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 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 11.1 Squares 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 Roots To square and to take the square root are opposite operations – they undo each other The square of 4 = = 16 The square root of 16 is 4√16 = 4

Section 1.3 Order 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 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 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 Properties Properties –Distributive Property A ( B + C) = AxB + AxC 3 ( ) = 3 x x 5 = = 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 Multiplicationa x b = b x a 4x3=3x4

Section 1.6 Algebra 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 Multiplicationax1=a –Number or letter keeps it’s identity (stays the same)

Section 1.7 Sequences Objective Objective To recognize and extend patterns for sequences To recognize and extend patterns for sequences Vocabulary Vocabulary Sequence – an ordered list of numbers Sequence – an ordered list of numbers Term – each number in a sequence 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. 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 # 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 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 # 9,18,36,72,…the next term is found by multiplying 2 by the previous #

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 10 b – Scientific Notation Form

1.9 Scientific Notation A x 10 b – 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=1cm100cm=1m 1000m=1km 1000mm=1m

1.8 Measurement: The Metric System  Vocabulary Gram – base unit of mass – how much it weighs  Milligram (mg), gram (g), kilogram (kg) 1000mg=1g1000g=1kg Liter – base unit of capacity – how much can fit inside  Milliliter (mL), Liter (L), Kiloliter (kL) 1000mL=1L1000L=1kL

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 Objective Objective To change units in the customary system To change units in the customary system Vocabulary Vocabulary Mass Mass Ounce(oz), Pound(lb), Ton(T) Ounce(oz), Pound(lb), Ton(T) 16oz=1 lb2,000lb=1T 16oz=1 lb2,000lb=1T Length Length Inch(in), Foot(ft),Yard(yd),Mile(mi) Inch(in), Foot(ft),Yard(yd),Mile(mi) 12in=1ft3ft=1yd5,280ft=1mi 12in=1ft3ft=1yd5,280ft=1mi

Section 6-7 Measurement: Customary Units Capacity Capacity Fluid Ounce(floz), Cup(c), Pint(pt), Quart(qt), Gallon(gal) Fluid Ounce(floz), Cup(c), Pint(pt), Quart(qt), Gallon(gal) 8floz=1c2c=1pt2pt=1qt4qt=1gal 8floz=1c2c=1pt2pt=1qt4qt=1gal To convert from larger units to smaller units, multiply To 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 2.3 Line Plots Objective Objective To construct and interpret line plots To construct and interpret line plots Vocabulary Vocabulary Line Plot – diagram that shows the frequency of data on a number line. The frequency is marked with an X. Line Plot – diagram that shows the frequency of data on a number line. The frequency is marked with an X.x xxxxxxxx xxxxxxxxxxxxxxxx

Section 2.3 Line Plots Cluster - data is grouped closely together Cluster - data is grouped closely together Outlier – a piece(s) of data that is separated from the rest of the data 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. Range – The difference between the highest and the lowest number in the data set. xxcluster xx outlier xxxxxxxxxxxxxxxxxxxx

Section 2.5 Stem and Leaf Plots Objective Objective To construct and interpret stem and leaf plots To construct and interpret stem and leaf plots Vocabulary Vocabulary Stem and Leaf Plots – a useful way to organize data as you collect it with data organized from least to greatest 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 Leaves – the digit in the least place value Stem – the digits in the higher place values Stem – the digits in the higher place values

Section 2.5 Stem and Leaf Plots 2 digit number – first number is a stem, second number is a leaf 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 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. 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 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 13,3,5 24,8 30,1,2,2,5,6,8,8,8 STEM LEAF The # of leaves equals #’s in data set

Section 2.6 Box and Whisker Plots ► 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 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 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 Plots ► Example  Data 2,3,5,12,17,20,49Median = 12  Lower quartile = 3Lower extreme = 2  Upper extreme = 49Upper quartile = st quartile 2 nd quartile 3 rd quartile 4 th quartile

Section 2.8 Misleading 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 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 Predict Percent Proportionap b100 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?78654x78÷100=a a=about 510 = =