No records

7.RP.2b 
7 
Ratios & Proportional Relationships 
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 


7.RP.2c 
7 
Ratios & Proportional Relationships 
Represent proportional relationships by equations. 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. 


7.RP.2d 
7 
Ratios & 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) where r is the unit rate. 


7.RP.3 
7 
Ratios & Proportional Relationships 
Analyze proportional relationships and use them to solve realworld and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 


6.RP.1 
6 
Ratios & Proportional Relationships 
Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes.. 


6.RP.2 
6 
Ratios & Proportional Relationships 
Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. (Expectations for unit rates in this grade are limited to noncomplex fractions.). 


6.RP.3 
6 
Ratios & Proportional Relationships 
Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 


6.RP.3a 
6 
Ratios & Proportional Relationships 
Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 


6.RP.3b 
6 
Ratios & Proportional Relationships 
Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?. 


6.RP.3c 
6 
Ratios & Proportional Relationships 
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. 


6.RP.3d 
6 
Ratios & Proportional Relationships 
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 


No records

6.SP.4 
6 
Statistics & Probability 
Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 


6.SP.5 
6 
Statistics & Probability 
Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered. 


7.SP.1 
7 
Statistics & Probability 
Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 


7.SP.2 
7 
Statistics & Probability 
Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 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. Gauge how far off the estimate or prediction might be. 


7.SP.3 
7 
Statistics & Probability 
Draw informal comparative inferences about two populations. 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. 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. 


7.SP.4 
7 
Statistics & Probability 
Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book. 


7.SP.5 
7 
Statistics & Probability 
Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 


7.SP.6 
7 
Statistics & Probability 
Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. 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. 


7.SP.7 
7 
Statistics & Probability 
Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 


7.SP.7a 
7 
Statistics & Probability 
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. 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. 


7.SP.7b 
7 
Statistics & Probability 
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?. 


7.SP.8 
7 
Statistics & Probability 
Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 


7.SP.8a 
7 
Statistics & Probability 
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. 


7.SP.8b 
7 
Statistics & Probability 
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. 


7.SP.8c 
7 
Statistics & Probability 
Design and use a simulation to generate frequencies for compound events. 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?. 


8.SP.1 
8 
Statistics & Probability 
Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 


8.SP.2 
8 
Statistics & Probability 
Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 


8.SP.3 
8 
Statistics & Probability 
Investigate patterns of association in bivariate data. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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. 


8.SP.4 
8 
Statistics & Probability 
Investigate patterns of association in bivariate data. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, 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?. 


6.SP.1 
6 
Statistics & Probability 
Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students' ages. 


6.SP.2 
6 
Statistics & Probability 
Develop understanding of statistical variability. 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. 


6.SP.3 
6 
Statistics & Probability 
Develop understanding of statistical variability. 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. 


No records

7.NS.1 
7 
The Number System 
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 


7.NS.1a 
7 
The Number System 
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 


7.NS.1b 
7 
The Number System 
Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts. 


7.NS.1c 
7 
The Number System 
Understand subtraction of rational numbers as adding the additive inverse, p  q = p + (q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts. 


7.NS.1d 
7 
The Number System 
Apply properties of operations as strategies to add and subtract rational numbers. 


7.NS.2 
7 
The Number System 
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 


7.NS.2a 
7 
The Number System 
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. Interpret products of rational numbers by describing realworld contexts. 


7.NS.2b 
7 
The Number System 
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers then (p/q) = (p)/q = p/(q). Interpret quotients of rational numbers by describing realworld contexts. 


7.NS.2c 
7 
The Number System 
Apply properties of operations as strategies to multiply and divide rational numbers. 


7.NS.2d 
7 
The Number System 
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. 


7.NS.3 
7 
The Number System 
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.). 


8.NS.1 
8 
The Number System 
Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 


8.NS.2 
8 
The Number System 
Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ?^2). For example, by truncating the decimal expansion of ?2 (square root of 2), show that ?2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 


6.NS.1 
6 
The Number System 
Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) Ã· (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) Ã· (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) Ã· (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. 


6.NS.2 
6 
The Number System 
Compute fluently with multidigit numbers and find common factors and multiples. Fluently divide multidigit numbers using the standard algorithm. 


6.NS.3 
6 
The Number System 
Compute fluently with multidigit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. 


6.NS.4 
6 
The Number System 
Compute fluently with multidigit numbers and find common factors and multiples. 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. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 


6.NS.5 
6 
The Number System 
Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 


6.NS.6 
6 
The Number System 
Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 


6.NS.6a 
6 
The Number System 
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., (3) = 3, and that 0 is its own opposite. 


6.NS.6b 
6 
The Number System 
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. 


6.NS.6c 
6 
The Number System 
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. 


6.NS.7 
6 
The Number System 
Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. 


6.NS.7a 
6 
The Number System 
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 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. 


6.NS.7b 
6 
The Number System 
Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write 3Â°C > 7Â°C to express the fact that 3Â°C is warmer than 7Â°C. 


6.NS.7c 
6 
The Number System 
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 realworld situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. 


6.NS.7d 
6 
The Number System 
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. 


6.NS.8 
6 
The Number System 
Apply and extend previous understandings of numbers to the system of rational numbers. Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

