chapter 2 arithmetic strategies & area. ch. 2 ---------- 2.1.1
TRANSCRIPT
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Chapter 2Arithmetic Strategies & Area
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Ch. 2----------
2.1.1
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Dot Plot- -A graphical display of data using dots-Similar to a bar graph
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Ch. 2----------
2.1.2
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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!
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Stem & Leaf Plots- A way of representing data by splitting numbers
----- ----- ----- ----- ----- ----- ----- ----- -----
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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’
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…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
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Be Sure You Know!:
*Venn Diagram- A visual way to compare & contrast 2 ‘things’ using 2 circles
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Ch. 2----------
2.2.1
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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.!
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A 3-sided polygon (a flat shape with straight sides).
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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!
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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!
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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
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Ch. 2----------
2.2.2
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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
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Plane Figure- Shapes that be drawn on a flat surface called a plane. A plane is like an endless piece of paper!
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Ch. 2----------
2.2.3
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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
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Ch. 2----------
2.3.1
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Product- The result of multiplication
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Ch. 2----------
2.3.2
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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
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Ch. 2----------
2.3.3
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-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
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-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!
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Ch. 2----------
2.3.4
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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:
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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
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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
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Ch. 1----------
1.1.2
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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
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Perimeter- The length of the boundary around a shape
Area & Perimeter Rock Video!
----- ----- ----- ----- ----- ----- ----- ----- -----Area- -The space that a shape covers
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Ch. 1----------
1.1.3
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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
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249.24
You already know & use place values!
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Ch. 1----------
1.1.4
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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
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Do you realize that you use rounding all the time?
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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!
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Ch. 1----------
1.2.1
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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
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As you write your expressions, keep in mind Order Of Operations rules!
Please
Excuse
My
Dear
Aunt
Sally
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Need extra help understanding Numerical Expressions & Order Of Operations?
----- ----- ----- ----- ----- ----- ----- ----- -----
This video explains Numerical Expressions
This video explains the basics of Order Of Operations rules!
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Conjecture- A statement that appears to be true-An educated guess…
----- ----- ----- ----- ----- ----- ----- ----- -----Justify- Give reasons why your conjecture makes sense
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Line Segment- A piece of a straight line
----- ----- ----- ----- ----- ----- ----- ----- -----
Examples
ABBCACADBDEtc.
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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
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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
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Ch. 1----------
1.2.2
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Remembering ‘Greater Than’ & ‘Less Than’ Symbols
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17
24
24
17
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Reviewing Symbols Used To Compare Quantities----- ----- ----- ----- ----- ----- ----- ----- -----
Greater Than
Less Than
Equal To
Less Than Or Equal To
Greater Than Or Equal To
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Ch. 1----------
1.2.3
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Rectangular Array- Visual model for showing a whole number using rows & columns
----- ----- ----- ----- ----- ----- ----- ----- -----
Rows
Columns Helpful for multiplication!
6
3
6
3
*
=18
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----- ----- ----- ----- ----- ----- ----- ----- -----Remainder- The amount ‘left over’ after dividing 2 numbers that do not divide evenly.
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----- ----- ----- ----- ----- ----- ----- ----- -----Remainder- The amount ‘left over’ after dividing 2 numbers that do not divide evenly.
7
3 R 1
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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
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Ch. 1----------
1.2.4
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Definitions Factor-
A factor is a number that divides evenly into another w/o a remainder
12 12
1 2
6
3
4
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Definitions Prime Number-
A number w/ 2 factors (1 & itself)-Cannot be divided evenly by any other numbers
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Definitions
Composite Number-
A number w/ more than 2 factors
Video explanation of prime & composite
numbers
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Definitions Factors-
Product-
Numbers that create new numbers when they are multiplied A number that results from multiplication
Factors
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Definitions Factor Pairs-
A pair of numbers that multiply to give a particular product
32 32
1 2
16
4
8
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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!
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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
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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!