Lesson 4: 1-6 Relations

How can you organize a set of ordered pairs into a table?
Describe the similarities and differences beteen a table and a mapping.
How would you use a set of ordered pairs to graph relations?
Suppose that two ordered pairs are aligned horizontally on your grpah. Explain how you would know this from a table.

Coordinate System
Coordinate Plane
x- and y-axes
Origin
Ordered Pair
x- and y-coordinates
Relation
Mapping
Domain
Range
Independent Variable
Dependent Variable

A.REI.10
D. Represent and solve equations and inequalities graphically
10. HSA-REI.D.10
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be
a line).

F.IF.1
A. Understand the concept of a function and use function notation
1. HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. 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. The graph of f is the graph of the equation y = f(x).

Chapter 1A (1-1 - 1-4) (Skip 1-3) 1B (1-6-1-8 skip end behavior) (Skip 1-5)

A relation can be represented as a set of ordered pairs, as an equation, a table, a mapping, or a graph. A mapping lists the x-values in the domain (independent variable) and the y-values in the range (dependent variable) with arrows drawn from the x-values to the corresponding y-values. A table lists the set of x-coordinates in the first column and their corresponding y-coordinates in the second column. A graph consists of a horizontal axis (x-axis), a vertical axis (y-axis), and the intersection of the axes (origin).

The deeper in the ocean you are, the greater pressure is on your body. This is because there is more water over you. The force of gravity pulls the water weight down, creating a greater pressure.

The equation that relates the total pressure of the water to the depth is P=rgh where
P=the pressure
r=the density of water
g=the acceleration due to gravity, and
h=the height of the water above you'

The number of calories you burn increase as the number of minutes that you walki increases.

Multiple Representations: Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs and search for regularity or trends. Encourage students to become familiar with and use multiple representations for relations.

You may want to spend extra time on independent and dependent variables, since an undertanding of these concepts provides the foundation for later work with functions. Have students work generate several real-world scenarios with idependent and dependent variables. Then have students work in small groups to compare and contrast variables.

Formative assessment: Exercises 1-8

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