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germantown-middle | MATH RESOURCES change/understand .. GO. Determining if a relationship is a function from a graph. Note: If you're learning about graphs, you're bound to see a bunch of linear equations, so it's a good idea to understand what makes an equation a linear. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or .

Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities e. Interpret scientific notation that has been generated by technology. Estimate the rate of change from a graph.

How Do You Make a Table of Values for a Linear Equation?

If f is a function and x is an element of its domain, then f x denotes the output of f corresponding to the input x. Ratios And Proportional Relationships 6. Construct a viable argument to justify a solution method. Seeing Structure In Expressions Interpret expressions that represent a quantity in terms of its context. Statistics And Probability 7. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 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. The Number System 6. 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. This video illustrates the relationships among these representations.

It is important for students to move freely among the various representations. By the end of the Unit, students should feel very comfortable with tables and graphs and with some simple equations.

Students should also have an appreciation of the advantages and disadvantages of each representation. Graphing Factor Pairs The Grade 6 Unit Prime Time covered the relationship between factor pairs of a number and rectangles with area equal to the number. By superimposing the factor-pair rectangles for a number on top of each other, students can see the symmetry of the factor pairs.

What is a Linear Equation? | Virtual Nerd

This video shows the inverse variation relationship that results when you graph those factor pairs as coordinates. Inverse variation refers to a nonlinear relationship in which the product of two variables is constant.

In the context of these rectangles, the two variables are length I and width w. Their area, or the product of the variables l and w, is constant. In an inverse variation, the values of one variable decrease as the values of the other variable increase. Identifying Correlation Coefficients The correlation coefficient is a number between 1 and —1 that tells how closely a pattern of data points fits a straight line.

This video shows the correlation coefficient of various sets of data points. This video shows a geometric proof of the Pythagorean Theorem.

Use functions to model relationships between quantities. | CC | 8 | 8.F | Virtual Nerd

Growing, Growing, Growing Exponential and Linear Functions When making tables, students usually generate each value in the table by working with the previous value. Either they add a constant to the previous value in the case of linear relationships or they multiply the previous value by a constant in the case of exponential relationships.

This process of generating a value from a previous value is called recursion, or iteration. It is important to distinguish between a constant growth factor multiplicativeas illustrated in an exponential function, and the constant additive pattern in linear functions. This video illustrates successive iterations for linear and exponential growth. Patterns in the Table of Powers In this Unit, students begin to develop understanding of the rules of exponents by examining patterns in the table of powers for the first 10 whole numbers.

This video describes some of these patterns. Frogs, Fleas, and Painted Cubes The Distributive Property and Equivalent Quadratic Expressions When a quadratic expression is written in factored form, its factors are often binomial expressions, or simply binomials.