chapter 1 survey of mathmccarronsite.net/m2374-ch3slides.pdf · proportion arithmetic standard...
TRANSCRIPT
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.