Working with Coordinate Planes


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1 Virtual Math Girl: Module 1 (Student) and 2 (Teacher) Working with Coordinate Planes Activities and Supplemental Materials The purpose of Virtual Math Girl Module 1 (Student) and 2 (Teacher) is to familiarize students with the four quadrant grid, or coordinate plane. A discussion of the distance formula for calculating length on a grid is included as an activity for extended learning. The activities are in order in which they are discussed in the VMG Module 2 (Teacher). Each page with graphics can be printed separately from this file by selecting Print from the File Menu and selecting the pages number(s) to be printed. Essential Vocabulary: quadrant, ordered pairs, coordinates plane, points, positive numbers, X axis, Y axis, and function table Grade 5 Ohio State Mathematics Standards addressed in this Module of Virtual Math Girl: Measurement Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature. Y2003.CMA.S02.G0507.BE.L05.I02 Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. Patterns, Functions and Algebra Students use patterns, relations, and functions to model, represent, and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs, and equations. Describe, extend, and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs, and other applications. Y2003.CMA.S04.G0507.BA.L05.I01 Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables, or graphs Represent, analyze, and generalize a variety of patterns and functions with tables, graphs, words, and symbolic rules. Y2003.CMA.S04.G0507.BB.L05.I03 Use variables as unknown quantities in general rules when describing patterns and other relationships. Use rules and variables to describe patterns, functions and other relationships. Y2003.CMA.S04.G0507.BE.L05.I03 Use variables as unknown quantities in general rules when describing patterns and other relationships. Use representations, such as tables, graphs, and equations, to model situations and to solve problems, especially those that involve linear relationships. Y2003.CMA.S04.G0507.BF.L05.I05 Model problems with physical materials and visual representations, and use models, graphs and 1
2 tables to draw conclusions and make predictions. Write, simplify, and evaluate algebraic expressions. Y2003.CMA.S04.G0507.BG.L05.I03 Use variables as unknown quantities in general rules when describing patterns and other relationships. Graph linear equations and inequalities. Y2003.CMA.S04.G0507.BK.L05.I05 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions Data Analysis and Probability Students pose questions and collect, organize, represent, interpret, and analyze data to answer those questions. Students develop and evaluate inferences, predictions, and arguments that are based on data. Read, create, and use line graphs, histograms, circle graphs, box and whisker plots, stem and leaf plots, and other representations when appropriate. Y2003.CMA.S05.G0507.BA.L05.I01 Read, construct, and interpret frequency tables, circle graphs and line graphs. 2
3 Virtual Math Girl  Activity 1 Plotting Positions on a Single Grid Quadrant Name You are helping to prepare a map for the town council so visitors will be able to find businesses in town. Plot the positions of these businesses in town from the function table below and label the ordered pairs associated with each business. Make sure to label each point with the name of the business and write the coordinates next to the point. x y Bank 1 3 Police Station 2 4 Restaurant 2 5 Pizza Place 3 2 Market 3 5 Movie 4 3 Skateboard Park 6 4 What is the most likely measure you would use in talking about this map to the town council, feet, kilometers, blocks, or inches? Why did you choose your answer? On the grid draw lines to show a route that a visitor might take from the restaurant to the movie. 3
4 Virtual Math Girl  Activity 2 Single Quadrant and Four Quadrant Grid Comparison Why is the first grid called a four quadrant grid? What similarities between the four quadrant grid and the single quadrant grid do you see? 4
5 Virtual Math Girl  Activity 3 Plotting Coordinates on a Four Quadrant Grid (page 1) This table is a function table. A function table has a place for an x coordinate and a y coordinate. The number in the left column is on the x axis and the number in the right column is on the y axis. This table is just another way of representing numbers on a grid. Points of interest x y Fountain 0 0 Grocery Fill in the function table from this grid. The fountain has coordinates of 0,0. Plot the points for other attractions in town. Bank School Outdoor Market Pharmacy Antique Shop Clothing Store 5
6 Plotting Coordinates on a Four Quadrant Grid (page 2) 6
7 Virtual Math Girl  Activity 4 Design Your Own Town (page 1) Your teacher will hand out a four quadrant grid for this activity. Design your own town using the function table and the four quadrant grid. Include six or seven different points of interest. Label each site with the name and coordinates of the point of interest and enter the information into the function table. Imagine that the lines on the grid are streets; create a route that a person traveling to all your points of interest might follow. Draw lines to show the route. Point of interest x y 7
8 Design Your Own Town (page 2) Map of your own town with walking routes to see all the sites. 8
9 Virtual Math Girl  Activity 5 Measuring Lines (page 1) Four lines have been plotted on the attached four quadrant grid. Measure the length of each line by counting on the grid. Enter the length in to the table below. What units are you using to measure the lines? Which is the longest? Which is the shortest? Confirm the line lengths as measured by calculating the line lengths using the distance formula. Function table for 8 ordered pairs x y Line length table Line name Length
10 Measuring Lines (page 2) 10
11 Virtual Math Girl  Activity 6 (Extended Activity) Measuring and Using the Distance Formula (page 1) Your teacher will hand out a four quadrant grid. Plot the eight ordered pairs from the function table. Then working from top to bottom and left to right, draw lines between the points. Label the lines A, B, C, and D. Measure the length of lines A, B, C, and D on the grid. Enter the length in the chart. Check the length you measured by finding the length using the distance formula. Enter your answers in the chart. Coordinates for left hand point Coordinates for right hand point Line A Line B Line C Line D DISTANCE FORMULA d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 d = distance x 2, x 1 = x axis points y 2, y 1 = y axis points Line name Measured length d Calculated length Line A Line B Line C Line D 11
12 Measuring and Using the Distance Formula (page 2) 12
13 Virtual Math Girl  Activity 7 (Extended Activity) Using the Distance Formula to Calculate Lengths of Diagonal Lines (page 1) Your teacher will hand out a four quadrant grid. Plot the points from the function table and connect the given points to create 3 diagonal lines with any points. Name each line by the points at either end of the line. Calculate the length of these lines using the distance formula. You will use a calculator to find the square root in the distance formula. Point x y A 11 B 23 C 4 3 D E DISTANCE FORMULA d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 d = distance x 2, x 1 = x axis points y 2, y 1 = y axis points F Line name d Length 13
14 Using the Distance Formula to Calculate Lengths of Diagonal Lines (page 2) 14
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