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Notes for the 1 st grading period. 6 th Advance and 7 th Average. Section 1.2 Powers and Exponents. Objective To use Powers and Exponents Vocabulary Exponent – the number that tells how many times the base is used as a factor

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Notes for the 1 st grading period

Notes for the 1st grading period

6th Advance and 7th Average


Section 1 2 powers and exponents
Section 1.2 Powers and Exponents

  • Objective

    • To use Powers and Exponents

  • Vocabulary

    • Exponent – the number that tells how many times the base is used as a factor

    • Base – the number, in a power, that is being used as the factor

    • Powers – numbers expressed using exponents


  • Section 1 2 powers and exponents1
    Section 1.2 Powers and Exponents

    • Vocabulary

      • Squared – term that means a number is used as a factor two times

      • Cubed – term that means a number is used as a factor three times

      • Evaluate – to find the value of an expression – to solve it

      • Standard Form – when a number is written without exponents

      • Exponential Form – when a number is written with exponents


    Section 11 1 squares and square roots
    Section 11.1Squares and Square Roots

    • Objective

      • To find squares of numbers and square roots of perfect squares

  • Vocabulary

    • Square – the product of a number and itself

      • Ex. 3 x 3 = 9(square also product)

    • Perfect Squares – squares of rational numbers

      • Ex 1,4,9,16,25,36…

    • Square roots – the factors multiplied to form perfect squares

      • Ex 2 is the square root of 4, 9 is the square root of 81

    • Radical sign – a symbol used to indicate the positive square root of a number.

      • Ex. √


  • Section 11 1 squares and square roots1
    Section 11.1Squares and Square Roots

    • To square and to take the square root are opposite operations – they undo each other

      • The square of 4 = 16 42 = 16

      • The square root of 16 is 4 √16 = 4


    Section 1 3 order of operations
    Section 1.3Order of Operations

    • Objective

      • To evaluate expressions using the order of operations

  • Vocabulary

    • Numerical expression – mathematical sentence that involves numbers and operations

    • Order of Operations – agreed upon steps to find the value of expressions


  • Section 1 3 order of operations1
    Section 1.3Order of Operations

    • Steps to solve

      • 1. Solve inside of the parentheses

      • 2. Evaluate the powers

      • 3. Multiply and divide from left to right

      • 4. Add and subtract from left to right


    Section 1 6 algebra properties
    Section 1.6Algebra Properties

    • Objective

      • To use addition and multiplication properties to solve problems

  • Vocabulary

    • Equivalent Expressions – expressions that have the same value

    • Properties – statements that are true for any number or variable


  • Section 1 6 algebra properties1
    Section 1.6Algebra Properties

    • Properties

      • Distributive Property

        • A ( B + C) = AxB + AxC

        • 3 ( 4 + 5 ) = 3 x 4 + 3 x 5 = 12 + 15 = 27

        • 2 ( Y – 8 ) = 2 x Y – 2 x 8 = 2Y – 16

      • Commutative Property

        • Of Addition a + b = b + a 5+1=1+5

        • Of Multiplication a x b = b x a 4x3=3x4


    Section 1 6 algebra properties2
    Section 1.6Algebra Properties

    • Properties

      • Associative Property

        • Of Addition (a+b)+c=a+(b+c)

        • Of Multiplication (axb)xc=ax(bxc)

          • Parentheses are switched

      • Identity Property

        • Of Addition a+0=a

        • Of Multiplication ax1=a

          • Number or letter keeps it’s identity (stays the same)


    Section 1 7 sequences
    Section 1.7 Sequences

    • Objective

      • To recognize and extend patterns for sequences

    • Vocabulary

      • Sequence – an ordered list of numbers

      • Term – each number in a sequence

      • Arithmetic Sequence – a sequence in which the next term is found by adding the same term to the previous term.

        • 7,11,15,19,…the next term is found by adding four to the previous #

      • Geometric Sequence – a sequence in which the next term is found by multiplying the previous term by the same number

        • 9,18,36,72,…the next term is found by multiplying 2 by the previous #


    1 9 scientific notation
    1.9 Scientific Notation

    • Objective

      • To write numbers greater than 100 in scientific notation and in standard form

    • Vocabulary

      • Scientific Notation – a number written as the product of a number and a power of ten. The number must be greater than or equal to 1 and less than 10

        • A x 10b – Scientific Notation Form


    1 9 scientific notation1
    1.9 Scientific Notation

    • A x 10b – Scientific Notation Form

      • A is the number greater or equal to one but less than ten

      • B is the number of times the decimal point was moved to make A - a number between 1 and 10

      • x 10 –constant – always there in scientific notation


    1 8 measurement the metric system
    1.8 Measurement:The Metric System

    • Objective

      • To change metric units of length, capacity, and mass

    • Vocabulary

      • Meter – Base unit of length – how long

        • Millimeter (mm), Centimeter (cm), Meter (m), Kilometer (km)

          • 10mm=1cm 100cm=1m 1000m=1km 1000mm=1m


    1 8 measurement the metric system1
    1.8 Measurement:The Metric System

    • Vocabulary

      • Gram – base unit of mass – how much it weighs

        • Milligram (mg), gram (g), kilogram (kg)

          • 1000mg=1g 1000g=1kg

      • Liter – base unit of capacity – how much can fit inside

        • Milliliter (mL), Liter (L), Kiloliter (kL)

          • 1000mL=1L 1000L=1kL


    1 8 measurement the metric system2
    1.8 Measurement:The Metric System

    • When converting units of measurements remember if the unit is changing from a big unit to a small unit the operation to use is multiplication

    • When converting from a small unit to a big unit – use division

    • Page 38 - diagram


    Section 6 7 measurement customary units
    Section 6-7Measurement: Customary Units

    • Objective

      • To change units in the customary system

    • Vocabulary

      • Mass

        • Ounce(oz), Pound(lb), Ton(T)

        • 16oz=1 lb 2,000lb=1T

      • Length

        • Inch(in), Foot(ft),Yard(yd),Mile(mi)

        • 12in=1ft 3ft=1yd 5,280ft=1mi


    Section 6 7 measurement customary units1
    Section 6-7Measurement: Customary Units

    • Capacity

      • Fluid Ounce(floz), Cup(c), Pint(pt), Quart(qt), Gallon(gal)

        • 8floz=1c 2c=1pt 2pt=1qt 4qt=1gal

          To convert from larger units to smaller units, multiply

          To convert from smaller units to larger units, divide


    Section 2 2 making predictions
    Section 2.2 Making Predictions

    • Objective

      • To make predictions from graphs

    • Vocabulary

      • Statistics – a branch of mathematics that deals with collection, organizing and interpreting data in charts, tables, and graphs

      • Data – pieces of information, often numerical

      • Frequency table – table showing with tally marks how often pieces of data occur within given intervals


    Section 2 2 making predictions1
    Section 2.2 Making Predictions

    • Vocabulary

      • Line graph – graph that shows how values change over a period of time. Useful for predicting future events

      • Scatterplot – two sets of related data plotted on the same graph. Useful in showing relationships in data.


    Section 2 3 line plots
    Section 2.3Line Plots

    • Objective

      • To construct and interpret line plots

    • Vocabulary

      • Line Plot – diagram that shows the frequency of data on a number line. The frequency is marked with an X.

        x

        x x

        x x x x


    Section 2 3 line plots1
    Section 2.3Line Plots

    • Cluster - data is grouped closely together

    • Outlier – a piece(s) of data that is separated from the rest of the data

    • Range – The difference between the highest and the lowest number in the data set.

      x x cluster

      x x outlier

      x x x x x


    Section 2 5 stem and leaf plots
    Section 2.5Stem and Leaf Plots

    • Objective

      • To construct and interpret stem and leaf plots

    • Vocabulary

      • Stem and Leaf Plots – a useful way to organize data as you collect it with data organized from least to greatest

      • Leaves – the digit in the least place value

      • Stem – the digits in the higher place values


    Section 2 5 stem and leaf plots1
    Section 2.5Stem and Leaf Plots

    • 2 digit number – first number is a stem, second number is a leaf

    • 3 digit number – first two numbers are stems, last number is a leaf

    • Only list the stem once for numbers that share the same stem and put the leaves in descending order from left to right.


    Section 2 5 stem and leaf plots2
    Section 2.5Stem and Leaf Plots

    Example 15,13,28,32,38,30,31,13,36,35,38,32,38,24 – 14 #’s

    Put in order least to greatest –make sure you have the same #

    13,13,15,24,28,30,31,32,32,35,36,38,38,38 – 14 #’s

    1 3,3,5

    2 4,8

    3 0,1,2,2,5,6,8,8,8

    STEM

    LEAF

    The # of leaves

    equals #’s in data

    set


    Section 2 6 box and whisker plots
    Section 2.6Box and Whisker Plots

    • Objective

      • To construct and interpret box and whisker plots

    • Vocabulary

      • Box and Whisker Plot – diagram that summarizes data by dividing it into 4 parts called quartiles

      • Lower Extreme – the lowest value in the data set

      • Upper Extreme – the highest value in the data set


    Section 2 6 box and whisker plots1
    Section 2.6Box and Whisker Plots

    • Median – the middle number in an ordered set of data, it splits the data into halves –lower and upper

    • Lower Quartile – in the lower part of the data, it is the median of that half

    • Upper Quartile – in the upper part of the data, it is the median of that half


    Section 2 6 box and whisker plots2
    Section 2.6Box and Whisker Plots

    • Steps

      • First order your data from least to greatest

      • Find the median which is the middle number in the data set

      • Find the lower and upper quartiles which are the middle numbers in the lower and upper halves

      • Find the lower and upper extremes

      • Then draw the plot on a number line


    Section 2 6 box and whisker plots3
    Section 2.6Box and Whisker Plots

    • Example

      • Data 2,3,5,12,17,20,49 Median = 12

      • Lower quartile = 3 Lower extreme = 2

      • Upper extreme = 49 Upper quartile = 20

        2 3 12 20 49

        1st quartile 2nd quartile 3rd quartile 4th quartile


    Section 2 8 misleading statistics
    Section 2.8Misleading Statistics

    Objective

    Recognize when statistics and graphs are misleading

    Ways to mislead

    No title, axes labels or scales, unequal intervals on the scale

    Pictures could distort the actual amount

    Exclusion of outliers – wrong representation of the data


    Section 8 3 using statistics to predict
    Section 8.3Using Statistics to Predict

    Objective – To predict actions of a larger group by using a sample

    Vocabulary

    Survey – a question or set of questions designed to collect data about the specific group of people

    Population – the specific group of people

    Random Sample – a sample chosen without preference


    Section 8 3 using statistics to predict1
    Section 8.3Using Statistics to Predict

    Percent Proportion a p

    b 100

    a=part of the population, b=entire population, p= percentage

    Multiply numbers diagonally across from each other and divide by remaining # to find missing #

    Example – A survey showed that 78% of students who take a bus to school carry a backpack. Predict how many of the 654 students who take a bus also carry a backpack.

    a=?, b=654, p=78 ? 78 654x78÷100=a

    654 100a=about 510

    =

    =


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