Prime Factors

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly.

Define: prime number, prime factor, integer

Read this lesson on prime factorization.

Do pages 14-18 in Math Makes Sense 8.

Mental Math and Problem Solving

Mental math is when you apply known math rules and facts in an undocumented way. People think of mental math as kids doing calculations in their head. How does this relate to problem solving? Well, what is:

1+1=2 

It is a problem that equates two quantities: "2" and "1+1".

In fact it is an equation that expresses a whole number in two different ways.

Because you can count and you possess intuitive number sense and you can understand the + sign you know that one plus one equals two.  Since you know one plus one equals two without using a calculator or a pencil you know it because of ...'mental math'.  Well what about:

6+16+26=48

6x8=48

6+6+6+4+26=48

6+16+10+10+6=48

6+6+6+4+6+4+6+4+6=48

6+6+6+6+6+4+4+4=48

6+6+6+6+6+12=48

6+6+6+6+6+6+6=48

2x3x2x2x2=48

3x2⁴=48

Over time, you're going to know that the prime factors of 48 are 3 and 2. You're going to know that the square root of 48 is not a whole number. Your new knowledge will be 'mental math'. 

You are going to be asked to 'justify'' your problem solving strategies. That usually means spelling out the mental math you used to find answers. Therefore 'mental math' often becomes personal knowledge that must be proven (in writing) every time you use it.  It must be acknowledged that personal knowledge is always subject to rounding errors: you're unique therefore your understanding of any fact may also be unique. Is your personal knowledge 'good unique' or 'bad unique'? That's what your teachers and colleagues want to know.

I'd like you to review these very elementary 'mental math' facts. Do you know them all? I bet you do!

Next, read page 11 in Math Makes Sense 8.

Comparing and Ordering Integers

Math Makes Sense 8, All Keywords

UNIT 1

expanded form

standard form

prime factorization

scientific notation

inverse operation

unit tiles

zero pair

variable tile

UNIT 2

equivalent ratios

unit rate

proportion

similar figures

discount

sales tax

commission

simple interest

principal

amount

UNIT 3

isometric diagram

pitorial diagram

triangular prism

surface area

volume

UNIT 4

reciprocals

terminating decimal

repeating decimal

UNIT 5

population

census

sample

Census at School

inference

histogram

UNIT 6

diameter

radius

circumference

irrational number

cylinder

volume

UNIT 7

complementary angles

complement

supplementary angles

supplement

opposite angles

perpendicular

transversal

alternate angles

corresponding angles

interior angles

bisect

bisector

perpendicular bisector

angle bisector

circumcentre

circumcircle

UNIT 8

square number

perfect square

square root

irrational number

leg

hypotenuse

Pythagorean Theorem

Pythagorean triple

UNIT 9

positive integer

negative integer

opposite integers

zero pair

rational number

coordinate grid

quandrants 

ordered pair

x-axis

y-axis

origin

UNIT 10

algebra

distributive property

expand

UNIT 11

experimental probability

relative frequency

theoretical probability

simulation

odds

ALPHABETICAL LIST

algebra

alternate angles

amount

angle bisector

bisect

bisector

census

Census at School

circumcentre

circumcircle

circumference

commission

complement

complementary angles

coordinate grid

corresponding angles

cylinder

diameter

discount

distributive property

equivalent ratios

expand

expanded form

experimental probability

histogram

hypotenuse

inference

interior angles

inverse operation

irrational number

irrational number

isometric diagram

leg

negative integer

odds

opposite angles

opposite integers

ordered pair

origin

perfect square

perpendicular

perpendicular bisector

pitorial diagram

population

positive integer

prime factorization

principal

proportion

Pythagorean Theorem

Pythagorean triple

quandrants

radius

rational number

reciprocals

relative frequency

repeating decimal

sales tax

sample

scientific notation

similar figures

simple interest

simulation

square number

square root

standard form

supplement

supplementary angles

surface area

terminating decimal

theoretical probability

transversal

triangular prism

unit rate

unit tiles

variable tile

volume

volume

x-axis

y-axis

zero pair

zero pair

Scientific Notation

Pre-requisite: EXPONENTS

Read this explanation.

Do this lesson and quiz and watch the video below.