Major project report on Tata Motors and its marketing strategies
Copy of Math 3.1.1 Linear and Non-Linear Sequences.pptx
1. Math Resilience 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).
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.
11. Linear sequences change the
same between terms.
NON-linear sequences do
not change the same a
constant amount between
terms.
12. Here are the first four terms of a sequence: 1, 3, 6, 10.
Is it linear or non-linear?
13. Is a square number sequence linear or non-linear? How do
you know?
14. Math Week 1
● Lesson 1.1
● I can describe linear and non-linear
sequence patterns.
16. With your group, choose a rule.
Write the first 4 terms on the
board. Do not write your rule.
17. 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...
18. 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?
29. 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 …
40. 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
41. 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
42. 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
43. 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
44. 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 0
45. 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...
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.
47. 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.
48. 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
49. 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
50. 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
51. 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
53. Main Idea: Sequences→Linear vs. Non-linear
The sequence shows square numbers,
1x1= 1, 2x2=4, 3x3=9, 4x4=16,
5x5=25
54. Main Idea: Sequences→Linear vs. Non-linear
The sequence shows square numbers,
1x1= 1, 2x2=4, 3x3=9, 4x4=16,
5x5=25
55. Activity: Make your own rule and sequence.
1. Choose a rule. Example: add 7 OR multiply by 5 OR subtract one more
each time.
2. Write down the first four terms of your sequence.
3. Share your sequence on Padlet and tell the rule.
4. Read two classmates’ padlet. Either continue the sequence for three
more terms OR name the rule.
Sequence:
9, 20, 31, 42
