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Standard Text At SchoolCCSS.Math.Content.HSG-GMD.A.3RUse volume formulas for cylinders, pyramids, cones, and spheres to solve problems.Attending and Exploring0visually attend to math materials and activitiesCCSS.Math.Content.HSG-CO.A.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.CCSS.Math.Content.HSG-CO.A.5Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.CCSS.Math.Content.HSG-GMD.B.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.CCSS.Math.Content.HSG-MG.A.1Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).CCSS.Math.Content.HSG-MG.A.3Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)./attempt to touch or tolerate math manipulativesexplore math manipulatives'request or choose a number song or bookCCSS.Math.Content.HSN-VM.A.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).CCSS.Math.Content.HSF-IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.gdemonstrate understanding of cause and effect by repeatedly taking an action in order to see the resultCCSS.Math.Content.HSG-CO.B.6Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.CCSS.Math.Content.HSS-ID.A.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).CCSS.Math.Content.HSS-ID.B.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.CCSS.Math.Content.HSS-ID.B.6bLInformally assess the fit of a function by plotting and analyzing residuals.CCSS.Math.Content.HSS-ID.C.8UCompute (using technology) and interpret the correlation coefficient of a linear fit.CCSS.Math.Content.HSS-IC.B.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.CCSS.Math.Content.HSS-IC.B.6Evaluate reports based on data.CCSS.Math.Content.HSS-CP.A.4Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.CCSS.Math.Content.HSS-CP.B.6Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model.CCSS.Math.Content.HSS-CP.B.7nApply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model.CCSS.Math.Content.HSS-CP.B.8Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.CCSS.Math.Content.HSS-MD.A.4Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.CCSS.Math.Content.HSS-MD.B.5b@Evaluate and compare strategies on the basis of expected values.CCSS.Math.Content.HSS-MD.B.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).[participate in simple problem solving activities by observing, then exploring manipulativesfattempts to imitate or join in clapping patterns, finger plays, actions, nursery rhymes, songs or rapsCCSS.Math.Content.HSN-Q.A.1Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.CCSS.Math.Content.HSS-ID.A.4"Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.CCSS.Math.Content.HSS-MD.A.1Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.Efollows routine placing/retrieving personal items in same place dailyCCSS.Math.Content.HSF-BF.A.1a_Determine an explicit expression, a recursive process, or steps for calculation from a context.CCSS.Math.Content.HSF-LE.B.5SInterpret the parameters in a linear or exponential function in terms of a context.CCSS.Math.Content.HSF-TF.B.7Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.CCSS.Math.Content.HSG-MG.A.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).CCSS.Math.Content.HSS-CP.A.5|Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.`anticipates holidays or events based on season (i.e. when it's cold asks when its going to snow)CCSS.Math.Content.HSA-CED.A.3Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.follows as schedule is read and anticipates favorite or regularly scheduled school activities with a smile or sigh and/or shows disappointment when routine is changed(match objects to duplicates to make sets+match objects by different color attributes)sort objects by color attribute into setsidentify primary colors by name"identify secondary colors by name(sort objects by size attribute into setsEfind objects in the environment that share 1 size or color attribute.&match duplicate two-dimensional shapesCCSS.Math.Content.HSG-CO.B.7Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.CCSS.Math.Content.HSG-CO.B.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.CCSS.Math.Content.HSG-SRT.A.2<Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.CCSS.Math.Content.HSG-SRT< .A.3oUse the properties of similarity transformations to establish the AA criterion for two triangles to be similar.CCSS.Math.Content.HSG-SRT.B.4Prove theorems about triangles.CCSS.Math.Content.HSG-SRT.B.5wUse congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.CCSS.Math.Content.HSG-SRT.C.6Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.CCSS.Math.Content.HSG-C.A.1#Prove that all circles are similar.&sort duplicate two-dimensional shapes.Fsort similar two-dimensional shapes with varying sizes and orientationFchoose one attribute (size, shape, or color) to sort shapes into sets.Fidentify 2 dimensional shapes: circle, square, rectangle and triangle*locate 2 dimensional shapes in environment5anticipate at least one special event on the calendaridentify 4 seasons of the yearGmatch appropriate clothing to hot and cold temperatures on thermometermatch sets of 1 and 2CCSS.Math.Content.HSN-Q.A.2FDefine appropriate quantities for the purpose of descriptive modeling.CCSS.Math.Content.HSN-Q.A.3_Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.identify amounts of 1 and 28connect numerals 1 and 2 to the quantity they represent.;write numerals 1 and 2 to match sets with these quantities.demonstrate 1-1 correspondencematch sets of 3 and 4identify sets of 3 and 4*construct a set to match numerals 3 and 4.;write numerals 3 and 4 to match sets with these quantities.!demonstrate cardinality of numberidentify sets of 5 and 6*construct a set to match numerals 5 and 6.;write numerals 5 and 6 to match sets with these quantities.understand concept of "0"CCSS.Math.Content.HSN-VM.C.10Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.CCSS.Math.Content.HSA-APR.B.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.CCSS.Math.Content.HSF-IF.C.7csGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.CCSS.Math.Content.HSF-IF.C.7dGraph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.CCSS.Math.Content.HSF-IF.C.8aUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. write "0"*compare and indicate 2 sets that are equalCCSS.Math.Content.HSN-CN.B.4Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number..join and separate sets and compare the result.CCSS.Math.Content.HSN-RN.B.3Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.CCSS.Math.Content.HSS-CP.A.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ).identify sets of 7 and 8+construct a set to match numerals 7 and 8 .;write numerals 7 and 8 to match sets with these quantities.identify sets of 9 and 10+construct a set to match numerals 9 and 10.=write numerals 9 and 10 to match sets with these quantities..Ordering NumbersAuse ordinal numbers from 1-6 to describe each position in a line.CCSS.Math.Content.HSS-ID.A.1YRepresent data with plots on the real number line (dot plots, histograms, and box plots)."locate numbers 1-10 on number lineplace numerals 1-10 in order.[identify relative position of numerals 1-10 using the words "before" "after" and "between".'state one more than a given number 1-10Omatch ABAB patterns using objects (shapes or colors) sound, movement or numbersCCSS.Math.Content.HSF-BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.CCSS.Math.Content.HSF-LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).^duplicate ABAB patterns in 2 ways using objects (shapes or colors) sound, movement or numbersPextend ABAB patterns using objects (shapes or colors) sound, movement or numbersRdescribe ABAB patterns using objects (shapes or colors) sound, movement or numbersrecord ABAB patterns.count number of units represented in a patterncompare equivalent patterns3find a given date on current month's calendar, 1-108identify 4 seasons given name of month within the seasonPuse the words "same" and "different" to describe attributes of 2 sets of objects?find object that doesn't belong in a set using chosen attributeMuse 2D shapes to build bars in an object bar graph based on color attributesCCSS.Math.Content.HSN-VM.C.6rUse matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.Oconstruct pictograph bars to display data based on size attributes of 2D shapes5interpret a graph by comparing amounts in a bar graphCCSS.Math.Content.HSS-ID.A.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.CCSS.Math.Content.HSS-IC.B.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.Prediction and Bar GraphsKmake 1 simple prediction about amounts based on 1 attribute of a given set.CCSS.Math.Content.HSS-IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.CCSS.Math.Content.HSS-MD.B.6bUse probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).?tally data of amounts based on 1 attribute in a set of objects.CCSS.Math.Content.HSS-IC.A.2tDecide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.CCSS.Math.Content.HSS-MD.A.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.@place data into a simple bar graph using symbolic representationZcompare amounts on graph using "more than" "less than" and "equal to" language and symbols-use data from graph to solve a simple problemidentify dice patterns?play simple board game with 1 die and moving pawn around spaces&solve addition problems with sums to 5Asolve addition problems using counting on or number line strategy&solve addition problems with sums 6-9Nsolve addition and subtraction problems with sums and corresponding sums of 100find the missing addend to make a quantity of 10(write addition and subtraction equationsCCSS.Math.Content.HSA-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.CCSS.Math.Content.HSF-IF.B.4For a function that mo< dels a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.CCSS.Math.Content.HSF-IF.C.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).2use a calculator to add and subtract to sums of 10CCSS.Math.Content.HSF-LE.A.4For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.CCSS.Math.Content.HSG-CO.A.2FRepresent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).Suse counting skills and/or other learned strategies to solve a simple word problem(construct a set to match numerals 11-15.9write numerals 11-15 to match sets with these quantities.quse "more than", "less than" and "equal to" symbols and symbolic language to compare quantities of numbers 11-20.0locate numbers 11-20 on number line and calendarplace numbers 11-20 in order(state one more than a given number 11-20'identify a line, side, angle and vertexCCSS.Math.Content.HSG-CO.A.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.CCSS.Math.Content.HSG-CO.A.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CCSS.Math.Content.HSG-CO.C.9&Prove theorems about lines and angles.CCSS.Math.Content.HSG-C.A.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.CCSS.Math.Content.HSG-GPE.B.6pFind the point on a directed line segment between two given points that partitions the segment in a given ratio.=draw a rectangle choosing between two sets of dots to connectCCSS.Math.Content.HSG-GPE.B.7zUse coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.place 2D shapes to fill an areaDuse attribute blocks to re-create a different block shape or designCCSS.Math.Content.HSG-CO.D.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).CCSS.Math.Content.HSG-CO.D.13YConstruct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.CCSS.Math.Content.HSG-C.A.4KConstruct a tangent line from a point outside a given circle to the circle.CCSS.Math.Content.HSG-GPE.B.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Efind three-dimensional shapes in the environment and match to samplesCCSS.Math.Content.HSG-GMD.A.2zGive an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures._identify three-dimensional shapes: cube, sphere, cylinder, rectangular prism, triangular prismHchoose a survey question with 2 possible responses for males and femalesCCSS.Math.Content.HSS-IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.*make a prediction about opinion-based data:tally data from males and females regarding their opinionsEuse categorical data chart to organize answers from males and femalesCCSS.Math.Content.HSS-ID.B.6afFit a function to the data; use functions fitted to data to solve problems in the context of the data.CCSS.Math.Content.HSS-ID.B.6cLFit a linear function for a scatter plot that suggests a linear association.[use symbolic representation to make a bar graph with data in categories according to genderXtalk or write about conclusions drawn from bar graph, including comparison to predictionskip count by tens to 100CCSS.Math.Content.HSA-APR.D.7Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.Measuring Tools and Money[identify common elements between measurement tools (numbers, numbers in order, lines, etc.)CCSS.Math.Content.HSG-SRT.D.11Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).%identify measurement tools given nameCCSS.Math.Content.HSF-TF.A.1iUnderstand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.CCSS.Math.Content.HSG-C.B.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.8match measurement attributes to the corresponding tools.Gmatch commonly used tools for measurement to every day life situations.Ncompare measurement attributes using a tool or by making relative comparisons.#combine 4 quarters to make a dollar9identify numbers that are 10 more than given number 20-509choose method to solve addition problems to sums of 11-159choose method to solve addition problems of sums of 16-20cdemonstrate using addition for a word problem for joining two groups, using terms "sum" and "total"Qchoose correct operation of addition or subtraction to solve simple word problemBdemonstrate commutative property of addition with simple equationsCCSS.Math.Content.HSN-CN.A.2Use the relation i = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.Hidentify addition problems that are doubles to sums 11-18 and solve them"add 3 or more single digit numbersparrange and re-arrange order of numbers in adding 3 or more single digit numbers to prove associative propertyCCSS.Math.Content.HSN-VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties..use a calculator to add 3 single-digit numbers2 Digit Numbers and Place ValueIstudent will identify numbers that are 10 more than a given number 51-100zestimate reasonable number to represent familiar sets in 1 and 2 digit numbers (ex candy in hand e vs. candy in a package)CCSS.Math.Content.HSA-REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.D3 Digit Place Value and Adding and Subtracting 2 and 3 Digit Numbers)add and subtract 10 from a 2 digit number*add and subtract 100 from a 3 digit number^use what is known about making ten to make a hundred using multiples of 10 (ex. 30 + 70 = 100):use a calculator to add and subtract 2 and 3 digit numbers3add and subtract 2 di< git numbers without regrouping3add and subtract 3 digit numbers without regrouping}estimate reasonable number to represent familiar sets up to 3 digit numbers (ex shoes in classroom vs. shoes in a shoe store)Dround numbers to estimate sums and differences to 10 s place valueCround numbers to estimate sums and differences to 100's place value0add and subtract 2 digit numbers with regrouping0add and subtract 3 digit numbers with regroupingestimate reasonable number to represent familiar sets up to 4 digit numbers (ex students in class, students in school, students in city)3add and subtract 4 digit numbers with a calculator(count common coin combinations to $1.00$Two Dimensional and Congruent Shapesmatch 2-D outline to one of the faces of a 3D object including square to cube, circle to cylinder, and triangle to triangular prism.identify congruent shapes\predict and confirm the results of sliding, flipping, and/or turning two-dimensional shapesCCSS.Math.Content.HSN-VM.C.11Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.CCSS.Math.Content.HSN-VM.C.12Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.ndescribe a motion or a series of motions (up, down, over, turn, left, right) to prove two shapes are congruent0identify line symmetrical two dimensional shapes3locate the line of symmetry in a symmetrical figure=identify a right angle as 90 degrees with perpendicular lines*identify polygons and quadrilateral subset/identify polygons: rhombus, hexagon and octagonThree Dimensional Shapes:identify three-dimensional shape faces, vertices and edgesycount three-dimensional shape faces, vertices and edges in cylinder, cube, sphere, triangular prism and rectangular prismeuse a table to organize and classify three dimensional shapes by number of faces, vertices and edges.7count sides and vertices visible on a 2D net for a cubenbuild and identify a cube from a 2-dimensional net and count to compare sides and vertices to 2D net amounts.\sort polyhedral shapes (only flat faces, ex. prisms ) from other shapes (cylinders, spheres)Mcollect data on the size of hands of individuals in class to the nearest inch1order the numerical data from smallest to largestgplot data on a line plot graph to determine the most common size of hands by the shape of the line plotCCSS.Math.Content.HSS-MD.A.2lCalculate the expected value of a random variable; interpret it as the mean of the probability distribution.Pidentify the highest and lowest measurements and subtract to determine the range determine the median of the data5use the median to compare hand size to another group.Kdescribe the shape of the graph, including greatest (mode) and least values Probability and Change Over Timepredict the probability of outcomes of simple experiments using words such as "likely" or "unlikely" "certain" and "impossible."CCSS.Math.Content.HSS-CP.A.3Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.7describe outcome of experiment, comparing to predictiondescribe outcome of applying a variable into a simple experiment by comparing before and after, using the terms "variable" and "result".Buse x- axis, then y-axis on a line graph to find coordinate pointsCCSS.Math.Content.HSN-CN.B.5Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.CCSS.Math.Content.HSA-REI.D.12
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.CCSS.Math.Content.HSF-IF.B.5rRelate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.CCSS.Math.Content.HSG-GPE.B.4AUse coordinates to prove simple geometric theorems algebraically.qinterpret a line graph to describe change over time with the overall shape (increasing, decreasing, staying same)zmake a prediction (using terms of probability) regarding change with a simple scientific experiment or everyday occurrencecollect data using a table from an experiment that measures change over time using both quantities (ex. time and plant growth, or time-distance for a runner)\plot data on a line graph to represent change over time, placing time amounts on the x-axis.talk or write about conclusions including comparison of results to predictions and the overall shape (increasing, decreasing, staying same)Puse notation for an equivalent expression using fact families (i.e. 2+3 @ 1 + 4)CCSS.Math.Content.HSA-SSE.A.2BUse the structure of an expression to identify ways to rewrite it.CCSS.Math.Content.HSA-APR.D.6/Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.CCSS.Math.Content.HSA-CED.A.1QCreate equations and inequalities in one variable and use them to solve problems.CCSS.Math.Content.HSF-IF.B.6Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.CCSS.Math.Content.HSF-BF.B.4a{Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.=complete a problem with a missing addend (i.e. 2 + ___ = 5)CCSS.Math.Content.HSA-REI.A.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.CCSS.Math.Content.HSA-REI.A.2zSolve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.CCSS.Math.Content.HSA-REI.B.3vSolve linear equations and inequalities in one variable, including equations with coefficients represented by letters.CCSS.Math.Content.HSA-REI.D.10Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).CCSS.Math.Content.HSF-BF.B.5Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.Csolve a simple addition equation with a variable (i.e. 2 + x = 5 )Bextend a number pattern with a constant increment (ex. 1,3,5,7,9& )?use a table representing constant change between two quantitiesCCSS.Math.Content.HSA-APR.C.4MProve polynomial identities and use them to describe numerical relationships.CCSS.Math.Content.HSF-BF.B.4ccRead values of an inverse function from a graph or a table, given that the function has an inverse.CCSS.Math.Content.HSF-LE.A.1aProve that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.CCSS.Math.Content.HSF-LE.A.1blRecognize situations in which one quantity changes at a constant rate per unit interval relative to another.CCSS.Math.Content.HSF-LE.A.1czRecognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.<CCSS.Math.Content.HSF-LE.A.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.CCSS.Math.Content.HSG-C.A.2NIdentify and describe relationships among inscribed angles, radii, and chords.Mdescribe number pattern present in a table depicting constant rate of changeMultiplication ModelsHuse repeated equal sets to demonstrate understanding of multiplicationLuse manipulatives to solve multiplication problems with factors 1-5 and zero}use 10:1 or 2:1 relationships to set up and solve a multiplication problem describing number of fingers or hands in a groupFuse skip counting by 5's, 2's or 10's to solve multiplication problemsXsolve multiplication problems with factors 6-9 using ? and X to denote multiplication.&write a simple multiplication equationCCSS.Math.Content.HSA-SSE.A.1aKInterpret parts of an expression, such as terms, factors, and coefficients.CCSS.Math.Content.HSA-SSE.A.1b[Interpret complicated expressions by viewing one or more of their parts as a single entity./solve multiplication problems with factor of 10!multiply with 10 and 100, to 1000[use multiplication to solve a repeated addition word problem that uses the word "product".9solve a 2 digit multiplication problem with a calculator.Hdemonstrate commutative property of multiplication with simple equationsbsolve division problems with corresponding factors 6-9 using /, ?, and to denote division.guse inverse relationship with multiplication to solve division problems with divisors and quotients 1-9 write a simple division equationNchoose correct operation of multiplication or division to solve a word problem@measure perimeter of a square, rectangle, triangle, and hexagon.7measure area of a square, and rectangle in square units;make different rectangular arrays with same number of tilesFdetermine volume of a box, using cubes and state the amount as 'cubed'Fidentify dry and liquid measured amounts of 1 cup, 1/2 cup and 1/4 cupWidentify tablespoon, teaspoon and 1/2 teaspoon, using standard T and tsp abbreviations.0measure dry ingredients with 1, 1/2 and 1/4 cups3measure liquid ingredients with 1, 1/2 and 1/4 cupsRmeasure dry and liquid ingredients with 1 tablespoon, 1 teaspoon. and 1/2 teaspoon+identify fractions with common denominators3add and subtract fractions with common denominators7add fractions with common denominators to total 1 whole7identify mixed number in terms of an amount in a recipeNsolve an addition problem using fraction models that results in a mixed numberNadd and subtract decimals as money terms from .10 to 2.00 on a calculatorAlgebra: PatternsAlgebra: Patterns and Units Algebra: Patterns and Units?Algebra: Missing Addends, Variables and Constant Rate of Change<Data Anaylsis & Probability: Pre-Math (Matching and Sorting),Data Anaylsis & Probability: Data and Graphs-Data Anaylsis & Probability: Data and Graphs =Data Anaylsis & Probability: Probability and Change Over Time*Geometry: Pre-Math (More About Attributes)"Geometry: Plane and Solid Shapes Geometry: ClassificationMeasurement: CalendarMeasurement: Time and MoneyMeasurement: Measurement ToolsMeasurement: Money'Measurement: Perimeter, Area and Volume:Numbers and Operations: Pre-Math (Attending and Exploring)1Numbers and Operations: Counting and Number Sense=Numbers and Operations: 2 and 3 Digit Numbers and Place Value6Numbers and Operations: Larger Numbers and Place Value.Numbers and Operations: Adding and Subtracting;Numbers and Operations: Rounding, Estimating and Regrouping-Numbers and Operations: Multiplication Models'Numbers and Operations: Division Models8Numbers and Operations: Adding and Subtracting Fractions8Numbers and Operations: Fractions, Decimals and Percents/,,/25 8e+<>BXE51H"JM#OPuURSZVt
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