Problem Solving: Lesson 12 Symmetry on a Coordinate Graph Lesson 12 Skills Maintenance

Transcription

1 Lesson 1 Skills Maintenance Lesson Planner Skills Maintenance Adding and Subtracting Positive and Negative Integers Symmetry on a Coordinate Graph We review the concept of symmetry and extend it to the coordinate graph. We discussed symmetry in this unit with respect to opposites. We see on a coordinate grid that there is a natural line of symmetry around each of the axes. The coordinate graph provides a nice context for symmetry because it allows us to study the coordinates of symmetrical points and see what kinds of patterns arise. These patterns involve opposites. Objective Students will identify symmetry on a coordinate graph. Homework Students compare two integers by writing > or < between the numbers, solve a mix of integer addition and subtraction problems, and draw three shapes on their paper and draw a line of symmetry in each shape. In Distributed Practice, students practice rational number conversions and decimal number and fraction computations. Name Date Skills Maintenance Adding and Subtracting Positive and Negative Integers Solve Skills Maintenance Adding and Subtracting Positive and Negative Integers (Interactive Text, page 307) Unit 8 Lesson Students solve a mix of integer operations. Encourage them to use number lines or red and black cards if necessary. Unit 8 Unit 8 Lesson 1 977

2 Lesson 1 Where do we find symmetry on a coordinate graph? (Student Text, pages 60 60) Connect to Prior Knowledge Begin by reviewing the concept of symmetry. Put three or four objects on the board, some with symmetry and some without. Here are some examples: Where do we find symmetry on a coordinate graph? CRASH BANG ENTERTAINMENT IS DEVELOPING A VIDEO GAME. THE GAME WILL ALLOW PLAYERS TO TRAVEL THROUGH SPACE, EXPLORE PLANETS FOR LIFE FORMS, AND KEEP ASTEROIDS FROM HITTING THE EARTH. IT IS AN EDUCATIONAL VIDEO GAME DESIGNED TO SHOW THE FUTURE OF SPACE EXPLORATION AND WHAT WE MIGHT FIND ON OTHER PLANETS. THE PROGRAMMERS WHO WORK FOR CRASH BANG ENTERTAINMENT ARE USING A COORDINATE GRAPH TO DESIGN THE MAIN SPACESHIP THAT WILL BE USED IN THE VIDEO GAME. Ask students to identify the shapes with symmetry and explain how they can tell. Listen for: It is symmetry when the line splits the shape into two parts that are exactly the same. It is not symmetry if you draw the line, and the parts are different on each side of the line. Link to Today s Concept Tell students that in today s lesson we extend our thinking about symmetry to the coordinate graph. The advantage is being able to compare the coordinates of symmetrical points and learn about symmetry from them. Demonstrate Engagement Strategy: Teacher Demonstration Demonstrate finding symmetry on a coordinate graph in one of the following ways: : Use the mbook Teacher Edition for pages of the Student Text Unit 8 Lesson 1 Overhead Projector: Display Transparency 17, and modify as discussed. Board: Draw the coordinate graph on the board, and modify as discussed. Look at the graphic on Student Text, page 60. Crash Bang Entertainment, a company we learned about earlier, is working on a video game entitled Space Quest Adventure! Players will be able to explore space from inside a rocket. The programmers at Crash Bang are using a coordinate graph to design the main rocket for the game. Have students think about symmetry and how it might apply to the coordinate graph. We can use any line on the coordinate graph to show symmetry, but the x-axis and y-axis are a natural place for looking at this concept. 978 Unit 8 Lesson 1

3 Demonstrate Have students look at page 603 of the Student Text. Note that programmers are designing the rocket on a coordinate graph. Look at the four points on the rocket labeled A, B, C, and D. Walk students through locating each of the coordinate points on the axes. Help students to observe the parts of the rocket that are formed from the coordinates. The programmers use the y-axis to ensure that what is on either side of the axis is the same. Tell students that we can use coordinates as a guide for symmetry. The first task is to make sure that the rocket used in many of the flights is well-designed. One way to check this is by confirming that the rocket is symmetrical. The programmers put the center of the rocket on the y-axis. They use the y-axis to make sure that what is on each side of the y-axis is the same. We can use coordinates to check for symmetry B C A = (, ) B = (, ) C = ( 5, 5) D = (5, 5) y A D x 603 Unit 8 Lesson Unit 8 Lesson 1 979

4 Lesson 1 Where do we find symmetry on a coordinate graph? (continued) Demonstrate Continue the discussion of the rocket shape on page 60 of the Student Text. Have students look carefully at the points, and explain that A and B are symmetrical, and C and D are symmetrical. Be sure they see that the line of symmetry is the y-axis. When this is the case, the y-values are the same in both sets of coordinates, and the x-values are opposites. Write these on the board or overhead for emphasis. The x-coordinates for A and B are and. They are opposites. The y-coordinates for A and B are both. The x-coordinates for C and D are 5 and 5. They are opposites. The y-coordinates for C and D are 5. They are the same. Also point out that the points are an equal distance from the axis. We can tell from observing the points, and we can be sure by checking their coordinates that they are indeed symmetrical points. 60 We can determine if the rocket is symmetrical in two ways. We can look at the rocket on the coordinate graph to see if it is symmetrical, estimating if both sides are an equal distance from the y-axis. The more precise way is to check the coordinates. 60 Unit 8 Lesson B C y A Coordinate graphs are an excellent way to check for symmetry. We used the y-axis in this example as our line of symmetry. We wanted to see if points on the left side of the axis were the same distance away from the y-axis as points on the right. Problem-Solving Activity Turn to Interactive Text, page 308. D x Look at Points A and B. Both move the same distance on the x-axis from the point of origin, (0, 0). Point A moves out to the right and Point B moves out to the left. They both move up the y-axis the same distance. They both move up. So, Points A and B are symmetrical. Compare Points C and D. Both move 5 away from the x-axis. Point C moves 5 to the left from the point of origin (0, 0), and Point D moves 5 to the right. Both points move down 5 on the y-axis. These two points on the rocket are exactly the same distance from the x- and the y-axes. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. How can you summarize symmetry around the y-axis? (The x-coordinates are opposites, and the y-coordinates are the same.) Check for Understanding Engagement Strategy: Think, Think Ask students the following questions about symmetry in the rocket. Tell them that you will call on one of them to answer a question after you ask it. Tell them to listen for their names. After each question, allow time for students to think of the answer. Then call on a student. Ask: What is the pattern of the coordinates of points C and D? (They both move five away from the x-axis; they both have the same y-coordinate.) 980 Unit 8 Lesson 1

5 Problem-Solving Activity Name Date Problem-Solving Activity (Interactive Text, page 308) Have students turn to page 308 in the Interactive Text and complete the activity. Students first determine the coordinates for the points A D. Then they are to answer questions about the symmetry of the design and the patterns in the coordinates. Monitor students work as they complete the activity. Watch for: Can students determine the coordinates for all the points? Can students see the patterns in the coordinates? Be sure to go over student answers when they are done with the Problem-Solving Activity. It is important that students have an opportunity to share their findings and hear other students findings after they have completed this exploration. Problem-Solving Activity Give the coordinates for each point labeled in the drawing. Then answer the questions. y A ( 3, 3) B (3, 3) 5 C ( 3, 8) A 3 B D (3, 8) 1 x x C 8 D y 1. What do points A and B have in common? What is different about these points? They are both on the 3 of the y-axis. On the x-axis, both 308 Unit 8 Lesson 1 are 3, but A is negative and B is positive.. What do points C and D have in common? What is different about these points? They are both on the 8 of the y-axis. On the x-axis, both are on 3, but C is negative and D is positive. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Reinforce Understanding Remind students that they can review lesson concepts by accessing the online mbook Study Guide. Unit 8 Lesson 1 981

6 Lesson 1 Homework Homework Go over the instructions on page 605 of the Student Text for each part of the homework. Students compare two integers by writing > or < between the numbers. Activity Students solve a mix of integer addition and subtraction problems. Activity 3 Students draw three shapes on their paper and draw a line of symmetry through each shape. Activity Distributed Practice Students practice decimal number, fraction, and percent conversions as well as operations involving fractions and decimal numbers. Remind students that we practice these skills on a regular basis so they continue to improve. Write > or < to show the larger number > 5. 5 > > > < > 30 Activity Add and subtract Activity 3 Draw three shapes on your paper and show a line of symmetry through each. Model See Additional Answers below. Activity Distributed Practice Solve. 1. Convert 1 5 to a percent. 0.. Convert 17% to a decimal number Convert 0.75 to a fraction Unit 8 Lesson Additional Answers Activity 3 Answers may vary. 98 Unit 8 Lesson 1