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Chapter 7 Inequalities

This chapter delves into the intricacies of inequalities, exploring concepts such as one-step inequalities involving addition, subtraction, multiplication, and division. Understanding inequalities as mathematical sentences that compare two quantities is crucial for mastering mathematical reasoning. Students will learn how to interpret inequalities on number lines and graph them accurately. Key terms like absolute value, positive and negative integers, and rational numbers are defined, enhancing foundational knowledge in algebra. Interactive group work and exit tickets reinforce learning and assess comprehension.

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Chapter 7 Inequalities

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  1. Chapter 7Inequalities

  2. Day….. • CRA s All Day • Writing Inequalities • Solving One-Step Inequalities (+ and - ) • Solving One-Step Inequalities (x and ÷ ) • No School

  3. Day 1

  4. Bell Work Justify your Response

  5. Vocabulary • A mathematical sentence indicating two quantities are not equal. Inequality - • The distance between a number and 0 on a number line. Absolute Value- Any number greater than 0. They can be written with or without the + sign and appear to the right or above the 0. Positive Integer- Negative Integer - Any number less than 0. They are written with a – sign and appear to the left or below 0 Any number that can be written as a fraction. Rational Number - Aline on which numbers are marked at intervals, used to illustrate simple numerical operations. Number Line - • Variable - A letter or symbol used to represent an unknown number.

  6. I Can…. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

  7. Interpreting and Writing Inequalities Essential Understanding: An inequality is a mathematical sentence that compares quantities using the symbols >, <, ≥, and ≤. Example:

  8. Group Work Please take out your maker boards

  9. Wrap it Up • Review • Questions • Exit Tickets

  10. Day 2

  11. Bell Work Justify your response.

  12. Homework Check

  13. Vocabulary • A mathematical sentence indicating two quantities are not equal. Inequality - • _________ • ___________ • ___________ • ____________ • _____________ • ___________ • ___________ Absolute Value- • The distance between a number and 0 on a number line. Any number greater than 0. They can be written with or without the + sign and appear to the right or above the 0. Positive Integer- Negative Integer- • Any number less than 0. They are written with a – sign and appear to the left or below 0. a number that can be written as a fraction Rational Number - a line on which numbers are marked at intervals, used to illustrate simple numerical operations. Number Line -

  14. I Can…. Write inequalities for a given number line representation.

  15. Writing and Graphing Inequalities Essential Understanding: • Inequalities can be graphed on a number line using an open or a closed dot and a ray ( ) • An open dot means the number is not included (used with < and > symbols) • A closed dot means the number is included (used with ≤ and ≥) • The direction of the ray or shaded area indicates the solution set _________________ -3 -2 -1 0 1 2 3 x > -1

  16. Watch This • http://learnzillion.com/lessons/1507-write-inequalities-given-a-number-line-representation ( 3 mins)

  17. Group Work Please take out your maker boards

  18. Wrap it Up • Review • Questions • Exit Tickets

  19. Day 3

  20. Bell Work Justify Your Response

  21. Homework Check

  22. Vocabulary • A mathematical sentence indicating two quantities are not equal. Inequality - • _________ • ___________ • ___________ • ____________ • _____________ • ___________ • ___________ Absolute Value- • The distance between a number and 0 on a number line. Any number greater than 0. They can be written with or without the + sign and appear to the right or above the 0. Positive Integer- Negative Integer- • Any number less than 0. They are written with a – sign and appear to the left or below 0. a number that can be written as a fraction Rational Number - a line on which numbers are marked at intervals, used to illustrate simple numerical operations. Number Line -

  23. I Can…. Solve one-step inequalities involving addition and subtraction

  24. Solving One-Step Inequalities Essential Understanding: Addition and subtraction and multiplication and division properties can be used to solve inequalities. • If the same number is added or subtracted from each side of an inequality, the inequality remains true. • If the same positive number is multiplied or divided from each side of an inequality, the inequality remains true. Examples: 3 < 6 3 < 6 x > 6 x > 6

  25. Solving Inequalities Essential Understanding: Inequalities can be solved by finding values for the variable that make the inequality true. Examples: X +2 < 8 = x < 6 8-2 = 6 or 6 + 2 = 8 X must be a number less than 6 to make this sentence true. Therefore, any number less than 6 (5,4,3,2,1,0,-1,-2, etc… would make the sentence true So…… x < 6 or x ≤ 5

  26. Your Turn…. • Clear your desk of everything but a calculator and a pencil.

  27. Wrap it Up • Review • Questions • Exit Tickets

  28. Day 4

  29. pOp Quiz • Take out a pencil and a calculator • Clear everything else from your desk

  30. Homework Check

  31. Vocabulary • A mathematical sentence indicating two quantities are not equal. Inequality - • _________ • ___________ • ___________ • ____________ • _____________ • ___________ • ___________ Absolute Value- • The distance between a number and 0 on a number line. Any number greater than 0. They can be written with or without the + sign and appear to the right or above the 0. Positive Integer- Negative Integer- • Any number less than 0. They are written with a – sign and appear to the left or below 0. a number that can be written as a fraction Rational Number - a line on which numbers are marked at intervals, used to illustrate simple numerical operations. Number Line -

  32. I Can…. Solve one-step inequalities involving multiplication and division.

  33. Solving One-Step Inequalities Essential Understanding: Inequalities can be solved by finding values for the variable that make the inequality true. Examples: 2x < 16 = x < 8 16 ÷ 2 = 8 or 8 x 2 = 16 X must be a number less than 8 to make this sentence true. Therefore, any number less than 8 (7.2, 8, 9 ½, 44, etc… ) would make the sentence true . So…… x < 8 or x ≤ 7

  34. Practice Please take out your maker boards

  35. Wrap it Up • Review • Questions • Exit Tickets

  36. Day 5

  37. Enjoy your Fall Break No School 

  38. Not Used this Week

  39. Computer Station • www.learnzillion.com (6 minutes per video) • www.tenmarks.com (10 questions per assignment)

  40. Station Rotations • Write your exit ticket. • Pack up everything but a pencil. • You will have 15 minutes to complete each rotation

  41. 1st Rotation

  42. 2nd Rotation

  43. 3rd Rotation

  44. 4th Rotation

  45. Group Work Before we begin……. • Complete an exit ticket. • Pack up everything except for your pencil and calculator. • Sit quietly unit everyone is ready.

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