Copy of Math 3.1.1 Linear and Non-Linear Sequences.pptx

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1. M a t h R e s i l i e n c e khả năng phục hồi toán học When you are struggling with a problem, ask: What have I already tried? What do need I know? What am I trying to find out? What else could I try?

2. Math Expectations ✅ Write the date and learning goal(s). ✅ Read the directions and find the question. ✅ Hunt for important words and numbers. (e.g,. star, circle, underline, arrow) ✅Show your thinking by writing down your calculations and drawings. ✅Circle your answer. ✅Check your answer by using inverse operations (backwards thinking).

3. Math Expectations ✅ Write the date and learning goal(s).

4. Math Expectations ✅ Read the directions and find the question.

5. Math Expectations ✅ Hunt for important words and numbers. (e.g,. star, circle, underline, arrow)

6. Math Expectations ✅Show your thinking by writing down your calculations and drawings.

7. Math Expectations ✅Circle your answer.

8. Math Expectations ✅Check your answer by using inverse operations (backwards thinking).

9. Word Wall - identify the term-to-term rule https://wordwall.net/resource/42444/maths/match-term-to-term-rule-to-sequence Math is Fun - What is a sequence? https://www.mathsisfun.com/algebra/sequences-series.html Math is Fun - Square Numbers https://www.mathsisfun.com/square-root.html Video: Math Antics Number Patterns https://www.youtube.com/watch?v=vV7C7bXm4VI&t=428s Game: https://mathsframe.co.uk/en/resources/resource/42/sequences

10. Linear sequences change the same between terms. NON-l inear sequences do not change the same a constant amount between terms.

11. Here are the first four terms of a sequence: 1, 3, 6, 10. Is it linear or non-linear?

12. Is a square number sequence linear or non-linear? How do you know?

13. Math Week 1 Lesson 1.1 I can describe linear and non-linear sequence patterns.

14. - Subtract Decrease Go down Count back + Add Increase Go up Count on

15. With your group, choose a rule. Write the first 4 terms on the board. Do not write your rule.

16. Unit 1 Vocabulary Sequence : A number pattern. A list of terms that follow a rule. 3, 6, 9, 12… or x, T, x, T, x, T… Term: the numbers, shapes, or items in a sequence. Linear sequence : a number pattern that increases or decreases by the same amount each time. 4, 2, 0, -2, -4, -6… Non-linear sequence : a number pattern that does not increase or decrease by the same amount each time. 5, 25, 125, 625... Rule : describes how numbers are connected. Add one more than you added last time: 1, 2, 4, 7, 11… Negative number: a number less than 0. 0, -1, -2, -3, → Zero, negative 1, negative 2, negative 3… Not minus one, minus 2, minus 3...

17. Unit 1 Vocabulary Difference: the “jump” size between terms in a sequence. The difference between these terms is +5 Spatial pattern: a pattern that includes drawings. Square number: the product of multiplying a number by itself . 2 x 2 = 4 , 9 x 9 = 81. The red numbers on this 100 chart are square numbers. Can you see how the row (<->) and column (↕)form a square?

18. Starter: Answer problems 1-3 (5 minutes)

19. Starter: Answer problems 1-3 (5 minutes)

20. Starter: The Number System 1a. The rule is - 5 (minus 5, subtract 5) 1b. The rule is +10 (add 10) 1c. The rule is -100 ( subtract 100)

21. Starter: Answer problems 1-3 (5 minutes)

22. Starter: The Number System 2a. Six hundred and one 2b. Two hundred and ninety-nine 3c. One hundred and eleven

23. Starter: Answer problems 1-3 (5 minutes)

24. Starter: The Number System 364 Three hundred and sixty-four 909 Nine hundred and nine

25. Starter: Answer problems 4-5 (2 minutes)

26. Starter: Answer problems 4-5 (2 minutes) 500 2 5 160 10

27. Main Idea: Sequences→number patterns that follow a rule

28. Main Idea: Sequences→number patterns that follow a rule Linear sequence (numbers change by the same amount each time) Sequence: 2, 4, 6, 8, 10, 12, 14 …

29. Main Idea: Sequences→number patterns that follow a rule

30. Main Idea: Sequences→number patterns that follow a rule

31. Main Idea: Sequences→number patterns that follow a rule

32. Main Idea: Sequences→number patterns that follow a rule

33. Main Idea: Sequences→number patterns that follow a rule

34. Main Idea: Sequences→number patterns that follow a rule

35. Main Idea: Sequences→number patterns that follow a rule

36. Main Idea: Sequences→number patterns that follow a rule

37. Main Idea: Sequences→number patterns that follow a rule

38. Main Idea: Sequences→number patterns that follow a rule ---

39. Main Idea: Sequences→number patterns that follow a rule 1a. The next term is 1046 rule + 100 + 100 + 100 + 100 term 946 1046 1146 1246

40. Main Idea: Sequences→number patterns that follow a rule 1a. The next term is 1046. 1b. The next term is 948. rule + 100 + 100 + 100 + 100 term 946 1046 1146 1246 rule - 100 - 100 - 100 - 100 term 1048 948 848 748

41. Main Idea: Sequences→number patterns that follow a rule 1c. The next term is 2989. rule + 1000 + 1000 + 1000 + 1000 term 1989 2989 3989 4989

42. Main Idea: Sequences→number patterns that follow a rule 1c. The next term is 2989. 1d . The next term is 8999. rule + 1000 + 1000 + 1000 + 1000 term 1989 2989 3989 4989 rule - 1000 - 1000 - 1000 - 1000 term 9999 8999 7999 6999

43. Main Idea: Sequences→number patterns that follow a rule 1e. The next term is -1 (negative one) rule - 1 - 1 - 1 -1 term 3 2 1

44. Main Idea: Sequences→Linear vs. Non-linear Linear sequence : a number pattern that increases or decreases by the same amount each time. 4, 2, 0, -2, -4, -6… Non-linear sequence : a number pattern that does not increase or decrease by the same amount each time . 5, 25, 125, 625...

45. Main Idea: Sequences→Linear vs. Non-linear Linear sequence : changes by same amount each time. Non-linear sequence : changes by different amount each time 5, 25, 125, 625... 7a. 19. The difference between each term is +5 so 14 + 5 = 19. This is linear because each term changes by +5.

46. Main Idea: Sequences→Linear vs. Non-linear Linear sequence : changes by same amount each time. Non-linear sequence : changes by different amount each time 5, 25, 125, 625... 7a. 19. The difference between each term is +5 so 14 + 5 = 19. This is linear because each term changes by +5. 7b. 8. The difference between each term is -4 so 12-4 =8. This is linear because each term changes by -4.

47. Main Idea: Sequences→Linear vs. Non-linear 7c. 8. The difference between each term is different so this sequence is non-linear. The term-to-term change is not the same. rule + 1 + 2 + 3 +4 +5 +6 term 2 3 5 8 12 17

48. Main Idea: Sequences→Linear vs. Non-linear 7d. 54. The difference between each term is different so this sequence is non-linear. The term-to-term change is not the same. rule x3 x3 x3 x3 x3 x3 term 2 6 18 54 162 486

49. Main Idea: Sequences→Linear vs. Non-linear 7e. 26. The difference between each term is different so this sequence is non-linear. The term-to-term change is not the same. rule -9 -8 -7 -6 -5 -4 term 50 41 33 26 21 17

50. Main Idea: Sequences→Linear vs. Non-linear 7f. 4. The difference between each term is different so this sequence is non-linear. The term-to-term change is not the same. rule ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 term 32 16 8 4 2 1 0.5 or ½ 0.25 or ¼

51. Main Idea: Sequences→Linear vs. Non-linear

52. Main Idea: Sequences→Linear vs. Non-linear The sequence shows square numbers, 1x1= 1, 2x2= 4, 3x3= 9, 4x4= 16, 5x5= 25

53. Main Idea: Sequences→Linear vs. Non-linear The sequence shows square numbers, 1x1= 1, 2x2= 4, 3x3= 9, 4x4= 16, 5x5= 25

54. Activity: Make your own rule and sequence. Choose a rule. Example: add 7 OR multiply by 5 OR subtract one more each time. Write down the first four terms of your sequence. Share your sequence on Padlet and tell the rule. Read two classmates’ padlet. Either continue the sequence for three more terms OR name the rule. Sequence: 9, 20, 31, 42

55. Activity: Padlet - Make your own rule and sequence.

56. Check your progress: What is easy for you? What are you still working on?

57. https://www.math-salamanders.com/negative-numbers-worksheet.html#What