Unit 5, Lesson 1: Interpreting Negative Numbers

Transcription

1 Unit 5, Lesson 1: Interpreting Negative Numbers Lesson Goals Locate rational numbers on the number line. Interpret positive and negative numbers in context. Compare rational numbers. Required Materials pre-printed slips, cut from copies of the blackline master 1.1: Using the Thermometer (5 minutes) Setup: Display the image. 1 minute of quiet think time and 1 minute of quiet work time, followed by a whole-class discussion. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 1

2 Student task statement Here is a weather thermometer. Three of the numbers have been left off. Possible responses 1. 25, 10, What numbers go in the boxes? 2. What temperature does the thermometer show? 2. About Anticipated misconceptions Some students may think the missing number between 0 and -10 needs to have a magnitude larger than -10, such as -15, because on the positive side of the number line, numbers increase in magnitude as you go up. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 2

3 1.2: Fractions of a Degree (5 minutes) Setup: Remind students about the weather thermometer. Instruct them to estimate. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 3

4 Student task statement 1. What temperature is shown on each thermometer? 2. Which thermometer shows the highest temperature? 3. Which thermometer shows the lowest temperature? Possible responses 1.,,, 2. The third thermometer 3. The second thermometer 4. It is colder because. 4. Suppose the temperature outside is. Is that colder or warmer than the coldest temperature shown? How do you know? Anticipated misconceptions Some students may struggle to estimate the temperature on the last thermometer, since it is between two markings. Ask them to tell what the temperature would be for the lines directly above and directly below the thermometer's level. Then ask what temperature would be halfway in between those two numbers. Some students may struggle with comparing to the temperatures shown on the thermometers. Prompt students to point out where would be on the thermometer that is showing Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 4

5 . Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 5

6 1.3: Seagulls Soar, Sharks Swim (10 minutes) Setup: Display the image for all to see. Tell students to measure to each animal's eyes, to the nearest meter. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 6

7 Student task statement Here is a picture of some sea animals. The number line on the left shows the vertical position of each animal above or below sea level, in meters. Possible responses 1. Seagull is at 10 m. Dolphin is at 3 m. Octopus is at -10 m. Shark is at -3 m. Fish is at -7 m. Penguin is at 0 m. 2. The albatross is a. 0 m above the dolphin b. 7 m below the seagull c. 13 m above the octopus 3. The seabird is a. 2 m above the dolphin 1. How far above or below sea level is each animal? Measure to their eye level. b. 5 m below the seagull 2. A mobula ray is 3 meters above the surface of the ocean. How does its distance from the surface of the ocean compare to the vertical distance from the eyes of: The jumping dolphin? The flying seagull? The octopus? c. 15 m above the octopus 4. The clownfish is a. 5 m below the dolphin 3. An albatross is 5 meters above the surface of the ocean. How does its distance from the surface compare to the vertical distance from the eyes of: b. 12 m below the seagull c. 8 m above the octopus Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 7

8 The jumping dolphin? The flying seagull? The octopus? 5. Either 0 m or 6 m. 4. A clownfish is 2 meters below the surface of the ocean. How does its distance from the surface compare to the vertical distance from the eyes of: The jumping dolphin? The flying seagull? The octopus? Anticipated misconceptions If students measure to the top or bottom of the animal, remind them that we are using the eyes of the animal to measure their height or depth. 5. The vertical distance of a new dolphin from the dolphin in the picture is 3 meters. What is its distance from the surface of the ocean? Some students may struggle to visualize where the albatross, seagull, and clownfish are on the graph. Consider having them draw or place a marker where the new animal is located while comparing it to the other animals in the picture. Are you ready for more? The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of the earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole? Possible Responses About 7,897 miles. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 8

9 1.4: Card Sort: Rational Numbers (Optional, 15 minutes) Setup: Students in groups of 3. Distribute the first set of cards. Wait until those are sorted to distribute the second set of cards. Student task statement 1. Your teacher will give your group a set of cards. Order the cards from least to greatest. 2. Pause here so your teacher can review your work. Then, your teacher will give you a second set of cards. 3. Add the new set of cards to the first set so that all of the cards are ordered from least to greatest. Possible responses , -10, -9, -7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 8, 10, 11, 15, 22, No answer needed ,,, -10, -9, -7.7, -7, -6,, -4, -3,, -2.5, -2,, -1,, 0,, 1,, 2, 2.5,, 3, 5,, 7.7, 8, 10,, 11, 15, 22,, 23 Anticipated misconceptions Some students may struggle with ordering the negative numbers. For example, they may put -2.5 to the right of -2 since they are used to seeing 2.5 to the right of 2. Help students visualize a number line and figure out which number should be farther away from 0. Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 9

10 Lesson Synthesis (5 minutes) Which of two negative numbers is greater? Which of a set numbers has the greater magnitude? How can we order negative numbers? 1.5: Signed Numbers (Cool-down, 5 minutes) Setup: None. Student task statement Here is a set of signed numbers: 7, -3,, -0.8, 0.8, -, -2 Possible responses 1. -3, -2, -0.8, -,, 0.8, 7 1. Order the numbers from least to greatest. 2. If these numbers represent temperatures in degrees Celsius, which is the coldest? If these numbers represent elevations in meters, which is the farthest away from sea level? Unit 5: Rational Number Arithmetic, Lesson 1: Interpreting Negative Numbers 10