© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2 Number Lines Integers and Rational Numbers © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers In each of these previous situations, you have been working with integers, which are positive numbers (1, 2, 3, . . . ), negative numbers (–1, –2, –3, . . . ) and 0, but not fractional amounts. 1. Place only the integers on the number line below. a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 H –5 5 –10 10 –15 –20 15 20 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers In each of these previous situations, you have been working with integers, which are positive numbers (1, 2, 3, . . . ), negative numbers (–1, –2, –3, . . . ) and 0, but not fractional amounts. 1. Place only the integers on the number line below. a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 H –5 5 –10 10 –15 –20 15 20 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers Rational numbers are numbers that are positive and negative and can be written as a fraction. All integers can also be written as a fraction, so they are also considered rational numbers. For example, 17 is also 17 1 or –12 can be written as − 12 1 . 2. Circle the following numbers that are rational numbers but not integers? a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 Rational numbers include decimals that terminate or repeat because they have a fraction equivalent. Irrational numbers are decimal numbers that are non-terminating and non-repeating. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers Rational numbers are numbers that are positive and negative and can be written as a fraction. All integers can also be written as a fraction, so they are also considered rational numbers. For example, 17 is also 17 1 or –12 can be written as − 12 1 . 2. Circle the following numbers that are rational numbers but not integers? a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 Rational numbers include decimals that terminate or repeat because they have a fraction equivalent. Irrational numbers are decimal numbers that are non-terminating and non-repeating. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers 3. Place each of the rational numbers that are not integers on the number line below. a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 H –5 5 –10 10 –15 –20 15 20 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Lesson 4a.2: Integers and Rational Numbers 3. Place each of the rational numbers that are not integers on the number line below. a. −12.3 b. 17 c. 1 1 2 e. −4.9 f. 19 g. −5 3 4 h. 0 i. −12 H –5 5 –10 10 –15 –20 15 20 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2: Here are three vertical number lines that each represent a different situation: temperature, profit/loss and sea level. 4. Place zero at the center of each number line. Make sure it is the same for each number line. 5. Place each of the following statements as a point on the appropriate number line. a. $2.50 e. –1.25 feet b. 3 ½ feet below sea level f. –$3.80 c. Owe $3.25 g. 2.7 degrees below zero d. 4.5 degrees h. 5.21 feet above sea level Temperature (C°) Profit/Loss Sea Level © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2: Here are three vertical number lines that each represent a different situation: temperature, profit/loss and sea level. 4. Place zero at the center of each number line. Make sure it is the same for each number line. 5. Place each of the following statements as a point on the appropriate number line. a. $2.50 e. –1.25 feet b. 3 ½ feet below sea level f. –$3.80 c. Owe $3.25 g. 2.7 degrees below zero d. 4.5 degrees h. 5.21 feet above sea level Temperature (C°) Profit/Loss Sea Level © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2: 6. Write one statement that uses a rational number that is not an integer for each situation (temperature, profit or loss, and sea level) and place that point on the appropriate number line. a. b. c. Temperature (C°) Profit/Loss Sea Level © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2: Profit/Loss Sea Level 5 $25 5,000 –5 –$25 –5,000 Temperature (C°) a b c Write a statement for each of the points on the number lines. (Use worksheet 2.1) 7. Temperature a. b. c. 8. Profit and Loss 9. Sea Level Students can approximate the numbers. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Lesson 4a.2: Review 10. Petra says that integers are rational numbers, but rational numbers are not integers. Use the definitions to explain whether she is correct or not. 11. Place 4 numbers on the number line below with the following rules: 2 numbers must be negative and 2 numbers must be positive and 2 numbers must be integers and 2 numbers must be non-integer rational numbers. 12. If the situation is money, write a statement that reflects each of the numbers you created in problem 11. Have students take notes in a math journal/notebook. –5 5 –10 10 –15 –20 15 20 © DMTI (2017) | Resource Materials | www.dmtinstitute.com