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# National STEM Standards Ninth Grade Mathematics resources

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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. Develop a deeper understanding of very large and very small numbers and of various representations of them.

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

1.1.2. Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

1.2. Understand meanings of operations and how they relate to one another.

1.2.1. Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

1.2.3. Develop an understanding of permutations and combinations as counting techniques.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

1.3. Compute fluently and make reasonable estimates.

1.3.1. Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

1.3.2. Judge the reasonableness of numerical computations and their results.

Flip Charts Algebra Skills

Flip Charts Math Grade 8

NCTM.2. Algebra

2.1. Understand patterns, relations, and functions.

2.1.2. Understand relations and functions and select, convert flexibly among, and use various representations for them.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

2.1.3. Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

2.1.5. Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

2.2. Represent and analyze mathematical situations and structures using algebraic symbols.

2.2.2. Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

2.2.3. Use symbolic algebra to represent and explain mathematical relationships.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

2.3. Use mathematical models to represent and understand quantitative relationships.

2.3.2. Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

2.3.3. Draw reasonable conclusions about a situation being modeled.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

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. Analyze properties and determine attributes of two- and three-dimensional objects.

Flip Charts Dot to Dot

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

3.1.2. Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.

Flip Charts Dot to Dot

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

Flip Charts Plane Geometry

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.2.1. Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

3.2.2. Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

3.3. Apply transformations and use symmetry to analyze mathematical situations.

3.3.1. Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

3.3.2. Use various representations to help understand the effects of simple transformations and their compositions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

NCTM.4. Measurement

4.2. Apply appropriate techniques, tools, and formulas to determine measurements.

4.2.2. Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders.

Flip Charts Algebra Skills

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

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.

5.1.2. Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

5.1.4. Understand histograms, parallel box plots, and scatterplots and use them to display data.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.1.5. Compute basic statistics and understand the distinction between a statistic and a parameter.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.2. Select and use appropriate statistical methods to analyze data.

5.2.1. For univariate measurement data, students should be able to display the distribution, describe its shape, and select and calculate summary statistics.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.2.2. For bivariate measurement data, students should be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.3. Develop and evaluate inferences and predictions that are based on data.

5.3.2. Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

5.3.3. Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

5.4. Understand and apply basic concepts of probability

5.4.4. Understand the concepts of conditional probability and independent events.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

NCTM.6. Problem Solving

6.1. Build new mathematical knowledge through problem solving.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

6.2. Solve problems that arise in mathematics and in other contexts.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

6.3. Apply and adapt a variety of appropriate strategies to solve problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

NCTM.7. Reasoning and Proof

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.2. Make and investigate mathematical conjectures.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.3. Develop and evaluate mathematical arguments and proofs.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.4. Select and use various types of reasoning and methods of proof.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

NCTM.9. Connections

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes