6th Grade "I CAN" Statements
EXPRESSIONS & EQUATIONS
6.EE.1 --I can write numerical expressions involving whole number exponents. Ex. 34 = 3x3x3x3 --I can evaluate numerical expressions involving whole number exponents. Ex. 34 = 3x3x3x3 = 81 --I can solve order of operation problems that contain exponents. Ex. 3+22 – (2+3) = 2 6.EE.2a --I can use numbers and variables to evaluate expressions. --I can translate written phrases into algebraic expressions. --I can translate algebraic expressions into written phrases. 6.EE.2b --I can identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient). --I can identify parts of an expression as a single entity, even if not a monomial. 6.EE.2c --I can substitute specific values for variables. --I can evaluate algebraic expressions including those that arise from real-world problems. --I can apply order of operations when there are no parentheses for expressions that include whole number exponents. 6.EE.3 --I can create equivalent expressions using the properties of operations (e.g. distributive property, associative property, adding like terms with the addition property or equality, etc.). --I can apply the properties of operations to create equivalent expressions. 6.EE.4 --I can recognize when two expressions are equivalent. --I can prove (using various strategies) that two expressions are equivalent no matter what number is substituted. 6.EE.5 --I can recognize solving an equation or inequality as a process of answering “which values from a specified set, if any, make the equation or inequality true?”. --I can use the solution to an equation or inequality to prove that the answer is correct. --I can use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.6 --I can recognize that a variable can represent an unknown number, or, depending on the scenario/situation, any number in a specific set. --I can relate variables to a context. --I can write expressions when solving a real-world or mathematical problem. 6.EE.7 --I can define an inverse operation. --I can use inverse operations to solve one step variable equations. --I can apply rules of the form x + p = q and px = q, for cases in which p, q and x are all nonnegative rational numbers, to solve real world and mathematical problems. (There is only one unknown quantity). --I can develop a rule for solving one-step equations using inverse operations with nonnegative rational coefficients. --I can solve and write equations for real-world mathematical problems containing one unknown. 6.EE.8 --I can identify the constraint or condition in a real-world or mathematical problem in order to set up an inequality. --I can recognize that inequalities of the form x>c or x<c have infinitely many solutions. --I can write an inequality of the form x>c or x<c to represent a constraint or condition in a real-world or mathematical problem. --I can represent solutions to inequalities or the form x>c or x<c, with infinitely many solutions, on the number line diagrams. 6.EE.9 --I can define independent and dependent variables . --I can use variables to represent two quantities in a real-world problem that change in relationship to one another. --I can write an equation to express one quantity (dependent) in terms of the other quantity (independent). --I can analyze the relationship between the dependent variable and independent variable using tables and graphs. --I can relate the data in a graph and table to the corresponding equation. GEOMETRY 6.G.1 --I can recognize and know how to compose and decompose polygons into triangles and rectangles. --I can compare the area of a triangle to the area of the composed rectangle. --I can apply the techniques of composing and/or decomposing to find the area of triangles, special quadrilaterals and polygons to solve mathematical and real world problems. --I can discuss, develop and justify formulas for triangles and parallelograms (6th grade introduction). 6.G.2 --I can calculate the volume of a right rectangular prism. --I can apply volume formulas for right rectangular prisms to solve real-world and mathematical problems involving rectangular prisms with fractional edge lengths. --I can model the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths. 6.G.3 --I can draw polygons in the coordinate plane. --I can use coordinates (with the same x-coordinate or the same y-coordinate) to find the length of a side of a polygon. --I can apply the technique of using coordinates to find the length of a side of a polygon drawn in the coordinate plane to solve real-world and mathematical problems. 6.G.4 --I can recognize that 3-D figures can be represented by nets. --I can represent three-dimensional figures using nets made up of rectangles and triangles. --I can apply knowledge of calculating the area of rectangles and triangles to a net. --I can combine the areas for rectangles and triangles in the net to find the surface area of a 3-dimensional figure. --I can solve real-world and mathematical problems involving surface area using nets. NUMBER SYSTEM 6.NS.1 --I can compute quotients of fractions divided by fractions (including mixed numbers). --I can interpret quotients of fractions. --I can figure out how to solve division problems with fractions in a real-world situation. --I can solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 6.NS.2 --I can divide multi-digit numbers using the standard algorithm with speed and accuracy, without any math tools (i.e., calculator, multiplication chart). 6.NS.3 --I can fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation with speed and accuracy, without math tools (i.e., calculator). 6.NS.4 --I can identify the factors of two whole numbers less than or equal to 100 and determine the Greatest Common Multiple. --I can identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple. --I can apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor. 6.NS.5 --I can identify an integer and its opposite. --I can use integers to represent quantities in real world situations (above/below sea level, etc). --I can explain where zero fits into a situation represented by integers. 6.NS.6 --I can identify a rational number as a point in the number line. 6.NS.6a --I can identify the location of zero on a number line in relation to positive and negative numbers. --I can recognize opposite signs of numbers as locations on opposite sides of 0 on the number line. --I can reason that a double negative, e.g., -(-2) is the opposite of that number itself. 6.NS.6b --I can recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located. --I can reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y axis, e.g., (x,y) and (x,-y). --I can recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x axis, e.g., (x,y) and (x,-y). --I can reason that when two ordered pairs differ only by signs, the locations of the points are related by reflections across both axes, e.g., (-x,-y) and (x,y). 6.NS.6c --I can find and position integers and other rational numbers on a horizontal or vertical number line diagram. --I can find a position pairs of integers and other rational numbers on a coordinate plane. 6.NS.7 --I can order rational numbers on a number line. 6.NS.7a --I can interpret statements of inequality as statements about relative position of two numbers on a number line diagram. 6.NS.7b --I can write, interpret, and explain statements of order for rational numbers in real-world contexts. 6.NS.7c --I can identify absolute value of rational numbers. --I can interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. 6.NS.7d --I can distinguish comparisons of absolute value from statements about order and apply to real world contexts. 6.NS.8 --I can calculate absolute value. --I can graph points in all four quadrants of the coordinate plane. --I can solve real-world problems by graphing points in all four quadrants of a coordinate plane. --I can calculate the distances between two points with the same first coordinate or the same second coordinate using absolute value, given only coordinates. RATIOS & PROPORTION 6.RP.1 --I can write ratio notation- __:__, __ to __, __/__ --I can explain how order matters when writing a ratio. --I can demonstrate how ratios can be simplified. --I can demonstrate how ratios compare two quantities; the quantities do not have to be the same unit of measure. --I can recognize that ratios appear in a variety of different contexts; part-to-whole, part-to-part, and rates. --I can generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship. --I can analyze context to determine which kind of ratio is represented. 6.RP.2 --I can identify and calculate a unit rate. --I can use appropriate math terminology as related to rate. --I can analyze the relationship between a ratio a:b and a unit rate a/b where b≠0. 6.RP.3 --I can make a table of equivalent ratios using whole numbers. --I can find the missing values in a table of equivalent ratios. --I can solve real-world and mathematical problems involving ratio and rate, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.3a --I can make a table of equivalent ratios using whole numbers. --I can find the missing values in a table of equivalent ratios. --I can plot pairs of values that represent equivalent ratios on the coordinate plane. --I can use tables to compare proportional quantities. 6.RP.3b --I can apply the concept of unit rate to solve real-world problems involving unit pricing. --I can apply the concept of unit rate to solve real-world problems involving constant speed. 6.RP.3c --I can demonstrate how a percent is a ratio of a number to 100. --I can find a percent of a number as a rate per 100. --I can solve real-world problems involving finding the whole, given a part and a percent. 6.RP.3d --I can apply ratio reasoning to convert measurement units in real-world and mathematical problems. --I can apply ratio reasoning to convert measurement units by multiplying or dividing in real-world and mathematical problems. 6.SP.1 --I can recognize that data has variability. --I can recognize a statistical question (examples versus non-examples). STATISTICS & PROBABILITY 6.SP.2 --I can identify that a set of data has distribution. --I can describe a set of data by its center, e.g., mean and median. --I can describe a set of data by its spread and overall shape, e.g. by identifying data clusters, peaks, gaps and symmetry. 6.SP.3 --I can recognize there are measures of central tendency for a data set, e.g., mean, median, mode. --I can recognize there are measures of variances for a data set , e.g., range, interquartile range, mean absolute deviation. --I can recognize that measure of central tendency for a data set summarizes the data with a single number. --I can recognize that measures of variation for a data set describe how its values vary with a single number. 6.SP.4 --I can identify the components of dot plots, histograms, and box plots. --I can find the median, quartile and interquartile range of a set of data. --I can analyze a set of data to determine its variance. --I can create a dot plot to display a set of numerical data. --I can create a histogram to display a set of numerical data. --I can create a box plot to display a set of numerical data. 6.SP.5a --I can report the number of observations in a data set or display. 6.SP.5b --I can organize and display data in tables and graphs. --I can describe the data being collected, including how it was measured and its units of measurement. 6.SP.5c --I can calculate quantitative measures of center, e.g., mean, median, mode. --I can calculate measures of variance, e.g., range interquartile range, mean absolute deviation. --I can choose the appropriate measure of central tendency to represent the data. 6.SP.5d --I can identify outliers. --I can determine the effect of outliers on quantitative measures of a set of data, e.g., mean, median, mode, range, interquartile range, mean absolute deviation. --I can analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context. |
7th Grade "I CAN" Statements
EXPRESSIONS & EQUATIONS
7.EE.1 · I can combine like terms with rational coefficients · I can factor and expand linear expressions with rational coefficients using the distributive property · I can apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 7.EE.2 · I can write equivalent expressions with fractions, decimals, percents, and integers · I can rewrite an expression in a equivalent form in order to provide insight about how quantities are related in a problem context 7.EE.3 · I can convert between numerical forms as appropriate · I can solve 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 · I can apply properties of operations to calculate with numbers in any form · I can assess the reasonableness of answers using mental computation and estimation strategies 7.EE.4a · I can identify the sequence of operations used to solve an algebraic equation of the form px + q=r and p(x + q) = r · I can fluently solve equations of the form px + q=r and p(x + q) = r with speed and accuracy · I can 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 · I can compare an algebraic solution to an arithmetic solution by identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm What is the width? This can be answered algebraically by using only the formula for perimeter (P=21+2w) to isolate w or by finding an arithmetic solution by substituting values into the formula 7.EE.4b · I can graph the solution set of the inequality of the form px + q>r or px + qr or px + q · I can use variables and construct equations to represent quantities of the form px + q=r and p(x + q) = r from real-world and mathematical problems · I can solve word problems leading to inequalities of the form px + q>r or px + q<r, where p, q, and r are specific rational numbers · I can interpret the solution set of an inequality in the context of the problem GEOMETRY 7.G.1 · I can use ratios and proportions to create scale drawing · I can identify corresponding sides of scaled geometric figures · I can compute lengths and areas from scale drawings using strategies such as proportions · I can solve problems involving scale drawings of geometric figures using scale factors · I can reproduce a scale drawing that is proportional to a given geometric figure using a different scale 7.G.2 · I can determine which conditions create unique triangles, more than one triangles, or no triangle · I can analyze given conditions based on the three measures of angles or sides of a triangle to determine when there is a unique triangle, more than one triangle or no triangle · I can construct triangles from three given angle measures to determine when there is a unique triangle, more than one triangle or no triangle using appropriate tools (freehand, rulers, protractors, and technology) · I can construct triangles from three given side measures to determine when there is a unique triangle, more than one triangle or no triangle using appropriate tools (freehand, rulers, protractors, and technology) 7.G.3 · I can define slicing as the cross-section of a 3D figure · I can describe the two-dimensional figures that result from slicing a three-dimensional figure such as a right rectangular prism or pyramid · I can analyze three-dimensional shapes by examining two dimensional cross-sections 7.G.4 · I can determine the parts of a circle including radius, diameter, area, circumference, center and chord · I can identify π · I can recognize the formulas for area and circumference of a circle · I can determine the formulas for area and circumference of a circle, find its area · I can find its circumference, given the area of a circle · I can justify that π can be derived from the circumference and diameter of a circle · I can apply the circumference or area formulas to solve mathematical and real-world problems · I can justify the formulas for area and circumference of a circle and how they relate to π · I can informally derive the relationship between circumference and area of a circle 7.G.5 · I can identify and recognize types of angles: supplementary, complementary, vertical, adjacent · I can determine complements and supplements of a given angle · I can determine unknown angle measures by writing and solving algebraic equations based on relationships between angles 7.G.6 · I can determine the formulas for area and volume and then procedure for finding surface area and when to use them in real-world and math problems for two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms · I can solve real-world and math problems involving area, surface area and volume of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms NUMBER SYSTEM 7.NS.1.a. · I can describe situations in which opposite quantities combine to make 0 · I can apply the principal of subtracting rational numbers in real-world contexts 7.NS.1.b. · I can represent and explain how a number and its opposite have a sum of 0 and are additive inverses · I can demonstrate and explain how adding two numbers, p + q, if q is positive, the sum of p and q will be lql spaces to the right of p on the number line · I can demonstrate and explain how adding two numbers, p + q, if q is negative, the sum of p and q will be lql spaces to the left of p on the number line · I can interpret sums of rational numbers by describing real-world contexts · I can explain and justify why the sum of p + q is located a distance of lql in the positive or negative direction from p on a number line · I can represent the distance between two rational numbers on a number line is the absolute vale of their difference and apply this principal in real-world contexts · I can apply properties of operations as strategies to add and subtract rational numbers 7.NS.1.c. · I can identify subtraction of rational numbers as adding the additive inverse property to subtract rational numbers, p-q= p+ (-q) · I can apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line · I can apply properties of operations as strategies to add and subtract rational numbers 7.NS.1.d. · I can identify properties of addition and subtraction when adding and subtracting rational numbers · I can apply properties of operations as strategies to add and subtract rational numbers 7.NS.2a · I can recognize that the process for multiplying fractions can be used to multiply rational numbers including integers · I can recognize and describe the rules when multiplying signed numbers · I can apply the properties of operations, particularly distributive property, to multiply rational numbers · I can interpret the products of rational numbers by describing real-world contexts 7.NS.2b · I can explain why integers can be divided except when the divisor is 0 · I can describe why the quotient is always a rational number · I can comprehend and describe the rules when dividing signed numbers, integers · I can recognize that –(p/q) = -p/q = p/-q · I can interpret the quotient of rational numbers by describing real-world contexts 7.NS.2c · I can identify how properties of operations can be used to multiply and divide rational numbers (such as distributive property, multiplicative inverse property, multiplicative identity, commutative property for multiplication, associative property for multiplication, etc.) · I can apply properties of operations as strategies to multiply and divide rational numbers 7.NS.2d · I can convert a rational number to a decimal using long division · I can explain the decimal form of a rational number terminates (stops) in zeroes or repeats 7.NS.3 · I can add rational numbers · I can subtract rational numbers · I can multiply rational numbers · I can divide rational numbers · I can solve real-world mathematical problems by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions RATIOS & PROPORTION 7.RP.1 · I can compute unit rates associated with ratios of fractions in like or different units · I can compute fractional by fractional quotients · I can apply fractional ratios to describe rates 7.RP.2.1 · I can determine that a proportion is a statement of equality between two ratios · I can analyze two ratios to determine if they are proportional to one another with a variety of strategies (e.g. using tables, graphs, pictures, etc.) 7.RP.2.2 · I can define constant of proportionality as a unit rate · I can analyze tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships to identify the constant of proportionality 7.RP.2.2 · I can represent proportional relationships by writing equations 7.RP.2.3 · I can recognize what (0,0) represents on the graph of a proportional relationship · I can recognize what (1,r) on a graph represents, where r is the unit rate · I can explain what the points on a graph of a proportional relationship means in terms of a specific situation 7.RP.3 · I can recognize situations in which percentage proportional relationships apply · I can apply proportional reasoning to solve multi-step ratio and percent problems, e.g., simple interest, tax, markups, markdowns, gratuities, commissions, fees, percent increase and decrease, percent error, etc STATISTICS & PROPORTIONALITY 7.SP.1 · I can apply statistics terms such as population, sample, sample size, random sampling, generalizations, valid, biased and unbiased · I can recognize sampling techniques such as convenience, random, systematic and voluntary · I can recognize that generalizations about a population from a sample are valid only if the sample is representative of that population · I can apply statistics to gain information about a population from a sample of the population · I can generalize that random sampling tends to produce representative samples and support valid inferences 7.SP.2 · I can define random sample · I can identify an appropriate sample size · I can analyze and interpret data from a random sample to draw inferences about a population with an unknown characteristic of interest · I can generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples 7.SP.3 · I can identify measures of central tendency (mean, median, and mode) in a data distribution · I can identify measures of variation including upper quartile, lower quartile, upper extreme-maximum, lower extreme minimum, range, interquartile range, and mean absolute deviation (i.e. box-and-whisker plots, line plot, dot plots, etc.) · I can compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap · I can compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability 7.SP.4 · I can find measures of central tendency (mean, median, and mode) and measures of variability (range, quartile, etc.) · I can analyze and interpret data using measures of central tendency and variability · I can draw informal comparative inferences about two populations from random sample 7.SP.5 · I can understand that probability is expressed as a number between 0 and 1 · I can understand that a random event with a probability of ½ is equally likely to happen · I can understand that as probability moves closer to 1 it is increasingly likely to happen · I can understand that as probability moves closer to 0 it is decreasingly likely to happen · I can draw conclusions to determine that a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes 7.SP.6 · I can determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed · I can determine the relationship between experimental and theoretical probabilities by using the law of large numbers · I can predict the relative frequency (experimental probability) of an event based on the (theoretical) probability 7.SP.7a · I can use models to determine the probability of events · I can recognize uniform (equally likely) probability · I can develop a uniform probability model and use it to determine the probability of each outcome/event 7.SP.7b · I can use models to determine the probability of events · I can develop a probability model (which may not be uniform) by observing frequencies in data generated from a change process · I can analyze a probability model and justify why it is uniform or explain the discrepancy if it is not 7.SP.8a · I can determine that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs · I can identify the outcomes in the sample space for an everyday event 7.SP.8b · I can define and describe a compound event · I can find probabilities of compound events using organized lists, tree diagrams, etc. and analyze the outcomes · I can choose the appropriate method such as organized lists, tables and tree diagrams to represent sample spaces for compound events 7.SP.8c · I can define simulation · I can design and use a simulation to generate frequencies for compound events |
8th Grade "I CAN" Statements
EXPRESSIONS & EQUATIONS
8.EE.1 · I can explain why a zero exponent produces a value of one. · I can explain how a number raised to an exponent of -1 is the reciprocal of that number. · I can explain the properties of integer exponents to generate equivalent numerical expressions. 1. Multiplying Exponents of the same base For example, 32 x 3-5 = 1/33 = 1/27 2. Dividing Exponents of the same base For example, 3²/ 3-1 = 1/33 = 1/27 3. Expand and exponent by another exponent For example ((2²)³ = 64 8.EE.2 · I can use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 =p, where p is a positive rational number. · I can evaluate square roots of small perfect squares. · I can evaluate cube roots of small perfect cubes. · I can understand that the square root of 2 is irrational. 8.EE.3 · I can express numbers as a single digit times an integer power of 10 (Scientific Notation). · I can use scientific notation to estimate very large and/or very small quantities. · I can multiply and divide numbers in scientific notation in order to compare growth or decay. · I can compare quantities to express how much larger one is compared to the other 8.EE.4 · I can perform operations using numbers expressed in scientific notations. · I can use scientific notation to express very large and very small quantities. · I can interpret scientific notation that has been generated by technology · I can choose appropriate units of measure when using scientific notation 8.EE.5 · I can determine the rate of change by the definition of slope. · I can graph proportional relationships. · I can compare two different proportional relationships represented in different ways. (For example, compare a distance-time graph to a distance-time equation to determine which of the two moving objects has greater speed) · I can interpret the unit rate of proportional relationships as the slope of a graph 8.EE.6 · I can find the slope of a line between a pair of distinct points. · I can determine the y-intercept of a line. · (interpreting unit rate as the slope of the graph is included in 8.EE) · I can analyze patterns for points on a line through the origin · I can derive an equation of the form y=mx for a line through the origin · I can analyze patterns for points on a line that does not pass through or include the origin · I can derive an equation of the form y=mx + b for a line intercepting the vertical axis at b (the y-intercept) · I can use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane 8.EE.7a · I can give examples of linear equations in one variable with one solution and show that the given example equation has one solution by successively transforming the equation into an equivalent equation of the form x=a · I can give examples of linear equations in one variable with infinitely many solutions and show that the given example has infinitely many solutions by successively transforming the equation into an equivalent equation of the form a=a · I can give examples of linear equations in one variable with no solution and show that the given example has no solution by successively transforming the equation into an equivalent equation of the form b=a, where a and b are different numbers. 8.EE.7b · I can solve linear equations with rational number coefficients. · I can solve equations whose solutions require expanding expressions using the distributive property and/or collecting like terms. 8.EE.8a · I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs. · I can describe the point(s) of intersection between two lines as the points that satisfy both equations simultaneously. 8.EE.8b · I can define “inspection” · I can solve a system of two equations (linear) in two unknowns algebraically. · I can identify cases in which a system of two equations in two unknowns has no solution · I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions · I can solve simple cases of systems of two linear equations in two variables by inspection. · I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations. 8.EE.8c · I can represent real-world and mathematical problems leading to two linear equations in two variables ( and…. All of the elements from 8.EE.8b). FUNCTIONS 8.F.1 · I can determine if an equation represents a function. · I can apply a function rule for any input that produces exactly one output. · I can generate a set of ordered pairs from a function and graph the function. 8.F.2 · I can identify functions algebraically including slope and y intercept · I can identify functions using graphs. · I can identify functions using tables. · I can identify functions using verbal descriptions. · I can compare and contrast two functions with different representations. · I can draw conclusions based on different representations of functions. 8.F.3 · I can recognize that a linear function is graphed as a straight line represented as an equation in the form y = mx + b. · I can recognize the equation y=mx+b is the equation of a function whose graph is a straight line where m is the slope and b is the y-intercept · I can provide examples of nonlinear functions using multiple representations (tables, graphs, and equations). · I can compare the characteristics of linear and nonlinear functions using various representations. 8.F.4 · I can recognize that slope is determined by the constant rate of change · I can recognize that the y-intercept is the initial value where x=0 · I can determine the rate of change (slope) from two (x,y) values, a verbal description, values in a table, or graph. · I can determine the initial value (y-intercept) from two (x,y) values, a verbal description, values in a table, or graph. · I can construct a function to model a linear relationship between two quantities. · I can relate the rate of change and initial value to real world quantities in a linear function in terms of the situation modeled and in terms of its graph or a table of values. 8.F.5 · I can sketch a graph given a verbal description of its qualitative features. · I can interpret the relationship between x and y values by analyzing a graph. · I can analyze a graph and describe the functional relationship between two quantities using the qualities of the graph. GEOMETRY 8.G.1 · I can define and identify rotations, reflections, and translations. · I can identify corresponding sides and corresponding angles of similar figures. · I can understand prime notation to describe an image after a translation, reflection, or rotation. · I can identify center of rotation. · I can identify direction and degree of rotation. · I can identify line of reflection. · I can use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (i.e. Lines are taken to lines and line segments to line segments of the same length). 8.G.1 · I can define and identify rotations, reflections, and translations · I can identify corresponding sides and corresponding angles · I can understand prime notation to describe an image after a translation, reflection, or rotation · I can identify center of rotation · I can identify direction and degree of rotation · I can identify line of reflection. · I can use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (i.e. angles are taken to angles of the same measure) 8.G.1 · I can define and identify rotations, reflections, and translations · I can identify corresponding sides and corresponding angles · I can understand prime notation to describe an image after a translation, reflection, or rotation · I can identify center of rotation · I can identify direction and degree of rotation · I can identify line of reflection. · I can use models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (i.e. parallel lines are taken to parallel lines). 8.G.2 · I can define congruency · I can identify symbols for congruency · I can apply the concept of congruency to write congruent statements. · I can reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotation, reflections, and translation. · I can describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words. 8.G.3 · I can define dilations as a reduction or enlargement of a figure. · I can identify scale factor of the dilation. · I can describe the effects of dilations, translations, rotations, and reflections on 2- D figures using coordinates. 8.G.4 · I can define similar figures as corresponding angles are congruent and corresponding side lengths are proportional. · I can recognize the symbol for similar. · I can apply the concept of similarity to write similarity statements · I can reason that a 2-D figure is similar to another if the second can be obtained by a sequence of rotations, reflections, translation or dilation · I can describe the sequence of rotations, reflections, translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols 8.G.5 · I can define similar triangles. · I can define and identify transversals. · I can identify angles created when a parallel line is cut by transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.). · I can justify that the sum of the interior angles equals 180. (For example, arrange three copies of the same triangle so that the three angles appear to form a line). · I can justify that the exterior angles of a triangle is equal to the sum of the two remote interior angles. · I can use Angle-Angle Criterion to prove similarity among triangles. (Give an argument in terms of transversals why this is so). 8.G.6 · I can define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a and b, hypotenuse, sides, right angle, converse, base, height, proof · I can identify the legs and hypotenuse of a right triangle · I can explain a proof of the Pythagorean Theorem · I can explain a proof of the converse of the Pythagorean Theorem 8.G.7 · I can recall the Pythagorean Theorem and its converse in order to apply it to realworld and mathematical problems (2 and 3 dimesional). · I can solve basic mathematical Pythagorean Theorem problems and its converse to find missing length of sides of triangles in two and there-dimensions. · I can apply Pythagorean Theorem in solving real-world problems dealing with two and three-dimensional shapes. 8.G.8 · I can determine how to create a right triangle from two points on a coordinate graph. · I can use the Pythagorean Theorem to solve for the distance between the two points. 8.G.9 · I can identify and define vocabulary: cone, cylinder, sphere, radius, diameter, circumference, area, volume, pi, base, height · I can recognize formulas for volume of cones, cylinders, and spheres. · I can compare the volume of cones, cylinders, and spheres · I can determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape · I can, given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate for Pi. NUMBER SYSTEM 8.NS.1 · I can define rational and irrational numbers. · I can show that the decimal expansion of rational numbers repeats eventually. · I can convert a decimal expansion which repeats eventually into a rational number · I can show informally that every number has a decimal expansion. 8.NS.2 · I can approximate irrational numbers as rational numbers · I can approximately locate irrational numbers on a number line · I can estimate the value of expression involving irrational numbers using rational. (Examples: Being able to determine the value of the √2 on a number line lies between 1 and 2, more accurately, between 1.4 and 1.5, and more accurately etc….) · I can compare the size of irrational numbers using rational approximations STATISTICS & PROPORTION 8.SP.1 · I can describe patterns such as clustering, outliers, positive or negative association, and nonlinear association. · I can construct scatter plots for bivariate measurement data. · I can interpret scatter plots for bivariate (two different variables such as distance and time) measurement data to investigate patterns of association between two quantities 8.SP.2 · I can show how straight lines are used to model relationships between two quantitative variables. · I can informally assess the model fit by judging the closeness of the data points to the line · I can fit a straight line within the plotted data. 8.SP.3 · I can find the slope and intercept of a linear equation in the context of bivariate measurement data. · I can interpret the meaning of the slope and intercept of a linear equation in terms of the situation. (For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height · I can solve problems using the equation of a linear model 8.SP.4 · I can recognize patterns shown in comparison of two sets of data. · I can show how to construct a two-way table. · I can interpret the data in the two-way table to recognize patterns. (For examples, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?). · I can use relative frequencies of the data to describe relationships (positive, negative, or no correlation). |