Chapter 2Arithmetic Strategies & Area

Ch. 2----------

2.1.1

Dot Plot- -A graphical display of data using dots-Similar to a bar graph

Ch. 2----------

2.1.2

Stem & Leaf Plots- A way of representing data by splitting numbers

-The leaf is typically the last digit of the data number-The stem is typically the ‘other’ numbers-The stem values are listed going down, & the leaf values next

to them-The stem groups the scores & the leaf indicates a specific score

within that group----- ----- ----- ----- ----- ----- ----- ----- -----

Click here for a 3 minute video explaining Stem & Leaf Plots!

Stem & Leaf Plots- A way of representing data by splitting numbers

----- ----- ----- ----- ----- ----- ----- ----- -----

Histogram- A way of representing data similar to a bar graph, but the data is grouped into ranges (Ex.- 40-49) & then plotted as bars ----- ----- ----- ----- ----- ----- ----- ----- ----- 2016 American League Home Run Data

Number Of HR’s

Numbers Of Players Reaching Each # of HR’s

These ranges are also referred to as ‘bins’

…So what’s the difference between a bar graph & a histogram?

----- ----- ----- ----- ----- ----- ----- ----- -----

The main difference is that histograms show RANGES of data & bar graphs show a specific category

Be Sure You Know!:

*Venn Diagram- A visual way to compare & contrast 2 ‘things’ using 2 circles

Ch. 2----------

2.2.1

Be Sure You Know!:

*Triangle- A 3-sided polygon (A polygon is a flat shape w/ straight sides)

-The angles of a triangle always add up to 180 degrees

A 3-sided polygon (a flat shape with straight sides).

Use this link to create different types of triangles & to see how the angles always add up to 180 deg.!

A 3-sided polygon (a flat shape with straight sides).

Be Sure You Know!:

*Hexagon- A 6-sided polygon

A 3-sided polygon (a flat shape with straight sides).

Look at this! You can make a hexagon with a series of triangles!

Be Sure You Know!:

*Rhombus- A flat shape with 4 equal straight sides

-Opposite sides are parallel & opposite angles are =

A 3-sided polygon (a flat shape with straight sides).

Take Note! Squares fit the definition of a rhombus!

Be Sure You Know!:*Trapezoid-

-A 4-sided flat shape w/ straight sides & a pair of opposite sides that are parallel

A 3-sided polygon (a flat shape with straight sides).

Fun Link! Use this link to create different types of trapezoids!

http://www.mathsisfun.com/definitions/trapezoid.html

Ch. 2----------

2.2.2

Square Units- -A unit of measure-Can be of different sizes (centimeters, inches, feet, yards, miles, etc.) & named for its length (linear measure)

Example 1 Example 2

Plane Figure- Shapes that be drawn on a flat surface called a plane. A plane is like an endless piece of paper!

Ch. 2----------

2.2.3

Base 10 Blocks- Blocks that help us learn math concepts that typically come in ‘1’s, 10’s, 100’s, & 1000’s’.

What number would be represented by the shown blocks?

364

Ch. 2----------

2.3.1

Product- The result of multiplication

Ch. 2----------

2.3.2

Generic Rectangles- - Refers to a model which helps us multiply ‘complicated’ numbers by helping us calculate the area of a rectangle that was cut into sections.

Click here for a 3 minute video explaining multiplication using generic rectangles

Ch. 2----------

2.3.3

-Common Factor- When you find all of the factors of 2 or more numbers, & then find some factors that are the same

(Remember, factors are numbers you multiply together to get another number)

----- ----- ----- ----- ----- ----- ----- ----- -----Greatest Common Factor (GCF)- The highest number that divides exactly into 2 or more numbers

-Look at these numbers :

----- ----- ----- ----- ----- ----- ----- ----- -----The greatest common factor would be:

12 12

1 2

6

3

4

30 30

1 2

15

3

10

65

6 Here is a link to an online 'calculator' to help you

find the GCF of 2 or 3 numbers!

Ch. 2----------

2.3.4

Distributive Property- States that the multiplier of a sum or difference can be ‘distributed to multiply each term

----- ----- ----- ----- ----- ----- ----- ----- -----

Try it with your own set of numbers!

a x (b + c) = a x b + a x c

Try it using these #’s!:A=2B=1C=3

2 x (1 + 3) = 2 x 1 + 2 x 3

Here is a 3 minute video to help you better understand the distributive property of multiplication:

Let’s try multiplying 5(26) using a Generic Rectangle & the

Distributive Property

Let’s try multiplying 5(26) using a Generic Rectangle & the

Distributive Property

20 6

5 20*5=100 6*5=30

100 + 30 = 130

26 * 5 = 130a x (b + c) = a x b + a x c

5(26) = 5 x 20 + 5 x 6

Try it using these #’s!:A=5

B=20C=6

130 = 130

Be Sure You Know!:*Rectangle- A Quadrilateral

(Has 4 sides)

-4 right angles

-Opposite sides are equal in length

-2 sides that meet at a right angle are length & width (base & height)

-Area of a rectangle is A=Length * Width

Ch. 1----------

1.1.2

Area- -The space that a 2-dimensional shape covers

The area of this shape can be found by using this formula: Area = Length x Width

Perimeter- The length of the boundary around a shape

Area & Perimeter Rock Video!

----- ----- ----- ----- ----- ----- ----- ----- -----Area- -The space that a shape covers

Ch. 1----------

1.1.3

Place Value- -The number assigned to each place that a digit occupies-Are all powers of 10 in our number system

Video For Place Value Explanation

249.24

You already know & use place values!

Ch. 1----------

1.1.4

Rounding- -Method used to shorten numbers-Involves either increasing or decreasing a number to

the next digit-Makes it easier to do ‘math in our head’-Allows us to get approximate numbers

Do you realize that you use rounding all the time?

Need More Help Understanding Rounding?

This short video explains the very basic of rounding!

This video explains how to round to place values such as 10,000 & even 1,000,000!

Ch. 1----------

1.2.1

Numerical Expression- Combination of numbers & one or more operation symbols that represents a particular number

----- ----- ----- ----- ----- ----- ----- ----- ----- Example- 4 + 20 – 7 represents what number?

17 Example- 6 + 2 (2+1) represents what number?

24

As you write your expressions, keep in mind Order Of Operations rules!

Please

Excuse

My

Dear

Aunt

Sally

Need extra help understanding Numerical Expressions & Order Of Operations?

----- ----- ----- ----- ----- ----- ----- ----- -----

This video explains Numerical Expressions

This video explains the basics of Order Of Operations rules!

Conjecture- A statement that appears to be true-An educated guess…

----- ----- ----- ----- ----- ----- ----- ----- -----Justify- Give reasons why your conjecture makes sense

Line Segment- A piece of a straight line

----- ----- ----- ----- ----- ----- ----- ----- -----

Examples

ABBCACADBDEtc.

Composite Number- A number w/ more than 2 factors-A number that can be arranged into more than 1 rectangular array

----- ----- ----- ----- ----- ----- ----- ----- -----Prime Number- A number that can only form 1 rectangular array / Can only be into 1 & itself

Even Numbers- A number that can be evenly divided by 2

----- ----- ----- ----- ----- ----- ----- ----- -----Odd Number- A number that leaves a remainder of 1 when divided by 2

Ch. 1----------

1.2.2

Remembering ‘Greater Than’ & ‘Less Than’ Symbols

----- ----- ----- ----- ----- ----- ----- ----- -----

17

24

24

17

Reviewing Symbols Used To Compare Quantities----- ----- ----- ----- ----- ----- ----- ----- -----

Greater Than

Less Than

Equal To

Less Than Or Equal To

Greater Than Or Equal To

Ch. 1----------

1.2.3

Rectangular Array- Visual model for showing a whole number using rows & columns

----- ----- ----- ----- ----- ----- ----- ----- -----

Rows

Columns Helpful for multiplication!

6

3

6

3

*

=18

----- ----- ----- ----- ----- ----- ----- ----- -----Remainder- The amount ‘left over’ after dividing 2 numbers that do not divide evenly.

----- ----- ----- ----- ----- ----- ----- ----- -----Remainder- The amount ‘left over’ after dividing 2 numbers that do not divide evenly.

7

3 R 1

Definitions

Short Clip to Explain Natural Numbers & Whole Numbers!

Natural Numbers-

Counting Numbers-

Whole Numbers-

1, 2, 3, 4, 5, 6, etc.

….just another term for natural numbers!

Natural numbers and 0

Ch. 1----------

1.2.4

Definitions Factor-

A factor is a number that divides evenly into another w/o a remainder

12 12

1 2

6

3

4

Definitions Prime Number-

A number w/ 2 factors (1 & itself)-Cannot be divided evenly by any other numbers

Definitions

Composite Number-

A number w/ more than 2 factors

Video explanation of prime & composite

numbers

Definitions Factors-

Product-

Numbers that create new numbers when they are multiplied A number that results from multiplication

Factors

Definitions Factor Pairs-

A pair of numbers that multiply to give a particular product

32 32

1 2

16

4

8

Definitions Frequency-

The number of times that an item appears in a set of data How often something happens (Usually within a period of time)

This link helps you understand Frequency by examining heartbeats!

Prime Factor-

A factor that is also a prime number

What is different about the numbers

that are circled compared to those

in squares?

….so the prime factors of 30 are 5, 2, & 3

Prime Factorization-

Writing a number as a product of only prime numbers

This short video gives more explanation on finding the prime

factorization of a number!