Math 110 - Kennedy (Quiz 2)

What are NCTM Process Standards

1. Problem Solving

2. Reasoning and Prof

3. Communication

4. Connections

5. Representation

What is the NCTM Standard Problem Solving?

Using math strategies to find a solution to a problem, especially unfamiliar problems

ex. having students figure out a problem their self before teaching them how to solve it

What is the NCTM Standard Reasoning and Prof?

Explaining why an answer is correct and making conjectures

ex. writing a paragraph on how you solved the problem

What is the NCTM Standard Communication?

Sharing mathematical thinking with others

ex. talking a a partner on how you solved a problem

What is the NCTM Standard Connections?

Relating mathematical concepts to each other and to real-world situations

ex. using fractions to divide a pizza

What is the NCTM Standard Representation?

Showing mathematical ideas in different ways

ex. using a number line, fractions, decimals

What is Place Value?

the value a digit has depending on its position within a number

What is the place value of 4,852?

Digit	Place	Value
4	Thousands	4,000
5	Hundreds	500
8	Tens	80
2	Ones	2

What is Expanded Notation?

Taking a number an expanding it using addition

Write 4,582 in expanded notation.

1. 4,000 + 500 + 80 + 2

2. 4(1,000) + 5(100) + 8(10) + 2(1)

3. four thousand + five hundred + eighty + two

4. (4×10³) + (5×10²) + (8×10^1) + 2

What are the early numeration additive systems?

1. Egyptian

2. Babylonian - had no zero

What are the early numeration positional systems?

1. Roman Numerals - no zero

2. Mayan - 1st to develop symbol for zero

Convert 23 to Base 2

Answer 10111two

Convert 39 to base two

Answer 100111two

Convert 11011two to base 10

Answer: 27

Convert 1010101two to base 10

Answer: 85

Write number in consecutive order staring at 1

1, 2, 3, 4, 5…

Factor

A whole number that divides another number evenly

ex. 3 is a factor of 12

Multiple

A result of multiplying a number by an integer

ex. 12 is a multiple of 3

Divisible

Divides evenly with no remainder

ex. 12 is divisible by 4

Prime

A whole number greater than 1 with exactly two positive factors

ex. 7, 13

Composite

A whole number greater than 1 with more than two positive factors

ex. 4, 6

What does a|b mean

a divides b evenly

ex. 3|12

What is a shortcut to finding all the factors of a number?

square rooting the number and only testing whole numbers up to that square root

ex. For 24, √(24) = 4.9 so test 1, 2, 3, and 4.

Divisibility Test

Number	Rule	Example
2	Last digit is even.	148
3	Sum of digits is divisible by 3.	123: (1+2+3=6) 6/3 = 2
4	The last two digits are divisible by 4.	316: 16 is divisible by 4
5	Last digit is 0 or 5.	235
6 8	Divisible by both 2 and 3. The last 3 digits are divisible by 3	114 913,032 32/8 = 4
9	Sum of digits is divisible by 9.	729: (7+2+9=18) 18/9 = 2
10	The last digit is 0.	450

Sieve of Eratosthenes

A method that finds the prime numbers in a range of whole numbers

*25 PRIME numbers under 100*

Prime Factorization

expresses a number as a product of primes

ex. 36 = 2×2×3×3

Use a factor tree to find the prime factors of 72

Answer: 72 = 2×2×2×3×3

Use a factor tree to simplify 24/40

Answer: 3/5

24 = 2×2×2×3

40 = 2×2×2×5

Cross off prime numbers that are in both the numerator and the denominator to get the answer

What is GCF (Greatest Common Factor)?

The largest factor shared by two or more numbers

What is the GCF of (36,45)

Answer: 9

What is the GCF of (12,18)?

Answer: 6

What is LCM (Least Common Multiple)?

The smallest positive multiple shared by two or more numbers

What is the LCM of (6,10)?

Answer: 30

What is the LCM of (120,180)?

ex. 360

What is a fraction?

A ratio of two numbers; the numerator and denominator

Is a fraction one number? True or False

True

What are the different ways to show fractions?

Paper folding, fraction circles, fraction strips, number line

Equivalent Fractions

fractions that have the same value, they are equal

What word is banned when talking about fractions?

Reduced!!!'

Say simplify instead