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| STANDARD | CHARACTERISTICS |
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Math standards are structured by grade level ranges. For a complete overview of the math standards -- click here.
| STANDARD |
CHARACTERISTICS |
GRADE 3-5 | GRADE 6-8 |
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DATA ANALYSIS AND PROBABILITY
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Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer
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• design investigations to address a question and consider how
data-collection methods affect the nature of the data set;
• collect data using observations, surveys, and experiments; • represent data using tables and graphs such as line plots, bar graphs, and line graphs; • recognize the differences in representing categorical and numerical data. |
• formulate questions, design studies, and collect data about
a characteristic shared by two populations or different
characteristics within one population;
• select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots. |
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Select and use appropriate statistical methods to analyze data
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• describe the shape and important features of a set of data
and compare related data sets, with an emphasis on how the
data are distributed;
• use measures of center, focusing on the median, and understand what each does and does not indicate about the data set; • compare different representations of the same data and evaluate how well each representation shows important aspects of the data. |
• find, use, and interpret measures of center and spread,
including mean and interquartile range;
• discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots |
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Develop and evaluate inferences and predictions that are based on data
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• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions |
• use observations about differences between two or more
samples to make conjectures about the populations from which
the samples were taken;
• make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit; • use conjectures to formulate new questions and plan new studies to answer them. |
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Understand and apply basic concepts of probability
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• describe events as likely or unlikely and discuss the degree
of likelihood using such words as certain, equally likely, and
impossible;
• predict the probability of outcomes of simple experiments and test the predictions; • understand that the measure of the likelihood of an event can be represented by a number from 0 to 1. |
• understand and use appropriate terminology to describe
complementary and mutually exclusive events;
• use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations; • compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. |
| STANDARD |
CHARACTERISTICS |
GRADE 3-5 | GRADE 6-8 |
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ALGEBRA
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Understand patterns, relations, and functions |
• describe, extend, and make generalizations about geometric
and numeric patterns;
• represent and analyze patterns and functions, using words, tables, and graphs.
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• represent, analyze, and generalize a variety of patterns
with tables, graphs, words, and, when possible, symbolic
rules;
• relate and compare different forms of representation for a relationship; • identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations |
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Represent and analyze
mathematical situations and structures using algebraic symbols
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• identify such properties as commutativity, associativity,
and distributivity and use them to compute with whole
numbers;
• represent the idea of a variable as an unknown quantity using a letter or a symbol; • express mathematical relationships using equations.
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• develop an initial conceptual understanding of different
uses of variables;
• explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; • use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; • recognize and generate equivalent forms for simple algebraic expressions and solve linear equations |
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Use mathematical models to
represent and understand quantitative relationships
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• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. | • model and solve contextualized problems using various representations, such as graphs, tables, and equations. | |
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Analyze change in various
contexts
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• investigate how a change in one variable relates to a change
in a second variable;
• identify and describe situations with constant or varying rates of change and compare them. |
• use graphs to analyze the nature of changes in quantities in linear relationships. | |
| STANDARD |
CHARACTERISTICS |
GRADE 3-5 | GRADE 6-8 |
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CONNECTIONS
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recognize and use connections among mathematical ideas;
understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics. |
recognize and use connections among mathematical ideas;
understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics. |
| STANDARD |
CHARACTERISTICS |
GRADE 3-5 | GRADE 6-8 |
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REPRESENTATION
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create and use representations to organize, record, and
communicate mathematical ideas;
select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena |
create and use representations to organize, record, and
communicate mathematical ideas;
select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena |
