Chapter 2 Arithmetic Strategies & Area

Ch. 2 ---------- 2.1.1

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

Ch. 2 ---------- 2.1.2

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

2016 American League Home Run Data 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 These ranges are also referred to as ‘bins’ Numbers Of Players Reaching Each # of HR’s

…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 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

What number would be represented by the shown blocks? Base 10 Blocks- Blocks that help us learn math concepts that typically come in ‘1’s, 10’s, 100’s, & 1000’s’. 364 What number would be represented by the shown blocks?

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 : 12 30 1 12 1 30 2 6 2 15 3 4 3 10 5 6 ----- ----- ----- ----- ----- ----- ----- ----- ----- The greatest common factor would be: 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

Try it with your own set of numbers! Distributive Property- States that the multiplier of a sum or difference can be ‘distributed to multiply each term ----- ----- ----- ----- ----- ----- ----- ----- ----- a x (b + c) = a x b + a x c 2 x (1 + 3) = 2 x 1 + 2 x 3 Try it using these #’s!: A=2 B=1 C=3 Try it with your own set of numbers! 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 20 5 20*5=100 6*5=30 Try it using these #’s!: A=5 B=20 C=6 100 + 30 = 130 26 * 5 = 130 a x (b + c) = a x b + a x c 5(26) = 5 x 20 + 5 x 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- -The space that a shape covers Area & Perimeter Rock Video!

Ch. 1 ---------- 1.1.3

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

You already know & use place values! 249.24

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? http://www.youtube.com/watch?v=YMcmSlO27pw 24

As you write your expressions, keep in mind Order Of Operations rules! Please Excuse My Dear Aunt Sally

This video explains Numerical Expressions 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 AB BC AC AD BD Etc.

----- ----- ----- ----- ----- ----- ----- ----- ----- 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 ----- ----- ----- ----- ----- ----- ----- ----- ----- 24 17 24 17

Reviewing Symbols Used To Compare Quantities ----- ----- ----- ----- ----- ----- ----- ----- ----- Greater Than Greater Than Or Equal To Less Than Less Than Or Equal To Equal To 17

Ch. 1 ---------- 1.2.3

Helpful for multiplication! Rectangular Array- Visual model for showing a whole number using rows & columns ----- ----- ----- ----- ----- ----- ----- ----- ----- 6 Columns Helpful for multiplication! 3 Rows 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. 3 R 1 7

Short Clip to Explain Natural Numbers & Whole Numbers! Definitions Natural Numbers- 1, 2, 3, 4, 5, 6, etc. ….just another term for natural numbers! Counting Numbers- Whole Numbers- Natural numbers and 0 Short Clip to Explain Natural Numbers & Whole Numbers!

Ch. 1 ---------- 1.2.4

Definitions Factor- A factor is a number that divides evenly into another w/o a remainder 12 1 12 2 6 3 4

Short Clip to Explain Natural Numbers & Whole Numbers! Definitions A number w/ 2 factors (1 & itself) -Cannot be divided evenly by any other numbers Prime Number- Short Clip to Explain Natural Numbers & Whole Numbers!

Definitions Composite Number- A number w/ more than 2 factors Video explanation of prime & composite numbers Short Clip to Explain Natural Numbers & Whole Numbers!

Definitions Factors- Product- Numbers that create new numbers when they are multiplied A number that results from multiplication Product- Factors

Definitions Factor Pairs- A pair of numbers that multiply to give a particular product 32 1 32 2 16 4 8

This link helps you understand Frequency by examining heartbeats! 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!

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