Elementary Ed. Math

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Week 7

Vocabulary:

• Square #s: Have an odd number of factors. 1, 4,9,16, and 25

• Composite #s: Numbers with more than two factors

A number can be both composite AND square

• Prime #s: Only have two factors. 1 and itself.

1 is not Prime or Composite

• Factorization: A method of breaking numbers into factors

• Prime Factorization: Break a number into numbers that are only prime numbers

Methods to find Greatest Common Factor and Least Common Multiple :

1.) Intersection of Sets

2.) Prime Factorization Method

3.) Venn Diagram Method

GCF and LCM

Factorization and Prime Factorization

Prime and Composite Numbers

Week 8

Used GCF and LCM to solve Word Problems

GCF and LCM Practice

Week 9

Vocabulary:

• Integer- Positive and Negative whole numbers including 0

• Origin- Beginning or Starting Point

• Absolute Value-Distance of the number from the origin

• Opposites- The number that is the same distance from the origin

Integer Addition Methods:

• Number Line Method- Walking forward (Positives) and Walking backwards (Negatives)

• Show using Chips

Methods for Adding Integers

Adding Integers

Week 10

Model for Multiplying Integers:

• Chip Model

Dividing Integers:

• If the dividend and the divisor have same signs then their quotient is positive
• If the dividend and the divisor have different signs then their quotient is negative

Fraction Parts:

numerator- how many of the whole we are talking about

denominator- how many pieces in the whole

Proper Fraction:

The numerator is smaller then the denominator

Improper Fraction:

The numerator is larger than the denominator

Equivalent Fractions:

Represent the same value, but use different numbers/size pieces

Fractions

Dividing Integers

Methods for Multiplying Integers

Multiplying Integers

Week 11

Comparing Fractions:

Same Denominator/ Same Size Pieces-

• If the denominator are the same, compare the numerators, which one has more of the same size pieces?

Same Numerator/Same Number of Pieces-

• If the fraction share the same numerator, compare the denominators:

-The bigger the denominator, the smaller the pieces

-The smaller the denominator, the bigger the pieces

In class practice drawing models for mixed numbers and improper fractions.

Fractions using Models

Comparing Fractions

Week 12

Sums and Differences of fractions using fraction bars as models.

IN CLASS PRACTICE

Week 13

Fraction Bars Practice with Irregular Fractions

Practice with drawing representations and equations to solve word problems

Writing equations

Drawing Representations

Fraction Bars Practice

Week 6

Vocabulary:

• Factor: Number being multiplied

• Multiple: The result you get from multiplying a number by a whole number (integer)

• Divisor: The number being used to divide, or a number that divides

• Divisible: Can be divided by a number without a remainder

Divisibility Rules:

2: A number is divisible by 2 if the units( ones) digit is even

EX: 254--------> 4 is even

3: A number is divisible by 3 if the sun of the digits is divisible by

EX: 2,571--------> 2+5+7+1=15 --------> 15 is divisible by 3

6: A number is divisible by 6 if the number is divisible by both 2 and 3

9: A number is divisible by 9 if the sum of the digits is divisible by 9.

EX: 720,936--------> 7+2+0+9+3+6=27--------> 27/9=3

5:A number is divisible by 5 if the units (ones) digit is divisible by 5

EX:2505--------> 5 is divisible by 5

10: A number is divisible by 10 if the units(ones) digit is divisible by 10

EX: 67830--------> 0/10=0

4: A number is divisible by 4 if the last two digits is a number that is divisible by 4.

EX: 344--------> 44/4=11

8: A number is divisible by 8 if the last 3 digits is a number that is divisible by 8.

EX: 2568--------> 568/8=71

11: A number is divisible by 11 if the sum of the odd power of 10 digits minus the sum of the even powers of 10 digits is divisible by 11

EX: 9482--------> (8+9) - (2+4)= 6-17=-11--------> -11/11=-1

7:No rule, Try division

Divisibility Rules

Vocabulary

Week 5

Algorithms for division

• Standard Algorithm: Divide, Multiply, Subtract, Bring Down.

• Partial Quotient: Can the divisor be put in the dividend 10 times? Work your way down the problem.

Start of Exam 2 Content:

Exponent Rules:

Power of a Power Rule:

• For every whole number a, and natural numbers m and n

Same Exponents:

• For whole numbers a and b, and natural numbers n

Order of Operations:

Parenthesis ( ), Brackets [ ], Braces { }

Exponents

Multiplication

Division

Addition

Subtraction

How would you explain odd numbers and even numbers to students?

• Match pairs in boxes-odd if there are any leftovers
• Share into two equal groups
• Making partners (with students)

Order of Operations

Exponent Rules

Start of Exam 2 Content

Division Algorithms

Week 4

Algorithms of Multiplication

-Standard Algorithm: Multiplying in Parts

-Expanded Algorithm: When doing multi-digit multiplication, separate the tens and ones and multiply.

EX: 35 X 15 --------------> 30 + 5

x10 + 5

525

-Partial Products: Multiply the digits in the ones place first and bring the answer down. Now multiply the digit in the ones place with the digit in the tens place and bring it below as well. Add the results of both together.

23 X 4 ----------------> 23

x 4

12

+80

92

-Division:

• Dividend: The amount you have that is being shared, divided up

• Divisor- How what you "have" is being shared, broken up

• Quotient- The result of division

Properties of Division that DO NOT hold:

• Associative Property
• Commutative Property
• Distributive Property

Division

Multiplication Algorithms

Week 3

-Subtraction: Taking away # from the Sum

• Minuend: The part you start with

• Subtrahend: The part being taken away

• Difference: The result of subtraction

-Take Away Model: Show using Chips/Coins/ Cubes

-Number Line Model

-Comparison Model:

"Sara is 3 feet tall. Her older brother is 5 feet tall. How much taller is Sara's older brother?"

-Missing Addend Model:

6 = 4 + ______

6 - 4 = 2

Properties of Subtraction that DO HOLD

-Closure Property:

Whole # + Whole # = Unique Whole #

-Identity Property:

5 - 0 = 5 = 0 + 5

Properties of Subtraction

Take-Away, Number Line, and Comparison Model

Subtraction

Week 2

-Base 10 Binary System/ Powers of 10

-Base 2 and Base 5 Binary Systems

-Addition:

• Addend- The numbers being added

• Sum- The result of being added

• Counting on Strategy- The use of the Number line

• Closure Property, Commutative Property, Associative Property, and Identity Property of Addition

Basics of Addition

Base 2 and 5 Binary Systems

Base 10 Binary System

Week 1

-Reviewed the Syllabus and designed our ideal classroom.

-Created a poster analyzing Standards for Mathematical Practice "Make Sense of Problems & Persevere In Solving Them".

-Discussion of the Number System and Roman Numerals

Roman Numerals

Standards for Mathematical Practice

Syllabus Review

Week 14

Continued practice drawing fractions and models to solve.

Use Arrays to show Multiplication

Arrays for multiplication