You will learn how to. In Function Junction your child will take a deeper look at functions and explore new functions. As they work through the Problems of this Unit, it will be helpful to keep asking questions such as:.
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Recognize linear and nonlinear relationships in tables and graphs. Use linear and inverse variation equations to model bivariate data Use residual analysis to measure the fit of linear and inverse variation models. Analyze, approximate, and solve linear equations. Use linear and inverse variation equations to solve problems and to make predictions and decisions Use scatter plots, two-way tables, and correlation coefficients to describe patterns of association in pairs of variables.
Use standard deviation to measure variability in data distributions. When your child encounters a new problem, it is a good idea to ask questions such as: What are the key variables in this situation?
If there is a pattern relating the variables, is it strong enough to allow me to make predictions? What is the pattern relating the variables? What kind of equation will express the relationship? How can I use the equation to answer questions about the relationship? They will learn how to: Develop strategies for finding the distance between two points on a coordinate grid Explain a proof of the Pythagorean Theorem Understand and use the Pythagorean Theorem to solve everyday problems Write fractions as repeating or terminating decimals Write decimals as fractions Recognize rational and irrational numbers Locate irrational numbers on a number line Relate the area of a square to its side length, and the volume of a cube to its side length Estimate square roots and cube roots When your student encounters a new problem, it is a good idea to ask questions such as: What are the quantities in this problem?
Is the Pythagorean Theorem useful and appropriate in this situation? How do I know? Do I need to find the distance between two points? How are the side length and the area of a square related? How can I estimate the square root or cube root of a number? The Investigations in this Unit will help them learn how to: Identify situations in which a quantity grows or decays exponentially Recognize the connections between the growth patterns in tables, graphs, and equations that represent exponential functions Construct equations to express the relationship between the variables in an exponential function in data tables, graphs, and problem situations Compare exponential and linear functions Develop and use rules for working with exponents, including scientific notation, to write and interpret equivalent expressions Solve problems about exponential growth and decay from a variety of different areas, including science and business As your child works on the Problems in this Unit, ask questions about situations that involve nonlinear relationships such as: How can I recognize whether the relationship between the variables is an exponential function?
What is the growth or decay factor? What equation models the data in the table, graph, or problem situation? What can I learn about this situation by studying a table or graph of the exponential function?
How can I answer questions about the problem situation by studying a table, graph, or equation that represents the exponential function? They will learn how to Recognize patterns of change for quadratic relationships Write equations for quadratic functions represented in tables, graphs, and problem situations Connect quadratic equations to the patterns in tables and graphs of quadratic functions Use a quadratic equation to identify the maximum or minimum value, the x- and y-intercepts, line of symmetry, and other important features of the graph of a quadratic function Recognize equivalent quadratic expressions Use the Distributive Property to write equivalent quadratic expressions in factored and expanded form Use tables, graphs, and equations of quadratic functions to solve problems in a variety of situations from geometry, science, and business Compare properties of quadratic, linear, and exponential functions When your child encounters a new problem, it is a good idea to ask questions such as: What are the independent and dependent variables?
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