Week One:
Polya's four steps to problem solving
1.) Understand the problem
2.) Devise a plan
3.) Carry out the plan
Look back (reflect)
Ask youeself what problem solving strategy are you going to use?
Guess and use check/trial and error
Draw a picture or a diagram
Act it out
Make the problem simpler
Look for the pattern
Work backwards
Make an organized list
When teaching make sure students
1.) Understand
2.) Plan
3.) Implement
Look back to check if results are reasonable
MTE 280
Whole Number Operations
Addition
Right to Left
American Standard
Partial Sums
Partial Sums with Place Value
Left to Right
Left to Right Algorithom
Expanded Notation
Place Value Explicit
Lattice
Meaning (Put together/Join)
1.) Identity Property: a+0=a
2.) Commutative Property: a+b=b+a
Associative Property: (a+b)+c=a+(b+c)
Week Three:
Week Five:
Subtraction
Right to Left
American Standard
European Mexican
Left to Right
Reverse Indian
Left to Right Algorithm
Expanded Notation
Intager Subtraction
Meanings
1.) Take Away 5-2=3
2.) Comparison
3.) Missing Add End
7-3=4
4 is the Difference
3 is the subtrahend
7 is the Minuend
Week 5:
Multiplication
Meaning: Repeated Addition
(3 x z) is 3 groups of z
Week Four:
Division
Week Four:
Week Two:
Numeration Systems
-Base-10 System
-The Value of the number depends on the place
-The numbers get bigger by 10 times (1/10) x (1/10)= (1/100)
Numbers to the right of the decimal are part of the unit
Expanded Notation
Week One:
Make sure students understand the problem by having them explain the problem in their own words or show how to complete it.
Make sure students:
1.) Understand
2.) Plan
3.) Implement
4.) Look back reasonably
Divisibility Rules
*Sum of Digits
-By 3: Sum of digits is divided by 3
*Ending
-By 2: 0,2,4,6,8
-By 5: 0,5
-By 10: 0
*Last Digits
-By 4: Last two digits are divided by 4
Week Six
Number Theory
-Types of Numbers
-Divisibility
-Factors-multiples>Fraction work
Prime numbers 1-60 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
Week Six
Prime Factorization
The "Fingerprint"or "DNA" of every composite number: always the same factoraztion tree.
Week Six
Week Seven
GCF (Greatest Common Factor) LCM (Least Common Multiple)
Week Eight
Fractions
Meanings
1.) Part-whole
3 divided by 4=3/4
Ratio
Models
1.) Surface Area
2.) Length
3.) Sets (groups of things)
Week Nine
Addition and Subtraction (common denominators)
Week Nine
Fraction word problems with models
Problem examples
Week Ten
Problem Solving with Fractions
Problem examples