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Standard Text At SchoolGrade 7CCSS.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.Attending and Exploring0visually attend to math materials and activitiesMathematical PracticesZMathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.Grade 6CCSS.Math.Content.6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.CCSS.Math.Content.6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.CCSS.Math.Content.6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.CCSS.Math.Content.6.G.A.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.CCSS.Math.Content.6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.CCSS.Math.Content.7.EE.B.4bSolve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.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.SP.B.3Informally 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.C.8bRepresent 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./attempt to touch or tolerate math manipulativesexplore math manipulatives'request or choose a number song or book
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.CCSS.Math.Content.6.NS.C.7b^Write, interpret, and explain statements of order for rational numbers in real-world contexts.CCSS.Math.Content.6.EE.A.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.CCSS.Math.Content.6.EE.B.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.CCSS.Math.Content.6.EE.B.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.CCSS.Math.Content.6.EE.B.8Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequa< lities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.CCSS.Math.Content.6.EE.C.9Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.CCSS.Math.Content.7.NS.A.3_Solve real-world and mathematical problems involving the four operations with rational numbers.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.4a&Solve 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.Grade 8CCSS.Math.Content.8.NS.A.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.CCSS.Math.Content.8.EE.C.8c\Solve real-world and mathematical problems leading to two linear equations in two variables.CCSS.Math.Content.8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.CCSS.Math.Content.8.G.C.9~Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.CCSS.Math.Content.8.SP.A.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.CCSS.Math.Content.8.SP.A.4Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.gdemonstrate understanding of cause and effect by repeatedly taking an action in order to see the resultCCSS.Math.Content.7.SP.A.2Use 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.C.5eUnderstand 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.[participate in simple problem solving activities by observing, then exploring manipulativesPatterns[enjoys or tolerates clapping patterns, finger plays, actions, nursery rhymes, songs or rapsfattempts to imitate or join in clapping patterns, finger plays, actions, nursery rhymes, songs or rapsEfollows routine placing/retrieving personal items in same place dailyCCSS.Math.Content.6.NS.C.5vUnderstand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.CCSS.Math.Content.6.NS.C.7cUnderstand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.CCSS.Math.Content.6.EE.A.2cCEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).CCSS.Math.Content.7.NS.A.1b&Understand 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.1cUnderstand 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.2aeUnderstand 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.2bUnderstand 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.`anticipates holidays or events based on season (i.e. when it's cold asks when its going to snow)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.More About Attributes&match duplicate two-dimensional shapesCCSS.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.CCSS.Math.Content.8.EE.B.6Use similar triangles to explain why t< he slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.CCSS.Math.Content.8.G.A.2Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.CCSS.Math.Content.8.G.A.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.CCSS.Math.Content.8.G.A.5Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.&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 thermometerCounting 1 and 2'recognize quantity of 2 is more than 1.CCSS.Math.Content.6.RP.A.3aMake tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.CCSS.Math.Content.6.NS.B.2AFluently divide multi-digit numbers using the standard algorithm.CCSS.Math.Content.6.NS.C.6cFind and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.CCSS.Math.Content.6.NS.C.7auInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram.CCSS.Math.Content.6.NS.C.7dFDistinguish comparisons of absolute value from statements about order.8connect numerals 1 and 2 to the quantity they represent.CCSS.Math.Content.8.NS.A.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi).;write numerals 1 and 2 to match sets with these quantities.demonstrate 1-1 correspondence*construct a set to match numerals 3 and 4.;write numerals 3 and 4 to match sets with these quantities.!demonstrate cardinality of number*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.6.NS.C.6aRecognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.CCSS.Math.Content.7.NS.A.1aCDescribe situations in which opposite quantities combine to make 0.identify a set that is more*compare and indicate 2 sets that are equalidentify sets with less ..join and separate sets and compare the result.CCSS.Math.Content.7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.+construct a set to match numerals 7 and 8 .;write numerals 7 and 8 to match sets with these quantities.+construct a set to match numerals 9 and 10.=write numerals 9 and 10 to match sets with these quantities..Ause ordinal numbers from 1-6 to describe each position in a line.CCSS.Math.Content.6.SP.B.4aDisplay numerical data in plots on a number line, including 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".Wcompare numbers 1-10 using "more than" "less than" and "equal to" language and symbols'state one more than a given number 1-10'state one less than a given number 1-10Omatch ABAB patterns using objects (shapes or colors) sound, movement or numbersCCSS.Math.Content.8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.^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 patternsCCSS.Math.Content.6.EE.B.5Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.Calendarname days of week in order4find days of the week in a given month on a calendarname months in order3find a given date on current month's calendar, 1-108identify 4 seasons given name of month within the seasonObject Graphs and PictographsPuse the words "same" and "different" to describe attributes of 2 sets of objectsMuse 2D shapes to build bars in an object bar graph based on color attributesOconstruct pictograph bars to display data based on size attributes of 2D shapes5interpret a graph by comparing amounts in a bar graphCCSS.Math.Content.6.SP.B.5bwDescribing the nature of the attribute under investigation, including how it was measured and its units of measurement.CCSS.Math.Content.6.SP.B.5cGiving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.Kmake 1 simple prediction about amounts based on 1 attribute of a given set.CCSS.Math.Content.6.SP.A.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.CCSS.Math.Content.6.SP.B.5dRelating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.?tally data of amounts based on 1 attribute in a set of objects.CCSS.Math.Content.6.SP.B.5a%Reporting the number of observations.CCSS.Math.Content.7.SP.A.1PUnderstand 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.@place data into a simple bar graph using symbolic representationZcompare amounts on graph using "more than" "less than" and "equal to" language and symbolsCCSS.Math.Content.6.SP.A.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.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.-use data from graph to solve a simple problem?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$count backwards from any number 1-10Lsolve subtraction problems with corresponding subtraction facts to sums to 5Esolve subtraction problem using counting back or number line strategy&solve addition problems with sums 6-9?solve subtraction problems with corresponding facts to 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.7.RP.A.2bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.CCSS.Math.Content.7.RP.A.2c2Represent proportional relationships by equations.CCSS.Math.Content.8.F.A.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).CCSS.Math.Content.8.F.B.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.2use a calculator to add and subtract to sums of 10CCSS.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.8.EE.A.4|Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.Yidentify doubles addition problems and use them to solve subtraction problems, sums 2- 10Suse counting skills and/or other learned strategies to solve a simple word problemidentify numerals 11-15identify numerals 16-208write numerals 16-20 to match sets with these quantitiesComparisons to 20quse "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(state one less than a given number 11-20Geometric Shapes and Figures'identify a line, side, angle and vertexCCSS.Math.Content.8.G.A.1aPLines are taken to lines, and line segments to line segments of the same length.CCSS.Math.Content.8.G.A.1b/Angles are taken to angles of the same measure.=draw a rectangle choosing between two sets of dots to connectplace 2D shapes to fill an areaDuse attribute blocks to re-create a different block shape or designEfind three-dimensional shapes in the environment and match to samples_identify three-dimensional shapes: cube, sphere, cylinder, rectangular prism, triangular prismHchoose a survey question with 2 possible responses for males and femalesCCSS.Math.Content.6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.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.8cHDesign and use a simulation to generate frequencies for compound events.*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.8.SP.A.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.[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 predictionDcompare sets of numbers 1-20 using :"greater" "fewer" "most" "least":order quantities from most to least and from least to mostidentify 2 digit numbers 21-50write numerals 21-50[identify common elements between measurement tools (numbers, numbers in order, lines, etc.)CCSS.Math.Content.6.RP.A.3dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.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.%identify measurement tools given name8match 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 20-50CCSS.Math.Content.7.NS.A.1dRApply properties of operations as strategies to add and subtract rational numbers.9identify numbers that are 10 less than given number 20-509choose method to solve addition problems to sums of 11-15Gchoose method to solve corresponding subtraction facts to sums of 11-159choose method to solve addition problems of sums of 16-20Dchoose method to solve corresponding subtraction facts to sums 16-20cdemonstrate using addition for a word problem for joining two groups, using terms "sum" and "total"\demonstrate using subtraction for word problems with removal using manipulatives or picturesdemonstrate using subtraction for word problems with comparison, using manipulatives or pictures, understanding 'difference' as a comparisonudemonstrate using subtraction for word problems with finding a missing part of a set, using manipulatives or picturesQchoose correct operation of addition or subtraction to solve simple word problemBdemonstrate commutative property of addition with simple equationsCCSS.Math.Content.6.EE.A.3FApply the properties of operations to generate equivalent expressions.CCSS.Math.Content.7.NS.A.2cUApply properties of operations as strategies to multiply and divide rational numbers.Hidentify addition problems that are doubles to sums 11-18 and solve themGsolve corresponding subtraction problems to sums of 11-18 using doubles"add 3 or more single digit numbersparrange and re-arrange order of numbers in adding 3 or more single digit numbers to prove associative property.use a calculator to add 3 single-digit numbers2 Digit Numbers and Place Valuerote count 1-100Istudent will identify numbers that are 10 more than a given number 51-100Istudent will identify numbers that are 10 less 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.8.EE.A.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.)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 digit 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=use symbols < > and = to compare large numbers up to 6 digitsduplicate ABBABB patternextend ABBABB patternskip count by 5'sskip count by 2'sNdetermine a missing unit in a pattern using shapes, colors objects, or numbers^use number patterns with simple skip counting (2's, 5's, 10's) fill in missing pattern element(count common coin combinations to $1.00CCSS.Math.Content.6.NS.B.3rFluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Weights and Lengths;identify pre-measured lines pictured with a ruler in inches2measure line with ruler recording length in inches>measure line with ruler and yardstick recording length in feet8measure line with meter stick reporting length in metersmatch 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.8.G.A.1c+Parallel lines are taken to parallel lines.CCSS.Math.Content.8.G.A.3xDescribe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.ndescribe a motion or a series of motions (up, down, over, turn, left, right) to prove two shapes are congruent*identify polygons and quadrilateral subset/identify polygons: rhombus, hexagon and octagon: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)Line Plot GraphMcollect 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 plotPidentify 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.7.SP.C.7aDevelop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.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.6.NS.C.6bUnderstand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.CCSS.Math.Content.6.NS.C.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.CCSS.Math.Content.7.RP.A.2aDecide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.CCSS.Math.Content.7.RP.A.2dExplain 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.8.F.B.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.CCSS.Math.Content.8.G.B.8]Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.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)CCSS.Math.Content.6.RP.A.3bSSolve unit rate problems including those involving unit pricing and constant speed.\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.6.EE.A.2a\Write expressions that record operations with numbers and with letters standing for numbers.CCSS.Math.Content.6.EE.A.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).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.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.8.EE.A.2Use square root and cube root symbols to represent solutions to equations of the form x = p and x = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.=complete a problem with a missing addend (i.e. 2 + ___ = 5)CCSS.Math.Content.8.EE.C.7aQGive examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).Csolve a simple addition equation with a variable (i.e. 2 + x = 5 )"identify equivalent and equal setsBextend a number pattern with a constant increment (ex. 1,3,5,7,9& )?use a table representing constant change between two quantitiesCCSS.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.8.SP.A.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.Mdescribe number pattern present in a table depicting constant rate of changeHuse repeated equal sets to demo<nstrate 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 groupCCSS.Math.Content.7.RP.A.3MUse proportional relationships to solve multistep ratio and percent problems.Fuse 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 equation/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 equationsCCSS.Math.Content.8.EE.C.7bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.Tidentify number sets that can and cannot be divided into equal groups greater than 1Buse an array model and grouping to demonstrate concept of divisionMuse manipulatives to solve division problems with divisors and quotients 1-5bsolve 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 equation+solve division problems with divisor of 10Ruse division to solve a word problem with equal sets that uses the word "quotient"Xdivide by 100 s and 10 s by identifying number of sets in a dividend or removing zero(s)Csolve a division problem with a 2 digit divisor using a calculator.Nchoose correct operation of multiplication or division to solve a word problem:identify factors and multiples and relate them to divisionMeasurement and Geometry7measure 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'+sort equal fraction pieces to make a whole.show 1/2 of an object and array@assemble and name matching equal fraction pieces to make a whole-identify 2 ways to make a square into fourths>define meaning of the numbers in the numerator and denominator[write a fraction name to match a fraction model with numerator of 1 and denominator of 2-8.identify , 1/3, of a setCommon FractionsJidentify fraction model amounts with a numerator greater than 1 (i.e. 3/4)8use fraction models to match basic equivalent fractionsGidentify fractions of a set with a numerator greater than 1 (i.e. 3/4)Iorder common fractions (i.e. 1/2, 1/4,3/4 1/3, 2/3) using measuring cupsRcompare common fractions to measuring cups to 0, 1/2 and 1 with symbols > < and =Midentify linear measurement that falls between whole numbers as 1/2" and 1/4" Adding and Subtracting Fractions+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 numberBuse fraction models to identify fraction amounts from 1/10 - 10/104divide fractions 1/10 to 1/10 to convert to decimalsCCSS.Math.Content.7.NS.A.2dConvert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.!read decimals in the tenths place(read decimals in money terms .10 to .99Nadd and subtract decimals as money terms from .10 to 2.00 on a calculatorvmatch decimals .50 and .25 to fractions of 1/2 and 1/4 and relate to money (quarters) and time (quarter and half-past)2match fractions to percentages 100%, 50% and 25%.CCSS.Math.Content.6.RP.A.3cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.Algebra: PatternsAlgebra: Patterns and UnitsAlgebra: Number Patterns?Algebra: Missing Addends, Variables and Constant Rate of Change1Data Anaylsis & Probability: Matching and Sorting:Data Anaylsis & Probability: Object Graphs and Pictographs6Data Anaylsis & Probability: Prediction and Bar Graphs3Data Anaylsis & Probability: Categorical Data Graph,Data Anaylsis & Probability: Line Plot Graph=Data Anaylsis & Probability: Probability and Change Over TimeGeometry: More About Attributes&Geometry: Geometric Shapes and Figures.Geometry: Two Dimensional and Congruent Shapes"Geometry: Three Dimensional Shapes.Geometry: Classification (Angles and Polygons)Measurement: CalendarMeasurement: Time and MoneyMeasurement: Measurement Tools&Measurement: Measuring Tools and Money Measurement: Weights and LengthsMeasurement: 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, Place Value6Numbers and Operations: Larger Numbers and Place Value1Numbers and Operations: Addition and Subtraction ;Numbers and Operations: Rounding, Estimating and Regrouping-Numbers and Operations: Multiplication Models'Numbers and Operations: Division Models,Numbers and Operations: Fractions and Wholes8Numbers and Operations: Adding and Subtracting Fractions8Numbers and Operations: Fractions, Decimals and Percents=++7<?GKPS* YӮ0+[ haAM@ 6A\:
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