Worksheets: 4Study Guides: 1Worksheets: 3Study Guides: 1Worksheets: 3Study Guides: 1Worksheets: 3Study Guides: 1### STEM.M. MATHEMATICS: National Council of Teachers of Mathematics (NCTM)

#### NCTM.1. Number and Operations

##### 1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

###### 1.1.1. Work flexibly with fractions, decimals, and percents to solve problems.

Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 ###### 1.1.2. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.

Worksheets :4Study Guides :1 ###### 1.1.3. Develop meaning for percents greater than 100 and less than 1.

Worksheets :4Study Guides :1 ###### 1.1.4. Understand and use ratios and proportions to represent quantitative relationships.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ###### 1.1.5. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1 ###### 1.1.6. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.

Worksheets :4Study Guides :1 ###### 1.1.7. Develop meaning for integers and represent and compare quantities with them.

Worksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 ##### 1.2. Understand meanings of operations and how they relate to one another.

###### 1.2.1. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 1.2.2. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Worksheets :4Study Guides :1 ##### 1.3. Compute fluently and make reasonable estimates.

###### 1.3.1. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ###### 1.3.2. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Worksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 1.3.4. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1 #### NCTM.2. Algebra

##### 2.1. Understand patterns, relations, and functions.

###### 2.1.1. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Worksheets :5Study Guides :1Worksheets :4Study Guides :1 ##### 2.2. Represent and analyze mathematical situations and structures using algebraic symbols.

###### 2.2.1. Develop an initial conceptual understanding of different uses of variables.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ###### 2.2.2. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

Worksheets :5Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 2.2.3. Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Worksheets :3Study Guides :1Worksheets :5Study Guides :1FreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. Read more...iWorksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :5Study Guides :1 ###### 2.2.4. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Worksheets :3Study Guides :1Worksheets :5Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 ##### 2.3. Use mathematical models to represent and understand quantitative relationships.

###### 2.3.1. Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

What are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :4Study Guides :1 ##### 2.4. Analyze change in various contexts.

###### 2.4.1. Use graphs to analyze the nature of changes in quantities in linear relationships.

Worksheets :4Study Guides :1 #### NCTM.3. Geometry

##### 3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

###### 3.1.1. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Read more...iWorksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. Read more...iWorksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 3.1.2. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 3.1.3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Worksheets :4Study Guides :1Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Read more...iWorksheets :3Study Guides :1Worksheets :3Study Guides :1Pythagorean Theorem is a fundamental relation in Euclidean geometry. Use the Pythagorean Theorem and its converse to solve problems. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ##### 3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

###### 3.2.1. Use coordinate geometry to represent and examine the properties of geometric shapes.

Worksheets :4Study Guides :1 ###### 3.2.2. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.

Worksheets :4Study Guides :1 ##### 3.3. Apply transformations and use symmetry to analyze mathematical situations.

###### 3.3.1. Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ###### 3.3.2. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations.

Worksheets :3Study Guides :1 ##### 3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.

###### 3.4.4. Use geometric models to represent and explain numerical and algebraic relationships.

Worksheets :3Study Guides :1Worksheets :4Study Guides :1Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. Read more...iWorksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 #### NCTM.4. Measurement

##### 4.1. Understand measurable attributes of objects and the units, systems, and processes of measurement.

###### 4.1.3. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Read more...iWorksheets :3Study Guides :1 ##### 4.2. Apply appropriate techniques, tools, and formulas to determine measurements.

###### 4.2.2. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Read more...iWorksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. Read more...iWorksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 4.2.3. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :4Study Guides :1 ###### 4.2.4. Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

Worksheets :4Study Guides :1Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. Read more...iWorksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 4.2.5. Solve problems involving scale factors, using ratio and proportion.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 4.2.6. Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1 #### NCTM.5. Data Analysis and Probability

##### 5.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

###### 5.1.1. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

Worksheets :3Study Guides :1FreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1 ###### 5.1.2. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 ##### 5.2. Select and use appropriate statistical methods to analyze data.

###### 5.2.1. Find, use, and interpret measures of center and spread, including mean and interquartile range.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ###### 5.2.2. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 ##### 5.3. Develop and evaluate inferences and predictions that are based on data.

###### 5.3.2. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ###### 5.3.3. Use conjectures to formulate new questions and plan new studies to answer them.

Worksheets :3Study Guides :1FreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1 ##### 5.4. Understand and apply basic concepts of probability

###### 5.4.2. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

Probability is the possibility that a certain event will occur. An event that is certain to occur has a probability of 1. An event that cannot occur has a probability of 0. Therefore, the probability of an event occurring is always between 0 and 1.Probability word problems worksheets. Read more...iWorksheets :4Study Guides :1FreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1 ###### 5.4.3. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.

Worksheets :3Study Guides :1 #### NCTM.6. Problem Solving

##### 6.1. Build new mathematical knowledge through problem solving.

Worksheets :3Study Guides :1 ##### 6.2. Solve problems that arise in mathematics and in other contexts.

Worksheets :3Study Guides :1 ##### 6.3. Apply and adapt a variety of appropriate strategies to solve problems.

Worksheets :3Study Guides :1 #### NCTM.7. Reasoning and Proof

##### 7.1. Recognize reasoning and proof as fundamental aspects of mathematics.

Worksheets :3Study Guides :1 ##### 7.2. Make and investigate mathematical conjectures.

Worksheets :3Study Guides :1 ##### 7.3. Develop and evaluate mathematical arguments and proofs.

Worksheets :3Study Guides :1 ##### 7.4. Select and use various types of reasoning and methods of proof.

Worksheets :3Study Guides :1 #### NCTM.9. Connections

##### 9.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

Worksheets :3Study Guides :1 #### NCTM.11. Grade 8 Curriculum Focal Points

##### 11.1. Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

###### 11.1.1. Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Worksheets :5Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1 ##### 11.2. Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

###### 11.2.1. Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.

Pythagorean Theorem is a fundamental relation in Euclidean geometry. Use the Pythagorean Theorem and its converse to solve problems. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ##### 11.3. Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

###### 11.3.1. Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1 #### NCTM.12. Connections to the Grade 8 Focal Points

##### 12.1. Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.

Worksheets :4Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ##### 12.2. Geometry: Given a line in a coordinate plane, students understand that all ''slope triangles'' - triangles created by a vertical ''rise'' line segment (showing the change in y), a horizontal ''run'' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line.

Worksheets :5Study Guides :1Worksheets :3Study Guides :1 ##### 12.3. Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.

Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :3Study Guides :1Worksheets :4Study Guides :1Worksheets :3Study Guides :1 ##### 12.4. Number and Operations: Students use exponents and scientific notation to describe very large and very small numbers. They use square roots when they apply the Pythagorean Theorem.

Worksheets :4Study Guides :1Pythagorean Theorem is a fundamental relation in Euclidean geometry. Use the Pythagorean Theorem and its converse to solve problems. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1Worksheets :4Study Guides :1 ### NewPath Learning resources are fully aligned to US Education Standards. Select a standard below to view correlations to your selected resource: