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1 Coordinate Pairs and Graphing Algebra Walk Student Activity Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development

2 Algebra Walk In this activity, students physically move around a large coordinate grid to model the plotting of coordinate pairs. Students graph the results on a coordinate plane. MATERIALS Transparency/Page: Dinograph Paper Transparencies/Pages: Graphs 1 6 Transparencies/Pages: Graphs 1 6 Answer Keys Transparency/Page: Summary Answer Key for Equations 1 6 blank transparency masking tape heavy string or rope three dinosaur counters chart paper VOCABULARY ordered pair coordinate pair coordinate plane TIME: 30 minutes Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 1

3 TEACHING TIP: The following must be prepared prior to the beginning of the activity. A large 4-quadrant coordinate plane made with masking tape on the floor. It must have 11 horizontal lines with the y-axis placed on line 6. It must have 19 vertical lines with the x-axis on line 9. 4 card tents, each labeled with 1 Quadrant name (e.g., Quadrant I) 1 card tent labeled (0, 0) 2 card tents, 1 labeled x-axis and 1 labeled y-axis Note: If classroom space is not adequate, consider preparing the coordinate plane in a hallway or outdoors. TEACHING TIP: This activity can be modified for youner students by creating and using the first quadrant only. INTRODUCE Dinograph Paper Copyright 2002 by the McGraw-Hill Companies McGraw-Hill Professional Development y Transparency: Dinograph Paper x Explain to students that, using the graph on the floor, they will plot lines by walking to points as they follow instructions from an equation. Display Transparency: Dinograph Paper. (Using this graph, you will model what students are going to do.) Put a dinosaur counter, facing toward QI and QII, on the point (2, 0) on the x-axis. Explain that the dinosaur is sitting on the input point the x-value (2) of an ordered pair. The dinosaur needs to move to the output point the y-value of the ordered pair. Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 2

4 Indicate that the rule that the dinosaur must follow is Multiply x by 2. Ask students what the output, or y-value, will be. (4) Announce that because the y-value is positive, the dinosaur is facing and will move 4 units in the positive direction. Move the dinosaur to the new point and announce the ordered pair that marks the spot: (2, 4), input 2 and output 4. Position another dinosaur at ( 2, 0). (The dinosaur should still be facing QI and QII.) Point out that the x-value, or input, is 2. Ask students what the y-value, or output, should be if the rule remains Multiply x by 2. ( 4) Announce that because the y-value is negative, the dinosaur must move backward (the opposite of positive) 4 units in the negative direction. Announce the ordered pair, when you have moved the dinosaur to the new point, that marks the spot: ( 2, 4), input 2, and output 4. Position a third dinosaur at (0, 0). Ask students what the input and output, or x-value and y-value, should be. (0 and 0) Lay string or rope across the 3 points on the graph to create a line. Tell students that they will now take the place of the dinosaurs and create a living-line graph. DISCUSS AND DO Move the class into position to view the coordinate plane that you have created on the floor. Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 3

5 Pass out the 7 card tents that you have created and ask student volunteer to place them on the graph. Clarify any misconceptions. Move 5 student volunteers to one side. TEACHING TIP: If the class would benefit from peer support, use 10 volunteers instead of 5. There will still be 5 individuals to move to the points, but each individual will have a partner with whom to consult. Have the rest of the students form groups of 3 or 4 and locate their Pages: Graphs 1 6. Walk to the graph. Select a point in each quadrant. Stand on each point in turn. Ask students to name the ordered pair that identifies the selected point in each quadrant on the graph. Ask the student volunteers to stand at various points along the x-axis, facing in the positive direction toward QI and QII. (They should be distributed across both negative values and positive values, with no value greater than + 4 and no value less than 4.) Have each student identify the ordered pair for his or her location (n, 0). Ask the student volunteers to apply the rule Multiply x by 2 to their x-coordinate and move to the spot for the correct y-coordinate. Those with negative x-values should move backward to their points. (Move in the opposite of the positive direction.) Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 4

6 TEACHING TIP: Suggest to members of the livingline that they compute the y-value, or output value, before they move to reduce the chance of confusion. Also, remind them that when calling out their ordered pairs, x is first and y is second. Have each student name the ordered pair for the spot on which he or she is standing. Have the observers verify the accuracy of the location. Have the observers record the points on their copy of Graph 1 as each student names his or her ordered pair. Have the observers include the ordered pair. Use a string or rope to connect each member of the living-line when all points are recorded. Have observers connect the dots on their graphs. Have observers write the rule below the graph. Have the graph members trade places with 5 observers. Have the members of the living-line repeat the same steps for each of the remaining five graphs: Line up along the x-axis. Call out the ordered pair. (n, 0) Apply the rule. Move to the new points. Call out the new points. Use rope to create the line. Have observers: verify the points when they are called graph the points on Graphs 1 6 draw the line write the graph number and the rule below the graph For each line, use 5 new students. Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 5

7 Repeat this activity until there are 6 lines and graphs. The rules for the 6 lines and graphs are: Graph 1 Multiply x by + 2. Graph 2 Multiply x by 2. Graph 3 Multiply x by + 2; then add + 1. Graph 4 Multiply x by + 2; then subtract + 1. Graph 5 Multiply x by + 1; then add + 1. Graph 6 Multiply x by 1; then add + 1. CONCLUDE 1 Graph 1 Answer Key Bring the class together to discuss the activity. Display, in order, Transparencies: Graphs 1 6 Answer Keys, permitting students to verify work. Display Transparency: Summary Answer Key for Equations 1 6. Ask students how the lines are affected by the rules. Sample responses include: Multiply x by + 2. Copyright 2002 by the McGraw-Hill Companies McGraw-Hill Professional Development Transparency: Graph 1 Answer Key Equations 1 6 Summary Answer Key Multiplying by a negative number causes the line to slope downward from left to right. Multiplying by a positive number causes the line to slope upward from left to right. Adding a number causes the line to cross the y-axis at that number. (When nothing is added to or subtracted from x, the line crosses at the origin.) The larger the multiplier, the steeper the line. Record students responses on chart paper, or a white board. END OF CONCLUDE 1 Copyright 2002 by the McGraw-Hill Companies McGraw-Hill Professional Development Transparency: Summary Answer Key for Equations 1 6 Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 6

8 CONCLUDE 2 ADVANCED Bring the class together to discuss the activity. Display, in order, Transparencies: Graphs 1 6 Answer Keys, permitting students to verify work. Point out that where these may not show the exact points that students have graphed, any two points on the same line will yield the same graph of the line. Ask students which lines sloped upward from left to right. (Redisplay the graphs when they are called out.) Graph 1 Graph 3 Graph 4 Graph 5 Ask them which lines sloped downward from left to right. (Redisplay the graphs when they are called out.) Graph 2 Graph 6 Display again Transparencies: Graphs 1 6 Answer Keys. Graph 1 Answer Key Ask students if they can see any relationship between the rules and the slopes of the graphed lines. If students do not mention it, point out that when an x-value was multiplied by a positive number, the line sloped upward (left to right). If the x-value was multiplied by a negative number, the line sloped downward (left to right). Multiply x by + 2. Copyright 2002 by the McGraw-Hill Companies McGraw-Hill Professional Development Transparencies: Graphs 1 6 Answer Keys Write on a blank transparency the equation y = mx + b. Explain to students that all linear equations can be written in this form. Redisplay, in order, Transparencies: Graphs 1 6 Answer Keys. Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 7

9 Rewrite the rules in an equation of the form y = mx + b below each rule. Point out that where there is no b, it is assumed that b is 0. Graph 1 Multiply x by + 2: y = + 2x. Graph 2 Multiply x by 2: y = 2x. Graph 3 Multiply x by + 2; then add + 1: y = + 2x Graph 4 Multiply x by + 2; then subtract + 1: y = + 2x + 1. Graph 5 Multiply x by + 1; then add + 1: y = x Graph 6 Multiply x by 1; then add + 1: y = x Point out that when m = 2, the line is steeper than when m = 1. Explain that m in the equation y = mx + b represents the slope of the line. Explain that slope is rise-over-run: the ratio of the change in y-values (rise) to the change in x-values (run). Redisplay, in order, Transparencies: Graphs 1 6 and: point out this relationship. use two different-colored pens to mark the run (change in x-values) and then the rise (change in y-values) on each graph. Suggest to students that there is another interesting feature to the equations of the form y = mx + b. Ask students to look at the place on each graph where the line crosses the y-axis. Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 8

10 Ask them what about each equation suggests where this will happen. (b is the y-intercept.) Point out, if not mentioned, that a negative b value means that the line crosses the y-axis below the x- axis, and that a positive b value means that the line crosses the y-axis above the x-axis. END OF CONCLUDE 2 End of Algebra Walk Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development 9