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# Minnesota Standards Ninth Grade Mathematics resources

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Algebra

9.2.1. Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.

9.2.1.1. Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain.

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

9.2.1.2. Distinguish between functions and other relations defined symbolically, graphically or in tabular form.

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

9.2.1.6. Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.

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

9.2.2. Recognize linear, quadratic, exponential and other common functions in real world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

9.2.2.3. Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.

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

9.2.2.4. Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

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

9.2.2.5. Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

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

9.2.3. Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.

9.2.3.2. Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

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

9.2.3.6. Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots.

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

9.2.4. Represent real world and mathematical situations using equations and inequalities involving linear, quadratic, exponential and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

9.2.4.2. Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.

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

Geometry & Measurement

9.3.1. Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.

9.3.1.1. Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.

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

9.3.1.4. Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k^2 and k^3, respectively.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

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

9.3.2. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.

9.3.2.1. Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.

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 Similarity and scale

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

9.3.3. Know and apply properties of geometric figures to solve real world and mathematical problems and to logically justify results in geometry.

9.3.3.1. Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

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

9.3.3.2. Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

9.3.3.6. Know and apply properties of congruent and similar figures to solve problems and logically justify results.

Flip Charts Math Grade 8

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 Ratios, proportions and percents

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

9.3.3.7. Use properties of polygons--including quadrilaterals and regular polygons--to define them, classify them, solve problems and logically justify results.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

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

9.3.3.8. Know and apply properties of a circle to solve problems and logically justify results.

Flip Charts Dot to Dot

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

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

9.3.4. Solve real-world and mathematical geometric problems using algebraic methods.

9.3.4.4. Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.

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

9.3.4.7. Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

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

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

Data Analysis & Probability

9.4.1. Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.

9.4.1.1. Describe a data set using data displays, including box-and whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data 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

9.4.1.3. Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

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

9.4.2. Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.

9.4.2.3. Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.

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

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

9.4.3. Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.

9.4.3.1. Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

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

9.4.3.2. Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

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