Ask: What happens to the equation if we replace x with 1? Elicit from students the equation 1 + 5 = 6.Label the first column x, the second column x + 5, and the third column y. Draw a table with four columns and five rows.Students should say that the equation means "a number plus five equals another number," or a comparable statement. Ask: How could you say this equation in words?.Write the equation x + 5 = y publicly for the class to see.They should also be able to recognize and interpret an equation. Prerequisite Skills and Concepts: Students should know about ordered pairs and locating points on a grid. Ensure all students have a copy of the grid. Label the x- and y-axes from 0 through 10. Preparation: Draw a coordinate grid where all students can see it. Materials: Poster paper or a way to display a coordinate grid publicly for the class straightedge one copy of a coordinate grid, a straightedge, and lined paper for each student Key Standard: Interpret an equation as a linear function, whose graph is a straight line. One example could read, " Rule: The first number plus three equals the second number ordered pairs: (2,5) (3,6) (4,7) and (5,8)."ĭeveloping the Concept Finding and Graphing Points for Linear RelationshipsĪt this level, students will begin to see the relationship between equations and straight-line graphs on a coordinate grid. Have students identify the rule and explain how to graph the points. Provide students with other examples of ordered pairs that follow a rule.Use a straightedge to connect the points. Students should see that a line will be formed. Ask: What figure do you think will be formed by connecting the points on the grid?.Emphasize the importance of moving right for the first number in the ordered pair and up for the second number. Have students verbalize how to locate the point for each of the other ordered pairs.Students should say to "start at 0, move 6 units to the right, then 4 units up." Mark this point on the grid for the class to see. Ask: How would you locate the point for (6,4) on the grid?.Say: Let's locate these ordered pairs on a grid.You can help them by using the rule to write each ordered pair as an equation: 6 – 2 = 4, 7 – 2 = 5, 8 – 2 = 6, 9 – 2 = 7. Students should notice that each ordered pair follows this rule. Ask: Does the same rule apply to the other ordered pairs?.Ask: What rule describes the relationship between the numbers in this ordered pair?Īlthough many rules work for this pair in isolation, elicit from students this rule: the first number minus two equals the second number.Write these ordered pairs where all students can see them: (6,4) (7,5) (8,6) and (9,7).Preparation: Draw a large coordinate grid that the entire class can see. Materials: Poster paper or a way to display a coordinate grid publicly for the class straightedge Key Standard: Graph points on the coordinate plane. A day spent plotting coordinates that fall in a straight line will be a day well spent. Your students may have encountered ordered pairs last year, but it's a good idea to start by reviewing how to locate a point on a grid from an ordered pair. We account for this on the graph by sketching a picture of a graph suggested by the points plotted.Introducing the Concept Finding and Graphing Points for Linear Relationships Recall that when a function is defined by an equation, we have a lot of inputs for \(x\) to choose from. Draw the function by connecting the dots.Use the ordered pairs to plot the graph of the function.Create ordered pairs from the inputs and their outputs add to table.Compute the outputs \(f(x)\) corresponding to each input \(x\) by plugging the \(x\) value into the rule for \(f(x)\) add these to the table.Choose several inputs to use to create ordered pairs convenient numbers such as -1, 0, 1 are good to include, and often times, 4-5 points is sufficient to get an idea of what the graph will look like.Create a table to keep track of inputs, outputs, and ordered pairs.To graph a function defined using an equation for its rule.
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