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Grade 6 TN Lesson: Ordering and Comparing Integers Use with MiC unit Models You Can Count On after page 60 TN Standard: MA.6.SPI 0606.3.1 Represent on a number line the solution of a linear inequality. CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd 5/14/09 10:27 AM Page 43 Focus On: Ordering and Comparing Integers Inequality Symbols Just as the equals sign (=) shows that two numbers have the same value, the following symbols show when two numbers have different values: < stands for “is less than” > stands for “is greater than” ≤ stands for “is less than or equal to” ≥ stands for “is greater than or equal to” You can use these symbols to order and compare integers. Use < or > to compare –5 and 3. –5 is negative and 3 is positive, so –5 is less than 3. –5 < 3 Use < or > to order and compare –2, –9, and –6. All three numbers are negative, so the numbers with the smaller absolute value are the greater numbers. –2 > –6 > –9 Showing Inequality on a Number Line A number line can show inequalities. A shaded dot and all of the points where the number line is thicker stand for possible values of x. An empty dot shows a number that is not a possible value. Use a number line to show all the values for x when x ≤ –2. Find the given number on the number line. Draw a shaded dot for ≤ or ≥. Thicken the line to the left of the number for ≤. Thicken the line to the right of the number for ≥. –8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 Use a number line to show all the values for x when x > –5. Find the given number on the number line. Draw an empty dot for < or >. Thicken the line to the left of the number for <. Thicken the line to the right of the number for >. –8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 Inequality Expressions Just like an equals sign can be used to write a number sentence or an expression, so can the inequality symbols. Use =, <, >, ≤, or ≥ to compare –2 and 3 - 6. Find the value of the difference. 3 - 6 = –3 Compare this value with the given value. –2 is greater than –3 Write a number sentence with the correct inequality sign. –2 > 3 - 6 © Encyclopædia Britannica, Inc. Use =, <, >, ≤, or ≥ to complete the number sentence x + 6 –1. The sentence is true when x = –8. Substitute the value of x and find the value of the sum. x + 6 = –8 + 6 = –2 Compare this value with the given value. –2 is less than –1 Write a number sentence with an inequality sign. x + 6 < –1 Integers 1 CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd 5/14/09 10:27 AM Page 44 Ordering and Comparing Integers Math Content Students will order and compare positive and negative numbers using inequality symbols and statements. 1. Compare each pair of numbers by filling in the box with < or >. 4. Which number line shows all the values that are less than or equal to –1? 5 2 A. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 b. –6 1 B. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 c. –14 –2 C. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 0 –8 D. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 a. d. 2. Shade each number line to show the possible values of x. a. x < –4 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 b. x ≤ 0 5. Which number line shows all the possible values for x > 3? A. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 B. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 C. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 D. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 c. x > –7 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 d. x ≥ –6 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 3. Which number is not a possible value of y when y ≤ 2? 6. Draw number lines to show the possible values of x. a. x < 0 A. 0 B. 1 C. 2 b. x ≤ 6 D. 3 2 TN Lesson © Encyclopædia Britannica, Inc. CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd 5/14/09 10:27 AM Page 45 Ordering and Comparing Integers 7. Complete each number sentence by filling in each box with <, =, or >. Then write the inequality using words. a. 2 - 4 9. Use < or > to order and compare each set of numbers. a. –8, –1, –5 0 b. 0, 2, –2 b. 8 + (–9) c. 4 - 12 –1 10. Catherine has a budget of $12 to buy a gift for her little sister. She would like to buy a picture book that costs $11. The price of the book plus tax (T) must be less than or equal to her budget in order for her to afford it. Write an expression using an inequality symbol to represent this situation. –1 - 8 8. a. Use =, <, >, ≤, or ≥ to complete the number sentence below, when x = –3. x+5 –4 b. Write the number sentence using words. © Encyclopædia Britannica, Inc. 11. Pedro currently has 65 points in math. He needs a score of at least 70 points to pass. How many points (P) will allow him to pass math? Write an inequality that represents this situation. Integers 3 CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd 5/14/09 10:27 AM Page 44 Ordering and Comparing Integers Answer Key 1a. 1b. 1c. 1d. 2a. > < < > –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 2b. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 2c. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 2d. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 3. D 4. A 5. D 6a. –8 –7 –6 –5 –4 –3 –2 –1 6b. 0 1 2 3 4 5 6 7 8 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 7a. <; Two minus four is less than zero. 7b. =; Eight plus negative nine is equal to negative one. 7c. >; Four minus twelve is greater than negative one minus eight. 8a. x + 5 > – 4 8b. –3 plus five is greater than negative four. 9a. –1 > –5 > –8 or –8 < –5 < –1 9b. 2 > 0 > –2 or –2 < 0 < 2 10. $11 + T ≤ $12 or $12 ≥ $11 + T 11. 65 + P ≥ 70 or 70 ≤ 65 + P 4 TN Lesson © Encyclopædia Britannica, Inc.