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Count forward beginning from a given number within the known sequence (instead of having to begin at 1). When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Understand the relationship between numbers and quantities; connect counting to cardinality.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Add up to four two-digit numbers using strategies based on place value and properties of operations.

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ? symbols appropriately. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object.

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Identify arithmetic patterns (including patterns in the addition table or multiplication table], and explain them using properties of operations.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Measure and estimate liquid volumes and masses of objects using standard units of grams (g], kilograms (kg], and liters (l). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a ? b and a ? c. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Draw points, lines, line segments, rays, angles (right, acute, obtuse], and perpendicular and parallel lines. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

A cube with side length 1 unit, called a ""unit cube,"" is said to have ""one cubic unit"" of volume, and can be used to measure volume.

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

Apply the formulas V = l ? w ? h and V = b ? h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Make 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 ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Understand 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. Find 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.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Understand 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.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Write expressions that record operations with numbers and with letters standing for numbers. Identify 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. Understand 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 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.

Solve 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. Use 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.

Find 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. Find 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. Draw 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. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand 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. Recognize 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.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Explain 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) wherer is the unit rate. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Understand 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. Understand 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. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Solve real-world and mathematical problems involving the four operations with rational numbers. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand 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.

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. 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 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. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know 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. Use 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. Solve 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. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Approximate 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.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3= p, where p is a positive rational number. Use 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.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. 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; 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.

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve real-world and mathematical problems leading to two linear equations in two variables. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Understand 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. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Understand 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 twodimensional figures, describe a sequence that exhibits the similarity between them. Use 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.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Know that straight lines are widely used to model relationships between two quantitative variables. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Students will alphabetize groups of three words by placing a number 1, 2, or 3 in front of each word.

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Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

The number of objects is the same regardless of their arrangement or the order in which they were counted.

For example, “Can you join these two triangles with full sides touching to make a rectangle?

For example, determine the unknown number that makes the equation true in each of the equations 8 + ? In this range, read and write numerals and represent a number of objects with a written numeral. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

For example, describe a context in which a total number of objects can be expressed as 5 ?7. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ?8. For example, determine the unknown number that makes the equation true in each of the equations 8 ? ?

For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Solve one- and two-step ""how many more"" and ""how many less"" problems using information presented in scaled bar graphs. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Solve problems involving addition and subtraction of fractions by using information presented in line plots.

When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.

Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Use operations on fractions for this grade to solve problems involving information presented in line plots.

Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours?

Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Apply the formulas V = l w h andV = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 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. 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 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.

Understand that random sampling tends to produce representative samples and support valid inferences. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 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. For example, estimate the population of the United States as 3 ? 10 8 and the population of the world as 7 ? 10 9 , and determine that the world population is more than 20 times larger. 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). For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1], (2,4) and (3,9], which are not on a straight line. 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. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

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. Just embarrassed it took me over a minute to figure out he wasn't speaking English xDi»?sanket jahagirdar: phadu method !!!!!!!!! Nothing from this site may be stored on Google Drive or any other online file storage system. Understand for these examples that decomposing into more equal shares creates smaller shares. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.

For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 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. No worksheet or portion thereof is to be hosted on, uploaded to, or stored on any other web site, blog, forum, file sharing, computer, file storage device, etc. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Understand the connections between proportional relationships, lines, and linear equations.

Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Understand the relationship between numbers and quantities; connect counting to cardinality.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Add up to four two-digit numbers using strategies based on place value and properties of operations.

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ? symbols appropriately. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object.

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Identify arithmetic patterns (including patterns in the addition table or multiplication table], and explain them using properties of operations.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Measure and estimate liquid volumes and masses of objects using standard units of grams (g], kilograms (kg], and liters (l). Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a ? b and a ? c. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Draw points, lines, line segments, rays, angles (right, acute, obtuse], and perpendicular and parallel lines. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

A cube with side length 1 unit, called a ""unit cube,"" is said to have ""one cubic unit"" of volume, and can be used to measure volume.

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

Apply the formulas V = l ? w ? h and V = b ? h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Make 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 ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Understand 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. Find 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.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Understand 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.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Write expressions that record operations with numbers and with letters standing for numbers. Identify 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. Understand 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 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.

Solve 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. Use 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.

Find 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. Find 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. Draw 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. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand 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. Recognize 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.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Explain 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) wherer is the unit rate. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Understand 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. Understand 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. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Solve real-world and mathematical problems involving the four operations with rational numbers. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand 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.

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. 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 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. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know 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. Use 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. Solve 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. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Approximate 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.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3= p, where p is a positive rational number. Use 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.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. 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; 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.

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve real-world and mathematical problems leading to two linear equations in two variables. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Understand 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. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Understand 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 twodimensional figures, describe a sequence that exhibits the similarity between them. Use 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.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Know that straight lines are widely used to model relationships between two quantitative variables. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Students will alphabetize groups of three words by placing a number 1, 2, or 3 in front of each word.

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Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

The number of objects is the same regardless of their arrangement or the order in which they were counted.

For example, “Can you join these two triangles with full sides touching to make a rectangle?

For example, determine the unknown number that makes the equation true in each of the equations 8 + ? In this range, read and write numerals and represent a number of objects with a written numeral. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

For example, describe a context in which a total number of objects can be expressed as 5 ?7. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ?8. For example, determine the unknown number that makes the equation true in each of the equations 8 ? ?

For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Solve one- and two-step ""how many more"" and ""how many less"" problems using information presented in scaled bar graphs. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Solve problems involving addition and subtraction of fractions by using information presented in line plots.

When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.

Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Use operations on fractions for this grade to solve problems involving information presented in line plots.

Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours?

Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Apply the formulas V = l w h andV = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 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. 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 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.

Understand that random sampling tends to produce representative samples and support valid inferences. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 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. For example, estimate the population of the United States as 3 ? 10 8 and the population of the world as 7 ? 10 9 , and determine that the world population is more than 20 times larger. 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). For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1], (2,4) and (3,9], which are not on a straight line. 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. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

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. Just embarrassed it took me over a minute to figure out he wasn't speaking English xDi»?sanket jahagirdar: phadu method !!!!!!!!! Nothing from this site may be stored on Google Drive or any other online file storage system. Understand for these examples that decomposing into more equal shares creates smaller shares. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.

For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 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. No worksheet or portion thereof is to be hosted on, uploaded to, or stored on any other web site, blog, forum, file sharing, computer, file storage device, etc. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Understand the connections between proportional relationships, lines, and linear equations.

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