8Unit Rates Essential Understanding: A unit rate is a rate that has been simplified to a denominator of 1.Example:Remember a rate is a ratio and it must be scaled down by division (not subtraction) to find its simplest form.However, the quickest way to determine a unit rate is to divide the numerator by the denominator and place the quotient over a 1.
9Create and determine equivalent ratios. I Can….Create and determine equivalent ratios.
10Reviewing Equivalent Ratios When:The question asks me if the ratios are equivalent .The question ask me if the ratios make a proportion.How:I can find their cross products.orI can determine their unit rates.I can scale them up or down.Example:I can check my answer by: by trying two or more ways.
11Find a missing quantity using a given ratio. I Can….Find a missing quantity using a given ratio.
12Reviewing Proportions When:The question gives 3 quantities and asks me to find the 4th quantity.The question asks me to use a ratio to find a quantity.The question asks me to find a larger or smaller ratio.How:I can use a proportion to organize my thoughts and give me a visual.I must be careful to list the quantities in the order they are asked in the question.I can figure out how the ratio is being scaled (up or down) and by how much.orI can also use a proportion to cross multiply and divide to find equivalent cross products.Examples:I can check my answer by: cross multiplying the original ratio and the ratio I created.
14Convert fractions to decimal. I Can….Convert fractions to decimal.
15Converting Fractions to Decimals Essential Understanding:To convert a fraction to a decimal you simply divide the numerator by the denominator.Examples:𝟐 𝟓 = 𝟏 𝟒 = 𝟏 𝟐 = 𝟕 𝟖 =
16Convert decimals to fractions. I Can….Convert decimals to fractions.
17Convert Decimals to Fractions Essential Understanding:To convert a decimal to a fraction you simply identify the place value of the last decimal place and use it as the denominator of the fraction.In other words, you write it like you read it. Simplify when possible.Examples:
18Convert decimals to percent. I Can….Convert decimals to percent.
19Converting Decimals to Percent. Essential Understanding:To convert a decimal to a percent, you simply multiply the decimal by 100 and add a percent sign (%).In other words, you move the decimal two places to the right and add a percent sign.Examples:.25 = .1 = = = =
20Convert percent to decimals. I Can….Convert percent to decimals.
21Converting Percent to a Decimal. Essential Understanding:To convert a percent to a decimal, you simply divide by 100 and remove the percent sign (%).In other words, move the decimal two places to the left and remove the percent sign.Examples:5% = % = % = % = =
23Finding the Percent of a Number Essential Understanding:To find the percent of a number, write the percent as a decimal, then multiply the decimal and given number.Remember “of” is sometimes a clue word for multiplication.Examples:What is 40% of 60?Find 25% of 120.Determine 33% of $690.
24I Can….solve problems involving finding the whole given a part and the percent
25Finding the whole given the part and percent. Essential Understanding:To find the whole, when given the part and percent, you simply change the percent to a decimal and divide the "part" by the percent.Examples:10 is 20% of what number?300 is 75% of what number?60 is 80% of what number?
28Compare and Order Rational Numbers Essential Understanding:It is easy to compare and order rational numbers(i.e. fractions, decimals, and percent).Begin by expressing all the given numbers in the same form. Decimal form is the quickest, but you can use fraction or percent, as well.Example:Next, use your knowledge of place value or common denominators to compare or list the numbers in the order they are asked (typically from least to greatest).
29Create and identify intervals on a number line. I Can….Create and identify intervals on a number line.
30Number Lines Essential Understanding: Number lines can be drawn horizontally to display numbers in order from least to greatest (left to right).Ex.Number lines can also be drawn vertically to display numbers from greatest to least (top to bottom).Number lines can be drawn to represent any number set (beginning and ending with any number).Number lines drawn to illustrate both positive and negative numbers, are created by placing a zero in the middle and continuing to number in each direction from there.Each tick mark represents a fraction of the number line. You can count these marks to determine the interval.
31Locate and place positive rational numbers on a number line. I Can….Locate and place positive rational numbers on a number line.
32Rational Numbers on a Number Line Essential Understanding:To determine the value of a plotted point, you first identify the value of each tick mark. This is done by counting the tick marks between two whole numbers. Begin counting with the first tick mark after a whole number and continue counting until you reach the next whole number (include the second whole number in your counting).ExampleThe number of tick marks counted represent the fraction the number line has been divided into.Example:You can use this knowledge to label each tick mark as a fraction, decimal, or percent and locate or identify given points.
34Apply the properties of operations to generate equivalent expressions. I Can….Apply the properties of operations to generate equivalent expressions.
35Algebraic Properties Essential Understanding: Algebraic properties can be used to rewrite expressions or generate equivalent expressions. For instance, the expression can be rewritten like this using commutative property of addition to rearrange the numbers.Examples of other algebraic properties:1 x 4 x 3 = 4 x 3 x 1(6 + 3) +8 = (8 +3) + 69 x (3 x 2) = (9 x 3) x 24(3 – 2)
36Apply the properties of operations to simplify expressions. I Can….Apply the properties of operations to simplify expressions.
37Distributive Property Essential Understanding:Distributive property can be used to rewrite algebraic expressions by multiplying the number outside the parenthesis by each number, term, or variable inside. For instance the expression 3(p+2) can be rewritten as 3p + 6Examples:2(3+7)(6-3)35(3+6d)(4-a)8(5b+6c)89(ab + 4c)
38combine like terms to simplify expressions. I Can….combine like terms to simplify expressions.
39Combining Like Terms Essential Understandings: Expressions that can not be solved , can often be simplified by combining like terms. To simplify like terms, you must begin by identifying the types of terms you have. Terms are defined by their variables or lack of one. They must have the exact same variable with exact same exponent to be considered like terms.Example:To give your self a visual, you can use shapes to code expression before combining the like terms. Be sure to keep the sign with the term.After you have coded the terms, you can rearrange them using your knowledge of commutative property. This will make combing the like terms easier.Once you have rearranged the terms, you can simply combine like terms. You should have the same number of terms in your final answer as the number of shapes you used to code the expression
40evaluate expressions using substitution. I Can….evaluate expressions using substitution.
41Evaluating Expressions Essential Understanding:To evaluate an expression using substitution, you simply replace the variable(s) with the defined quantity.Examples:3x + 5 when x=24w +5w when w=82abc when a=3, b=4, and c=57y – 3p when y=7 and p =2
42I Can….Identify key terms for addition, subtraction, multiplication, and division.
43Key Terms for Addition Increased + Added + Combine + Plus + And + Climbed +Rose +Together +Sum ( + )Average ( + ) then ÷
45Key Terms for Multiplication Times xEach xOf xMultiply xHalf x½Double x2Twice x2Triple x3Product ( x )
46Example: 18 ÷ 3 will be written as 𝟏𝟖 𝟑 Key Terms for DivisionDivided ÷Shared ÷Cut ÷Split ÷Ratio of ÷Quotient ( ÷ )*****Remember division is written in fraction form in algebra*****Example: 18 ÷ 3 will be written as 𝟏𝟖 𝟑
47Key Terms for Exponents Squared 𝑥 2Cubed 𝒙 𝟑To the fourth power 𝒙 𝟒To the fifth power 𝒙 𝟓Etc.….
48Key Terms for Order Than switch Sum ( + ) Difference ( - ) Product ( x )Quotient ( ÷ )FirstThenNextLast
49Key Terms for Equations Is =Equals =Equivalent =
50Key Terms for Inequalities Greater than ≥Less than ≤Is not equal to ≠
51Translate written expressions to numerical form. I Can….Translate written expressions to numerical form.
52Verbal Expressions Essential Understanding: Algebraic word problems are just expressions written in word form. They are used to describe real life situations and to solve real life problems.Example:The key to successfully solving an algebraic word problem is to translate the expression from word form to numerical form. To do this, we follow a few very simple steps.Step 1: Know your vocabulary.Step 2: Read the problem CAREFULLY.Step 3: Code the problem.Step 4: Determine what is know (what numbers are given)Step 5: Determine what is unknown (what variables are given)Step 6: Determine what operation(s) to used based on what the question is asking/telling.Step 7: Translate expression/equationStep 8: Solve if necessaryExamples:
53Locate and graph positive and negative integers. I Can….Locate and graph positive and negative integers.
54Locating Integers on a Number Line Essential Understanding:On a horizontal number line, integers are ordered from least to greatest.So, the negative integers are to the left of zero and the positive integers are to the right of zero.Therefore, the farther left an integer is, on a number line, the smaller it is.Think “left is less”Example:On a vertical number line, integers are ordered from greatest to least.So, the positive integers are above the zero and the negative integers are below the zero.Therefore, the lower an integers is, on a number line, the smaller it is.Think of thermometers and temperatures “below zero”
55Determine absolute value and identify opposites. I Can….Determine absolute value and identify opposites.
56Absolute Value Essential Understanding: The absolute value of a number is its distance from zero.Model:The absolute value of a number is written like this −6Examples:The absolute value of − 6 𝑎𝑛𝑑 6 are the same because they are both 6 places from zero.Numbers that have the same absolute value are called opposites. Therefore, 7 and -7 are opposites.
58Identify misleading features on graphs. I Can….Identify misleading features on graphs.
59Misleading Graphs Essential Understandings: In statistics, a misleading graph, also known as a distorted graph, is a graph in which data is misrepresented. This misrepresentation results in the reader drawing an incorrect conclusion about the data.Graphs can be misleading by accident, due to poor construction, but often graphs are created to be misleading on purpose.Advertisers and statisticians often use data to prove a point, and they can easily twist that data in their favor.The following things are important to consider, when analyzing a graph:1. Title : Is it there? Is it biased?2. Labels: Are both axes labeled? Are all sections of a pie chart labeled with a category and a numerical value or is there a category key?3. Source of the data: Is it a bias source? How was the data obtained?4. Key to a pictograph : Is each picture worth the same value? Are they the same size for the same value?6. Scale: Does the graph start with zero?7. Breaks: Is there a break in either axis?8. Spacing: Are the numbers/categories equally spaced?9. Intervals: Does the scale go up/down consistently?
60Read, create, and interpret pie charts I Can….Read, create, and interpret pie charts
61Circle Graph Essential Understandings: In a circle graph (or pie chart), each part of the data is represented by a “slice” of the circle. In a circle graph, the size of each sector is determined by the fractional value of the data it represents. Circle graphs illustrate a part to whole comparison. Percentages and category keys are used to analyze the given data set. One of the most common uses for a circle graph is to display poll results and surveys.Example:
62Circle Graph Essential Understandings: In sixth grade you are expected to be able to do 4 things with circle graphs:Create themExample:Read themDetermine the number in each category using the % and the whole (i.e. % of a number)Determine the % each category represents using the part and the whole (i.e. 𝑥 𝑦 = .xy = xy%
63Identify types of surveys and survey methods. I Can….Identify types of surveys and survey methods.
64Surveys Essential Understandings: Turn on the television, radio or open a newspaper and you will often see the results from a survey. Gathering information is an important way to help people make decisions about topics of interest. Surveys can help decide what needs changing, where money should be spent, what products to buy, what problems there might be, or lots of other questions you may have at any time.The best part about surveys is that they can be used to answer any question about any topic. You can survey people (through questionnaires, opinion polls, etc) or things (like pollution levels in a river, or traffic flow).Here are four steps to a successful survey:Step one: create the questionsStep two: ask the questionsStep three: tally the resultsStep four: present the results
65Identify bias in survey methods and results. I Can….Identify bias in survey methods and results.
66Bias Surveys Essential Understandings: There are two main reasons surveys result in bias conclusions.1) The first reason is biases found in questioning, such as:Loaded questions- Questions using words or thoughts that cause the reader to lean toward a particular response.Example: Do you think we should build a bigger and better school?Nonresponsive bias- occurs when individuals chosen for the sample are unwilling or unable to participate in the survey.Example: using an internet or mail delivered survey.2) The second reason is sampling bias, such as:Convenience Sample- consists of members of a population that are easily accessed.Example: Surveying the people in your class, about a change that would affect the whole school.Voluntary Response Sample- involves only those who want to participate in the sampling.Example: Comment boxes at local businesses
67Identify an unbiased survey. I Can….Identify an unbiased survey.
68Unbiased Surveys Essential Understandings: Unbiased surveys follow three simple guidelines:Unbiased questions (avoid adjectives)Unbiased survey methods (avoid the mail, comment boxes, the internet, and phone calls when possible)An unbiased samplingThere are 3 types of unbiased sampl :Simple Random Sample- In which each item or person in the population is as likely to be chosen as any other.Example: Putting names in a hatStratified Random Sample- In which the population is divided into similar, non-overlapping groups. A simple random sample is then selected from each groupExample: Surveying 10 from 8th grade, 10 from 7th grade, and 10 from 6th gradeSystematic Random Sample- In which the items or people are selected according to a specific time or item interval.Example: Surveying every 5th person through the front door
69Identify the population and sample when given a survey method. I Can….Identify the population and sample when given a survey method.
70Population and Sample Essential Understandings: The population is the entire group the survey’s results intend to represent.Example: Conducting a survey of Tennessee’s graduation rates for the past 5 years, by surveying every 20th senior from an alphabetical list of all seniors. The population would be every high school senior to graduate or not graduate from school in the past 5 years.The sample is the group of items or individuals chosen to participate in the survey.Example: Conducting a survey of Tennessee’s graduation rates for the past 5 years, by surveying every 20th senior from an alphabetical list of all seniors for the past 5 years. The sample would be every 20th senior.
71Identify biased and unbiased samples. I Can….Identify biased and unbiased samples.
72Bias/Unbiased Samples Essential Understandings:Unbiased samples:1. Simple Random Sample- In which each item or person in the population is as likely to bechosen as any other.Example: Putting names in a hatStratified Random Sample- In which the population is divided into similar, non-overlapping groups. A simple random sample is then selected from each groupExample: Surveying 10 students from 8th grade, 10 from 7th grade, and 10 from 6th gradeSystematic Random Sample- In which the items or people are selected according to aspecific time or item interval.Example: Surveying every 5th person through the front doorBiased samplesConvenience Sample- consists of members of a population that are easily accessed.Example: Surveying the people in your class only, about a change involving the whole school.Voluntary Response Sample- involves only those who want to participate in the sampling.Example: Comment boxes at local businesses
75You will be given 10 minutes to complete the provided Quick Quiz Bell WorkYou will be given 10 minutes to complete the provided Quick Quiz
76Relate my prior knowledge to the current sixth grade standards. I Can….Relate my prior knowledge to the current sixth grade standards.
77Station Rotation You will complete 4 station rotations today. You will have 15 minutes to work in each station.You are expected to record your answers on blank piece of paper.Be sure to include station and task numbers for each answer set.You may choose which task you would like to work on for each station, but you must complete at least oneIf you finish your first task, before time is up, you are expected to move on to another task in your station.When the timer ringers, you must stop where you are and quickly and silently clean your station.I will announce when it is time to switch to the next station.