are you not much more valuable than they?

Matthew 6:25-26

Warm Up

All Texans wear boots. No one who

wears boots is a wimp.

Some doctors have nice handwriting.

All teachers have nice handwriting.

Today

Homework Stumpers

Shipwreck

Where we are going

Positional number system

Quiz

Movie Next Week

Ben Carson

Pediatric Neurosurgeon

Speaker at National Prayer Breakfast

» 1997

» 2013*

Presidential Medal of Freedom 2008

*comments made him political figure

Homework Stumpers Deconstruction

The Year: 1500 AD

The Yucatan Positional Number System

Each system has a special number called the

“base”

Each position has a place value, determined

by powers of the base

Each digit in a written number has a value,

the digit times the place value.

value = digit place value

The End of Mayan Numbers

Finish Mayan number

worksheet for next time.

Reflection

Humble yourselves, therefore, under God's mighty hand, that he may lift you up in due time.

1 Peter 5:6

Reflection

When pride comes, then comes disgrace,

but with humility comes wisdom.

Proverbs 11:2

Warm up

Convert Mayan number to base 10:

Today

Warm up

Stumpers

Mathematical Manipulatives

Concrete models for numbers

Number words

Changing Bases

Don’t Forget

Pick up today

» Mayan Practice

» Assignment Sheet

Turn in today

» HW 2.3C

» Euler Worksheet

Homework Stumpers “Flipping”

Many of the Exercises from the book for

chapter 3 will be more appropriate as in

class work rather than homework.

Please have at least one person per

table bring the book to class.

Homework will include worksheets.

Review: Positional Number System

Each system has a special number called the “base”

Each position has a place value, determined by powers of the base

Each digit in a written number has a value, the digit times the place value. value = digit place value

Example: 5327

Mathematical Manipulatives

Physical models for abstract concepts

Many, many manipulatives on the

market

At a particular grade level, focus on a

few tools

Abstract Concrete Semi Concrete

Base 10 Blocks

Units (1 cubic cm)

10 Units = 1 Long (aka “rod”)

10 Longs = 1 Flat (aka “tile”)

10 Flats = 1 Block

Another Manipulative

Read about “bundles” on page 133.

Three Way Connection

Physical

Model

Numerical

Representation

Words

Make the Connection

Physical

Model

3527

Words

Write in expanded form

1. 36,713

2. 5098

3. 210,521

4. 2,131,101

Write in expanded form

1. 211three

2. 25seven

3. 213five

4. 1101two

Number words

Commas appear in wording where commas appear in numerical representation Five thousand, two hundred twenty-one

Hyphen is used in number words for twenty-one to ninety-nine

“and” is only used for the decimal point or other fractions (follow your text book)

Page 132

Spelling!

TEKS & Place Value Expansions

Grade 3: Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:

(A) compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate;

Worksheet

Quiz 7

Euler Circles

Mayan numbers Base Ten

Base Ten Mayan

Mayan Addition

Numbers Words

Words Numbers

Write in words

1. 36,713

2. 5098

3. 210,521

4. 2,131,101

5. 8,740,231,764

Reflection

What causes fights and quarrels among you? Don't they come from your desires that battle within you? You want something but don't get it. You kill and covet, but you cannot have what you want. You quarrel and fight. You do not have, because you do not ask God. When you ask, you do not receive, because you ask with wrong motives, that you may spend what you get on your pleasures.

James 4:1-3

Warm up

Expanded form:

2134five

Equal to what number base 10?

Warm up

Write in base 10:

5 blocks, 7 flats, 3 units

Write the number in words: 764,328,170,915

Warm up

Convert Mayan number to base 10:

Today

Homework Stumpers

Change of base

Quiz

Standard Addition Algorithm

Trading Up

Standard Subtraction Algorithm

Trading Down

Properties of Addition

Models for (introducing) subtraction

Don’t Forget

Pick up today

» Wksht 3.2

Turn in today

» Place Value wksht

Exam 2

» Postponed to 11/5

Homework Stumpers Remember: expanded form

1. 324five

2. 1011two

Convert Base 10 to Base 5

23

57

119

348

The End of Section 3.1

Finish homework from

section 3.1 and skim

section 3.2 for next time.

Numeration Systems

These systems are testable:

» Base Ten

» Base Five

» Mayan

Other systems will appear in lecture and

homework, not on quizzes or exams.

Kindergarten Counting

Forward counting prepares children

for…?

Backward counting prepares children

for…?

Skip counting prepares children for …?

Algorithm

What does it mean?

What is a “standard algorithm”?

Texas standards vs. Common Core

Standard Base 10 Addition

1578 + 2715

Now model with base ten blocks

Addition

134five + 232five

Now model with base five blocks

Game

Trading up

Standard Base 10 Subtraction

3575 1728

Now model with base five blocks

Addition

231five 132five

Now model with base five blocks

Game

Trading down

The End of Section 3.2

Finish homework from

section 3.2 and skim

section 3.3 for next time.

Properties of Addition of Whole Numbers

Closure property

Identity property

Commutative property

Associative property

Closure Property

The sum of two whole numbers is a whole

number.

5335

:Example

addition) (of

abba

Commutative Property

235235

:Example

addition) (of

cbacba

Associative Property

505

:Example

0addition) (of

aa

Identity Property

3535 6.

13013 5.

327273 4.

3232.3

202.2

5665.1

yxyx

xx

Practice

Identify the property (or properties) being used.

In Class Exercises

P. 159, #15-16

Standard Base 10 Addition

1578 + 2715

Worksheet

Reflection

Carry each other’s burdens, and in this way you will fulfill the law of Christ.

Galatians 6:2

Today

Homework Stumpers

Properties of Addition

Standard Addition Algorithm

Models for (introducing) subtraction

Standard Subtraction Algorithm

Quiz

Don’t Forget

Pick up today

» Exam 2 study questions

Turn in today

» HW 3.1

Mayan Math

» Dr. Kathryn Brown

» 11/18 (Mon) 6-7 PM

» BSH 129

Good worksheet?

Self-correcting

Cognitive Load

» It takes substantial practice to learn a schema

» Why is practice boring?

» How do you make practice interesting yet not

distracting from the goal skill?

A Word on Standard Algorithms

P. 144 Line 6 “Since calculators…”

P. 145 top (NCTM)

I have counted 8 “standard” algorithms for multi-digit multiplication in the Common Core p. 167)

Gender bias

A teacher who knows alternate ways of doing knows alternate ways of explaining

Reflection

I have much more to say to you, more

than you can now bear.

John 16:12

Today

Standard Subtraction Algorithm

Mental Models for Subtraction

Standard Multiplication Algorithm

Learning Multiplication

Mental Models for

Concrete activities for

Symbolic (Semi-concrete) activities

Don’t Forget

Pick up today

» Quiz

» Essay

» HW 3.1

Turn in today

»

Exam 2

Standard Base 10 Subtraction

3575 1728

Conceptual Subtraction

(Mental Models: Ways to introduce

subtraction, descriptions you can return

to when a student struggles)

Take away

Comparison

Missing addend

Worksheet In Class Exercises

The “Old Faithful” of Semi-concrete

(symbolic) representations:

P. 158-159, #9, 10, 11, 12

In Class Exercises

P. 159, #17, 18

The End of Section 3.2

Finish worksheet 3.2

and read section 3.2

for next time.

Standard Base 10 Multiplication

548 36

Conceptual Multiplication

(Mental Models: Ways to introduce

multiplication)

Repeated Addition

Area Model

Repeated Addition

At the Bear Volleyball tournament, there were

four teams of six bears each. How many

bears played in the tournament?

Area Model

This can be done with concrete objects

(base 10 blocks), but it is clunky & students

don’t necessarily connect the activity to

multiplication. (See p. 166-167 in book)

Grid paper is symbolic and works better.

Example: 412

Worksheet

Which are using

repeated addition

and which are

using area?

The End of Section 3.3

Finish worksheet 3.3

and read section 3.3

for next time.

Where Are We?

K 1st 2nd 3rd 4th 5th 6th

Count Add Subtract Multiply Divide &

Fractions

Decimals Ratio/

Proportion

Arithmetic Standard Milestones

Other Curriculum Threads

Geometry

Data, Probability, and Statistics

Money and Finance

Terminology

divisor dividend quotient

11555

Equivalent To

11555

11555

Terminology

9728

divisor

dividend

quotient

Equivalent To

9728

divisor

dividend

quotient

7298

Practice:

7284

Write 2 other

ways and label

Terminology

8425

divisor

dividend

quotient

2Rremainder

Equivalent To

8425

2R

42285

Practice

910911

10R

Scaffolding

What is it?

Long Division

Estimate Products to find the largest p such

that p divisor < dividend

Multiply p divisor

Subtract

Repeat

Stop when remainder < divisor

Cognitive Load Practice:

142 455

Practice:

423 726

Practice:

1687 2305

Practice:

275 466

Practice:

914 1238

Practice:

4012 8119

Practice:

53123 81135

There is no substitute for Conceptual Division

(Mental Models: Ways to introduce

division)

Inverse (Undoing) Multiplication

Sharing (partitive) concept

Measurement (repeated subtraction)

concept

24 3

Inverse (Undoing) Multiplication

Sharing (partitive) concept

Measurement (repeated subtraction)

concept

Long Division is not optional

2325632 2342 xxxxxx

The End of Section 3.4

Finish worksheet 3.4

and read section 3.4

for next time.