Notes for the 1 st grading period 6 th Advance and 7 th Average

Notes for the 1st grading period

6th Advance and 7th 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 Base – the number, in a power, that is being used

as the factor Powers – numbers expressed using exponents

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 11.1Section 11.1Squares and Square RootsSquares and Square Roots

Objective Objective To find squares of numbers and square roots of To find squares of numbers and square roots of perfect squaresperfect squares

VocabularyVocabularySquare – the product of a number and itselfSquare – the product of a number and itself

– Ex. 3 x 3 = 9(square also product)Ex. 3 x 3 = 9(square also product)Perfect Squares – squares of rational numbersPerfect Squares – squares of rational numbers

– Ex 1,4,9,16,25,36…Ex 1,4,9,16,25,36…Square roots – the factors multiplied to form perfect Square roots – the factors multiplied to form perfect squaressquares

– Ex 2 is the square root of 4, 9 is the square root of 81Ex 2 is the square root of 4, 9 is the square root of 81Radical sign – a symbol used to indicate the positive Radical sign – a symbol used to indicate the positive square root of a number.square root of a number.

– Ex. Ex. √√

Section 11.1Section 11.1Squares and Square RootsSquares and Square Roots

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

The square of 4 = 16 The square of 4 = 16 442 2 = 16= 16

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

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 1.3Order 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 1.6Algebra 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 1.6Algebra 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 1.6Algebra 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 Section 1.7 SequencesSequences

ObjectiveObjective To recognize and extend patterns for sequencesTo recognize and extend patterns for sequences

VocabularyVocabulary Sequence – an ordered list of numbersSequence – an ordered list of numbers Term – each number in a sequenceTerm – each number in a sequence Arithmetic Sequence – a sequence in which the next term is Arithmetic Sequence – a sequence in which the next term is

found by found by addingadding the same term to the previous term. the same term to the previous term. 7,11,15,19,…the next term is found by adding four to the previous # 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 Geometric Sequence – a sequence in which the next term is found by found by multiplyingmultiplying the previous term by the same number the previous term by the same number

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

1.9 Scientific Notation1.9 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 Notation1.9 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

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


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


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

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Section 6-7Section 6-7Measurement: Customary UnitsMeasurement: Customary Units

ObjectiveObjective To change units in the customary systemTo change units in the customary system

VocabularyVocabulary MassMass

Ounce(oz), Pound(lb), Ton(T)Ounce(oz), Pound(lb), Ton(T) 16oz=1 lb16oz=1 lb 2,000lb=1T2,000lb=1T

LengthLength Inch(in), Foot(ft),Yard(yd),Mile(mi)Inch(in), Foot(ft),Yard(yd),Mile(mi) 12in=1ft12in=1ft 3ft=1yd3ft=1yd 5,280ft=1mi5,280ft=1mi

Section 6-7Section 6-7Measurement: Customary UnitsMeasurement: Customary Units

CapacityCapacity Fluid Ounce(floz), Cup(c), Pint(pt), Quart(qt), Fluid Ounce(floz), Cup(c), Pint(pt), Quart(qt),

Gallon(gal)Gallon(gal) 8floz=1c8floz=1c 2c=1pt2c=1pt 2pt=1qt2pt=1qt 4qt=1gal4qt=1gal

To convert from larger units to smaller units, multiplyTo convert from larger units to smaller units, multiplyTo convert from smaller units to larger units, divideTo convert from smaller units to larger units, divide

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 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 2.3Section 2.3Line PlotsLine Plots

ObjectiveObjectiveTo construct and interpret line plotsTo construct and interpret line plots

VocabularyVocabularyLine Plot – diagram that shows the frequency Line Plot – diagram that shows the frequency

of data on a number line. The frequency is of data on a number line. The frequency is marked with an X.marked with an X.

xxxx xx

xx xx xx xx

Section 2.3Section 2.3Line PlotsLine Plots

Cluster - data is grouped closely togetherCluster - data is grouped closely together Outlier – a piece(s) of data that is separated Outlier – a piece(s) of data that is separated

from the rest of the datafrom the rest of the data Range – The difference between the highest Range – The difference between the highest

and the lowest number in the data set.and the lowest number in the data set.xx xx clustercluster

xx xx outlieroutlier

xx xx xx xx xx

Section 2.5Section 2.5Stem and Leaf PlotsStem and Leaf Plots

ObjectiveObjective To construct and interpret stem and leaf plotsTo construct and interpret stem and leaf plots

VocabularyVocabulary Stem and Leaf Plots – a useful way to organize Stem and Leaf Plots – a useful way to organize

data as you collect it with data organized from data as you collect it with data organized from least to greatestleast to greatest

Leaves – the digit in the least place valueLeaves – the digit in the least place value Stem – the digits in the higher place valuesStem – the digits in the higher place values


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

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

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


Example 15,13,28,32,38,30,31,13,36,35,38,32,38,24 – 14 #’sPut 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 3,3,52 4,83 0,1,2,2,5,6,8,8,8

STEM LEAF The # of leaves equals #’s in dataset

Section 2.6Section 2.6Box and Whisker PlotsBox and Whisker Plots

►Objective Objective To construct and interpret box and whisker To construct and interpret box and whisker

plotsplots►VocabularyVocabulary

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

Lower Extreme – the lowest value in the Lower Extreme – the lowest value in the data setdata set

Upper Extreme – the highest value in the Upper Extreme – the highest value in the data setdata set


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

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

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


►StepsSteps First order your data from least to greatestFirst order your data from least to greatest Find the median which is the middle Find the median which is the middle

number in the data setnumber in the data set Find the lower and upper quartiles which Find the lower and upper quartiles which

are the middle numbers in the lower and are the middle numbers in the lower and upper halvesupper halves

Find the lower and upper extremesFind the lower and upper extremes Then draw the plot on a number lineThen draw the plot on a number line


► Example Example Data 2,3,5,12,17,20,49Data 2,3,5,12,17,20,49 Median = 12Median = 12 Lower quartile = 3Lower quartile = 3 Lower extreme = 2Lower extreme = 2 Upper extreme = 49Upper extreme = 49 Upper quartile = 20Upper quartile = 20

22 33 12 12 2020

49 49

11stst quartile quartile 2 2ndnd quartile 3 quartile 3rdrd quartile quartile 4 4thth quartile quartile

Section 2.8Section 2.8Misleading StatisticsMisleading Statistics

ObjectiveObjective

Recognize when statistics and graphs are Recognize when statistics and graphs are misleadingmisleading

Ways to misleadWays to mislead

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

Pictures could distort the actual amountPictures could distort the actual amount

Exclusion of outliers – wrong representation Exclusion of outliers – wrong representation of the dataof the data

Section 8.3Section 8.3Using Statistics to Using Statistics to PredictPredict

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

Vocabulary Vocabulary Survey – a question or set of questions Survey – a question or set of questions designed to collect data about the specific designed to collect data about the specific group of peoplegroup of peoplePopulation – the specific group of peoplePopulation – the specific group of peopleRandom Sample – a sample chosen without Random Sample – a sample chosen without preferencepreference

Section 8.3Section 8.3Using Statistics to Using Statistics to PredictPredict

Percent ProportionPercent Proportion aa pp

bb 100100a=part of the population, b=entire population, p= percentagea=part of the population, b=entire population, p= percentage

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

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

a=?, b=654, p=78a=?, b=654, p=78 ?? 7878 654x78654x78÷100=a÷100=a

654654 100100 a=about 510 a=about 510

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Documents

Notes for the 1 st grading period 6 th Advance and 7 th Average