07 Q1 Mathematics: CCSS.MATH.CONTENT.7.RP.A.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. CCSS.MATH.CONTENT.7.RP.A.2Recognize and represent proportional relationships between quantities.CCSS.MATH.CONTENT.7.RP.A.2.ADecide whether two quantities are in a proportional relationship.CCSS.MATH.CONTENT.7.RP.A.2.BIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.CCSS.MATH.CONTENT.7.RP.A.2.CRepresent proportional relationships by equations. CCSS.MATH.CONTENT.7.RP.A.2.DExplain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.CCSS.MATH.CONTENT.7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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07 Q1 MATHEMATICS PROCESS PRODUCT/ASSESSMENTElementary SkillsHow do we apply the basic operations of mathematics to integers and fractions?What are negative numbers and how do we perform operations on these values?What are variables and how do they represent unknown values?What are the families of numbers in the real number system?

Elementary SkillsPerform operations without a calculator to add, subtract, multiply, divide and apply exponents towards positive integers.Recognize that negative numbers represent numbers less than zero.Establish operatory rules for negative numbers.Apply operations upon negative numbers without the use of calculators.Establish operatory rules for variables and coefficients.Classify numbers appropriately within the real number system.

Elementary SkillsCompletion of a variety of tasks based around operationsNotes and graphic organizers developed with help of staff to help recall and address prior informationSimplification of expressions with and without variables, coefficients and exponents.

MeasurementWhat are the appropriate units of measurement for a given situation?What tools do we use for various types of measurement?When tools are unavailable or do not apply to a situation, how can we calculate unknown values?How do metric measurements differ from standard measurements?How does distance related to area and volume?What are the formulas associated with area and volume?How do formulas influence the units of measurement?How can we convert units of measurement?

MeasurementIdentify and utilize the appropriate unit of measurement for a given situation.Implement the appropriate tool in a real world situation.Perform measurements with tools such a ruler, compass, protractor, caliper, measuring tape, clock etcCalculate unknown values of measurements.Derive and apply formulas for area and volume of non circular figures.Recognize that 2 dimensional figures are present in 3 dimensional figures.Apply operations and equations to units of measurement.

MeasurementCreation of graphs and tables to record data gathered based upon a given situation Completion of assignments linking measurement to science and real world situationDevelopment of graphic organizers used to convert units of measurement

RateHow do ratios show comparisons between two sets of numbers?What is a rational number?How can two units of measurement be combined to create a rate?When can rates be represented by a single number?What are common rates that are used and how can they be applied to real world situations?

RateCreate ratios for given situations.Differentiate between rational numbers and irrational numbers.Create a rate for a given situation be comparing two units of measurementExplore common rates and apply them towards real world situation.

RateCharts that order information to fit a given situationCreation of units of rate for a variety of real world situations..

Graphing RateWhat is a graph on a coordinate plane and how does it compare two values?How can we create graphs that represent rates?How can we determine which measurements determine the x and y values on a Cartesian plane?What is the difference between an independent and dependent variable?What are the distinct characteristics of a linear graph?When are relationships linear?When are relationships proportional?

Graphing RateUnderstand that two values together create a relationship that may or may not be linear. Graph these relationships and determine whether a relationship is linear.Determine whether a ratio is proportional based upon the characteristics of its graph.Predict the shape of a graph from a given table of values.Create a table of values to represent a given situation.

Graphing RateGraphs that represent information that is given and or created by students.Completion of tables related to these graphs

07 Q1 MATHEMATICS VOCABULARY:Ratio, length, area, proportional, relationship, unit rate, graph, equation, expression, percent, identity, element, operation, inverse, rational, irrational, associative, distributive, factor, integer, real number system, unit of measurement, metric system, volume, surface area, convert, Cartesian plane, independent, dependent, variable, algebra, coefficient, evaluate, simplify, order of operations

07 Q2 Mathematics: CCSS.MATH.CONTENT.7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.CCSS.MATH.CONTENT.7.EE.A.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."CCSS.MATH.CONTENT.7.EE.B.3Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. CCSS.MATH.CONTENT.7.EE.B.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.CCSS.MATH.CONTENT.7.EE.B.4.ASolve word problems leading to equations of the form px + q = r and p(x + q) =r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. CCSS.MATH.CONTENT.7.G.A.3Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.CCSS.MATH.CONTENT.7.G.B.4Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.CCSS.MATH.CONTENT.7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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07 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTSolving EquationsWhen can we use substitution to solve and simplify equations and expressions?What are inverse operations?How do we solve for unknown values of variables by isolation?How can we verify answers using substitution?What are the best courses of action to solve one step equations?How must we modify our approach to solve for variables in two step equations?When can we identify factors to simplify solution of two step equations?Why can we not solve for two variables in a single equation?

Solving EquationsSubstitute defined variables into an equation or expression to simplify or verify values.Perform appropriate inverse operation on each side of an equation to isolate variables by transposition.Solve for variables and appropriately express answers.Verify obtained answers using substitution.Determine an appropriate inverse operation to utilize for a given one step equation.Predict operations to be used for a two or more step equation.Factor a like term and divide to solve a multistep equation.Determine whether an equation can be solved based upon the given information.

Solving EquationsCompletion of one and two step equations.Application of algebraic concepts to real world situationsCreation of notes and graphic organizers used as reference materials related to this area of study.

Manipulating EquationsHow can we isolate variables for a given situation?What operations can be performed on variables without coefficients or exponents?What operations cannot be performed on variables without coefficients or exponents?How can we apply these concepts towards creating new equations?How can we apply equation creation to known equations for area, volume and rate?When is it appropriate to use manipulated equations in areas of science?

Manipulating EquationsSolve for values in reference to other variables as opposed to numbers.Determine whether operations can perform upon a given equation based upon form of terms.Create new equations based on given informationRecognize that multiple forms of the same equation are used to solve for different variables.Isolate variables in known equations.Apply these concepts to science such as density.

Manipulating EquationsCreation of new equations to be utilized for given situations.Completion of cross curricular activities related to science, density and buoyancy.

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07 Q2 MATHEMATICS PROCESS PRODUCT/ASSESSMENTCirclesWhat are the important characteristics and vocabulary terms associated with circles?What is pi?How can we use pi to create equations about circles?What formulas are used for area and circumference of a circle?How can we apply equations of circles towards creation of equations for cylinders and spheres?What is surface area?Why is surface area of spheres important to all aspects of life on earth?

CirclesUse appropriate vocabulary and terminology when discussing circles.Understand that the defining characteristic of a circle is a constant radius.Derive the ratio of pi.Create equations for diameter and circumference using pi as a known value.Understand that pi is not equal to 3.14.Determine area and circumference of circles.Apply knowledge of circles to cones, cylinders and spheres.Determine surface area of 3 dimensional figures.Describe conservation of space.

CirclesCompletion of work based upon circles and their applications in real world situation.Measurement of properties of circles.Establishment of pi as a result of circumference divided by diameter.Comparisons of surface area of figures with the same volume.

RadicalsWas is a radical expression?How are square roots simplified?When is it appropriate to use only the principle square root?How can we evaluate square roots that are not perfect squares?When is it beneficial to express in radical form rather than evaluated numeric form?How can we simplify radical expressions in simplest radical form?When can we apply square roots to solve for unknown values?What is a cube root?How does a cube root differ from a square root?

RadicalsDescribe the characteristics of rational expressions and square roots.Simplify perfect squares to a single numeric value.Simplify radicals to simplest radical form.Understand that radicals have two answers and that negative numbers do not have real solutions.Solve simple equations featuring square roots.Understand that cube roots are similar to square roots but have some different characteristics.

Radicals Solution of equations and simplification of expressions related to radicalsCreation of notes and graphic organizers used as reference materials related to this area of study.

07 Q2 MATHEMATICS VOCABULARY:Linear equation, increase, solve, simplify, arithmetic, sequence, circumference, area, pi, volume, surface area, isolation, chord, radius, diameter, transposition, square root, principle square root, cube root, radical

07 Q3 Mathematics: CCSS.MATH.CONTENT.7.G.A.1Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.CCSS.MATH.CONTENT.7.G.A.2Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.CCSS.MATH.CONTENT.7.G.B.5Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.CCSS.MATH.CONTENT.7.NS.A.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.CCSS.MATH.CONTENT.7.NS.A.1.ADescribe situations in which opposite quantities combine to make 0. For CCSS.MATH.CONTENT.7.NS.A.1.BUnderstand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.CCSS.MATH.CONTENT.7.NS.A.1.CUnderstand subtraction of rational numbers as adding the additive inverse, p - q = p+ (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.CCSS.MATH.CONTENT.7.NS.A.1.DApply properties of operations as strategies to add and subtract rational numbers.CCSS.MATH.CONTENT.7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.CCSS.MATH.CONTENT.7.NS.A.2.AUnderstand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.CCSS.MATH.CONTENT.7.NS.A.2.BUnderstand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.CCSS.MATH.CONTENT.7.NS.A.2.CApply properties of operations as strategies to multiply and divide rational numbers.CCSS.MATH.CONTENT.7.NS.A.2.DConvert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.CCSS.MATH.CONTENT.7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.

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07 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTConstructionsWhat are the physical tools that we use to construct figures and how do they work?How do we use fractions for standard units of measurement?How can we use the base ten system of decimals to read metric rulersWhen can we use protractors to measure angle magnitudes?How do compasses help us to construct circles and bisectors?When can technology be used to construct more accurate drawings of physical representations?What is scale and how is it used in design?How can we change the attributes of figures through scaling?

ConstructionsFollow and create step by step processes for drawing particular figures.Describe steps taken to create a given angle, shape or other figure.Utilize rational number system to work with American Standard units of measurement.Utilize rational and decimal numbers to work with metric units of measurement.Choose the appropriate tools to use for a given situation.Construct various angles and shapes both with and without measurement.Appropriately use a compass to construct a circle Understand that the compass expresses the defining characteristic of a circle: a constant radius.Using a ratio, scale a figure understanding that while side lengths change, angles remain constant.

Constructions- Students will use appropriate tools to draw both

physically and using technology.- Create visual representations using tools that

demonstrate an understanding of the properties of the shapes and figures that they create.

- Create scaled drawings with appropriate lengths and angle measurements.

Properties of AnglesWhat is a proof?How do proofs help us to apply information to many different situations?What are the properties of a straight angle?How can complimentary and supplementary angles proven to be true?What are vertical angles?What are the unique properties of a transversal?How can we prove that a triangle has 180 degrees?

Properties of AnglesRead and understand that mathematical proofs are processes by which mathematicians make defined rules that can be applied to other figures.View and write simple proofs, understanding the relation of this idea to other subject areas.Create figures and make observations and generalizations about the created illustrations.Develop equations for complimentary and supplementary angles.Using supplementary angles prove properties of vertical angles.Make generalizations about the relations between angles of right triangles.Use one of various methods to prove that a triangle has 180 degrees.

Properties of AnglesCreate simple proofs showing that certain attributes are definite and true.Develop and utilize equations for supplementary and complimentary angles in both pure mathematics and real world situations.Illustrate the properties of transversals and vertical angles by creating diagrams and labeling key information appropriately.Draw and prove that a triangle has 180 degrees based upon known information.

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07 Q3 MATHEMATICS PROCESS PRODUCT/ASSESSMENTNumber SystemsWhat is a real number?How can we break the real number system into other divisions?What is the difference between a rational and irrational number?How are integers a subset of rational numbers?When are the appropriate situations to use natural and whole number systems?When operations are performed on different subsets of numbers, how are the results influenced?How can we convert between rational and decimal forms of given numbers?How do we perform operations on ratios?

Number SystemsUnderstand that there are different classifications of numbers that can be used for a variety of different situations.Observe that while only real number systems are used in grade level mathematics, there are non-real number systems.Compare the properties of rational and irrational numbers to show how they have distinctly different attributes.Show that there are numbers in the rational set that can be expressed as single representations, not fractions.Review the properties of integers.Apply the natural and whole number systems to appropriate situations.Perform operations on different families of numbers and observe that there are certain relationships which exist between them (i.e. rational * rational always yields rational while irrational * irrational can yield irrational or rational)Perform indicated operations on decimals and rational umbers expressed as fractions.

Number SystemsCreate illustrations of the different families of number systems in relation pictorially.Classify given numbers.Read and create puzzles which require knowledge of different number systems to create appropriate solutions.Perform operations within the same family of numbers and with numbers in other sets.

Properties What is the associative property and how does it apply to addition and multiplication?What is the commutative property?Why do the associative and commutative properties not apply to subtraction and division?How do properties of numbers influence order of operations?How does order of operations influence real world situations?What are the results when we perform indicated operations on different families of number systems?

PropertiesEstablish that there are different properties that can be proven about numbers and their relationships.Define algorithm as a set of operations with an input and output that are related.Use the associative property to solve mathematical and real world problems.Apply the fact that the associative and commutative properties only hold true for the operations of addition and subtraction.Utilize order of operations and other properties to perform complicated operations on different families of numbers.

PropertiesApply the given properties to a variety of different mathematical and real world situations. Perform appropriate operations for a given situation.

07 Q3 MATHEMATICS VOCABULARY:Compass, ruler, protractor, angle, construction, proof, bisect, complimentary, supplementary, vertical, transversal, alternate interior, alternate exterior, corresponding, proof, real number, rational, irrational, decimal, whole, natural, set, associative property, commutative property, operation

07 Q4 Mathematics: CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.CCSS.MATH.CONTENT.7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. CCSS.MATH.CONTENT.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. CCSS.MATH.CONTENT.7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. CCSS.MATH.CONTENT.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.CCSS.MATH.CONTENT.7.SP.C.6Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. CCSS.MATH.CONTENT.7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.CCSS.MATH.CONTENT.7.SP.C.7.A Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. CCSS.MATH.CONTENT.7.SP.C.7.B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. CCSS.MATH.CONTENT.7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.CCSS.MATH.CONTENT.7.SP.C.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.CCSS.MATH.CONTENT.7.SP.C.8.B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.CCSS.MATH.CONTENT.7.SP.C.8.C Design and use a simulation to generate frequencies for compound events. 

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07 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTProbability IntroductionWhat are the historical origins of probability?How do ratios explain the basic meaning of probability?What are the outcomes that can be associated with a single event?What are the relationships that exist between all of the possible outcomes of a single event?What is the relationship between an outcome of an event happening and the outcome of the event not happening.How can we assure that all of the possible outcomes are covered?What is geometric probability?How can we apply our knowledge of geometric shapes and formulas to the world of probability?

Probability IntroductionExplore the origins of probability with Descartes and Pascal.Express simple probability examples as desired outcomes divided by the total number of outcomes.Determine the total number of outcomes for a variety of different situations.Understand that probabilities have a minimum of zero and a maximum of one and can be expressed as percents.Differentiate between more likely, less likely and equally likely outcomes.Perform summations to express all of the possible outcomes of a given situation.Explore probability expressed with geometric figures.Apply probability to areas of two dimensional figures.

Probability IntroductionStudents will perform accurate calculations based around single events.Upon completing basic calculations, students will be able to express both verbally and using formulas whether or not certain outcomes are more or less likely than others.

ProbabilityWhat are compound events?How does performing the same type of event in succession change the meaning of the total outcome?How can we extend our knowledge of single events to compound events?What is replacement and why is it important in compound events?What are mutually exclusive events and what are their implications?What is the difference between empirical and experimental probability?How can we use probability to draw conclusions about an event?How can we limit factors using the scientific

ProbabilityExplore compound probability as the process of performing multiple events which may or may not be related.Determine whether events are independent or dependent based upon given information.Use formulas for independent and dependent events to determine outcomes.Identify context clues to determine whether events are dependent or independent events.Determine whether events are mutually exclusive or inclusive based on a given situation.Perform experimental probability tests.Draw conclusions about a performed experiment based upon results.Understand that outside influences on an experiment can cause inaccurate results.Use the scientific method to determine whether bias or other errors cause mistakes in an experiment.

ProbabilityBuilding upon their knowledge of single events, students will be able to use various formulas and notations for compound probability. In addition to deciphering information, students will also be able to perform operations on fractions which they develop from given information.

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07 Q4 MATHEMATICS PROCESS PRODUCT/ASSESSMENTStatisticsWhat is statistics?How can statistics help us to make inferences about a population?What are some of the key vocabulary terms associated with statistics?What are the measures of central tendency?How can we record and display information about a sample group?How can we determine the measure of error to assure that we can draw valid conclusions?What is a normal distribution?What types of situations create a standard distribution curve?When can we calculate standard deviation?When are certain numbers outliers or not important?How are statistical experiments developed and performed?

StatisticsDefine statistics as an area of mathematics.Identify similarities between probability and statistics.Utilize appropriate vocabulary and symbols associated with basic statistics.Determine the measures of central tendency associated with a given set of data.Understand bias and how it can cause inaccurate results when performing statistics studies.Determine whether information gathered is important and identify parties who would utilize gathered information from a given experiment.Determine a measure of error for a given set of information to draw and express value and statistical relevance.Identify a standard normal distribution curve.Understand key vocabulary associated with standard normal distribution.Calculate standard deviations and determine their relevance to percentages of a given population.Understand that outliers occur and may or may not be statistically relevant to information gathered.Gather, record, chart and analyze information for a student created study.

StatisticsStudents will calculate various values associated with statistics including mean, median, mode, midrange and standard deviation.Students will be able to express why certain biases may occur in given situations and determine ways to limit or eliminate the biases.Interpretation of standard normal distribution will be undertaken using distribution curves and standard deviation.

07 Q4 MATHEMATICS VOCABULARY:Probability, event, outcome, compound probability, independent events, dependent events, replacement, mutually exclusive, inclusive, empirical probability, experimental probability, statistics, measure of central tendency, mean, median, mode, midrange, normal distribution, normal distribution curve, standard deviation.